Finding a type for Redis commands

Arriving at a type for Redis commands required a bit of exploration. I had some ideas early on that I for various reasons ended up dropping on the way. This is a post about my travels, hopefully someone finds it worthwhile reading.

The protocol

The Redis Serialization Protocol (RESP) initially reminded me of JSON and I thought that following the pattern of aeson might be a good idea. I decided up-front that I'd only support the latest version of RESP, i.e. version 3. So, I thought of a data type, Resp with a constructor for each RESP3 data type, and a pair of type classes, FromResp and ToResp for converting between Haskell types and RESP3. Then after some more reflection I realised that converting to RESP is largely pointless. The main reason to convert anything to RESP3 is to assemble a command, with its arguments, to send to Redis, but all commands are arrays of bulk strings so it's unlikely that anyone will actually use ToResp.¹ So I scrapped the idea of ToResp. FromResp looked like this

class FromResp a where
    fromResp :: Value -> Either FromRespError a

When I started defining commands I didn't like the number of ByteString arguments that resulted in, so I defined a data type, Arg, and an accompanying type class for arguments, ToArg:

newtype Arg = Arg {unArg :: [ByteString]}
    deriving (Show, Semigroup, Monoid)

class ToArg a where
    toArg :: a -> Arg

Later on I saw that it might also be nice to have a type class specifically for keys, ToKey, though that's a wrapper for a single ByteString.

Implementing the functions to encode/decode the protocol were straight-forward applications of attoparsec and bytestring (using its Builder).

A command is a function in need of a sender

Even though supporting pipelining was one of the goals I felt a need to make sure I'd understood the protocol so I started off with single commands. The protocol is a simple request/response protocol at the core so I settled on this type for commands

type Cmd a = forall m. (Monad m) => (ByteString -> m ByteString) -> m (Either FromRespError a)

that is, a command is a function accepting a sender and returning an a.

I wrote a helper function for defining commands, sendCmd

sendCmd :: (Monad m, FromResp a) => [ByteString] -> (ByteString -> m ByteString) -> m (Either FromRespError a)
sendCmd cmdArgs send = do
    let cmd = encode $ Array $ map BulkString cmdArgs
    send cmd <&> decode >>= \case
        Left desc -> pure $ Left $ FromRespError "Decode" (Text.pack desc)
        Right v -> pure $ fromValue v

which made it easy to define commands. Here are two examples, append and mget:

append :: (ToArg a, ToArg b) => a -> b -> Cmd Int
append key val = sendCmd $ ["APPEND"] <> unArg (toArg key <> toArg val)

-- | https://redis.io/docs/latest/commands/mget/
mget :: (ToArg a, FromResp b) => NE.NonEmpty a -> Cmd (NE.NonEmpty b)
mget ks = sendCmd $ ["MGET"] <> unArg (foldMap1 toArg ks)

The function to send off a command and receive its response, sendAndRecieve, was just a call to send followed by a call to recv in network (the variants for lazy bytestrings).

I sort of liked this representation – there's always something pleasant with finding a way to represent something as a function. There's a very big problem with it though: it's difficult to implement pipelining!

Yes, Cmd is a functor since (->) r is a functor, and thus it's possible to make it an Applicative, e.g. using free. However, to implement pipelining it's necessary to

1. encode all commands, then
2. concatenate them all into a single bytestring and send it
3. read the response, which is a concatenation of the individual commands' responses, and
4. convert each separate response from RESP3.

That isn't easy when each command contains its own encoding and decoding. The sender function would have to relinquish control after encoding the command, and resume with the resume again later to decode it. I suspect it's doable using continuations, or monad-coroutine, but it felt complicated and rather than travelling down that road I asked for ideas on the Haskell Discourse. The replies lead me to a paper, Free delivery, and a bit later a package, monad-batcher. When I got the pointer to the package I'd already read the paper and started implementing the ideas in it, so I decided to save exploring monad-batcher for later.

A command for free delivery

The paper Free delivery is a perfect match for pipelining in Redis, and my understanding is that it proposes a solution where

1. Commands are defined as a GADT, Command a.
2. Two functions are defined to serialise and deserialise a Command a. In the paper they use String as the serialisation, so show and read is used.
3. A type, ActionA a, is defined that combines a command with a modification of its a result. It implements Functor.
4. A free type, FreeA f a is defined, and made into an Applicative with the constraint that f is a Functor.
5. A function, serializeA, is defined that traverses a FreeA ActionA a serialising each command.
6. A function, deserializeA, is defined that traverses a FreeA ActionA a deserialising the response for each command.

I defined a command type, Command a, with only three commands in it, echo, hello, and ping. I then followed the recipe above to verify that I could get it working at all. The Haskell used in the paper is showing its age, and there seems to be a Functor instance missing, but it was still straight forward and I could verify that it worked against a locally running Redis.

Then I made a few changes…

I renamed the command type to Cmd so I could use Command for what the paper calls ActionA.

data Cmd r where
    Echo :: Text -> Cmd Text
    Hello :: Maybe Int -> Cmd ()
    Ping :: Maybe Text -> Cmd Text

data Command a = forall r. Command !(r -> a) !(Cmd r)

instance Functor Command where
    fmap f (Command k c) = Command (f . k) c

toWireCmd :: Cmd r -> ByteString
toWireCmd (Echo msg) = _
toWireCmd (Hello ver) = _
toWireCmd (Ping msg) = _

fromWireResp :: Cmd r -> Resp -> Either RespError r
fromWireResp (Echo _) = fromResp
fromWireResp (Hello _) = fromResp
fromWireResp (Ping _) = fromResp

(At this point I was still using FromResp.)

I also replaced the free applicative defined in the paper and started using free. A couple of type aliases make it a little easier to write nice signatures

type Pipeline a = Ap Command a

type PipelineResult a = Validation [RespError] a

and defining individual pipeline commands turned into something rather mechanical. (I also swapped the order of the arguments to build a Command so I can use point-free style here.)

liftPipe :: (FromResp r) => Cmd r -> Pipeline r
liftPipe = liftAp . Command id

echo :: Text -> Pipeline Text
echo = liftPipe . Echo

hello :: Maybe Int -> Pipeline ()
hello = liftPipe . Hello

ping :: Maybe Text -> Pipeline Text
ping = liftPipe . Ping

One nice thing with switching to free was that serialisation became very simple

toWirePipeline :: Pipeline a -> ByteString
toWirePipeline = runAp_ $ \(Command _ c) -> toWireCmd c

On the other hand deserialisation became a little more involved, but it's not too bad

fromWirePipelineResp :: Pipeline a -> [Resp] -> PipelineResult a
fromWirePipelineResp (Pure a) _ = pure a
fromWirePipelineResp (Ap (Command k c) p) (r : rs) = fromWirePipelineResp p rs <*> (k <$> liftError singleton (fromWireResp c r))
fromWirePipelineResp _ _ = Failure [RespError "fromWirePipelineResp" "Unexpected wire result"]

Everything was working nicely and I started adding support for more commands. I used the small service from work to guide my choice of what commands to add. First out was del, then get and set. After adding lpush I was pretty much ready to try to replace hedis in the service from work.

data Cmd r where
    -- echo, hello, ping
    Del :: (ToKey k) => NonEmpty k -> Cmd Int
    Get :: (ToKey k, FromResp r) => k -> Cmd r
    Set :: (ToKey k, ToArg v) => k -> v -> Cmd Bool
    Lpush :: (ToKey k, ToArg v) => k -> NonEmpty v -> Cmd Int

However, when looking at the above definition started I thinking.

• Was it really a good idea to litter Cmd with constraints like that?
• Would it make sense to keep the Cmd type a bit closer to the actual Redis commands?
• Also, maybe FromResp wasn't such a good idea after all, what if I remove it?

That brought me to the third version of the type for Redis commands.

Converging and simplifying

While adding new commands and writing instances of FromResp I slowly realised that my initial thinking of RESP3 as somewhat similar to JSON didn't really pan out. I had quickly dropped ToResp and now the instances of FromResp didn't sit right with me. They obviously had to "follow the commands", so to speak, but at the same time allow users to bring their own types. For instance, LSPUSH returns the number of pushed messages, but at the same time GET should be able to return an Int too. This led to Int's FromResp looking like this

instance FromResp Int where
    fromResp (BulkString bs) =
        case parseOnly (AC8.signed AC8.decimal) bs of
            Left s -> Left $ RespError "FromResp" (TL.pack s)
            Right n -> Right n
    fromResp (Number n) = Right $ fromEnum n
    fromResp _ = Left $ RespError "FromResp" "Unexpected value"

I could see this becoming worse, take the instance for Bool, I'd have to consider that

• for MOVE Integer 1 means True and Integer 0 means False
• for SET SimpleString "OK" means True
• users would justifiably expect a bunch of bytestrings to be True, e.g. BulkString "true", BulkString "TRUE", BulkString "1", etc

However, it's impossible to cover all ways users can encode a Bool in a ByteString so no matter what I do users will end up having to wrap their Bool with newtype and implement a fitting FromResp. On top of that, even thought I haven't found any example of it yet, I fully expect there to be, somewhere in the large set of Redis commands, at least two commands each wanting an instance of a basic type that simply can't be combined into a single instance, meaning that the client library would need to do some newtype wrapping too.

No, I really didn't like it! So, could I get rid of FromResp and still offer users an API where they can user their own types as the result of commands?

To be concrete I wanted this

data Cmd r where
    -- other commands
    Get :: (ToKey k) => k -> Cmd (Maybe ByteString)

and I wanted the user to be able to conveniently turn a Cmd r into a Cmd s. In other words, I wanted a Functor instance. Making Cmd itself a functor isn't necessary and I just happened to already have a functor type that wraps Cmd, the Command type I used for pipelining. If I were to use that I'd need to write wrapper functions for each command though, but if I did that then I could also remove the ToKey~/~ToArg constraints from the constructors of Cmd r and put them on the wrapper instead. I'd get

data Cmd r where
    -- other commands
    Get :: Key -> Cmd (Maybe ByteString)

get :: (ToKey k) => k -> Command (Maybe ByteString)
get = Command id . Get . toKey

I'd also have to rewrite fromWireResp so it's more specific for each command. Instead of

fromWireResp :: Cmd r -> Resp -> Either RespError r
fromWireResp (Get _) = fromResp
...

I had to match up exactly on the possible replies to GET

fromWireResp :: Cmd r -> Resp -> Either RespError r
fromWireResp _ (SimpleError err desc) = Left $ RespError (T.decodeUtf8 err) (T.decodeUtf8 desc)
fromWireResp (Get _) (BulkString bs) = Right $ Just bs
fromWireResp (Get _) Null = Right Nothing
...
fromWireResp _ _ = Left $ RespError "fromWireResp" "Unexpected value"

Even though it was more code I liked it better than before, and I think it's slightly simpler code. I also hope it makes the use of the API is a bit simpler and clear.

Here's an example from the code for the service I wrote for work. It reads a UTC timestamp stored in timeKey, the timestamp is a JSON string so it needs to be decoded.

readUTCTime :: Connection -> IO (Maybe UTCTime)
readUTCTime conn =
    sendCmd conn (maybe Nothing decode <$> get timeKey) >>= \case
        Left _ -> pure Nothing
        Right datum -> pure datum

What's next?

I'm pretty happy with the command type for now, though I have a feeling I'll have to revisit Arg and ToArg at some point.

I've just turned the Connection type into a pool using resource-pool, and I started looking at pub/sub. The latter thing, pub/sub, will require some thought and experimentation I think. Quite possibly it'll end up in a post here too.

I also have a lot of commands to add.

Footnotes:

¹

Of course one could use RESP3 as the serialisation format for storing values in Redis. Personally I think I'd prefer using something more widely used, and easier to read, such as JSON or BSON.

Tags: haskell redis

June 20, 2025 09:40 PM

GHC activities report: March–May 2025

This is the twenty-seventh edition of our GHC activities report, which describes the work Well-Typed are doing on GHC, Cabal, HLS and other parts of the core Haskell toolchain. The current edition covers roughly the months of March 2025 to May 2025. You can find the previous editions collected under the ghc-activities-report tag.

Sponsorship

We offer Haskell Ecosystem Support Packages to provide commercial users with support from Well-Typed’s experts, while investing in the Haskell community and its technical ecosystem including through the work described in this report. To find out more, read our recent announcement of these packages in partnership with the Haskell Foundation. We need funding to continue this essential maintenance work!

Many thanks to our Haskell Ecosystem Supporters: Channable and QBayLogic; to our existing clients who also contribute to making this work possible: Anduril, Juspay and Mercury; and to the HLS Open Collective for supporting HLS release management.

Team

The Haskell toolchain team at Well-Typed currently includes:

• Andreas Klebinger
• Ben Gamari
• Matthew Pickering
• Rodrigo Mesquita
• Sam Derbyshire
• Hannes Siebenhandl
• Zubin Duggal
• Mikolaj Konarski

In addition, many others within Well-Typed contribute to GHC, Cabal and HLS occasionally, or contribute to other open source Haskell libraries and tools.

GHC

Highlights

Explicit level imports

Following on from our best paper prize at TFP 2025, Matthew implemented Explicit Level Imports (GHC proposal #682, !14241).

This feature allows one to specify whether imports are needed for running Template Haskell splices, or for generating Template Haskell quotes. This cleanly separates which modules are required at compile-time vs those that are required at runtime. For example, the pandoc package uses the Template Haskell deriveJSON function from the aeson package. This function can be imported using a splice import:

{-# LANGUAGE ExplicitLevelImports #-}
{-# LANGUAGE TemplateHaskell #-}
module Text.Pandoc.App.Opt where
import splice Data.Aeson.TH (deriveJSON, defaultOptions)
-- + many other non-splice imports

data XYZ = ...
$(deriveJSON defaultOptions ''XYZ)

Declaring the Data.Aeson.TH import as a splice import informs GHC that this module is required only at compile-time, and (crucially) that other, non-splice, imports, are not needed at compile time. This hugely improves the performance of tools that use -fno-code (such as HLS), as GHC is no longer required to pessimistically assume that all modules imported in a module enabling TemplateHaskell are required at compile-time.

GHCi support for primops

Andreas significantly improved GHCi performance by implementing certain GHC primops (such as integer arithmetic operations) directly in the bytecode interpreter (!13978).

Reductions in runtime of up to 50% have been observed, with GHC-in-GHCi speeding up by about 15%.

Improvements to the debugger

Rodrigo has made numerous improvements to the GHCi debugger, which had accumulated many bugs over the years due to lack of maintenance (!14246, !14195, !14160, !14106, !14196, !14195, !13997). Usability is improved across the board, with quality-of-life fixed such as adding breakpoints to all statements in a do block to make debugging more predictable (#25932) to significant performance improvements to :steplocal (#25779).

Rodrigo also published the ghc-debugger package including an executable ghc-debug-adapter. This implements the Debug Adapter Protocol, enabling Haskell programs to be stepped-through and debugged from editors such as Visual Studio Code. ghc-debug-adapter depends on many recent changes to GHC, so it is compatible only with the upcoming GHC 9.14.

Expressions in SPECIALISE pragmas

Sam worked with Simon Peyton Jones to finalise MR !12319 “Expressions in SPECIALISE pragmas”. This change means that a SPECIALISE pragma is no longer required to simply be a type signature, it can be an arbitrary expression. For full details, see GHC proposal #493, but two particular idioms are worth noting. Firstly, the type at which to specialise can now be specified by a type application, e.g.

myFunction :: forall a. Num a => a -> Maybe a -> (a, a)
myFunction = ...
{-# SPECIALISE myFunction @Int #-}

This specialise pragma is much more concise than:

{-# SPECIALISE :: Int -> Maybe Int -> (Int, Int) #-}

and less prone to breakage when the type of myFunction changes.

Secondly, the syntax enables value specialisation, for example:

mainFunction :: Bool -> ...
mainFunction debug = if debug then ... else ...
{-# SPECIALISE mainFunction False #-}

This tells GHC to optimise the non-debug code path, without the debug logic potentially getting in the way.

Multiple Home Units support in GHCi

GHC 9.14 is fully compatible with multiple home units, including all GHCi commands and the GHCi debugger, thanks to work by Hannes about which we recently published a blog post (!14231). Our new design generalises the architecture of GHCi so that multi-unit and single-unit sessions are handled in the same way. The uniform handling will make sure that multi-unit sessions work correctly as GHCi evolves.

GHC Releases

• Ben released GHC 9.12.2 in March.

• Thanks to Luite Stegeman from IOG who released GHC 9.6.7 in March.

• Zubin released GHC 9.10.2 in May.

• The team are now working towards the release of GHC 9.14.1 later this year.

• After various community discussions, GHC HQ are planning to start designating some major release series as Long Term Support. This means increasing the length of the support window for LTS releases and reducing it for non-LTS releases.

Frontend

• Sam fixed a regression in the implementation of QuickLook in GHC 9.12 that would cause valid programs to be rejected (#26030, #25950, !14235).

• Sam fixed a problem in which HasCallStack evidence was incorrectly cached in GHC, causing GHC to bogusly report identical call stacks (#25529, !14084).

• Sam rectified several oversights in the initial implementation of the NamedDefaults language extension laid out in GHC proposal #409:

  • an issue with exporting named defaults (#25857, !14142),
  • lack of support for named default declarations for poly-kinded typeclasses such as Typeable (#25882, !14143),
  • an oversight in which NamedDefaults changed the behaviour of existing programs (#25775, !14075, ghc-proposals#694).

• Sam fixed duplicate record fields sometimes being reported as unused when they are actually used (#24035, !14066).

• Sam improved the error message emitted by GHC when one attempts to write a non-class at the head of a typeclass instance (#22688, !14105).

• Sam fixed several issues with the renaming of export lists:

  • one issue involved the TypeData extension (#24027, !14119),
  • another was to do with bundled pattern synonyms (#25892, !14154).

• Sam made “illegal term-level use” error messages more user friendly (#23982, !14122). That MR also improved the way GHC reports name qualification to the user, preferring to display the user-written qualification in error messages.

• Sam fixed GHC creating unnecessary cycle-breaker variables, which could cause problems for type-checking plugins that weren’t expecting them (#25933, !14206).

• Sam implemented the deprecation described in GHC proposal #448: the combination of ScopedTypeVariables and TypeApplications no longer enables the use of type applications in constructor patterns, requiring instead the TypeAbstractions extension (!13551).

• Sam fixed an issue in which equal types compared non-equal under TypeRep-equality by implementing a suggestion by Krzysztof Gogolewski (#25998, !14281).

• Sam improved the documentation surrounding defaulting in the user’s guide, providing a high-level overview of the different mechanisms in GHC for defaulting ambiguous type variables (#25807, !14057).

Backend

• Ben and Sam investigated testsuite failures in the LLVM backend (#25769). They identified many different issues:

  • #25730 concerned incorrect type annotations in the generated LLVM, fixed in !13936.
  • #25770, #25773 were symptoms of a serious bug in the implementation of floating-point register padding (fixed in !14134),
  • !14129 fixed incorrect type annotations in the LLVM for atomic operations, adding new tests to Cmm Lint to avoid similar bugs in the future.
  • Most of the other bugs involved initializers/finalizers, which were due to incorrect linkage annotation for builtin arrays (fixed in !14157).

• Rodrigo worked with Simon Peyton Jones to fix an issue in which the presence or absence of unrelated RULES could affect compilation, leading to non-deterministic compilation (#25170, !13884).

• Andreas fixed a bug in which GHC would construct over-saturated constructor applications, which caused a panic when building the xmonad-contrib package (#23865, !14036).

• Andreas made GHC constant-fold away invalid tagToEnum# calls to a particular error expression, which unlocks dead-code elimination opportunities and makes it easier to debug issues that arise from invalid use of tagToEnum# (#25976, !14254)

• Andreas added -fhuge-code-sections, an off-by-default flag that provides a workaround for AArch64 users running into bug #24648.

• Matthew overhauled the driver to bring one-shot compilation and make mode in line with each other, by consistently using the module graph to answer queries related to the module import structure (!14198, !14209). This was partly motivated by implementation requirements of the “Explicit Splice Imports” proposal, for which module graph queries are a central component.

• Matthew added support for “fixed” nodes in the module graph, which can be used for modules without corresponding source-files that are e.g. generated via the GHC API (#25920, !14187).

• Rodrigo moved some DynFlags consistency checks in order to consolidate the logic into the core makeDynFlagsConsistent function.

• Ben changed how GHC prints Uniques to the user to avoid NULL characters (#25989, !14265).

Compiler performance

• Matthew improved the performance of the bytecode assembler by ensuring the code is properly specialised (!13983).

• Matthew made sure that forceModIface properly forced all fields of ModIface in order to avoid space leaks (!14078).

• Matthew removed unused mi_used_th and mi_hpc fields from interfaces, which were needlessly bloating interface files (!14073).

• Matthew avoided allocation of intermediate ByteStrings when serialising FastStrings (#25861, !14107).

Recompilation checking

• Matthew overhauled the ModIface datatype, splitting it up in a more logical way which makes it easier to identify which parts contribute to recompilation checking (!14102). This allowed fixing several issues with recompilation checking in !14118, such as:

  • it ignored changes in exported named default declarations (#25855),
  • it did not take into account changes to COMPLETE pragmas (#25854).

• Matthew added the -fwrite-if-self-recomp flag which controls whether to include self-recompilation information, which avoids writing recompilation information in cases such as producing binary distributions for which recompilation is not a concern (#10424, #22188, !8604).

• Matthew refactored the implementation of recompilation-checking to ensure that all flags that influence recompilations are correctly taken into account (#25837, !14085).

• Sam improved recompilation checking for export lists in !14178 (#25881). In practice, this means that modules with explicit import lists will no longer always trigger the recompilation of a module they depend on when that module’s export list changes, as long as the explicitly imported items are preserved.

• Matthew improved the output of -dump-hi-diff to properly display the precise change in flags which caused recompilation (#25571, !13792).

Runtime system

• Ben fixed a bug in which the WinIO I/O manager was being inconsistently selected (#25838, !14088).

• Ben diagnosed and fixed a linking issue affecting global offset table usage on macOS that manifested in incorrect runtime results when using the GHC API (#25577, !13991).

• Ben fixed an issue in which GHC’s RTS linker was too eager to load shared objects which refer to undefined symbols (#25943, !14290).

• Ben significantly improved the performance of the RTS linker, culminating in a reduction in GHCi startup time from 2.5s to 250ms on Windows (#26052, #26009, !14339).

GHCi & bytecode interpreter

• Andreas fixed several endianness issues in the interpreter (#25791, !14172).

• Matthew implemented a fix for the mishandling of stack underflow frames (#25750, !13957). A remaining issue was subsequently identified (#25865) and fixed by Andreas’ work on the interpreter (!13978).

• Matthew ensured that all top-level functions are visible when loading a module in the interpreter, not only exported functions (!14032).

• Matthew fixed a bug in the simplifier that caused Core Lint failures when compiling certain programs (#25790, !14019).

• Matthew fixed a regression in the way that GHCi would import modules that involved Cabal mixins stanzas (#25951, !14222).

Libraries

• Ben exposed the constructors and fields of the Backtrace datatype in base (#26049, !14351).

• Ben brought base changelog entries up to date in !14320.

Build system & packaging

• Sam fixed GHC not working properly if the installation path contains spaces on Windows (#25204, !14137).

• Ben fixed a couple of issues relating to the llvm-as flag:

  • the value of the field was incorrectly set (#25856, !14104),
  • the information in the field was passed incorrectly to clang (#25793, !14025).

Testsuite

• Andreas fixed a bug in which tests requiring the interpreter would be run even if the compiler didn’t support it (#25533, !14201).

• Matthew fixed an issue with tests that used Template Haskell in the profiled dynamic way (#25947, !14215).

Cabal

• Mikolaj prepared the 3.14.2.0 bugfix release to the Cabal package suite (including the Cabal library and cabal-install).

• Matthew fixed all known regressions in the 3.14.1.0 release of cabal-install:

  • Issue #10759 to do with picking up unwanted environment files #10828.
  • Duplication of environment variables (#10718, #10827).
  • Interaction of multi-repl with internal dependencies (#10775, #10841).
  • A working directory oversight (#10772, #10800).
  • The pkgname_datadir environment variable incorrectly using a relative path (#10717, #10830).

• Matthew updated the outdated and gen-bounds commands to work with the v2- project infrastructure (#10878, #10840).

• Matthew ensured that C++ environment variables are passed to configure scripts (#10797, #10844).

• Matthew added a module name validity check to the cabal check command (#10295, #10816).

• Matthew updated the Cabal CI to use GHC 9.12.2 and GHC 9.6.7 (#10893).

• Matthew improved the testsuite output to make it more readable (#8419, #10837).

• Matthew fixed an issue in which changes to the PATH environment variable would incorrectly not trigger recompilation (#2015, #10817).

HLS

• Hannes prepared the HLS release 2.10.0.0 (#4448)

• Zubin prepared the HLS release 2.11.0.0 (#4585)

• Zubin added support for GHC 9.12.2 in HLS (#4527)

• Zubin reworked the HLS release CI infrastructure (#4481)

Haskell.org infrastructure

Ben worked to refactor and migrate a variety of core haskell.org services from Equinix Metal to new infrastructure at OpenCape:

• hoogle.haskell.org has been Nixified and now periodically reindexes automatically.

• Haskell.org’s primary mail server, mail.haskell.org, has been Nixified and updated.

• Haskell.org’s many mailing lists have been migrated to Mailman 3

• gitlab.haskell.org has been migrated to OpenCape and updated

• The Hackage documentation builder has been completely revamped with a more maintainable deployment strategy and a broader set of native packages available, enabling more Hackage packages to benefit from automatically-built documentation.

With these maintainability improvements we hope that haskell.org’s core infrastructure team can be more easily grown in the future.

by adam, andreask, ben, hannes, matthew, mikolaj, rodrigo, sam, zubin at June 20, 2025 12:00 AM

Why I'm writing a Redis client package

A couple of weeks ago I needed a small, hopefully temporary, service at work. It bridges a gap in functionality provided by a legacy system and the functionality desired by a new system. The legacy system is cumbersome to work with, so we tend to prefer building anti-corruption layers rather than changing it directly, and sometimes we implement it as separate services.

This time it was good enough to run the service as a cronjob, but it did need to keep track of when it ran the last time. It felt silly to spin up a separate DB just to keep a timestamp, and using another service's DB is something I really dislike and avoid.¹ So, I ended up using the Redis instance that's used as a cache by a OSS service we host.

The last time I had a look at the options for writing a Redis client in Haskell I found two candidates, hedis and redis-io. At the time I wrote a short note about them. This time around I found nothing much has changed, they are still the only two contenders and they still suffer from the same issues

• hedis has still has the same API and I still find it as awkward.
• redis-io still requires a logger.

I once again decided to use hedis and wrote the service for work in a couple of days, but this time I thought I'd see what it would take to remove the requirement on tinylog from redis-io. I spent a few evenings on it, though I spent most time on "modernising" the dev setup, using Nix to build, re-format using fourmolu, etc. I did the same for redis-resp, the main dependency of redis-io. The result of that can be found on my gitlab account:

• https://gitlab.com/magus/redis-resp
• https://gitlab.com/magus/redis-io

At the moment I won't take that particular experiment any further and given that the most recent change to redis-io was in 2020 (according to its git repo) I don't think there's much interest upstream either.

Making the changes to redis-io and redis-resp made me a little curious about the Redis protocol so I started reading about it. It made me start thinking about implementing a client lib myself. How hard could it be?

I'd also asked a question about Redis client libs on r/haskell and a response led me to redis-schema. It has a very good README, and its section on transactions with its observation that Redis transactions are a perfect match for Applicative. This pushed me even closer to start writing a client lib. What pushed me over the edge was the realisation that pipelining also is a perfect match for Applicative.

For the last few weeks I've spent some of my free time reading and experimenting and I'm enjoying it very much. We'll see where it leads, but hopefully I'll at least have bit more to write about it.

Footnotes:

¹

One definition of a microservice I find very useful is "a service that owns its own DB schema."

Tags: haskell redis

June 17, 2025 08:43 PM

Two Pointer Algorithms

We’re now on to part 5 of our series comparing Haskell and Rust solutions for LeetCodeproblems. You can also look at the previous parts (Part 1, Part 2, Part 3, Part 4) to get some more context on what we’ve learned so far comparing these two languages.

For a full look at problem solving in Haskell, check out Solve.hs, our latest course! You’ll get full breakdowns on the processes for solving problems in Haskell, from basic list and loop problems to advanced algorithms!

The Problem

Today we’ll be looking at a problem called Trapping Rain Water. In this problem, we’re given a vector of heights, which form a sort of 1-dimensional topology. Our job is to figure out how many units of water could be collected within the topology.

As a very simple example, the input [1,0,2] could collect 1 unit of water. Here’s a visualization of that system, where x shows the topology and o shows water we collect:

x
xox

We can never collect any water over the left or right “edges” of the array, since it would flow off. The middle index of our array though is lower than its neighbors. So we take the lower of these neighboring values, and we see that we can collect 1 unit of water in this system.

For a bigger example that collects water, we might have the input [4, 2, 1, 1, 3, 5]. Here’s what that looks like:

x
x o o o o x
x o o o x x 
x x o o x x
x x x x x x

The total water here is 9.

A flat system like [2,2,2], or a system that looks like a peak [1,2,3,2,1] cannot collect any water, so we should return 0 in these cases.

The Algorithm

There are a couple ways to solve this. One approach would be a two-pass solution, similar to what we used in Product of Array Except Self. We loop from the left side, tracking the maximum water we can store in each unit based on its left neighbors. Then we loop again from the right side and compare the maximum we can store based on the right neighbors to the prior value from the left. This solution is O(n) time, but O(n) space as well.

A more optimal solution for this problem is a two-pointer approach that can use O(1) additional space. In this kind of solution, we look at the left and right of the input simultaneously. Each step of the way, we make a decision to either increase the “left pointer” or decrease the “right pointer” until they meet in the middle. Each time we move, we get more information about our solution.

In this particular problem, we’ll track the maximum value we’ve seen from the left side and the maximum value we’ve seen from the right side. As we traverse each index, we update both sides for the current left and right indices if we have a new maximum.

The crucial step is to see that if the current “left max” is smaller than the current “right max”, we know how much water can be stored at the left index. This is just the left max minus the left index. Then we can increment the left index.

If the opposite is true, we calculate how much water can be stored at the right index, and decrease the right index.

So we keep a running tally of these sums, and we end our loop when they meet in the middle.

Rust Solution

We can describe our algorithm as a simple while loop. This loop goes until the left index exceeds the right index. The loop needs to track 5 values:

1. Left Index
2. Right Index
3. Left Max
4. Right Max
5. Total sum so far

So let’s write the setup portion of the loop:

pub fn trap(height: Vec<i32>) -> i32 {
    let mut leftMax = -1;
    let mut rightMax = -1;
    let mut leftI = 0;
    let mut rightI = height.len() - 1;
    let mut total = 0;
    while leftI <= rightI {
        ...
    }
}

A subtle thing…the constraints on the LeetCode problem are that the length is at least 1. But to handle length 0 cases, we would need a special case. Rust uses unsigned integers for vector length, so taking height.len() - 1 on a length-0 vector would give the maximum integer, and this would mess up our loop and indexing.

Within the while loop, we run the algorithm.

1. Adjust leftMax and rightMax if necessary.
2. If leftMax is not larger, recurse, incrementing leftI and adding to total from the left
3. If rightMax is smaller, decrement rightI and add total from the right

And at the end, we return our total!

pub fn trap(height: Vec<i32>) -> i32 {
    let n = height.len();
    if n <= 1 {
        return 0;
    }
    let mut leftMax = -1;
    let mut rightMax = -1;
    let mut leftI = 0;
    let mut rightI = n - 1;
    let mut total = 0;
    while leftI <= rightI {
        // Step 1
        leftMax = std::cmp::max(leftMax, height[leftI]);
        rightMax = std::cmp::max(rightMax, height[rightI]);
        if leftMax <= rightMax {
            // Step 2
            total += leftMax - height[leftI];
            leftI += 1;
        } else {
            // Step 3
            total += rightMax - height[rightI];
            rightI -= 1;
        }
    }
    return total;
}

Haskell Solution

Now that we’ve seen our Rust solution with a single loop, let’s remember our process for translating this idea to Haskell. With a two-pointer loop, the way in which we traverse the elements of the input is unpredictable, thus we need a raw recursive function, rather than a fold or a map.

Since we’re tracking 5 integer values, we’ll want to write a loop function that looks like this:

-- (leftIndex, rightIndex, leftMax, rightMax, sum)
loop :: (Int, Int, Int, Int, Int) -> Int

Knowing this, we can already “start from the end” and figure out how to invoke our loop from the start of our function:

trapWater :: V.Vector Int -> Int
trapWater input = loop (0, n - 1, -1, -1, 0)
  where
    n = V.length input

    loop :: (Int, Int, Int, Int, Int) -> Int
    loop = undefined

In writing our recursive loop, we’ll start with the base case. Once leftI is the bigger index, we return the total.

trapWater :: V.Vector Int -> Int
trapWater input = loop (0, n - 1, -1, -1, 0)
  where
    n = V.length input

    loop :: (Int, Int, Int, Int, Int) -> Int
    loop (leftI, rightI, leftMax, rightMax, total) = if leftI > rightI then total
      else …

Within the else case, we just follow our algorithm, with the same 3 steps we saw with Rust.

trapWater :: V.Vector Int -> Int
trapWater input = loop (0, n - 1, -1, -1, 0)
  where
    n = V.length input

    -- (leftIndex, rightIndex, leftMax, rightMax, sum)
    loop :: (Int, Int, Int, Int, Int) -> Int
    loop (leftI, rightI, leftMax, rightMax, total) = if leftI > rightI then total
      else
        -- Step 1
        let leftMax' = max leftMax (input V.! leftI)
            rightMax' = max rightMax (input V.! rightI)
        in  if leftMax' <= rightMax'
              -- Step 2
              then loop (leftI + 1, rightI, leftMax', rightMax', total + leftMax' - input V.! leftI)
              -- Step 3
              else loop (leftI, rightI - 1, leftMax', rightMax', total + rightMax' - input V.! rightI)

And we have our Haskell solution!

Conclusion

If you’ve been following this whole series so far, hopefully you’re starting to get a feel for comparing basic algorithms in Haskell and Rust (standing as a proxy for most loop-based languages). In general, we can write loops as recursive functions in Haskell, capturing the “state” of the list as the input parameter for that function.

In particular cases where each iteration deals with exactly one element of an input list, we can employ folds as a tool to simplify our functions. But the two-pointer algorithm we explored today falls into the general recursive category.

To learn the details of understanding these problem solving techniques, take a look at our course, Solve.hs! You’ll learn everything from basic loop and list techniques, to advanced data structures and algorithms!

by James Bowen at June 16, 2025 08:30 AM

Making GHCi compatible with multiple home units

GHC’s support for compiling multiple units in a single invocation is essential for tooling to work well with real-world Haskell projects. Loading your whole project into a single GHCi session allows you to get feedback quickly on changes to any part of your project, without having to restart the REPL. Until now, not all of GHCi worked with multiple home units, and this was a source of confusion for many users.

We’re now happy to announce that in 9.14.1, GHCi will fully support multiple home units. This post contains a brief overview of the changes.

Multiple Home Units

Work on multiple home units has been ongoing for a while. This is the latest chapter in our efforts to update the ecosystem to support this feature.

• GSOC 2020: Multiple Home Units (Hannes)
• The Interface for Multiple Home Units (Matthew)
• Multi Component support for cabal repl (Matthew)
• Multi Component support in HLS with cabal-install 3.12 (Zubin)

The main way to start a multi-unit GHCi session is by using cabal repl --enable-multi-repl with a selector that selects multiple components in the project, such as all:

> cabal repl --enable-multi-repl all

This will start a GHCi session with a home unit for each selected component. Until now, support in the REPL was essentially limited to reloading modules to get feedback about changes. Almost all other commands were unsupported when using multiple home units.

GHCi Supports Multiple Home Units

Following our changes, GHCi now fully supports multiple home units in its REPL. The experience of a user is now the same whether they are using a single home unit or multiple home units. In particular, the following features have been fixed or enabled:

• Usual REPL usage such as evaluating expressions
• All GHCi commands
  • :seti/:set
  • :browse
  • :module [+/-] [*]Mod1 ...
  • … and many more!
• The GHCi debugger
  • :break, :steplocal, :continue, etc…

Implementing Multi Unit Support in GHCi

To fully support multiple home units, GHCi needed a new internal model of how different contexts interact during a session. There are three key contexts:

• the prompt (the context in which expressions are evaluated),
• the script context (in which scripts loaded by :load are executed), and
• the unit context (the home units specified on the command line, e.g. the components of the Cabal packages being loaded).

Distinguishing these three different contexts is the key to our design. Before, each GHCi session only had a single home unit, and so commands would always be interpreted relative to that unit. In a multi-unit session, one of the units was chosen as the “active” unit, and commands would be interpreted relative to that unit. Now since it is possible to talk precisely about the different contexts, the dependencies between them and where commands should be interpreted, we can properly implement all GHCi commands.

Virtual home units

Our design adds virtual home units for the prompt and script contexts. Therefore, every GHCi session is a multi-unit session, and all commands are modified to support this.

This virtual home unit for the prompt is called interactive-ghci. All user input is interpreted in the context of interactive-ghci (it is the “active” unit). Since it always depends on all user-given home units (i.e. those given on the command line), we can import modules, run code, and execute GHCi commands as usual.

The virtual home unit for scripts is called interactive-session. It is similar in structure to interactive-ghci, namely that it depends on all user-given home units. This allows scripts to use packages from the current GHCi REPL session. Additionally, interactive-ghci depends on interactive-session, allowing the user to load and execute the script modules from the prompt.

Why do we need two virtual home units? When a script is loaded via :load Mod.hs, this Mod.hs needs to be interpreted relative to some home unit. We do not want to guess which home unit Mod.hs should be added to, since the behaviour is hard to predict in a multiple home unit session. However, we also can’t add Mod.hs to the interactive-ghci home unit, as we want to be able to maintain a different set of GHC options for the prompt (i.e. interactive-ghci) and scripts.

Adding these two virtual home units to the GHCi REPL session yields the following Home Unit Graph. We mark interactive-ghci to indicate that it is the “active” context of the GHCi prompt.

Examples

Now that we know how the GHCi session will work, let’s show a couple of concrete examples.

We assume a regular cabal project, initialised via the command:

> mkdir mhu-example && cd mhu-example
> cabal init -n --tests --libandexe

This creates a cabal project with three components:

• lib:mhu-example: The main library.
• exe:mhu-example: An executable.
• test:mhu-example-test: A test-suite.

From the perspective of GHC, a unit is essentially identical to a single component (with some hand-waving).

When we load only the library into a GHCi session, then the library is the single user-specified home unit in the GHCi session. For example, the cabal invocation

cabal repl lib:mhu-example

invokes the following GHC command:

ghc --interactive -this-unit-id lib-mhu-example -package base -package containers ...

This creates a home unit graph with three home units: interactive-ghci, interactive-session and mhu-example-library.

In the case of more than one user-specified home unit, the graph is extended in an intuitive way. For example, the cabal invocation

cabal repl --enable-multi-repl lib:mhu-example exe:mhu-example test:mhu-example-test

will result in the following GHC invocation:¹

ghc --interactive -unit @lib-mhu-example -unit @exe-mhu-example -unit @test-mhu-example-test

GHCi internally structures this as the following:

Naturally, home units can have dependencies on other home units, e.g. test:mhu-example-test and exe:mhu-example both depend on lib:mhu-example.

Setting REPL Options

The GHCi commands :set and :seti are used to change the GHC options of the home units and the ghc options for the prompt respectively. In the new architecture, the :set command applies the new options to all home units except interactive-ghci. :seti, on the other hand, applies changes only to the interactive-ghci home unit.

In the future, we may want to extend the capabilities of the :set command to change the GHC options only for certain home units.

Summary

GHCi is now fully compatible with multiple home units, including all GHCi commands and the GHCi debugger. Our new design generalises the architecture of GHCi so that multi-unit and single-unit sessions are handled in the same way. The uniform handling will make sure that multi-unit sessions work correctly as GHCi evolves.

This work has been performed in collaboration with Mercury, who have a long-term commitment to the scalability and robustness of the Haskell ecosystem. Well-Typed are always interested in projects and looking for funding to improve GHC and other Haskell tools. Please contact info@well-typed.com if we might be able to work with you!

---

1. The unit arguments are passed using response files. The file exe-mhu-example contains the arguments for the exe:mhu-example home unit, and similarly for the other files.↩︎

by hannes, matthew at June 16, 2025 12:00 AM

Monads are not like burritos

Monads are not like burritos

Posted on June 16, 2025
Tagged monad, pedagogy, meme, burrito, analogy, Haskell

In January 2009, while just a baby first-year PhD student, I wrote a blog post titled Abstraction, intuition, and the “monad tutorial fallacy”. In it, I made the argument that humans tend to learn best by first grappling with concrete examples, and only later proceeding to higher-level intuition and analogies; hence, it’s a mistake to think that clearly presenting your intuition for a topic will help other people understand it. Analogies and intuition can help, but only when accompanied by concrete examples and active engagement. To illustrate the point, I made up a fictitious programmer with a fictitious analogy.

But now Joe goes and writes a monad tutorial called “Monads are Burritos,” under the well-intentioned but mistaken assumption that if other people read his magical insight, learning about monads will be a snap for them. “Monads are easy,” Joe writes. “Think of them as burritos.” Joe hides all the actual details about types and such because those are scary, and people will learn better if they can avoid all that difficult and confusing stuff. Of course, exactly the opposite is true, and all Joe has done is make it harder for people to learn about monads…

My intention was to choose a fictitious analogy which was obviously ridiculous and silly, as a parody of many of the monad tutorials which existed at the time (and still do). Mark Jason Dominus then wrote a blog post, Monads are like burritos, pointing out that actually, monads are kinda like burritos. It’s really funny, though I don’t think it’s actually a very good analogy, and my guess is that Mark would agree: it was clearly written as a silly joke and not as a real way to explain monads.

In any case, from that point the “monads are burritos” meme took on a life of its own. For example:

• Chris Done made a webcomic about it
• Ed Morehouse wrote a ridiculous paper exploring the categorical foundations of burritos
• Someone made a burrito library in Rust
• Dr Eugenia Cheng tweeted about it

I even joined in the fun and made this meme image about bad monad tutorials:

Of course there are lots of people who still understand that it was all just a silly joke. Recently, however, I’ve seen several instances where people apparently believe “monads are burritos” is a real, helpful thing and not just a joke meme. For example, see this thread on lobste.rs, or this Mastodon post.

So, to set the record straight: “monads are burritos” is not a helpful analogy!Yes, I am writing a blog post because People Are Wrong On The Internet, and I know it probably won’t make any difference, but here we are.

Why not, you ask? To expand on my reasons from a 10-year-old Reddit comment:

• The burrito analogy strongly implies that a value of type m a somehow “contains” a value (or values) of type a. But that is not true for all monads (e.g. there is no sense in which a value of type IO String contains a String).
• Relatedly, the analogy also implies that a value of type m a can be “unwrapped” to get an a, but this is impossible for many monads.
• It is not actually very easy to take a burrito containing a burrito and merge it into a single-level burrito. At least this is not in any sense a natural operation on burritos. Perhaps you could argue that it is always easy to remove outer tortilla layers (but not the innermost one since the food will all fall out), but this is a bad analogy, since in general join does not just “remove” an outer layer, but somehow merges the effects of two layers into one.

Actually, burritos are a great analogy for the Identity monad! …but not much beyond that.

On a more positive note, my sense is that the average pedagogical quality of Haskell materials, and monad tutorials in particular, has indeed gone up significantly since 2009. I’d love to think this can be at least partially attributed to my original blog post, though of course it’s impossible to know that for sure.

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by Brent Yorgey at June 16, 2025 12:00 AM

PenroseKiteDart User Guide

Introduction

(Updated June 2025 for PenroseKiteDart version 1.4)

PenroseKiteDart is a Haskell package with tools to experiment with finite tilings of Penrose’s Kites and Darts. It uses the Haskell Diagrams package for drawing tilings. As well as providing drawing tools, this package introduces tile graphs (Tgraphs) for describing finite tilings. (I would like to thank Stephen Huggett for suggesting planar graphs as a way to reperesent the tilings).

This document summarises the design and use of the PenroseKiteDart package.

PenroseKiteDart package is now available on Hackage.

The source files are available on GitHub at https://github.com/chrisreade/PenroseKiteDart.

There is a small art gallery of examples created with PenroseKiteDart here.

Index

1. About Penrose’s Kites and Darts
2. Using the PenroseKiteDart Package (initial set up).
3. Overview of Types and Operations
4. Drawing in more detail
5. Forcing in more detail
6. Advanced Operations
7. Other Reading

1. About Penrose’s Kites and Darts

The Tiles

In figure 1 we show a dart and a kite. All angles are multiples of (a tenth of a full turn). If the shorter edges are of length 1, then the longer edges are of length , where is the golden ratio.

Aperiodic Infinite Tilings

What is interesting about these tiles is:

It is possible to tile the entire plane with kites and darts in an aperiodic way.

Such a tiling is non-periodic and does not contain arbitrarily large periodic regions or patches.

The possibility of aperiodic tilings with kites and darts was discovered by Sir Roger Penrose in 1974. There are other shapes with this property, including a chiral aperiodic monotile discovered in 2023 by Smith, Myers, Kaplan, Goodman-Strauss. (See the Penrose Tiling Wikipedia page for the history of aperiodic tilings)

This package is entirely concerned with Penrose’s kite and dart tilings also known as P2 tilings.

Legal Tilings

In figure 2 we add a temporary green line marking purely to illustrate a rule for making legal tilings. The purpose of the rule is to exclude the possibility of periodic tilings.

If all tiles are marked as shown, then whenever tiles come together at a point, they must all be marked or must all be unmarked at that meeting point. So, for example, each long edge of a kite can be placed legally on only one of the two long edges of a dart. The kite wing vertex (which is marked) has to go next to the dart tip vertex (which is marked) and cannot go next to the dart wing vertex (which is unmarked) for a legal tiling.

Correct Tilings

Unfortunately, having a finite legal tiling is not enough to guarantee you can continue the tiling without getting stuck. Finite legal tilings which can be continued to cover the entire plane are called correct and the others (which are doomed to get stuck) are called incorrect. This means that decomposition and forcing (described later) become important tools for constructing correct finite tilings.

2. Using the PenroseKiteDart Package

You will need the Haskell Diagrams package (See Haskell Diagrams) as well as this package (PenroseKiteDart). When these are installed, you can produce diagrams with a Main.hs module. This should import a chosen backend for diagrams such as the default (SVG) along with Diagrams.Prelude.

    module Main (main) where
    
    import Diagrams.Backend.SVG.CmdLine
    import Diagrams.Prelude

For Penrose’s Kite and Dart tilings, you also need to import the PKD module and (optionally) the TgraphExamples module.

    import PKD
    import TgraphExamples

Then to ouput someExample figure

    fig::Diagram B
    fig = someExample

    main :: IO ()
    main = mainWith fig

Note that the token B is used in the diagrams package to represent the chosen backend for output. So a diagram has type Diagram B. In this case B is bound to SVG by the import of the SVG backend. When the compiled module is executed it will generate an SVG file. (See Haskell Diagrams for more details on producing diagrams and using alternative backends).

3. Overview of Types and Operations

Half-Tiles

In order to implement operations on tilings (decompose in particular), we work with half-tiles. These are illustrated in figure 3 and labelled RD (right dart), LD (left dart), LK (left kite), RK (right kite). The join edges where left and right halves come together are shown with dotted lines, leaving one short edge and one long edge on each half-tile (excluding the join edge). We have shown a red dot at the vertex we regard as the origin of each half-tile (the tip of a half-dart and the base of a half-kite).

The labels are actually data constructors introduced with type operator HalfTile which has an argument type (rep) to allow for more than one representation of the half-tiles.

    data HalfTile rep 
      = LD rep -- Left Dart
      | RD rep -- Right Dart
      | LK rep -- Left Kite
      | RK rep -- Right Kite
      deriving (Show,Eq)

Tgraphs

We introduce tile graphs (Tgraphs) which provide a simple planar graph representation for finite patches of tiles. For Tgraphs we first specialise HalfTile with a triple of vertices (positive integers) to make a TileFace such as RD(1,2,3), where the vertices go clockwise round the half-tile triangle starting with the origin.

    type TileFace  = HalfTile (Vertex,Vertex,Vertex)
    type Vertex    = Int  -- must be positive

The function

    makeTgraph :: [TileFace] -> Tgraph

then constructs a Tgraph from a TileFace list after checking the TileFaces satisfy certain properties (described below). We also have

    faces :: Tgraph -> [TileFace]

to retrieve the TileFace list from a Tgraph.

As an example, the fool (short for fool’s kite and also called an ace in the literature) consists of two kites and a dart (= 4 half-kites and 2 half-darts):

    fool :: Tgraph
    fool = makeTgraph [RD (1,2,3), LD (1,3,4)   -- right and left dart
                      ,LK (5,3,2), RK (5,2,7)   -- left and right kite
                      ,RK (5,4,3), LK (5,6,4)   -- right and left kite
                      ]

To produce a diagram, we simply draw the Tgraph

    foolFigure :: Diagram B
    foolFigure = draw fool

which will produce the diagram on the left in figure 4.

Alternatively,

    foolFigure :: Diagram B
    foolFigure = labelled drawj fool

will produce the diagram on the right in figure 4 (showing vertex labels and dashed join edges).

When any (non-empty) Tgraph is drawn, a default orientation and scale are chosen based on the lowest numbered join edge. This is aligned on the positive x-axis with length 1 (for darts) or length (for kites).

Tgraph Properties

Tgraphs are actually implemented as

    newtype Tgraph = Tgraph [TileFace]
                     deriving (Show)

but the data constructor Tgraph is not exported to avoid accidentally by-passing checks for the required properties. The properties checked by makeTgraph ensure the Tgraph represents a legal tiling as a planar graph with positive vertex numbers, and that the collection of half-tile faces are both connected and have no crossing boundaries (see note below). Finally, there is a check to ensure two or more distinct vertex numbers are not used to represent the same vertex of the graph (a touching vertex check). An error is raised if there is a problem.

Note: If the TilFaces are faces of a planar graph there will also be exterior (untiled) regions, and in graph theory these would also be called faces of the graph. To avoid confusion, we will refer to these only as exterior regions, and unless otherwise stated, face will mean a TileFace. We can then define the boundary of a list of TileFaces as the edges of the exterior regions. There is a crossing boundary if the boundary crosses itself at a vertex. We exclude crossing boundaries from Tgraphs because they prevent us from calculating relative positions of tiles locally and create touching vertex problems.

For convenience, in addition to makeTgraph, we also have

    makeUncheckedTgraph :: [TileFace] -> Tgraph
    checkedTgraph   :: [TileFace] -> Tgraph

The first of these (performing no checks) is useful when you know the required properties hold. The second performs the same checks as makeTgraph except that it omits the touching vertex check. This could be used, for example, when making a Tgraph from a sub-collection of TileFaces of another Tgraph.

Main Tiling Operations

There are three key operations on finite tilings, namely

    decompose :: Tgraph -> Tgraph
    force     :: Tgraph -> Tgraph
    compose   :: Tgraph -> Tgraph

Decompose

Decomposition (also called deflation) works by splitting each half-tile into either 2 or 3 new (smaller scale) half-tiles, to produce a new tiling. The fact that this is possible, is used to establish the existence of infinite aperiodic tilings with kites and darts. Since our Tgraphs have abstracted away from scale, the result of decomposing a Tgraph is just another Tgraph. However if we wish to compare before and after with a drawing, the latter should be scaled by a factor times the scale of the former, to reflect the change in scale.

We can, of course, iterate decompose to produce an infinite list of finer and finer decompositions of a Tgraph

    decompositions :: Tgraph -> [Tgraph]
    decompositions = iterate decompose

Force

Force works by adding any TileFaces on the boundary edges of a Tgraph which are forced. That is, where there is only one legal choice of TileFace addition consistent with the seven possible vertex types. Such additions are continued until either (i) there are no more forced cases, in which case a final (forced) Tgraph is returned, or (ii) the process finds the tiling is stuck, in which case an error is raised indicating an incorrect tiling. [In the latter case, the argument to force must have been an incorrect tiling, because the forced additions cannot produce an incorrect tiling starting from a correct tiling.]

An example is shown in figure 6. When forced, the Tgraph on the left produces the result on the right. The original is highlighted in red in the result to show what has been added.

Compose

Composition (also called inflation) is an opposite to decompose but this has complications for finite tilings, so it is not simply an inverse. (See Graphs,Kites and Darts and Theorems for more discussion of the problems). Figure 7 shows a Tgraph (left) with the result of composing (right) where we have also shown (in pale green) the faces of the original that are not included in the composition – the remainder faces.

Under some circumstances composing can fail to produce a Tgraph because there are crossing boundaries in the resulting TileFaces. However, we have established that

• If g is a forced Tgraph, then compose g is defined and it is also a forced Tgraph.

Try Results

It is convenient to use types of the form Try a for results where we know there can be a failure. For example, compose can fail if the result does not pass the connected and no crossing boundary check, and force can fail if its argument is an incorrect Tgraph. In situations when you would like to continue some computation rather than raise an error when there is a failure, use a try version of a function.

    tryCompose :: Tgraph -> Try Tgraph
    tryForce   :: Tgraph -> Try Tgraph

We define Try as a synonym for Either ShowS (which is a monad) in module Tgraph.Try.

type Try a = Either ShowS a

(Note ShowS is String -> String). Successful results have the form Right r (for some correct result r) and failure results have the form Left (s<>) (where s is a String describing the problem as a failure report).

The function

    runTry:: Try a -> a
    runTry = either error id

will retrieve a correct result but raise an error for failure cases. This means we can always derive an error raising version from a try version of a function by composing with runTry.

    force = runTry . tryForce
    compose = runTry . tryCompose

Elementary Tgraph and TileFace Operations

The module Tgraph.Prelude defines elementary operations on Tgraphs relating vertices, directed edges, and faces. We describe a few of them here.

When we need to refer to particular vertices of a TileFace we use

    originV :: TileFace -> Vertex -- the first vertex - red dot in figure 2
    oppV    :: TileFace -> Vertex -- the vertex at the opposite end of the join edge from the origin
    wingV   :: TileFace -> Vertex -- the vertex not on the join edge

A directed edge is represented as a pair of vertices.

    type Dedge = (Vertex,Vertex)

So (a,b) is regarded as a directed edge from a to b.

When we need to refer to particular edges of a TileFace we use

    joinE  :: TileFace -> Dedge  -- shown dotted in figure 2
    shortE :: TileFace -> Dedge  -- the non-join short edge
    longE  :: TileFace -> Dedge  -- the non-join long edge

which are all directed clockwise round the TileFace. In contrast, joinOfTile is always directed away from the origin vertex, so is not clockwise for right darts or for left kites:

    joinOfTile:: TileFace -> Dedge
    joinOfTile face = (originV face, oppV face)

In the special case that a list of directed edges is symmetrically closed [(b,a) is in the list whenever (a,b) is in the list] we can think of this as an edge list rather than just a directed edge list.

For example,

    internalEdges :: Tgraph -> [Dedge]

produces an edge list, whereas

    boundary :: Tgraph -> [Dedge]

produces single directions. Each directed edge in the resulting boundary will have a TileFace on the left and an exterior region on the right. The function

    dedges :: Tgraph -> [Dedge]

produces all the directed edges obtained by going clockwise round each TileFace so not every edge in the list has an inverse in the list.

Note: There is now a class HasFaces (introduced in version 1.4) which includes instances for both Tgraph and [TileFace] and others. This allows some generalisations. In particular the more general types of the above three functions are now

    internalEdges :: HasFaces a => a -> [Dedge]
    boundary      :: HasFaces a => a -> [Dedge] 
    dedges        :: HasFaces a => a -> [Dedge]   

Patches (Scaled and Positioned Tilings)

Behind the scenes, when a Tgraph is drawn, each TileFace is converted to a Piece. A Piece is another specialisation of HalfTile using a two dimensional vector to indicate the length and direction of the join edge of the half-tile (from the originV to the oppV), thus fixing its scale and orientation. The whole Tgraph then becomes a list of located Pieces called a Patch.

    type Piece = HalfTile (V2 Double)
    type Patch = [Located Piece]

Piece drawing functions derive vectors for other edges of a half-tile piece from its join edge vector. In particular (in the TileLib module) we have

    drawPiece :: Piece -> Diagram B
    dashjPiece :: Piece -> Diagram B
    fillPieceDK :: Colour Double -> Colour Double -> Piece -> Diagram B

where the first draws the non-join edges of a Piece, the second does the same but adds a dashed line for the join edge, and the third takes two colours – one for darts and one for kites, which are used to fill the piece as well as using drawPiece.

Patch is an instances of class Transformable so a Patch can be scaled, rotated, and translated.

Vertex Patches

It is useful to have an intermediate form between Tgraphs and Patches, that contains information about both the location of vertices (as 2D points), and the abstract TileFaces. This allows us to introduce labelled drawing functions (to show the vertex labels) which we then extend to Tgraphs. We call the intermediate form a VPatch (short for Vertex Patch).

    type VertexLocMap = IntMap.IntMap (Point V2 Double)
    data VPatch = VPatch {vLocs :: VertexLocMap,  vpFaces::[TileFace]} deriving Show

and

    makeVP :: Tgraph -> VPatch

calculates vertex locations using a default orientation and scale.

VPatch is made an instance of class Transformable so a VPatch can also be scaled and rotated.

One essential use of this intermediate form is to be able to draw a Tgraph with labels, rotated but without the labels themselves being rotated. We can simply convert the Tgraph to a VPatch, and rotate that before drawing with labels.

    labelled draw (rotate someAngle (makeVP g))

We can also align a VPatch using vertex labels.

    alignXaxis :: (Vertex, Vertex) -> VPatch -> VPatch 

So if g is a Tgraph with vertex labels a and b we can align it on the x-axis with a at the origin and b on the positive x-axis (after converting to a VPatch), instead of accepting the default orientation.

    labelled draw (alignXaxis (a,b) (makeVP g))

Another use of VPatches is to share the vertex location map when drawing only subsets of the faces (see Overlaid examples in the next section).

4. Drawing in More Detail

Class Drawable

There is a class Drawable with instances Tgraph, VPatch, Patch. When the token B is in scope standing for a fixed backend then we can assume

    draw   :: Drawable a => a -> Diagram B  -- draws non-join edges
    drawj  :: Drawable a => a -> Diagram B  -- as with draw but also draws dashed join edges
    fillDK :: Drawable a => Colour Double -> Colour Double -> a -> Diagram B -- fills with colours

where fillDK clr1 clr2 will fill darts with colour clr1 and kites with colour clr2 as well as drawing non-join edges.

These are the main drawing tools. However they are actually defined for any suitable backend b so have more general types.

(Update Sept 2024) As of version 1.1 of PenroseKiteDart, these will be

    draw ::   (Drawable a, OKBackend b) =>
              a -> Diagram b
    drawj ::  (Drawable a, OKBackend) b) =>
              a -> Diagram b
    fillDK :: (Drawable a, OKBackend b) =>
              Colour Double -> Colour Double -> a -> Diagram b

where the class OKBackend is a check to ensure a backend is suitable for drawing 2D tilings with or without labels.

In these notes we will generally use the simpler description of types using B for a fixed chosen backend for the sake of clarity.

The drawing tools are each defined via the class function drawWith using Piece drawing functions.

    class Drawable a where
        drawWith :: (Piece -> Diagram B) -> a -> Diagram B
    
    draw = drawWith drawPiece
    drawj = drawWith dashjPiece
    fillDK clr1 clr2 = drawWith (fillPieceDK clr1 clr2)

To design a new drawing function, you only need to implement a function to draw a Piece, (let us call it newPieceDraw)

    newPieceDraw :: Piece -> Diagram B

This can then be elevated to draw any Drawable (including Tgraphs, VPatches, and Patches) by applying the Drawable class function drawWith:

    newDraw :: Drawable a => a -> Diagram B
    newDraw = drawWith newPieceDraw

Class DrawableLabelled

Class DrawableLabelled is defined with instances Tgraph and VPatch, but Patch is not an instance (because this does not retain vertex label information).

    class DrawableLabelled a where
        labelColourSize :: Colour Double -> Measure Double -> (Patch -> Diagram B) -> a -> Diagram B

So labelColourSize c m modifies a Patch drawing function to add labels (of colour c and size measure m). Measure is defined in Diagrams.Prelude with pre-defined measures tiny, verySmall, small, normal, large, veryLarge, huge. For most of our diagrams of Tgraphs, we use red labels and we also find small is a good default size choice, so we define

    labelSize :: DrawableLabelled a => Measure Double -> (Patch -> Diagram B) -> a -> Diagram B
    labelSize = labelColourSize red

    labelled :: DrawableLabelled a => (Patch -> Diagram B) -> a -> Diagram B
    labelled = labelSize small

and then labelled draw, labelled drawj, labelled (fillDK clr1 clr2) can all be used on both Tgraphs and VPatches as well as (for example) labelSize tiny draw, or labelCoulourSize blue normal drawj.

Further drawing functions

There are a few extra drawing functions built on top of the above ones. The function smart is a modifier to add dashed join edges only when they occur on the boundary of a Tgraph

    smart :: (VPatch -> Diagram B) -> Tgraph -> Diagram B

So smart vpdraw g will draw dashed join edges on the boundary of g before applying the drawing function vpdraw to the VPatch for g. For example the following all draw dashed join edges only on the boundary for a Tgraph g

    smart draw g
    smart (labelled draw) g
    smart (labelSize normal draw) g

When using labels, the function rotateBefore allows a Tgraph to be drawn rotated without rotating the labels.

    rotateBefore :: (VPatch -> a) -> Angle Double -> Tgraph -> a
    rotateBefore vpdraw angle = vpdraw . rotate angle . makeVP

So for example,

    rotateBefore (labelled draw) (90@@deg) g

makes sense for a Tgraph g. Of course if there are no labels we can simply use

    rotate (90@@deg) (draw g)

Similarly alignBefore allows a Tgraph to be aligned on the X-axis using a pair of vertex numbers before drawing.

    alignBefore :: (VPatch -> a) -> (Vertex,Vertex) -> Tgraph -> a
    alignBefore vpdraw (a,b) = vpdraw . alignXaxis (a,b) . makeVP

So, for example, if Tgraph g has vertices a and b, both

    alignBefore draw (a,b) g
    alignBefore (labelled draw) (a,b) g

make sense. Note that the following examples are wrong. Even though they type check, they re-orient g without repositioning the boundary joins.

    smart (labelled draw . rotate angle) g      -- WRONG
    smart (labelled draw . alignXaxis (a,b)) g  -- WRONG

Instead use

    smartRotateBefore (labelled draw) angle g
    smartAlignBefore (labelled draw) (a,b) g

where

    smartRotateBefore :: (VPatch -> Diagram B) -> Angle Double -> Tgraph -> Diagram B
    smartAlignBefore  :: (VPatch -> Diagram B) -> (Vertex,Vertex) -> Tgraph -> Diagram B

are defined using

    restrictSmart :: Tgraph -> (VPatch -> Diagram B) -> VPatch -> Diagram B

Here, restrictSmart g vpdraw vp uses the given vp for drawing boundary joins and drawing faces of g (with vpdraw) rather than converting g to a new VPatch. This assumes vp has locations for vertices in g.

Overlaid examples (location map sharing)

The function

    drawForce :: Tgraph -> Diagram B

will (smart) draw a Tgraph g in red overlaid (using <>) on the result of force g as in figure 6. Similarly

    drawPCompose  :: Tgraph -> Diagram B

applied to a Tgraph g will draw the result of a partial composition of g as in figure 7. That is a drawing of compose g but overlaid with a drawing of the remainder faces of g shown in pale green.

Both these functions make use of sharing a vertex location map to get correct alignments of overlaid diagrams. In the case of drawForce g, we know that a VPatch for force g will contain all the vertex locations for g since force only adds to a Tgraph (when it succeeds). So when constructing the diagram for g we can use the VPatch created for force g instead of starting afresh. Similarly for drawPCompose g the VPatch for g contains locations for all the vertices of compose g so compose g is drawn using the the VPatch for g instead of starting afresh.

The location map sharing is done with

    subVP :: VPatch -> [TileFace] -> VPatch

so that subVP vp fcs is a VPatch with the same vertex locations as vp, but replacing the faces of vp with fcs. [Of course, this can go wrong if the new faces have vertices not in the domain of the vertex location map so this needs to be used with care. Any errors would only be discovered when a diagram is created.]

For cases where labels are only going to be drawn for certain faces, we need a version of subVP which also gets rid of vertex locations that are not relevant to the faces. For this situation we have

    restrictVP:: VPatch -> [TileFace] -> VPatch

which filters out un-needed vertex locations from the vertex location map. Unlike subVP, restrictVP checks for missing vertex locations, so restrictVP vp fcs raises an error if a vertex in fcs is missing from the keys of the vertex location map of vp.

5. Forcing in More Detail

The force rules

The rules used by our force algorithm are local and derived from the fact that there are seven possible vertex types as depicted in figure 8.

Our rules are shown in figure 9 (omitting mirror symmetric versions). In each case the TileFace shown yellow needs to be added in the presence of the other TileFaces shown.

Main Forcing Operations

To make forcing efficient we convert a Tgraph to a BoundaryState to keep track of boundary information of the Tgraph, and then calculate a ForceState which combines the BoundaryState with a record of awaiting boundary edge updates (an update map). Then each face addition is carried out on a ForceState, converting back when all the face additions are complete. It makes sense to apply force (and related functions) to a Tgraph, a BoundaryState, or a ForceState, so we define a class Forcible with instances Tgraph, BoundaryState, and ForceState.

This allows us to define

    force :: Forcible a => a -> a
    tryForce :: Forcible a => a -> Try a

The first will raise an error if a stuck tiling is encountered. The second uses a Try result which produces a Left string for failures and a Right a for successful result a.

There are several other operations related to forcing including

    stepForce :: Forcible a => Int -> a -> a
    tryStepForce  :: Forcible a => Int -> a -> Try a

    addHalfDart, addHalfKite :: Forcible a => Dedge -> a -> a
    tryAddHalfDart, tryAddHalfKite :: Forcible a => Dedge -> a -> Try a

The first two force (up to) a given number of steps (=face additions) and the other four add a half dart/kite on a given boundary edge.

Update Generators

An update generator is used to calculate which boundary edges can have a certain update. There is an update generator for each force rule, but also a combined (all update) generator. The force operations mentioned above all use the default all update generator (defaultAllUGen) but there are more general (with) versions that can be passed an update generator of choice. For example

    forceWith :: Forcible a => UpdateGenerator -> a -> a
    tryForceWith :: Forcible a => UpdateGenerator -> a -> Try a

In fact we defined

    force = forceWith defaultAllUGen
    tryForce = tryForceWith defaultAllUGen

We can also define

    wholeTiles :: Forcible a => a -> a
    wholeTiles = forceWith wholeTileUpdates

where wholeTileUpdates is an update generator that just finds boundary join edges to complete whole tiles.

In addition to defaultAllUGen there is also allUGenerator which does the same thing apart from how failures are reported. The reason for keeping both is that they were constructed differently and so are useful for testing.

In fact UpdateGenerators are functions that take a BoundaryState and a focus (list of boundary directed edges) to produce an update map. Each Update is calculated as either a SafeUpdate (where two of the new face edges are on the existing boundary and no new vertex is needed) or an UnsafeUpdate (where only one edge of the new face is on the boundary and a new vertex needs to be created for a new face).

    type UpdateGenerator = BoundaryState -> [Dedge] -> Try UpdateMap
    type UpdateMap = Map.Map Dedge Update
    data Update = SafeUpdate TileFace 
                | UnsafeUpdate (Vertex -> TileFace)

Completing (executing) an UnsafeUpdate requires a touching vertex check to ensure that the new vertex does not clash with an existing boundary vertex. Using an existing (touching) vertex would create a crossing boundary so such an update has to be blocked.

Forcible Class Operations

The Forcible class operations are higher order and designed to allow for easy additions of further generic operations. They take care of conversions between Tgraphs, BoundaryStates and ForceStates.

    class Forcible a where
      tryFSOpWith :: UpdateGenerator -> (ForceState -> Try ForceState) -> a -> Try a
      tryChangeBoundaryWith :: UpdateGenerator -> (BoundaryState -> Try BoundaryChange) -> a -> Try a
      tryInitFSWith :: UpdateGenerator -> a -> Try ForceState

For example, given an update generator ugen and any f:: ForceState -> Try ForceState , then f can be generalised to work on any Forcible using tryFSOpWith ugen f. This is used to define both tryForceWith and tryStepForceWith.

We also specialize tryFSOpWith to use the default update generator

    tryFSOp :: Forcible a => (ForceState -> Try ForceState) -> a -> Try a
    tryFSOp = tryFSOpWith defaultAllUGen

Similarly given an update generator ugen and any f:: BoundaryState -> Try BoundaryChange , then f can be generalised to work on any Forcible using tryChangeBoundaryWith ugen f. This is used to define tryAddHalfDart and tryAddHalfKite.

We also specialize tryChangeBoundaryWith to use the default update generator

    tryChangeBoundary :: Forcible a => (BoundaryState -> Try BoundaryChange) -> a -> Try a
    tryChangeBoundary = tryChangeBoundaryWith defaultAllUGen

Note that the type BoundaryChange contains a resulting BoundaryState, the single TileFace that has been added, a list of edges removed from the boundary (of the BoundaryState prior to the face addition), and a list of the (3 or 4) boundary edges affected around the change that require checking or re-checking for updates.

The class function tryInitFSWith will use an update generator to create an initial ForceState for any Forcible. If the Forcible is already a ForceState it will do nothing. Otherwise it will calculate updates for the whole boundary. We also have the special case

    tryInitFS :: Forcible a => a -> Try ForceState
    tryInitFS = tryInitFSWith defaultAllUGen

Efficient chains of forcing operations.

Note that (force . force) does the same as force, but we might want to chain other force related steps in a calculation.

For example, consider the following combination which, after decomposing a Tgraph, forces, then adds a half dart on a given boundary edge (d) and then forces again.

    combo :: Dedge -> Tgraph -> Tgraph
    combo d = force . addHalfDart d . force . decompose

Since decompose:: Tgraph -> Tgraph, the instances of force and addHalfDart d will have type Tgraph -> Tgraph so each of these operations, will begin and end with conversions between Tgraph and ForceState. We would do better to avoid these wasted intermediate conversions working only with ForceStates and keeping only those necessary conversions at the beginning and end of the whole sequence.

This can be done using tryFSOp. To see this, let us first re-express the forcing sequence using the Try monad, so

    force . addHalfDart d . force

becomes

    tryForce <=< tryAddHalfDart d <=< tryForce

Note that (<=<) is the Kliesli arrow which replaces composition for Monads (defined in Control.Monad). (We could also have expressed this right to left sequence with a left to right version tryForce >=> tryAddHalfDart d >=> tryForce). The definition of combo becomes

    combo :: Dedge -> Tgraph -> Tgraph
    combo d = runTry . (tryForce <=< tryAddHalfDart d <=< tryForce) . decompose

This has no performance improvement, but now we can pass the sequence to tryFSOp to remove the unnecessary conversions between steps.

    combo :: Dedge -> Tgraph -> Tgraph
    combo d = runTry . tryFSOp (tryForce <=< tryAddHalfDart d <=< tryForce) . decompose

The sequence actually has type Forcible a => a -> Try a but when passed to tryFSOp it specialises to type ForceState -> Try ForseState. This ensures the sequence works on a ForceState and any conversions are confined to the beginning and end of the sequence, avoiding unnecessary intermediate conversions.

A limitation of forcing

To avoid creating touching vertices (or crossing boundaries) a BoundaryState keeps track of locations of boundary vertices. At around 35,000 face additions in a single force operation the calculated positions of boundary vertices can become too inaccurate to prevent touching vertex problems. In such cases it is better to use

    recalibratingForce :: Forcible a => a -> a
    tryRecalibratingForce :: Forcible a => a -> Try a

These work by recalculating all vertex positions at 20,000 step intervals to get more accurate boundary vertex positions. For example, 6 decompositions of the kingGraph has 2,906 faces. Applying force to this should result in 53,574 faces but will go wrong before it reaches that. This can be fixed by calculating either

    recalibratingForce (decompositions kingGraph !!6)

or using an extra force before the decompositions

    force (decompositions (force kingGraph) !!6)

In the latter case, the final force only needs to add 17,864 faces to the 35,710 produced by decompositions (force kingGraph) !!6.

6. Advanced Operations

Guided comparison of Tgraphs

Asking if two Tgraphs are equivalent (the same apart from choice of vertex numbers) is a an np-complete problem. However, we do have an efficient guided way of comparing Tgraphs. In the module Tgraph.Rellabelling we have

    sameGraph :: (Tgraph,Dedge) -> (Tgraph,Dedge) -> Bool

The expression sameGraph (g1,d1) (g2,d2) asks if g2 can be relabelled to match g1 assuming that the directed edge d2 in g2 is identified with d1 in g1. Hence the comparison is guided by the assumption that d2 corresponds to d1.

It is implemented using

    tryRelabelToMatch :: (Tgraph,Dedge) -> (Tgraph,Dedge) -> Try Tgraph

where tryRelabelToMatch (g1,d1) (g2,d2) will either fail with a Left report if a mismatch is found when relabelling g2 to match g1 or will succeed with Right g3 where g3 is a relabelled version of g2. The successful result g3 will match g1 in a maximal tile-connected collection of faces containing the face with edge d1 and have vertices disjoint from those of g1 elsewhere. The comparison tries to grow a suitable relabelling by comparing faces one at a time starting from the face with edge d1 in g1 and the face with edge d2 in g2. (This relies on the fact that Tgraphs are connected with no crossing boundaries, and hence tile-connected.)

The above function is also used to implement

    tryFullUnion:: (Tgraph,Dedge) -> (Tgraph,Dedge) -> Try Tgraph

which tries to find the union of two Tgraphs guided by a directed edge identification. However, there is an extra complexity arising from the fact that Tgraphs might overlap in more than one tile-connected region. After calculating one overlapping region, the full union uses some geometry (calculating vertex locations) to detect further overlaps.

Finally we have

    commonFaces:: (Tgraph,Dedge) -> (Tgraph,Dedge) -> [TileFace]

which will find common regions of overlapping faces of two Tgraphs guided by a directed edge identification. The resulting common faces will be a sub-collection of faces from the first Tgraph. These are returned as a list as they may not be a connected collection of faces and therefore not necessarily a Tgraph.

Empires and SuperForce

In Empires and SuperForce we discussed forced boundary coverings which were used to implement both a superForce operation

    superForce:: Forcible a => a -> a

and operations to calculate empires.

We will not repeat the descriptions here other than to note that

    forcedBoundaryECovering:: Tgraph -> [Tgraph]

finds boundary edge coverings after forcing a Tgraph. That is, forcedBoundaryECovering g will first force g, then (if it succeeds) finds a collection of (forced) extensions to force g such that

• each extension has the whole boundary of force g as internal edges.
• each possible addition to a boundary edge of force g (kite or dart) has been included in the collection.

(possible here means – not leading to a stuck Tgraph when forced.) There is also

    forcedBoundaryVCovering:: Tgraph -> [Tgraph]

which does the same except that the extensions have all boundary vertices internal rather than just the boundary edges.

Combinations and Explicitly Forced

We introduced a new type Forced (in v 1.3) to enable a forcible to be explictily labelled as being forced. For example

    forceF    :: Forcible a => a -> Forced a 
    tryForceF :: Forcible a => a -> Try (Forced a)
    forgetF   :: Forced a -> a

This allows us to restrict certain functions which expect a forced argument by making this explicit.

    composeF :: Forced Tgraph -> Forced Tgraph

The definition makes use of theorems established in Graphs,Kites and Darts and Theorems that composing a forced Tgraph does not require a check (for connectedness and no crossing boundaries) and the result is also forced. This can then be used to define efficient combinations such as

    compForce:: Tgraph -> Forced Tgraph      -- compose after forcing
    composeForce = composeF . forceF

    allCompForce:: Tgraph -> [Forced Tgraph] -- iterated (compose after force) while not emptyTgraph
    maxCompForce:: Tgraph -> Forced Tgraph   -- last item in allCompForce (or emptyTgraph)

Tracked Tgraphs

The type

    data TrackedTgraph = TrackedTgraph
       { tgraph  :: Tgraph
       , tracked :: [[TileFace]] 
       } deriving Show

has proven useful in experimentation as well as in producing artwork with darts and kites. The idea is to keep a record of sub-collections of faces of a Tgraph when doing both force operations and decompositions. A list of the sub-collections forms the tracked list associated with the Tgraph. We make TrackedTgraph an instance of class Forcible by having force operations only affect the Tgraph and not the tracked list. The significant idea is the implementation of

    decomposeTracked :: TrackedTgraph -> TrackedTgraph

Decomposition of a Tgraph involves introducing a new vertex for each long edge and each kite join. These are then used to construct the decomposed faces. For decomposeTracked we do the same for the Tgraph, but when it comes to the tracked collections, we decompose them re-using the same new vertex numbers calculated for the edges in the Tgraph. This keeps a consistent numbering between the Tgraph and tracked faces, so each item in the tracked list remains a sub-collection of faces in the Tgraph.

The function

    drawTrackedTgraph :: [VPatch -> Diagram B] -> TrackedTgraph -> Diagram B

is used to draw a TrackedTgraph. It uses a list of functions to draw VPatches. The first drawing function is applied to a VPatch for any untracked faces. Subsequent functions are applied to VPatches for the tracked list in order. Each diagram is beneath later ones in the list, with the diagram for the untracked faces at the bottom. The VPatches used are all restrictions of a single VPatch for the Tgraph, so will be consistent in vertex locations. When labels are used, there is also a drawTrackedTgraphRotated and drawTrackedTgraphAligned for rotating or aligning the VPatch prior to applying the drawing functions.

Note that the result of calculating empires (see Empires and SuperForce ) is represented as a TrackedTgraph. The result is actually the common faces of a forced boundary covering, but a particular element of the covering (the first one) is chosen as the background Tgraph with the common faces as a tracked sub-collection of faces. Hence we have

    empire1, empire2 :: Tgraph -> TrackedTgraph
    
    drawEmpire :: TrackedTgraph -> Diagram B

Figure 10 was also created using TrackedTgraphs.

7. Other Reading

Previous related blogs are:

• Diagrams for Penrose Tiles – the first blog introduced drawing Pieces and Patches (without using Tgraphs) and provided a version of decomposing for Patches (decompPatch).
• Graphs, Kites and Darts intoduced Tgraphs. This gave more details of implementation and results of early explorations. (The class Forcible was introduced subsequently).
• Empires and SuperForce – these new operations were based on observing properties of boundaries of forced Tgraphs.
• Graphs,Kites and Darts and Theorems established some important results relating force, compose, decompose.

by readerunner at June 15, 2025 03:32 PM

Browsing Stackage with VS Code and Glean

Browsing Stackage with VS Code and Glean

June 11, 2025

Have you ever wished you could browse all the Haskell packages together in your IDE, with full navigation using go-to-definition and find-references? Here’s a demo of something I hacked together while at ZuriHac 2025 over the weekend:

In the previous post I talked about how to index all of Hackage (actually Stackage, strictly speaking, because it’s not in general possible to build all of Hackage together) using Glean. Since that post I made some more progress on the indexer:

• The indexer now indexes types. You can see type-on-hover working in the demo. The types are similar to what you see in the Haddock-generated hyperlinked source, except that here it’s always using the type of the definition and not the type at the usage site, which might be more specific. That’s a TODO for later.

• Fixed a bunch of things, enriched the index with details about constructors, fields and class methods, and made indexing more efficient.

The DB size including types is now about 850MB, and it takes just under 8 minutes on my 9-year-old laptop to index the nearly 3000 packages in my stackage LTS 21.21 snapshot. (Note: the figures here were updated on 12-06-2025 when I redid the measurments).

Hooking it up to VS Code

The architecture looks like this:

The LSP server is a modified version of static-ls, which is already designed to provide an LSP service based on static information. I just reimplemented a few of its handlers to make calls to Glass instead of the existing hie/hiedb implementations. You can see the changes on my fork of static-ls. Of course, these changes are still quite hacky and not suitable for upstreaming.

Glass is a “Language-agnostic Symbol Server”. Essentially it provides an API abstraction over Glean with operations that are useful for code navigation and search.

Where to next?

There remain a few issues to solve before this can be useful.

• Make Glean more easily installable. There’s a general concensus that cabal install glean would lower the barrier to entry significantly; in order to do this we need to build the folly dependency using Cabal.

• Clean up and ship the LSP server, somehow. Once Glean is cabal-installable, we can depend on it from an LSP server package.

• Think about continuous integration to build the Glean DB. Perhaps this can piggyback off the stackage CI infra? If we can already build a complete stackage snapshot, and Glean is easily installable, then indexing would be fairly straightforward. I’d love to hear suggestions on how best to do this.

And looking forwards a bit further:

• Think about how to handle multiple packages versions. There’s no fundamental problem with indexing multiple package versions, except that Glass’s SymbolID format currently doesn’t include the package version but that’s easily fixable. We could for example build multiple stackage LTS instances and index them all in a single Glean DB. There would be advantages to doing this, if for instance there were packages in common between two Stackage instances then the Glean DB would only contain a single copy. A lot of the type structure would be shared too.

• Provide search functionality in the LSP. Glean can provide simple textual search for names, and with some work could also provide Hoogle-like type search.

• Think about how to index local projects and local changes. Glean supports stacked and incremental DBs, so we could build a DB for a local project stacked on top of the full Stackage DB. You would be able to go-to-definition directly from a file in your project to the packages it depends on in Stackage. We could re-index new .hie files as they are generated, rather like how static-ls currently handles changes.

• Integrate with HLS? Perhaps Glean could be used to handle references outside of the current project, switching seamlessly from GHC-based navigation to Glean-based navigation if you jump into a non-local package.

More use cases?

I talked with a few people at ZuriHac about potential use cases for Glean within the Haskell ecosystem. Using it in haskell.org came up a few times, as a way to power search, navigation and analysis. Also mentioned was the possibility of using it as a Hoogle backend. Potentially we could replace the Haddock-generated hyperlinked sources on haskell.org with a Glean-based browser, which would allow navigating links between packages and find-references.

Another use cases that came up was the possibility of doing impact analysis for core library changes (or any API changes really). Some of this is already possible using find-references, but more complex cases such as finding instances that override certain methods aren’t possible yet until we extend the indexer to capture richer information.

If you’re interested in using Glean for something, why not jump on the Glean discord server and tell us about it!

June 11, 2025 12:00 AM

Introduction to competitive programming in Haskell

Introduction to competitive programming in Haskell

Posted on June 10, 2025
Tagged Kattis, competitive programming, haskell

A few days ago I gave a talk at ZuriHac 2025 entitled Haskell for Competitive Programming, a basic introduction to competitive programming in general, and the joy of using Haskell for competitive programming in particular. This is an expanded version of my talk in blog post form. (For an even gentler introduction to competitive programming in Haskell, see this old blog post from 2019.)

Competitive Programming

First of all, what is competitive programming? It’s a broad term, but when I talk about competitive programming I have something in mind along the following lines:

• There are well-specified input and output formats, usually with a few examples, and a precise specification of what the output should be for a given input.
• Your job is to write a program which transforms input meeting the specification into a correct output.
• You submit your program, which is tested on a number of inputs and declared correct if and only if it yields the correct output for all the tested inputs.
• There is often time pressure involved—that is, you have a limited amount of time in which to write your program. However, it is also possible to participate “recreationally”, simply for the joy of problem-solving, without time pressure (in fact, the vast majority of the competitive programming I do is of this form, though I have occasionally participated in timed contests).

There are many variations: whether you are allowed to use code libraries prepared ahead of time, or must type everything from scratch; outputs can be scored according to some criteria rather than simply being judged right or wrong; and so on.

There are many sites which allow you to participate in contests and/or solve competitive programming problems recreationally. My favorite is Open Kattis; I mention some others at the end of this post.

Pot: a first example

As an introductory example, let’s look at Pot. As usual, there’s a silly story, but what it boils down to is that we will be given a sequence of numbers, and we should interpret the last digit of each number as an exponent, then sum the results. For example, if given 125, we should interpret it as \(12^5\), and so on.

Dealing with I/O via interact

An imperative approach to such a problem would involve doing a sequence of input commands, some computation, and a sequence of output commands—possibly interleaved with one another—and we might immediately think to start using functions like getLine and putStrLn to do the required I/O in Haskell. However, there is a much more fruitful functional perspective: we are simply being asked to implement a particular (partial) function of type String -> String. The fact that the function’s input and output should be hooked up to the program’s standard input and output is just an implementation detail. Competitive programming is functional at heart!

It turns out that Haskell’s standard library already has the perfect built-in function for this scenario:

interact :: (String -> String) -> IO ()

interact takes a pure String -> String function and turns it into an IO action which reads from standard input, passes the input to the given String -> String function, and prints the result to standard output. It even does this using lazy I/O—that is, the input is read lazily, as demanded by the function, so that the output and input can be automatically interleaved depending on which parts of the output depend on which parts of the input. In particular, this means that that the entire input need not be stored in memory at once. If the inputs can be processed into outputs in a streaming fashion—as is the case in the example problem we are currently considering—then the input and output will be interleaved. In general, this kind of lazy I/O is problematic and even unsafe, but it’s perfect for this scenario.

Solving the problem with a pipeline

So interact does all the IO for us, and all we have to do is write a pure String -> String function which transforms the input to the output. In this case, we can split the input into lines, drop the first line (we don’t need to know how many lines of input there are—we just get a list of all of them, since interact will read until EOF), read each number and turn it into the first digits raised to the power of the last digit, then sum them and show the result. The full solution is below. Notice how I use the “backwards composition” operator (>>>), since I find it more convenient to type from left to right as I’m thinking about transforming from input to output.

import Control.Category ((>>>))

main = interact $
  lines >>> drop 1 >>> map (read >>> process) >>> sum >>> show

process :: Integer -> Integer
process n = (n `div` 10) ^ (n `mod` 10)

I use Integer here since raw performance doesn’t matter much for this easy problem, and Integer avoids any potential problems with overflow. However, using Int instead of Integer can make a big difference for some compute-intensive problems. On Kattis, Int will always be 64 bits, but last time I checked Int can be 32 bits on Codeforces.

Shopping List: wholemeal programming and ByteString

Let’s consider Shopping List as a second example. In this problem, we are given a list of shopping lists, where each shopping list consists of a list of space-separated items on a single line. We are asked to find the items which are common to all the shopping lists, and print them in alphabetical order.

Wholemeal programming with standard data structures

This problem is very amenable to a “wholemeal programming” approach, where we work entirely at the level of whole data structure transformations rather than looping over individual elements. We can turn each shopping list into a set, then find the intersection of all the sets. Moreover, if we use Data.Set, which uses an ordering on the elements, we will get the result in alphabetical order “for free” (“free” as in the amount of code we have to write, not necessarily runtime cost). Haskell has a decent collection of data structures in the containers library ((Int)Set, (Int)Map, Seq, Tree, and even Graph) with a large collection of standard methods to construct and manipulate them, which are bread and butter for many competitive programming problems.

{-# LANGUAGE ImportQualifiedPost #-}

import Control.Category ((>>>))
import Data.Set (Set)
import Data.Set qualified as S

main = interact $
  lines >>> drop 1 >>> map (words >>> S.fromList) >>>
  foldr1 S.intersection >>>
  (\s -> show (S.size s) : S.toList s) >>> unlines

ByteString vs String

Unfortunately, when we try submitting this code, we get a Time Limit Exceeded error! What’s wrong?

The issue is our use of String, which is an actual linked list of characters and is very slow, especially when we have many short strings, as in this problem. In the worst case, we could have 100 shopping lists, each with 5000 items of length 10, for a total of up to 5 MB of input; with that much input data to read, any overhead associated with reading and parsing the input can make a significant difference.

Switching to ByteString is much faster. Why not Text, you ask? Well, Text has to do a bunch of extra work to deal properly with Unicode encodings, but in 99.99% of all competitive programming problems I’ve ever seen, the input is guaranteed to be ASCII. So not only do we not need Text, we can get away with a version of ByteString that simply assumes every character is a single 8-bit byte!

Once we import it, all we need to do is replace a bunch of String operations with corresponding ByteString ones.

{-# LANGUAGE ImportQualifiedPost #-}

import Control.Category ((>>>))
import Data.Set (Set)
import Data.Set qualified as S
import Data.ByteString.Lazy.Char8 qualified as BS

main = BS.interact $
  BS.lines >>> drop 1 >>> map (BS.words >>> S.fromList) >>>
  foldr1 S.intersection >>>
  (\s -> BS.pack (show (S.size s)) : S.toList s) >>> BS.unlines

A Favourable Ending: input parsing and lazy recursive structures

As a last example, let’s look at A Favourable Ending. This problem consists of a number of test cases; each test case describes a choose-your-own-adventure book with a number of sections, where each section is either an ending (either good or bad), or allows the reader to choose among three sections to proceed to next. For each test case, we are asked how many distinct stories there are with good endings.

More abstractly, since we are guaranteed that there are no loops, the sections of the book form a DAG, and we are asked to count the number of distinct paths in a DAG from a distinguished start node to any of a distinguished set of “good” leaves.

Parsing with Scanner

Parsing the input for this problem is trickier than the other examples so far. In theory, we could still ignore the first number specifying the number of test cases, and just continue reading test cases until EOF. However, each test case begins with a number specifying the number of sections in the book, and we cannot ignore this number: we need to know how many lines to read before the start of the next test case. Doing this manually involves pattern-matching on a list of lines, using splitAt to split off the lines for each test case, and manually passing around the list of the remaining lines: tedious.

Fortunately, Haskell is great at building abstractions to insulate us from such tedium. I’ve developed a simple Scanner abstraction which works well in this context.

We begin by creating some data types to represent the input in structured form:

type Book = Map Int Section

data Section = End Disposition | Choice [Int]
  deriving (Eq, Show)

data Disposition = Favourably | Catastrophically
  deriving (Eq, Show, Read)

Now we can write a Scanner to read a Book:

book :: Scanner Book
book = do
  s <- int
  M.fromList <$> s >< ((,) <$> int <*> section)

section :: Scanner Section
section = do
  t <- peek
  if isDigit (BS.head t)
    then Choice <$> (3 >< int)
    else End . readLower . BS.unpack <$> str

readLower :: Read a => String -> a
readLower = read . onHead toUpper

onHead :: (a -> a) -> [a] -> [a]
onHead _ [] = []
onHead f (x : xs) = f x : xs

(readLower and onHead are functions in my personal competitive programming template, included here for completeness).

One more piece of boilerplate we can write at this point is the main function, which simply consists of running the Scanner to read all the test cases, solving each test case, and formatting the output.

main = BS.interact $ runScanner (numberOf book) >>> map (solve >>> showB) >>> BS.unlines

DP + topsort with a lazy recursive map

With all that framework out of the way, we can turn to actually solving the problem. And here is where something really fun happens. In a typical imperative language, we would have to first topologically sort the book sections, then use dynamic programming to compute the number of good stories beginning at each section, starting with the leaves and proceeding backwards through the topological sort to the start—dozens of lines of code. However, in Haskell we can get all of this for free, just by defining a lazy, recursive map!

solve :: Book -> Int
solve book = endings ! 1
  where
    endings = M.fromList [(p, endingsFrom (book!p)) | p <- M.keys book]
    endingsFrom (End d) = if d == Favourably then 1 else 0
    endingsFrom (Choice ps) = sum $ map (endings !) ps

endings is a Map from each book section to the number of favorable stories starting with that section. Notice how its values are defined via the endingsFrom function, which is in turn defined, in the Choice case, by looking up the values of the choices in the endings map and summing them. endings is thus defined recursively, which works because it is lazy in the values. When we demand the value of endings ! 1, the runtime system starts evaluating thunks in the map as needed, implicitly doing a topological sort for us.

Here’s another way to think about this: what we really want is the function endingsFrom : Section -> Int, which tells us how many good endings there are starting at a given section. It can be defined via a recurrence; however, if we were to literally implement it as a recursive function, our program would spend a ridiculous amount of time recomputing the same values over and over again. So, we insert a lazy map in the middle to memoize it (there are other data structures that can be used for this purpose as well).

Resources

Here are some resources in case you’re interested in exploring more.

• Open Kattis has a collection of thousands of high-quality problems which can be solved in Haskell (or many other languages). If you just want to try solving some problems for fun, it’s a great place to start.
• There are also other sites which accept Haskell, such as Codeforces. Check these out if you want to actually participate in timed contests.
• My public listing of Kattis problems I have solved, with my own personal rating system.
• I’ve written a series of blog posts about competitive programming in Haskell, on a variety of topics.
• I also have a repository of modules I’ve developed specifically for competitive programming. Many of the modules are documented in one or more blog posts.
• Soumik Sarkar has an even larger collection of Haskell libraries for competitive programming.

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by Brent Yorgey at June 10, 2025 12:00 AM

Spatial Reasoning with Zigzag Patterns!

Today we’re continuing our study of Rust and Haskell solutions to basic coding problems. This algorithm is going to be a little harder than the last few we’ve done in this series, and it will get trickier from here!

For a complete study of problem solving techniques in Haskell, make sure to check out Solve.hs. This course runs the gamut from basic solving techniques to advanced data structures and algorithms, so you’ll learn a lot!

The Problem

Today’s problem is Zigzag Conversion. This is an odd problem that stretches your ability to think iteratively and spatially. The idea is that you’re given an input string and a number of “rows”. You need to then imagine the input word written as a zig-zag pattern, where you write the letters in order first going down, and then diagonally up to the right until you get back to the first row. Then it goes down again. Your output must be characters re-ordered in “row-order” after this zig-zag rearrangement.

This makes the most sense looking at examples. Let’s go through several variations with the string MONDAYMORNINGHASKELL. Here’s what it looks like with 3 rows.

M   A   R   G   K
O D Y O N N H S E L
N   M   I   A   L

So to get the answer, we read along the top line first (MARGK), then the second (ODYONNHSEL), and then the third (NMIAL). So the final answer is MARGKODYONNHSELNMIAL.

Now let’s look at the same string in 4 rows:

M     M     G     L
O   Y O   N H   E L
N A   R I   A K
D     N     S

The answer here is MMGLOYONHELNARIAKDNS.

Here’s 5 rows:

M       R       K
O     O N     S E
N   M   I   A   L
D Y     N H     L
A       G

The answer here is MRKOONSENMIALDYNHLAG.

And now that we have the pattern, we can also consider 2 rows, which doesn’t visually look like a zig-zag as much:

M N A M R I G A K L
O D Y O N N H S E L

This gives the answer MNAMRIGAKLODYONNHSEL.

Finally, if there’s only 1 row, you can simply return the original string.

The Algorithm

So how do we go about solving this? The algorithm here is a bit more involved than the last few weeks!

Our output order is row-by-row, so for our solution we should think in a row-by-row fashion. If we can devise a function that will determine the indices of the original string that belong in each row, then we can simply loop over the rows and append these results!

In order to create this function, we have to think about the zig-zag in terms of “cycles”. Each cycle begins at the top row, goes down to the bottom row, and then up diagonally to the second row. The next element to go at the top row starts a new cycle. By thinking about cycles, we’ll discover a few key facts:

1. With n rows (n >= 2), a complete cycle has 2n - 2 letters.
2. The top and bottom row get one letter per cycle.
3. All other rows get two letters per cycle.

Now we can start to think mathematically about the indices that belong in each row. It’s easiest to think about the top and bottom rows, since they only get one letter each cycle. Each of these has a starting index (0 and n - 1, respectively), and then we add the cycle length 2n - 2 to these starting indices until it exceeds the length.

The middle rows have this same pattern, only now they have 2 starting indices. They have the starting index from the “down” direction and then their first index going up and to the right. The first index for row i is obviously i - 1, but the second index is harder to see.

The easiest way to find the second index is backwards! The next cycle starts at 2n - 2. So row index 1 has its second index at 2n - 2 - 1, and row index 2 has its second index at 2n - 2 - 2, and so on! The pattern of adding the “cycle number” will work for all starting indices.

Once we have the indices for each row, our task is simple. We build a string for each row and combine them together in order.

So suppose we have our 4-row example.

M     M     G     L
O   Y O   N H   E L
N A   R I   A K
D     N     S

The “cycle num” is 6 (2 * 4 - 2). So the first row has indices [0, 6, 12, 18]. The fourth row starts with index 3, and so its indices also go up by 6 each time: [3, 9, 15].

The second row (index 1) has starting indices 1 and 5 (6 - 1). So its indices are [1, 5, 7, 11, 13, 17, 19]. Then the third row has indices [2, 4, 8, 10, 14, 16].

A vector input will allow us to efficiently use and combine these indices.

As a final note, the “cycle num” logic doesn’t end up working with only 1 row. The cycle length using our calculation would be 0, not 1 as it should. The discrepancy is because our “cycle num” logic really depends on having a “first” and “last” row. So if we only have 1 row, we’ll hardcode that case and return the input string.

Rust Solution

In our rust solution, we’ll accumulate our result string in place. To accomplish this we’ll do a few setup steps:

1. Handle our base case (1 row)
2. Get the string length and cycle number
3. Make a vector of the input chars for easy indexing (Rust doesn’t allow string indexing)
4. Initialize our mutable result string

pub fn convert(s: String, num_rows: i32) -> String {
    if (num_rows == 1) {
        return s;
    }
    let n = s.len();
    let nr = num_rows as usize; // Convenience for comparison
    let cycleLen: usize = (2 * nr - 2);
    let sChars: Vec<char> = s.chars().collect();
    let mut result = String::new();
    ...
}

Now we have to add the rows in order. Since the logic differs for the first and last rows, we have 3 sections: first row, middle rows, and last row. The first and last row are straightforward using our algorithm. Each is a simple while loop.

pub fn convert(s: String, num_rows: i32) -> String {
   if (num_rows == 1) {
       return s;
   }
   let n = s.len();
   let nr = num_rows as usize; // Convenience for comparison
   let cycleLen: usize = (2 * nr - 2);
   let sChars: Vec<char> = s.chars().collect();
   let mut result = String::new();
   
   // First Row
   let mut i = 0;
   while i < n {
       result.push(sChars[i]);
       i += cycleLen;
   }

   // Middle Rows
   ...

   // Last Row
   i = (nr - 1);
   while i < n {
       result.push(sChars[i]);
       i += cycleLen;
   }
   return result;
}

Now the middle rows section is similar. We loop through each of the possible rows in the middle. For each of these, we’ll do a while loop similar to the first and last row. These loops are different though, because we have to track two possible values, the “first” and “second” of each cycle.

If the “first” is already past the end of the vector, then we’re already done and can skip the loop. But even if not, we still need an “if check” on the “second” value as well. Each time through the loop, we increase both values by cycleLen.

pub fn convert(s: String, num_rows: i32) -> String {
   if (num_rows == 1) {
       return s;
   }
   let n = s.len();
   let nr = num_rows as usize; // Convenience for comparison
   let cycleLen: usize = (2 * nr - 2);
   let sChars: Vec<char> = s.chars().collect();
   let mut result = String::new();
   
   // First Row
   let mut i = 0;
   while i < n {
       result.push(sChars[i]);
       i += cycleLen;
   }

   // Middle Rows
   for row in 1..(nr - 1) {
       let mut first = row;
       let mut second = cycleLen - row;
       while first < n {
           result.push(sChars[first]);
           if second < n {
               result.push(sChars[second]);
           }
           first += cycleLen;
           second += cycleLen;
       }
   }

   // Last Row
   i = (nr - 1);
   while i < n {
       result.push(sChars[i]);
       i += cycleLen;
   }
   return result;
}

And that’s our complete solution!

Haskell Solution

The Haskell solution follows the same algorithm, but we’ll make a few stylistic changes compared to Rust. In Haskell, we’ll go ahead and define specific lists of indices for each row. That way, we can combine these lists and make our final string all at once using concatMap. This approach will let us demonstrate the power of ranges in Haskell.

We start our defining our base case and core parameters:

zigzagConversion :: String -> Int -> String
zigzagConversion input numRows = if numRows == 1 then input
  else ...
  where
    n = length input
    cycleLen = 2 * numRows - 2

    ...

Now we can define index-lists for the first and last rows. These are just ranges! We have the starting element, and we know to increment it by cycleLen. The range should go no higher than n - 1. Funny enough, the range can figure out that it should be empty in the edge case that our input is too small to fill all the rows!

zigzagConversion :: String -> Int -> String
zigzagConversion input numRows = if numRows == 1 then input
  else ...
  where
    n = length input
    cycleLen = 2 * numRows - 2

    firstRow :: [Int]
    firstRow = [0,cycleLen..n - 1]

    lastRow :: [Int]
    lastRow = [numRows - 1, numRows - 1 + cycleLen..n - 1]

    ...

In Rust, we used a while-loop with two state values to calculate the middle rows. Hopefully you know from this series now that this while loop translates into a recursive function in Haskell. We’ll accumulate our list of indices as a tail argument, and keep the two stateful values as our other input parameters. We’ll combine all our lists together into one big list of int-lists, allRows.

zigzagConversion :: String -> Int -> String
zigzagConversion input numRows = if numRows == 1 then input
  else ...
  where
    n = length input
    cycleLen = 2 * numRows - 2

    firstRow :: [Int]
    firstRow = [0,cycleLen..n - 1]

    lastRow :: [Int]
    lastRow = [numRows - 1, numRows - 1 + cycleLen..n - 1]

    middleRow :: Int -> Int -> [Int] -> [Int]
    middleRow first second acc = if first >= n then reverse acc
      else if second >= n then reverse (first : acc)
      else middleRow (first + cycleLen) (second + cycleLen) (second : first : acc)

    middleRows :: [[Int]]
    middleRows = map (\i -> middleRow i (cycleLen - i) []) [1..numRows-2]

    allRows :: [[Int]]
    allRows = firstRow : middleRows <> [lastRow]

    ...

Now we bring it all together with one final step. We make a vector from our input, and define a function to turn a single int-list into a single String. Then at the top level of our function (the original else branch), we use concatMap to bring these together into our final result String.

zigzagConversion :: String -> Int -> String
zigzagConversion input numRows = if numRows == 1 then input
  else concatMap rowIndicesToString  allRows
  where
    n = length input
    cycleLen = 2 * numRows - 2

    firstRow :: [Int]
    firstRow = [0,cycleLen..n - 1]

    lastRow :: [Int]
    lastRow = [numRows - 1, numRows - 1 + cycleLen..n - 1]

    middleRow :: Int -> Int -> [Int] -> [Int]
    middleRow first second acc = if first >= n then reverse acc
      else if second >= n then reverse (first : acc)
      else middleRow (first + cycleLen) (second + cycleLen) (second : first : acc)

    middleRows :: [[Int]]
    middleRows = map (\i -> middleRow i (cycleLen - i) []) [1..numRows-2]

    allRows :: [[Int]]
    allRows = firstRow : middleRows <> [lastRow]

    inputV :: V.Vector Char
    inputV = V.fromList input

    rowIndicesToString :: [Int] -> String
    rowIndicesToString = map (inputV V.!)

Conclusion

This comparison once again showed how while loops in Rust track with recursive functions in Haskell. We also saw some nifty Haskell features like ranges and tail recursion. Most of all, we saw that even with a trickier algorithm, we can still keep the same basic shape of our algorithm in a functional or imperative style.

To learn more about these problem solving concepts, take a look at Solve.hs, our comprehensive course on problem solving in Haskell. You’ll learn about recursion, list manipulation, data structures, graph algorithms, and so much more!

by James Bowen at June 09, 2025 08:30 AM

Funding the Haskell toolchain with Ecosystem Support Packages

Well-Typed are delighted to be working in partnership with the Haskell Foundation to offer Haskell Ecosystem Support Packages, which include:

• Investment in open-source maintenance work for core Haskell tools (GHC, Cabal, HLS, …)
• Access to Well-Typed’s team of Haskell experts for private development or technical support
• Funding the Haskell Foundation to sustain key community infrastructure¹
• Acknowledgement of the sponsor’s contribution to the Haskell community

We would like to gratefully acknowledge our first Haskell Ecosystem Supporters:

• Channable
• QBayLogic

They, along with our other clients who contribute to funding our open-source work, are making a real difference to Haskell’s sustainability. If your company uses Haskell and is not already funding its development, why not join them?

Introduction

The Haskell language has just turned 35 years old, and the vibrant Haskell community continues to thrive thanks to the efforts of dedicated volunteers across many different roles and open source projects. Haskell has always been a collective, community-driven project without a controlling corporate sponsor, which has many benefits. But it leads to challenges funding some activities that are crucial to the sustainability of the ecosystem:

• Maintenance of core parts of the Haskell toolchain: large, complex open-source projects need full-time paid maintainers to function effectively and avoid the “Nebraska problem”.

• Community-building and infrastructure support: from running servers for crucial services, to coordinating volunteers and assisting open-source projects, to organizing events.

Well-Typed has a well-established track record maintaining GHC and other core Haskell tools alongside our commercial consulting work; read more in our GHC activities reports. The Haskell Foundation undertakes a wide range of activities to support the community and broaden the adoption of Haskell.

Both Well-Typed and the Haskell Foundation rely on funding from commercial users of Haskell to make this possible. Thus we are happy to be working in partnership to make it easy for companies to contribute back and support all this important work, while receiving tangible benefits themselves. Haskell Ecosystem Supporter companies make a single contract and in return get support with their specific needs, work to sustain the Haskell tools on which they rely, and sponsor the Haskell Foundation. You can find out more about the approach we’ve agreed in the Foundation’s announcement of Ecosystem Partnerships.

Well-Typed have been keen supporters and sponsors of the Haskell Foundation since it was established five years ago, and Andres Löh from Well-Typed is currently Chair of the Foundation Board. We would be delighted to see other companies supporting the Haskell Foundation and the wider Haskell community through similar partnerships.

Our offer

Well-Typed offer multiple tiers of support, to meet the needs of clients of different sizes:

Tier	Bronze	Silver	Gold
Open-source maintenance for core Haskell toolchain	✅	✅✅	✅✅✅
Support for Haskell Foundation	✅	✅✅	✅✅✅
Engineering meetings	Quarterly	Monthly	Fortnightly
Technical support channel	-	Email	Chat
Developer time included	10 hours/month	1/5 FTE	1/2 FTE
Time reserved for private support or development	-	4 hours/month	16 hours/month
Publicity	Name	Small logo + link	Medium logo + link
Monthly (ex VAT)	$1,500	$3,850	$11,000
Annual (ex VAT)	$16,500	$42,000	$120,000

Next steps

If this sounds like something you or your company would be interested in, and you would like to help support the Haskell ecosystem, then:

• Read about our offer in more detail
• Talk to us in person at ZuriHac
• Contact us by email to info@well-typed.com

---

1. More specifically: for these packages, 20% of the purchase price will be donated to Haskell.org for the Haskell Foundation.↩︎

by adam at June 03, 2025 12:00 AM

Starting from the End: Solving “Product Except Self”

Today we continue our series exploring LeetCode problems and comparing Haskell and Rust solutions. We’re staying in the realm of list/vector manipulation, but the problems are going to start getting more challenging!

If you want to learn more about problem solving in Haskell, you should take a closer look at Solve.hs! You’ll particularly learn how to translate common ideas from loop-based into Haskell’s recursive ideas!

The Problem

Today’s problem is Product of Array Except Self. The idea is that we are given a vector of n integers. We are supposed to return another vector of n integers, where output[i] is equivalent to the product of all the input integers except for input[i].

The key constraint here is that we are not allowed to use division. If we could use division, the answer would be simple! We would find the product of the input numbers and then divide this product by each input number to find the corresponding value. But division is more expensive than most other numeric operations, so we want to avoid it if possible!

The Algorithm

The approach we’ll use in this article relies on “prefix products” and “suffix products”. We’ll make two separate vectors called prefixes and suffixes, where prefixes[i] is the product of all numbers strictly before index i, and suffixes[i] is the product of all numbers strictly after index i.

Then, we can easily produce our results. The value output[i] is simply the product of prefixes[i] and suffixes[i].

As an example, our input might be [3, 4, 5]. The prefixes vector should be [1, 3, 12], and the suffixes vector should be [20, 5, 1]. Then our final output should be [20, 15, 12].

prefixes: [1, 3, 12]
suffixes: [20, 5, 1]
output: [20, 15, 12]

Rust Solution

Here’s our Rust solution:

impl Solution {
    pub fn product_except_self(nums: Vec<i32>) -> Vec<i32> {
        let n = nums.len();
        let mut prefixes = vec![0; n];
        let mut suffixes = vec![0; n];
        let mut totalPrefix = 1;
        let mut totalSuffix = 1;

        // Loop 1: Populate prefixes & suffixes
        for i in 0..n {
            prefixes[i] = totalPrefix;
            totalPrefix *= nums[i];
            suffixes[n - i - 1] = totalSuffix;
            totalSuffix *= nums[n - i - 1];
        }

        let mut results = vec![0; n];

        // Loop 2: Populate results
        for i in 0..n {
            results[i] = prefixes[i] * suffixes[i];
        }
        return results;
    }
}

The two for-loops provide this solution with its shape. The first loop generates our vectors prefixes and suffixes. We keep track of a running tally of the totalPrefix and the totalSuffix. Each of these is initially 1.

let n = nums.len();
let mut prefixes = vec![0; n];
let mut suffixes = vec![0; n];
let mut totalPrefix = 1;
let mut totalSuffix = 1;

On each iteration, we assign the current “total prefix” to the prefixes vector in the front index i, and then the “total suffix” to the suffixes vector in the back index n - i - 1. Then we multiply each total value by the input value (nums) from that index so it’s ready for the next iteration.

// Loop 1: Populate prefixes & suffixes
for i in 0..n {
    prefixes[i] = totalPrefix;
    totalPrefix *= nums[i];
    suffixes[n - i - 1] = totalSuffix;
    totalSuffix *= nums[n - i - 1];
}

And now we calculate the result, by taking the product of prefixes and suffixes at each index.

let mut results = vec![0; n];

// Loop 2: Populate results
for i in 0..n {
    results[i] = prefixes[i] * suffixes[i];
}
return results;

Haskell Solution

In Haskell, we can follow this same template. However, a couple differences stand out. First, we don’t use for-loops. We have to use recursion or recursive helpers to accomplish these loops. Second, when constructing prefixes and suffixes, we want to use lists instead of modifying mutable vectors.

When performing recursion and accumulating linked lists, it can be tricky to reason about which lists need to be reversed at which points in our algorithm. For this reason, it’s often very helpful in Haskell to start from the end of our algorithm.

Let’s write out a template of our solution that leaves prefixes and suffixes as undefined stubs. Then the first step we’ll work through is how to get the solution from that:

productOfArrayExceptSelf :: V.Vector Int -> V.Vector Int
productOfArrayExceptSelf inputs = solution ???
  where
    n = V.length inputs

    solution :: ??? -> V.Vector Int

    prefixes :: [Int]
    prefixes = undefined

    suffixes :: [Int]
    suffixes = undefined

So given prefixes and suffixes, how do we find our solution? The ideal case is that both these lists are already in reverse-index order with respect to the input vector (i.e. n - 1 to 0). Then we don’t need to do an additional reverse to get our solution.

We can then implement solution as a simple tail recursive helper function that peels one element off each input and multiplies them together. When we’re out of inputs, it returns its result:

productOfArrayExceptSelf :: V.Vector Int -> V.Vector Int
productOfArrayExceptSelf inputs = solution (prefixes, suffixes, [])
  where
    n = V.length inputs

    -- Loop 2: Populate Results
    solution :: ([Int], [Int], [Int]) -> V.Vector Int
    solution ([], [], acc) = V.fromList acc
    solution (p : ps, s : ss, acc) = solution (ps, ss, p * s : acc)
    solution _ = error “Prefixes and suffixes must be the same size!”

    prefixes :: [Int]

    suffixes :: [Int]

So now we’ve done “Loop 2” already, and we just have to implement “Loop 1” so that it produces the right results. Again, we’ll make a tail recursive helper, and this will produce both prefixes and suffixes at once. It will take the index, as well as the “total” prefix and suffix so far, and then two accumulator lists. At the end of this, we want both lists in reverse index order.

productOfArrayExceptSelf :: V.Vector Int -> V.Vector Int
productOfArrayExceptSelf inputs = solution (prefixes, suffixes, [])
  where
    n = V.length inputs

    -- Loop 2: Populate Results
    solution :: ([Int], [Int], [Int]) -> V.Vector Int

    prefixes :: [Int]
    suffixes :: [Int]
    (prefixes, suffixes) = mkPrefixSuffix (0, 1, [], 1, [])

    -- Loop 1: Populate prefixes & suffixes
    mkPrefixSuffix :: (Int, Int, [Int], Int, [Int]) -> ([Int], [Int])
    mkPrefixSuffix (i, totalPre, pres, totalSuff, suffs) = undefined

Now we fill in mkPrefixSuffix as we would any tail recursive helper. First we satisfy the base case. This occurs once i is at least n. We’ll return the accumulated lists.

mkPrefixSuffix :: (Int, Int, [Int], Int, [Int]) -> ([Int], [Int])
mkPrefixSuffix (i, totalPre, pres, totalSuff, suffs) = if i >= n then (pres, reverse suffs)
  else ...

But observe we’ll need to reverse suffixes! This becomes clear when we map out what each iteration of the loop looks like for a simple input. Doing this kind of “loop tracking” is a very helpful problem solving skill for walking through your code!

input = [3, 4, 5]
i = 0: (0, 1, [], 1, [])
i = 1: (1, 3, [1], 5, [1])
i = 2: (2, 12, [3, 1], 20, [5, 1])
i = 3: (3, 60, [12, 3, 1], 60, [20, 5, 1])

Our prefixes are [12, 3, 1], which is properly reversed, but the suffixes are [20, 5, 1]. We don’t want both lists ending in 1! So we reverse the suffixes.

Now that we’ve figured this out, it’s simple enough to fill in the recursive case using what we already know from “Loop 1” in the Rust solution. We get the “front” index of input with i, and the “back” index with n - i - 1, use these to get the new products, and then save the old products in our list.

mkPrefixSuffix :: (Int, Int, [Int], Int, [Int]) -> ([Int], [Int])
mkPrefixSuffix (i, totalPre, pres, totalSuff, suffs) = if i >= n then (pres, reverse suffs)
  else
    let nextPre = nums V.! i
        nextSuff = nums V.! (n - i - 1)
    in mkPrefixSuffix (i + 1, totalPre * nextPre, totalPre : pres, totalSuff * nextSuff, totalSuff : suffs)

Here’s our complete Haskell solution!

productOfArrayExceptSelf :: V.Vector Int -> V.Vector Int
productOfArrayExceptSelf inputs = solution (prefixes, suffixes, [])
  where
    n = V.length inputs

    solution :: ([Int], [Int], [Int]) -> V.Vector Int
    solution ([], [], acc) = V.fromList acc
    solution (p : ps, s : ss, acc) = solution (ps, ss, p * s : acc)
    solution _ = error "Invalid solution!"

    prefixes :: [Int]
    suffixes :: [Int]
    (prefixes, suffixes) = mkPrefixSuffix (0, 1, [], 1, [])


    mkPrefixSuffix:: (Int, Int, [Int], Int, [Int]) -> ([Int], [Int])
    mkPrefixSuffix (i, totalPre, pres, totalSuff, suffs) = if i >= n then (pres, reverse suffs)
      else
        let nextPre = inputs V.! i
            nextSuff = inputs V.! (n - i - 1)
        in  mkPrefixSuffix (i + 1, totalPre * nextPre, totalPre : pres, totalSuff * nextSuff, totalSuff : suffs)

Conclusion

In this comparison, we saw a couple important differences in problem solving with a loop-based language like Rust compared to Haskell.

1. For-loops have to become recursion in Haskell
2. We want to use lists in Haskell, not mutable vectors
3. It takes a bit of planning to figure out when to reverse lists!

This led us to a couple important insights when solving problems in Haskell.

1. “Starting from the end” can be very helpful in plotting out our solution
2. “Loop tracking” is a very helpful skill to guide our solutions

For an in-depth look at these sorts of comparisons, check out our Solve.hs course. You’ll learn all the most important tips and tricks for solving coding problems in Haskell! In particular you’ll get an in-depth look at tail recursion, a vital concept for solving problems in Haskell.

by James Bowen at June 02, 2025 08:30 AM

Vibe coding case study: ScubaDuck

A lot of strong engineers that I know haven't really taken a serious look at AI coding; they've used LLMs to ask questions or write simple scripts and appreciate that it is a useful tool, but haven't actually tried building a nontrivial application entirely from scratch in vibe coding style (here, I use the term in its original meaning: when you do AI coding without carefully reviewing the output). This is understandable: if you're not working on a green field project, there aren't that many opportunities to write code in this style--standard practice for established projects is that someone else needs to review all of the code you write: this is a bad match for vibe coding! So in this post, I want to give a concrete case study of a nontrivial system that was entirely vibe coded (ScubaDuck), to argue the following claims:

1. AI coding can be done on a manager's schedule: you don't need continuous blocks of coding time and context-switching is considerably less harmful. ScubaDuck was implemented in three days of part time work, where all of the work happened when the baby was napping.
2. AI coding substantially lowers the cost of doing projects in tech stacks you are less familiar with. ScubaDuck is mostly JavaScript UI code, which is not something I write on a day-to-day basis.
3. AI coding is an unlock for "sidequests": support software that's ancillary to your main task that is nice to have, but not essential. If previously you would have decided the cost outweighed the benefit, AI coding reducing the cost means you should redo these calculations.
4. Vibe coding works and can produce working software. ScubaDuck is an existence proof that vibe coding is a viable strategy for generating JavaScript UI code (NB: I don't claim vibe coding will work for all domains, nor do I claim this is the only domain for it works. Hopefully you can also build some intuition for where it is more or less likely to work). You will not one shot it (ScubaDuck was 150 prompts in the end) but if you are prompting the LLM to also generate tests, you can reliably fix issues without causing regressions to existing code.
5. Vibe coding is good for situations where buggy software is low impact; be on the lookout for ways to engineer this sort of situation. ScubaDuck is a read-only interface, where the only downside to being buggy is you can't issue the queries you want to issue.

Update: You can see all of my prompts and the resulting agent trajectories at scubaduck-prompts.

What is ScubaDuck?

ScubaDuck is a discount implementation of Meta's internal Scuba realtime database system. You can read more about what exactly this is on GitHub, but it's not so important for the purposes of this post: the key details you need to know about ScubaDuck is that it consists of a Python server that exposes an API to perform queries against a DuckDB database, and an HTML and JavaScript frontend application which implements the forms for building these queries and rendering of the output data. Both the forms and output data rendering have nontrivial JavaScript enhancements: some form inputs are chip inputs and support autocomplete, and the time series view is an SVG chart. All of these components were coded from scratch, so the project has no third-party JavaScript dependencies.

So on the one hand, this project is pretty simple. There are no stringent performance or uptime requirements, it's a pretty standard server-client program that the LLM has seen millions of times before (this is good!) On the other hand, the exact behavior of the frontend UI is quite intricate and would be very difficult to one-shot in a single prompt. Indeed, as I was coding and testing the application, I frequently ran into situations that I didn't anticipate in my original specification, and that I had to ask Codex to refine. Another way to put it is that ScubaDuck is a relatively simple functional specification (although this too was not one shot), but I did a lot of polishing of small behaviors so that the interface behaved in the way that I expected Scuba to behave. Here, it was helpful that I had a very clear idea of what I wanted (since I've used Scuba quite a lot at work).

Going into ScubaDuck, I had a pretty good sense that this project should be a good fit for LLMs. HTML, JavaScript and Python are all extremely high resource languages, and I'd heard lots of people raving about how good LLMs were at transforming wireframes and mockups into fully functional websites. It is also fully self contained and straightforward-ish to test (only "ish" because you do have to use something like Playwright to actually test the frontend UI, which honestly is a slog. But fortunately, the LLM can write the tests for you!) One design decision I made, which I didn't originally anticipate but worked out in the end, was the decision to not use any third-party JavaScript libraries. This was by accident: Python has no native of bundling third party JavaScript, but I wanted the tool to work offline. I wasn't sure if you could vibe code an SVG charting library from scratch, but apparently you can and it's quite easy!

Agent setup

ScubaDuck was implemented with OpenAI Codex in the cloud (not the CLI tool). Codex's cloud offering requires you to initialize a hermetic environment which the coding agent can execute commands in. It's pretty well known now that AI coding agents work much better if they are able to run the code they write and see if it worked or not, so this is quite an important part of the process. Unfortunately, this was somewhat time consuming trial and error to setup. I had a fairly detailed initial prompt, and what I would do was submit it to Codex, watch it fail, read over the trajectory (the agent logs) to see what happened (Codex wanted to use npm! Codex couldn't download something from the internet! Codex tried to use a package that wasn't available!) and then fixed whatever environment misconfiguration had caused it to fail, or edited AGENTS.md to instruct it to not do some behavior. According to my history, the first day of the project was spent unsuccessfully trying to get the project setup, and my first successful Codex PR only happened on May 19.

At the end of setup, I had the following:

1. A pyproject.toml with exactly the dependencies I wanted to be used (duckdb, flask and python-dateutil), a lockfile for it (since I was using uv) and my preferred configuration for various tools (pytest, ruff). I'm a big fan of pytest-xdist for vibe coded projects, since you can prompt the LLM to write tests that will work when run in parallel and it does a pretty good job at this. Later I'd also add a pyright configuration, though initially I left it out because I saw Codex doing some strange things on account of duckdb being untyped, and I didn't want to debug it at the time (the fix, by the way, is instructing the LLM to define stubs as necessary in this case.)
2. An AGENTS.md file with some basic instructions to try to get Codex to stop doing things I saw it doing in the initial trajectories that I didn't want it to do. Nothing fancy, just if you see Codex do something bad, tell it not to do it in AGENTS.md. A good example of this is the "There are no nested AGENTS.md files, this is the only agents file": Codex is post-trained to look for nested AGENTS.md files, but you can save a few tool calls if you tell it there aren't any. (Note: folklore for Claude 3.7 is that instruction following for this sort of rules following was not great. Word on the street is that both Codex and Claude 4 are substantially better at this. Extra note: For uv users, another notable instruction in AGENTS.md is how to activate the venv, since at time of writing I couldn't get Codex to make this happen automatically.)
3. A setup script for the environment. This took the most debugging, because Codex runs all Internet access through a proxy and sometimes it works imperfectly.

After I got my initial prompt to generate a first draft of the application, I was able to begin vibe coding in earnest.

The Human-Agent loop

The basic vibe coding loop works like this:

1. Interact with the application and find things that are broken
2. Prompt the LLM to fix them
3. Repeat

For example, after the very first PR, some very mild poking around immediately revealed the bugs fixed in #2:

There's a race condition in the current test logic for matching against table contents in run_query. Specifically, if there were previously valid results in lastResults, and for some reason Dive doesn't do anything, then we will still see the old results. The testing framework should explicitly clear lastResults before attempting an interaction.

...and #3:

Filter functionality does not work. We will first add a failing test, and then fix it. The failing test should click "Add Filter", then select "user" as the field, and then add an "alice" chip (by typing alice in the text box and pressing ENTER). Then when we dive, we should see two alice rows. Right now, NO request is issued at all when we click Dive. Diagnose and then fix the problem.

Prompt the agent to write tests. It's very helpful to prompt the agent to generate tests for whatever bugs its fixing. For frontend code, I decided to use playwright to write these tests. An example in #11:

def test_header_and_tabs(page: Any, server_url: str) -> None:
    page.goto(server_url)
    page.wait_for_selector("#order_by option", state="attached")

    header = page.text_content("#header")
    assert "sample.csv" in header
    assert "events" in header

    assert page.is_visible("#settings")
    assert page.is_hidden("#columns")
    page.click("text=Columns")
    assert page.is_visible("#columns")
    cols = page.locator("#column_list li").all_inner_texts()
    assert "timestamp" in cols
    assert "event" in cols
    page.click("text=View Settings")
    assert page.is_visible("#settings")

    btn_color = page.evaluate("getComputedStyle(document.querySelector('#dive')).backgroundColor")
    assert "rgb(0, 128, 0)" == btn_color

    sidebar_overflow = page.evaluate("getComputedStyle(document.querySelector('#sidebar')).overflowY")
    view_overflow = page.evaluate("getComputedStyle(document.querySelector('#view')).overflowY")
    assert sidebar_overflow == 'auto'
    assert view_overflow == 'auto'

This is kind of a very manual and somewhat brittle test. I doubt I would have had the patience to manually write and debug this. But the LLM will happily do it. There is also a fear that the test might not actually be testing anything for real. But because these tests are all generated from bug reports, you can prompt the model to write the test first, check that it's failing, and then fix the problem. I didn't instruct this in the above prompt, but I did instruct it for #155, for example. The trajectory shows that the LLM demonstrates it can repro the bug before fixing the issue:

I’ll add a case-insensitive test for "samples" to check server behavior with lowercase input.

(scubaduck) root@5b69743466e4:/workspace/scubaduck# python - <<'EOF'
> import json
> from scubaduck import server
>
> app = server.app
> client = app.test_client()
> payload = {
>     "table": "events",
>     "start": "2024-01-01 00:00:00",
>     "end": "2024-01-03 00:00:00",
>     "graph_type": "table",
>     "order_by": "samples",  # lowercase
>     "order_dir": "DESC",
>     "limit": 10,
>     "columns": [],
>     "group_by": ["user"],
> }
> rv = client.post("/api/query", data=json.dumps(payload), content_type="application/json")
> print('status', rv.status_code)
> print('data', rv.get_json())
> EOF
status 400
data {'error': 'Unknown column: samples'}
(scubaduck) root@5b69743466e4:/workspace/scubaduck#

I’ve found the bug happens when "Samples" is lowercase. I’ll adjust the query to handle case insensitivity and add a test for it. Time to modify server.py to fix the issue!

Beware BC-breaking changes. The LLM generated tests worked well when I didn't need to change behavior in a BC-breaking way. Example prompt:

Change time column to default to none unconditionally. (I want to default it to a time column if we find a good candidate but this threshold needs tuning and I don't have the tuning right now.)

This hit a Codex timeout:

This attempt to update the default time column led to extensive frontend test failures that require deeper changes. The environment made it difficult to fully diagnose the Playwright test behaviors within the time available, so the work could not be completed.

In standard software engineering practice, when this happens, decouple the BC compatible and BC breaking changes!

Make it so that Time Column can be set to (none). When it is set this way, the Start/End fields are hidden and we don't apply a filter on time range. (#115)

and then later instead of defaulting the time column to none, I added a heuristic to pick a column that looked like time, which picked the same column that all of the existing tests had also expected to be called with.

Refactors have to be split up. Codex's timeout means that you can't ask it to do too much in one go. Here's a prompt that timed out:

scubaduck/index.html has gotten a bit long. Let's split out some of the JS code into dedicated JS files for their functionality. Also setup the necessary Flask scaffolding to serve these JS files. I think splitting out these specific components would be good:

• Dropdown implementation
• Sidebar resizing
• JS controlling the View Settings (e.g., updateDisplayTypeUI, as well as one off interactions on form elements, columns handling, filter handling, the actual Dive implementation (including query updating), reading in defaults from query string)
• Table rendering (e.g., formatNumber, sorting)
• Chip input implementation
• Chart rendering (showTimeSeries)

Make changes to AGENTS.md or README.md describing the structure so you can quickly find where the components you need are

I eventually did manage the refactor by prompting Codex to individually move out the pieces I wanted to extract one-by-one. This is a place where I think Claude Code probably would have performed better.

Parallelizing tasks. As you can see from the lengths of my prompts, it does take a while to write a good prompt; you're basically writing a bug report with enough detail that the LLM can repro it and then fix it. So sometimes I would be bottlenecked on prompt writing. However, sometimes the prompts were quite short. In those cases, Codex encourages you to submit more tasks that can run in parallel. I found this worked well, and I'd sometimes have as many as five instances going (once again, rate limited by discovering problems, making designs and typing prompts!) One irritation is when the tasks end up conflicting with each other. Sometimes the conflicts are easy to fix, but if it feels nontrivial, it's often better to just ask Codex to redo one of the PRs on latest main after the other has landed. To avoid merge conflicts, it helps to have only one "main feature" agent going at any time, and then ask the agent to do random bugfixes in parallel with it. Once you have no more tasks to get running, you can go do something else while you wait for the agents to finish (manager schedule!)

Prompting

As a reminder, I've posted all of my prompts (including the ones that failed) at scubaduck-prompts, and I think it's helpful to skim through them to get a flavor of what I was asking the LLM. But to summarize, what did I spend most of my time on prompting Codex to do? My general vibe (ahem) is that I spent most of my time doing minor enhancements, where I instructed Codex to make some part of the program work slightly differently, in a way that was previously unspecified from the previous prompt. The metaphor I had in my head while I was working on the project was like that of a sculptor chiseling away marble: in the beginning, anything is possible, but as I kept prompting, I continuously narrowed down the space of possible programs I had until I had exactly the one I wanted. One big thing I want to note is that Codex rarely needed to make updates to my tests; for the most part, tests that were added never got taken away, because I never "changed my mind". I suspect that the vibe coding process would have been rockier if I was having to change behavior frequently.

One of the things that surprised me the most about the process was how easy it was to implement a line chart in SVG with Codex. My first prompt resulted in a chart that looked broken on the test data:

We're going to add a new View type, to go along with Samples and Table: Time Series. Time Series supports all the fields that Table supports, and a few more:

• X-axis: Main group by dimension, e.g., the x-axis on time series view. This is our custom dropdown selector, but only time columns are populated here. It should prefer a default setting from the following list, most preferred first: "time", "timestamp"
• Granularity: Choose the time interval between data points on the chart. For example, a granularity of 1 hour means there will be a data point every 60 minutes that is aggregated with the chosen Aggregate function over the data for the granularity period before point. This is a plain drop down. The valid values are: Auto, Fine, 1 second, 5 seconds, 10 seconds, 30 seconds, 1 minute, 4 minutes, 5 minutes, 10 minutes, 15 minutes, 30 minutes, 1 hour, 3 hours, 6 hours, 1 day, 1 week, 30 days. The semantics of the Auto setting is that it sets the interval to whatever would result in maximum 100 buckets (if there are not enough data points for that many buckets, it just picks the finest time interval that makes sense), and Fine which sets the interval to 500 buckets.
• Fill Missing Buckets: This is a dropdown. For now, it has the settings "Fill with 0 (Per Series)" (default), "Connect (Per Series)" and "Leave blank".

Additionally, the default setting of Limit is 7, as it controls how many elements from group by will be plotted (the actual number of lines plotted could be a multiple of this, as we will plot every selected Column).

Unlike Samples and Table, we will instead display a line chart in the right panel. To plot the line chart, we will implement it by hand with JS and SVG, similar to how highcharts implements it. We will not use any third party dependencies. Lines will be plotted as paths, no smoothing, no dots for individual data points. Each series (as generated by group by) should be plotted with a different color, assigned using a best practices color palette for graph design. There should be a rendering of x-axis and y-axis; the x-axis should have slanted labels to aid readability. When we mouse over the chart, a vertical line should snap to the center of the time bucket that we are closest to. We should also display a crosshair on all of the series showing us their values at that data point, and highlight the closest point we are on, and increase the thickness of the series that point is on. To the left of the graph (still in the right panel), there should be a legend. The legend looks like this:

[GROUP BY VALUE] [AGGREGATE]
[First Column name, with series color]
[Number of samples for the first column]
[Second Column name, with series color]
[Number of samples for the second column]
... for all columns
----
... for all group by values (up to the limit)

So for example, if I group by user, I might see:

Alice AVG
value
4 (samples)

The highlighted series (which has a thicker line) should also be highlighted in the legend).

This was kind of terrifying, because I initially thought I didn't have a good way to test the SVG outputs. But after doing some regular old-fashioned debugging and reading the code (yes, this part not vibe coded), I figured out the problem, and also realized that Playwright can test that an SVG path is not just entirely straight. After the initial bugs were fixed, I mostly had to add missing features like x-axis/y-axis and interactivity features (amusingly, Codex ignored most of the instructions in the latter half of the prompt, giving only the barest bones legend. I suspect this was because I had some files which were too long). My general take after this was that JS chart libraries are going to become obsolete: it's much easier to vibe code a bespoke implementation and then customize the heck out of it.

Conclusion

ScubaDuck was implemented in about 150 Codex prompts. As you can see from the sample prompts above, the prompts are recognizably programming, they just happen to be in plain English language. This is a big help, because I never had to keep track of the nest of callbacks and state machines for implementing complex UI elements in JavaScript. I had to be fluent in what I wanted my program to do, and a good QA tester for the application to discover new problems that needed to be fixed, but I did not have to worry at all about the vagaries of SVG DOM elements or pixel position computation minutiae. It's hard to say how long it would have taken to code this by hand, but I think reproducing a UI that's been in production for years at Meta in three (part-time) days is pretty good!

Despite having done a bit of AI coding before, I also learned a bit from working on Codex. Codex made it blindingly clear that the parallel modality (and subsequent conflict resolution) is important. It made me adjust up my estimation of the capability of LLMs to write raw HTML/JS and evoked a future where people vibe code components in place of taking on a third party dependency. I was very appreciative of no rate limit Codex (though I doubt it's going to last.) It also reminded me how difficult it will be to setup agent environments for "real" projects (like PyTorch).

Hopefully, this case study has given you some ideas for things to try. Go forth and vibe code, responsibly!

by Edward Z. Yang at June 02, 2025 04:31 AM

Building Industrial Strength Software without Unit Tests

I don't know about you, but testing isn't my favourite part of software development.

It's usually the last thing standing between me and shipping a shiny new feature, and writing tests is often an annoying process with a lot of boilerplate and fighting against your system to get your app into a good start starting for the test or mocking out whichever services your app depends on.

Much ink has been spilled about how to organize your code in order to make this easier, but the fact that so many blog posts and frameworks exist for this express purpose suggests to me that we as a community of software developers haven't quite solved this issue yet.

Keep reading to see how I've solved this problem for myself by simply avoiding unit testing altogether.

An alternative testing method

When I first started at Unison Computing I was submitting my first feature when I learned there were precious few unit tests. I found it rather surprising for a codebase for a compiler for a programming language! How do you prevent regressions without unit tests?

The answer is what the Unison team has dubbed transcript tests. These are a variation on the concept of golden-file tests.

A Unison transcript is a markdown file which explains in standard what behaviour it is going to test, then intersperses code-blocks which outline the steps involved in testing that feature using a mix of Unison code and UCM commands (UCM is Unison's CLI tool). After that comes the magic trick; UCM itself can understand and run these transcript files directly and record the results of each block.

When running a transcript file with the ucm transcript command UCM produces a deterministic output file containing the result of processing each code block. Unless the behaviour of UCM has changed since the last time it was run the resulting file will always be the same.

Each block in the markdown file is either a command, which is sent to the UCM shell tool, or it represents an update to a file on the (virtual) file-system, in which case it will be typechecked against the state of the codebase.

Here's a quick example of a transcript for testing UCM's view command so you can get a feel for it.

# Testing the `view` command

First, let's write a simple definition to view:

``` unison
isZero = cases
  0 -> true
  _ -> false
```

Now we add the definition to the codebase, and view it.

``` ucm
scratch/main> update
scratch/main> view isZero
```

We run this transcript file with ucm transcript my-transcript.md which produces the my-transcript.output.md file.

Notice how compiler output is added inline, ignore the hashed names, It's because I'm skipping the step which adds names for Unison's builtins.

# Testing the `view` command

First, let's write a simple definition to view:

``` unison
isZero = cases
  0 -> true
  _ -> false
```

``` ucm :added-by-ucm
  Loading changes detected in scratch.u.

  I found and typechecked these definitions in scratch.u. If you
  do an `add` or `update`, here's how your codebase would
  change:

    � These new definitions are ok to `add`:
    
      isZero : ##Nat -> ##Boolean
```

Now we add the definition to the codebase, and view it.

``` ucm
scratch/main> update

  Done.

scratch/main> view isZero

  isZero : ##Nat -> ##Boolean
  isZero = cases
    0 -> true
    _ -> false
```

Feel free to browse through the collection of transcripts we test in CI to keep UCM working as expected.

Testing in CI

Running transcript tests in CI is pretty trivial; we discover all markdown files within our transcript directory and run them all. After the outputs have been written we can use git diff --exit-code which will then fail with a non-zero code if anything of the outputs have changed from what was committed. Conveniently, git will also report exactly what changed, and what the old output was.

This failure method allows the developer to know exactly which file has unexpected behaviour so they can easily re-run that file or recreate the state in their own codebase if they desire.

Transcript tests in other domains

I liked the transcript tests in UCM so much that when I was tasked with building out the Unison Share webapp I decided to use transcript-style testing for that too. Fast forward a few years and Unison Share is now a fully-featured package repository and code collaboration platform running in production without a single unit test.

If you're interested in how I've adapted transcript tests to work well for a webapp, I'll leave a few notes at the end of the post.

Benefits of transcript tests

Here's a shortlist of benefits I've found working with transcript tests over alternatives like unit tests.

You write a transcript using the same syntax as you'd interact with UCM itself.

This allows all your users to codify any buggy behaviour they've encountered into a deterministic transcript. Knowing exactly how to reproduce the behaviour your users are seeing is a huge boon, and having a single standardized format for accepting bug reports helps reduce a lot of the mental work that usually goes into reproducing bug reports from a variety of sources. This also means that the bug report itself can go directly into the test suite if we so desire.

All tests are written against the tool's external interface.

The tests use the same interface that the users of your software will employ, which means that internal refactors won't ever break tests unless there's a change in behaviour that's externally observable.

This has been a huge benefit for me personally. I'd often find myself hesitant to re-work code because I knew that at the end I'd be rewriting thousands of lines of tests. If you always have to rewrite your tests at the same time you've rewritten your code, how do you have any confidence that the tests still work as intended?

Updating tests is trivial

In the common case where transcripts are mismatched because some help message was altered, or perhaps the behaviour has changed but the change is intended, you don't need to rewrite any complex assertions, or mock out any new dependencies. You can simply look at the new output, and if it's reasonable you commit the changed transcript output files.

It can't be understated how convenient this is when making sweeping changes; e.g. making changes to Unison's pretty printer. We don't need to manually update test-cases, we just run the transcripts locally and commit the output if it all looks good!

Transcript changes appear in PR reviews

Since all transcript outputs are committed, any change in behaviour will show up in the PR diff in an easy-to-read form. This allows reviewers to trivially see the old and new behaviour for each relevant feature.

Transcript tests are documentation

Each transcript shows how a feature is intended to be used by end-users.

Transcripts as a collaboration tool

When I'm implementing new features in Unison Share I need to communicate the shape of a JSON API with our Frontend designer Simon. Typically I'll just write a transcript test which exercises all possible variants of the new feature, then I can just point at the transcript output as the interface for those APIs.

It's beneficial for both of us since I don't need to keep an example up-to-date for him, and he knows that the output is actually accurate since it's generated from an execution of the service itself.

Transcript testing for Webapps

I've adapted transcript testing a bit for the Unison Share webapp. I run the standard Share executable locally with its dependencies mocked out via docker-compose. I've got a SQL file which resets the database with a known set of test fixtures, then use a zsh script to reset my application state in between running each transcript.

Each transcript file is just a zsh script that interacts with the running server using a few bash functions which wrap curl commands, but save the output to json files, which serve as the transcript output.

I've also got helpers for capturing specific fields from an API call into local variables which I can then interpolate into future queries, this is handy if you need to, for example, create a project then switch it from private to public, then fetch that project via API.

Here's a small snippet from one of my transcripts for testing Unison Share's project APIs:

#!/usr/bin/env zsh

# Fail the transcript if any command fails
set -e

# Load utility functions and variables for user credentials
source "../../transcript_helpers.sh"

# Run a UCM transcript to upload some code to load in projects.
transcript_ucm transcript prelude.md

# I should be able to see the fixture project as an unauthenticated user.
fetch "$unauthenticated_user" GET project-get-simple '/users/test/projects/publictestproject'

# I should be able to create a new project as an authenticated user.
fetch "$transcripts_user" POST project-create '/users/transcripts/projects/containers' '{
    "summary": "This is my project",
    "visibility": "private",
    "tags": []
}'

fetch "$transcripts_user" GET project-list '/users/transcripts/projects'

You can see the output files generated by the full transcript in this directory.

Requirements of a good transcript testing tool

After working with two different transcript testing tools across two different apps I've got a few criteria for what makes a good transcript testing tool, if you're thinking of adding transcript tests to your app consider the following:

Transcripts should be deterministic

This is critical. Transcripts are only useful if they produce the same result on every run, on every operating system, at every time of day.

You may need to make a few changes in your app to adapt or remove randomness, at least when in the context of a transcript test.

In Share there were a lot of timestamps, random IDs, and JWTs (which contain a timestamp). The actual values of these weren't important for the tests themselves, so I solved the issue by piping the curl output through a sed script before writing to disk. The script matches timestamps, UUIDs, and JWTs and replaces them with placeholders like <TIMESTAMP>, <UUID>, and <JWT> accordingly.

A special mode in your app for transcript testing which avoids randomness can be useful, but use custom modes sparingly lest your app's behaviour differ too much during transcripts and you can't test the real thing.

I also make sure that the data returned by APIs is always sorted by something other than randomized IDs, it's a small price to pay, and reduces randomness and heisenbugs in the app as a helpful byproduct.

Transcripts should be isolated

Each individual transcript should be run in its own pristine environment. Databases should be reset to known state, if the file-system is used, it should be cleared or even better, a virtual file-system should be used.

Transcripts should be self-contained

Everything that pertains to a given test-case's state or configuration should be evident from within the transcript file itself. I've found that changes in behaviour from the file's location or name can just end up being confusing.

Difficulties working with Transcripts

Transcripts often require custom tooling

In UCM's case the transcript tooling has evolved slowly over many years, it has it's own parser, and you can even test UCM's API server by using special code blocks for that.

Share has a variety of zsh utility scripts which provide helpers for fetching endpoints using curl, and filtering output to capture data for future calls. It also has a few tools for making database calls and assertions.

Don't shy away from investing a bit of time into making transcript testing sustainable and pleasant, it will pay dividends down the road.

Intensive Setup**

As opposed to unit tests which are generally pretty lightweight; transcript tests are full integration tests, and require setting up data, and sometimes executing entire flows so that we can get the system into a good state for testing each feature.

You can mitigate the setup time by testing multiple features with each transcript.

I haven't personally found transcript tests to take too much time in CI, largely because I think transcript testing tends to produce fewer tests, but of higher value than unit testing. I've seen many unit test suites bogged down by particular unit tests which generate hundreds of test cases that aren't actually providing real value. Also, any setup/teardown is going to be more costly on thousands of unit-tests as compared to dozens or hundreds of transcript tests.

Service Mocking

Since transcript tests run against the system-under-test's external interface, you won't have traditional mocking/stubbing frameworks available to you. Instead, you'll mock out the system's dependencies by specifying custom services using environment variables, or wiring things up in docker-compose.

Most systems have a setup for local development anyways, so integrating transcript tests against it has the added benefit that they'll ensure your local development setup is tested in CI, is consistent for all members of your team, and continues to work as expected.

In Summary

Hopefully this post has helped you to consider your relationship with unit tests and perhaps think about whether other testing techniques may work better for your app.

Transcript tests surely aren't ideal for all possible apps or teams, but my last few years at Unison have proven to me that tests can be more helpful, efficient, and readable than I'd previously thought possible.

Let me know how it works out for you!

Hopefully you learned something �! Did you know I'm currently writing a book? It's all about Lenses and Optics! It takes you all the way from beginner to optics-wizard and it's currently in early access! Consider supporting it, and more posts like this one by pledging on my Patreon page! It takes quite a bit of work to put these things together, if I managed to teach your something or even just entertain you for a minute or two maybe send a few bucks my way for a coffee? Cheers! �

June 02, 2025 12:00 AM

65: Andy Gordon

Andy Gordon from Cogna is interviewed by Sam and Matti. We learn about Andy’s influential work including the origins of the bind symbol in haskell, and the introduction of lambdas in Excel. We go onto discuss his current work at Cogna on using AI to allow non-programmers to write apps using natural language. We delve deeper into the ethics of AI and consider the most likely AI apocalypse.

by Haskell Podcast at May 30, 2025 02:00 PM

Quantifying the impact of an AI tool in our company

As software engineers at Modus Create, we are always on the lookout for tools that can enhance our productivity and code quality. The advent of AI-powered coding assistants such as GitHub Copilot has sparked excitement in the development community. Copilot code completions propose snippets at the current cursor that the user can quickly insert, while Copilot Chat allows users to discuss their code with an AI.

These tools promise to revolutionize software development, allowing engineers to focus on higher-level tasks while delegating implementation details to machines. However, their adoption also raises questions:

• Do they genuinely improve developer productivity?
• How do they affect code quality and maintainability?
• Which users and tasks benefit the most from these AI-driven coding assistants?

This blog post explores the challenges of measuring the impact of AI tools in our software engineering practices, with a focus on GitHub Copilot. Note that the data discussed in the post was collected in Q2 2024. We expect that GitHub Copilot has improved since then; we have also not yet had the opportunity to quantitatively investigate newer interfaces to AI development, like Cursor or Windsurf.

“Developer Productivity”

At Modus Create, we’re passionate about improving the experience of developers, both for our own teams and those at clients. We have been working for years on tools that we think improve developer productivity, for instance with Nix, Bazel, Python, and many more. But measuring developer productivity is a notoriously difficult task.

At the heart of this question lies the nature of software development itself. Is it a productive activity that can fit scientific management, be objectively measured, and be optimized? Part of the research on developer productivity goes down this path, trying to measure things like the time it takes to complete standardized tasks. Another trend suggests that developers themselves can be their own assessors of productivity, where frameworks like SPACE are used to guide self-assessment. Each of these angles has strengths and weaknesses. To get as broad a picture as possible, we tried to use a bit of both. We found, though, that data collection issues made our task timings unusable (more on this below). Therefore, all our conclusions are drawn from self-assessments.

Our in-house experiment

To gain a deeper understanding of the impact of GitHub Copilot at Modus Create, we designed and conducted an in-house experiment.

We managed to recruit 22 participants in total, ranging from Junior to Principal software engineers. They had a wide range of programming experience.

The experiment consisted of four coding tasks that participants needed to complete using Python within an existing codebase. The tasks were designed to evaluate different aspects of software development:

1. Data ingestion: Loading and parsing data from a file into a Pandas DataFrame
2. Data analysis: Performing statistical computations and aggregations using Pandas’ groupby operations
3. Test development: Writing tests using Python’s unittest framework
4. Data visualization: Creating interactive plots using the Streamlit library

Participants had varied levels of experience with the required tools. Most participants had at least a little bit of Python experience, but Pandas experience was less common and hardly anyone had used Streamlit before.¹

Upon completion of the assigned tasks, all participants completed a comprehensive survey to provide detailed feedback on their experience. The survey consisted of approximately 50 questions designed to assess multiple dimensions of the development process, including:

• Assessment of participant expertise levels regarding task requirements, AI tooling and GitHub Copilot proficiency
• Evaluation of task-specific perceived productivity
• Analysis of the impact on learning and knowledge acquisition
• Insights into potential future GitHub Copilot adoption

Perceived productivity gains

We asked participants the following questions.

Question	Choices
If you didn't have Copilot, reaching the answer for task X would have taken...	Less time About the same time More time

This question was core to our study, as it allowed us to directly measure the perceived productivity gain of using Copilot versus not using it.

The result was clear: almost every Copilot user felt more productive using Copilot on every task.

We also broke out the same data by Python experience level, and found that more experienced Python users found less productivity gain than less experienced users. In this plot, we grouped the “no Python experience” and “beginner” users into the “less experienced” group, with the rest of the users in the “more experienced group”.

To better understand how participants tackled these tasks, we collected information by asking for each task:

Question	Choices
Which of the following have you used to complete task X?	Copilot code completions Copilot Chat Google search Library documentation My knowledge

We were also interested in comparing these usages across profiles of developers, so we asked this question as well:

Question	Choices
How would you describe your Python level?	No Python experience Beginner Intermediate Advanced

We could then visualize how participants who felt more productive with Copilot solved each problem, and see if there were variations depending on their profile. Since each participant could choose multiple options, sometimes there are more responses than participants.

Apparently, people don’t like library documentation. Also, we thought it was strange that the most experienced Python users never reported using their own knowledge. It would be interesting to dig more into this, but we don’t have the data available. One theory is that when reviewing AI suggestions everyone relied on their own Python knowledge, but experienced users took that knowledge for granted and so didn’t report using it.

Among people who felt more productive on tasks “Write unit tests” and “Plot with Streamlit”, we really see more usage of Copilot Chat than other sources.

Our hypothesis is that these tasks typically require making more global changes to the code or adding code in places that are not obvious at first. In these scenarios, Copilot Chat is more useful because it will tell you where and what code to add. In other tasks, it was clearer where to add code, so participants could likely place their cursor and prompt Copilot for a suggestion.

This is supported by the questions we asked:

Question	Choices
Which of the following do you think is true?	Copilot is better with acceleration: it helps accelerate work that I already know how to do. Copilot is better with exploration: it helps me explore the problem and how to solve it when I am not sure how to proceed.

This question uses checkboxes, so respondents were not restricted to a single answer.

On average, participants thought Copilot was suited for both acceleration and exploration, but with some notable differences depending on experience level: experienced Pythonistas strongly favored Copilot for acceleration, while less experienced users thought it was better for exploration.

We also found that the participants’ perspective on acceleration versus exploration seems related to the usage of Copilot Chat.

The most interesting part of this chart is that participants who think Copilot is good for exploration or bad for acceleration relied most heavily on Copilot Chat. This suggests that users find the autocomplete features more useful for acceleration, while the chat features — which allow general questions, divorced from a specific code location — are useful for exploration. But it is interesting to note how usage of Copilot Chat versus autocomplete is correlated with how users perceive Copilot as a whole.

For more on acceleration versus exploration with Copilot, this OOPSLA23 talk which inspired to ask this question is worth watching.

Copilot will make code flow

The SPACE framework mentions “flow” as an important aspect of productivity.

Some research associates productivity with the ability to get complex tasks done with minimal distractions or interruptions. This conceptualization of productivity is echoed by many developers when they talk about “getting into the flow” […].

This concept of flow is really interesting, because it is a way to measure productivity that is not based on outputs, but rather on the experience of the developers themselves. And although “flow” might be subjective and perceptual, studies have linked it to higher productivity and reduced stress; see this open-access book chapter for a readable overview of the research.

To get an idea of Copilot’s impact on flow, we asked the following questions:

Question	Choices
Did Copilot decrease your need to switch out of your IDE (for example to search for answers or check the documentation)?	Significantly A bit No
Did Copilot enhance your capacity to stay in your development flow?	Significantly A bit No

The results were unambiguous: most users found that Copilot helped significantly, and a strong majority found that it helped at least a little.

Learnings from organizing the experiment

Although the experiment went well overall, we noted a few challenges worth sharing.

First, ensuring active participation in the experiment required a collective effort within the company. Spreading the word internally about the experiment and looking for participants is an effort not to be underestimated. In our case, we benefited from great support from internal leaders and managers who helped communicate with and recruit participants. Even so, we would have liked to have more participants. It turns out that engineers are sometimes just too busy!

Second, keeping participants focused on the experiment was harder than expected. We had asked participants to make a git commit at the end of each task, thinking that we could use this data to quantify the time it took for each participant to complete their tasks. When looking at the data, we were surprised to see that the time between commits varied widely and was often much longer than expected. When asked, several participants reported that they had to interrupt our experiment to deal with higher-priority tasks. In the end, we discarded the timing data: they were too limited and too heavily influenced by external factors to provide useful conclusions. For the same reason, we haven’t even mentioned yet that our study had a control group: since the timing data wasn’t useful, we’ve omitted the control group entirely from the data presented here.

The ideal scenario of securing dedicated, uninterrupted time from a large pool of engineers proved impractical within our organizational context. Nevertheless, despite these limitations, we successfully gathered a meaningful dataset that contributes valuable perspectives to the existing body of research on AI-assisted development.

Further references

Speaking of other work out there, there’s a lot of it! It turns out that many people are excited by the potential of code assistants and want to understand them better. Who knew? Here is some further reading that we found particularly interesting:

• Experiments at Microsoft and Accenture introduced Copilot into engineers’ day-to-day workflow and measured the impact on various productivity metrics, like the number of opened pull requests; they found that Copilot usage significantly increased the number of successful builds. They had a much larger sample size than we did — Microsoft and Accenture have a lot of engineers — but unlike us they didn’t specifically consider the uptake of unfamiliar tools and libraries.

• A research team from Microsoft and MIT recruited developers from Upwork, gave them a task, and measured the time it took with and without Copilot’s help; they found that Copilot users were about 50% faster. They did a better job than we did at measuring completion time (they used GitHub Classroom), but we think our exit survey asked more interesting questions.

• The Pragmatic Engineer ran a survey about how engineers are using AI tooling, covering popular tools and their perceived impact on development.

Conclusion

Our experiment provided valuable insights into the impact of GitHub Copilot on developer experiences at Modus Create. Overall, developers reported increased productivity and a more seamless workflow. Participants used Copilot extensively in specific coding scenarios, such as automated testing and modifying code that used libraries they were unfamiliar with, and they felt more productive in those cases.

It was particularly interesting to see how the interface to the AI assistant (chat vs. completion) affected participants’ opinions on what the assistant was useful for, with chat-heavy users prioritizing exploration over acceleration and completion-heavy users the other way around. As interfaces and tooling continue to evolve — faster than we can design and run experiments to test them — we expect them to play a huge role in the success of AI-powered code assistants.

---

1. We made a small mistake with the wording in Pandas and Streamlit questions: we gave them the options “I have never used it”, “I have heard of it”, “I have used it before in a limited way”, “I am comfortable with it”, and “I am an advanced user”. The problem, of course, is that these responses aren’t mutually exclusive. Given the order the responses were presented in, we think it’s reasonable to interpret “I have never used it” responses to mean that they’d heard of it but never used it. For the plot, we’ve combined “I have never used it” and “I have heard of it” into “Never used it”.↩

May 29, 2025 12:00 AM

Threshold Strategy in Approval and Range Voting

How to turn polling insight into an optimal ballot — and why anything else is wasted.

I have written previously about how approval and range voting methods are intrinsically tactical. This doesn’t mean that they are more tactical than other election systems (nearly all of which are shown to sometimes be tactical by Gibbard’s Theorem when there are three or more options). Rather, it means that tactical voting is unavoidable. Voting in such a system requires answering the question of where to set your approval threshold or how to map your preferences to a ranged voting scale. These questions don’t have more or less “honest� answers. They are always tactical choices.

But I haven’t dug deeper into what these tactics look like. Here, I’ll do the mathematical analysis to show what effective voting looks like in these systems, and make some surprising observations along the way.

Mathematical formalism for approval voting

We’ll start by assuming an approval election, so the question is where to put your threshold. At what level of approval do you switch from voting not to approve a candidate to approving them?

We’ll keep the notation minimal:

• As is standard in probability, I’ll write â„™[X] for the probability of an event X, and ğ�”¼[X] for the expected value of a (numerical) random variable X.
• I will use B to refer to a random collection (multiset) of ballots, drawn from some probability distribution reflecting what we know from polling and other information sources on other voters. B will usually not include the approval vote that you’re considering casting, and to include that approval, we’ll write B ∪ {c}, where c is the candidate you contemplate approving.
• I’ll write W(·) to indicate the winner of an election with a given set of ballots. This is the candidate with the most approvals. We’ll assume some tiebreaker is in place that’s independent of individual voting decisions; for instance, candidates could be shuffled into a random order before votes are cast, in in the event of a tie for number of approvals, we’ll pick the candidate who comes first in that shuffled order.
• U(·) will be your utility function, so U(c) is the utility (i.e., happiness, satisfaction, or perceived social welfare) that you personally will get from candidate c winning the election. This doesn’t mean you have to be selfish, per se, as accomplishing some altruistic goal is still a form of utility, but we evaluate that utility from your point of view even though other voters may disagree.

With this notation established, we can clearly state, almost tautologically, when you should approve of a candidate c. You should approve of c whenever:

�[U(W(B ∪ {c}))] > �[U(W(B))]

That’s just saying you should approve of c if your expected utility from the election with your approval of c is more than your utility without it.

The role of pivotal votes and exact strategy

This inequality can be made more useful by isolating the circumstances in which your vote makes a difference in the outcome. That is, W(B ∪ {c}) ≠ W(B). Non-pivotal votes contribute zero to the net expectation, and can be ignored.

In approval voting, approving a candidate can only change the outcome by making that candidate the winner. This means a pivotal vote is equivalent to both of:

• W(B ∪ {c}) = c
• W(B) ≠ c

It’s useful to have notation for this, so we’ll define V(B, c) to mean that W(B ∪ {c}) ≠ W(B), or equivalently, that W(B ∪ {c}) = c and W(B) ≠ c. To remember this notation, recall that V is the pivotal letter in the word “pivot�, and also visually resembles a pivot.

With this in mind, the expected gain in utility from approving c is:

• ğ�”¼[U(W(B ∪ {c}))] - ğ�”¼[U(W(B))]. But since the utility gain is zero except for pivotal votes, this is the same as
• â„™[V(B, c)] · (ğ�”¼[U(W(B ∪ {c})) | V(B, c)] - ğ�”¼[U(W(B)) | V(B, c)]). But since V(B, c) implies that W(B ∪ {c}) = c, so this simplifies to
• â„™[V(B, c)] · (U(c) - ğ�”¼[U(W(B)) | V(B, c)])

Therefore, you ought to approve of a candidate c whenever

U(c) > �[U(W(B)) | V(B, c)]

This is much easier to interpret. You should approve of a candidate c precisely when the utility you obtain from c winning is greater than the expected utility in cases where c is right on the verge of winning (but someone else wins instead).

There are a few observations worth making about this:

• The expectation clarifies why the threshold setting part of approval voting is intrinsically tactical. It involves evaluating how likely each other candidate is to win, and using that information to compute an expectation. That means advice to vote only based on internal feelings like whether you consider a candidate acceptable is always wrong. An effective vote takes into account external information about how others are likely to vote, including polling and understanding of public opinion and mood.
• The conditional expectation, assuming V(B, c), tells us that the optimal strategy for whether to approve of some candidate c depends on the very specific situation where c is right on the verge of winning the election. If c is a frontrunner in the election, this scenario isn’t likely to be too different from the general case, and the conditional probability doesn’t change much. However, if c is a long-shot candidate from some minor party, but somehow nearly ties for a win, we’re in a strange situation indeed: perhaps a major last-minute scandal, a drastic polling error, or a fundamental misunderstanding of the public mood. Here, the conditonal expected utility of an alternate winner might be quite different from your unconditional expectation. If, say, voters prove to have an unexpected appetite for extremism, this can affect the runner-ups, as well.
• Counter-intuitively, an optimal strategy might even involve approving some candidates that you like less than some that you don’t approve! This can happen because different candidates are evaluated against different thresholds. Therefore, a single voter’s best approval ballot isn’t necessarily monotonic in their utility rankings. This adds a level of strategic complexity I hadn’t anticipated in my earlier writings on strategy in approval voting.

Approximate strategy

The strategy described above is rigorously optimal, but not at all easy to apply. Imagining the bizarre scenarios in which each candidate, no matter how minor, might tie for a win, is challenging to do well. We’re fortunate, then, that there’s a good approximation. Remember that the utility gain from approving a candidate was equal to

ℙ[V(B, c)] · (U(c) - �[U(W(B)) | V(B, c)])

In precisely the cases where V(B, c) is a bizarre assumption that’s difficult to imagine, we’re also multiplying by ℙ[V(B, c)], which is vanishingly small, so this vote is very unlikely to make a difference in the outcome. For front-runners, who are relatively much more likely to be in a tie for the win, the conditional probability changes a lot less: scenarios that end in a near-tie are not too different from the baseline expectation.

This happens because ℙ[V(B, c)] falls off quite quickly indeed as the popularity of c decreases, especially for large numbers of voters. For a national scale election (say, about 10 million voters), if c expects around 45% of approvals, then ℙ[V(B, c)] is around one in a million. That’s a small number, telling us that very large elections aren’t likely to be decided by a one-vote margin anyway. But it’s gargantuan compared to the number if c expects only 5% of approvals. Then ℙ[V(B, c)] is around one in 10^70. That’s about one in a quadrillion-vigintillion, if you want to know, and near the scale of possibly picking one atom at random from the entire universe! The probability of casting a pivotal vote drops off exponentially, and by this point it’s effectively zero.

With that in mind, we can drop the condition on the probability in the second term, giving us a new rule: Approve of a candidate c any time that:

U(c) > �[U(W(B))]

That is, approve of any candidate whose win you would like better than you expect to like the outcome of the election. In other words, imagine you have no other information on election night, and hear that this candidate has won. If this would be good news, approve of the candidate on your ballot. If it would be bad news, don’t.

• This rule is still tactical. To determine how much you expect to like the outcome of the election, you need to have beliefs about who else is likely to win, which still requires an understanding of polling and public opinion and mood.
• However, there is one threshold, derived from real polling data in realistic scenarios, and you can cast your approval ballot monotonically based on that single threshold.

This is no longer a true optimal strategy, but with enough voters, the exponential falloff in ℙ[V(B, c)] as c becomes less popular is a pretty good assurance that the incorrect votes you might cast by using this strategy instead of the optimal ones are extremely unlikely to matter. In practice, this is probably the best rule to communicate to voters in an approval election with moderate to large numbers of voters.

We can get closer with the following hypothetical: Imagine that on election night, you have no information on the results except for a headline that proclaims: Election Too Close To Call. With that as your prior, you ask of each candidate, is it good or bad news to hear now that this candidate has won. If it would be good news, then you approve of them. This still leaves one threshold, but we’re no longer making the leap that the pivotal condition for front-runners is unnecessary; we’re imagining a world in which at least some candidates, almost surely the front-runners, are tied. If this changes your decision (which it likely would only in very marginal cases), you can use this more accurate approximation.

Reducing range to approval voting

I promised to look at strategy for range voting, as well. Armed with an appreciation of approval strategy, it’s easy to extend this to an optimal range strategy, as well, for large-scale elections.

The key is to recognize that a range voting election with options 0, 1, 2, …, n is mathematically equivalent to an approval election where everyone is just allowed to vote n times. The number you mark on the range ballot can be interpreted as saying how many of your approval ballots you want to mark as approving that candidate.

Looking at it this way presents the obvious question: why would you vote differently on some ballots than others? In what situation could that possibly be the right choice?

• For small elections, say if you’re voting on places to go out and eat with your friends or coworkers, it’s possible that adding in a handful of approvals materially changes the election so that the optimal vote is different. Then it may well be optimal to cast a range ballot using some intermediate number.
• For large elections, though, you’re presented with pretty much exactly the same question each time, and you may as well give the same answer. Therefore, in large-scale elections, the optimal way to vote with a range ballot is always to rate everyone either the minimum or maximum possible score. This reduces a range election exactly to an approval election. The additional expressiveness of a range ballot is a siren call: by using it, you always vote less effectively than you would have by ignoring it and using only the two extreme choices.

Since we’re discussing political elections, which have relatively large numbers of voters, this answers the question for range elections, as well: Rate a candidate the maximum score if you like them better than you expect to like the outcome of the election. Otherwise, rate them the minimum score.

Summing it up

What we’ve learned, then, is that optimal voting in approval or range systems boils down to two nested rules.

• Exact rule (for the mathematically fearless): approve c iff U(c) > ğ�”¼[ U(W(B)) | your extra vote for c is pivotal ]. This Bayesian test weighs each candidate against the expected utility in the razor-thin worlds where they tie for first.
• Large-electorate shortcut (for everyone else): because those pivotal worlds become astronomically rare as the field grows, the condition shrinks to a single cutoff: approve (or give a maximum score) to every candidate whose victory you expect to enjoy more than you expected to like the result. (If you can, imagine only cases where you know the election is close.)

We’ve seen why the first rule is the gold standard; but the second captures virtually all of its benefit when millions are voting. Either way, strategy is inseparable from sincerity: you must translate beliefs about polling into a utility threshold, and then measure every candidate against it. We’ve also seen by a clear mathematical equivalence why range ballots add no real leverage in large-scale elections, instead only offering false choices that are always wrong.

The entire playbook fits on a sticky note: compute the threshold, vote all-or-nothing, and let the math do the rest.

by Chris Smith at May 28, 2025 08:25 PM

The Provocateurs: Brave New Bullshit

Following two sell-out shows at the Fringe last year, I'm on at the Fringe again:

11.25 Monday 4 August, Stand 2 w/Lucy Remnant and Susan Morrison

17.40 Sunday 17 August, Stand 4 w/Smita Kheria and Sarah-Jane Judge

17.40 Tuesday 19 August, Stand 4 w/Cameron Wyatt and Susan Morrison

Shows are under the banner of The Provocateurs (formerly Cabaret of Dangerous Ideas). Tickets go on sale Wednesday 7 May, around noon. The official blurb is brief:

Professor Philip Wadler (The University of Edinburgh) separates the hopes and threats of AI from the chatbot bullshit.

by Philip Wadler (noreply@blogger.com) at May 28, 2025 11:16 AM

Learning from Multiple Solution Approaches

Welcome to the second article in our Rust vs. Haskell problem solving series. Last week we saw some basic differences between Rust loops and Haskell recursion. We also saw how to use the concept of “folding” to simplify a recursive loop function.

This week, we’ll look at another simple problem and consider multiple solutions in each language. We’ll consider what a “basic” solution looks like, using relatively few library functions. Then we’ll consider more “advanced” solutions that make use of library functionality, and greatly simplify the structure of our solutions.

To learn more about problem solving in Haskell, including the importance of list library functions, take a look at our course Solve.hs! You’ll write most of Haskell’s list API from scratch so you get an in-depth understanding of the functions that are available!

The Problem

This week’s problem is Reverse Words in a String. The idea is simple. Our input is a string, which naturally has “words” separated by whitespace. We want to return a string that has all the words reversed! So if the input is ”A quick brown fox”, the result should be ”fox brown quick A”.

Notice that all whitespace is truncated in our output. We should only have a single space between words in our answer, with no leading or trailing whitespace.

The Algorithm

The algorithmic idea is simple and hardly needs explanation. We want to gather letters from the input word until we encounter whitespace. Then we append this buffered word to a growing result string, and keep following this process until we run out of input.

There is one wrinkle, which is whether we want to accumulate our answer in the forward or reverse direction. This changes across languages!

In Haskell, it’s actually more efficient to accumulate the “back” of our resulting string first, meaning we should start by iterating from the front of the input. This is more consistent with linked list construction.

In Rust, we’ll iterate from the back of the input so that we can accumulate our result from the “front”.

Basic Rust Solution

In our basic solution, we’re going to consider a character-by-character approach. As outlined in our algorithm, we can accomplish this task with a single loop, with two stateful values. First, we have the “current” word we’re accumulating of non-whitespace characters. Second, we have the final “result” we’re accumulating.

It’s efficient to append to the end of strings, meaning we want to construct our result from front-to-back. This means we’ll loop through the characters of our string in reverse, as shown with .rev() here:

pub fn reverse_words(s: String) -> String {
    let mut current = String::new();
    let mut result = String::new();
    for c in s.chars().rev() {
        ...
    }
}

Within the loop, we now just have to consider what to do with each character. If the character is not whitespace, the answer is simple. We just append this character to our “current” word. Because we’re looping through the input in reverse, our “current” word will also be in reverse!

pub fn reverse_words(s: String) -> String {
    let mut current = String::new();
    let mut result = String::new();
    for c in s.chars().rev() {
        if !c.is_whitespace() {
            current.push(c);
        } else {
            ...
        }
    }
}

So what happens when we encounter whitespace? There’s a few conditions to consider:

1. If “current” is empty, do nothing.
2. If “result” is empty, append “current” (in reverse order) to result.
3. If “result” is not empty, add a space and then append “current” in reverse.
4. Regardless, clear “current” and prepare to gather a new string.

Here’s what the code looks like:

pub fn reverse_words(s: String) -> String {
    let mut current = String::new();
    let mut result = String::new();
    for c in s.chars().rev() {
        if !c.is_whitespace() {
            current.push(c);
        } else {
            // Step 1: Skip if empty
            if !current.is_empty() {
                // Step 2/3 Only push an empty space is result is not empty
                if !result.is_empty() {
                    result.push(' ');
                }
                // Step 2/3 Reverse current and append
                for b in current.chars().rev() {
                    result.push(b);
                }
                // Step 4: Clear “current”
                current.clear();
            }
        }
    }
}

There’s one final trick. Unless the word begins with whitespace, we’ll still have non-empty current at the end and we will not have appended it. So we do one final check, and once again append “current” in reverse order.

Here’s our final basic solution:

pub fn reverse_words(s: String) -> String {
    let mut current = String::new();
    let mut result = String::new();
    for c in s.chars().rev() {
        if !c.is_whitespace() {
            current.push(c);
        } else {
            // Step 1: Skip if empty
            if !current.is_empty() {
                // Step 2/3 Only push an empty space is result is not empty
                if !result.is_empty() {
                    result.push(' ');
                }
                // Step 2/3 Reverse current and append
                for b in current.chars().rev() {
                    result.push(b);
                }
                // Step 4: Clear “current”
                current.clear();
            }
        }
    }
   if !current.is_empty() {
        if !result.is_empty() {
            result.push(' ');
        }
        for b in current.chars().rev() {
            result.push(b);
        }
    }
    return result;
}

Advanced Rust Solution

Looping character-by-character is a bit cumbersome. However, since basic whitespace related operations are so common, there are some useful library functions for dealing with them.

Rust also prioritizes the ability to chain iterative operations together. This gives us the following one-line solution!

pub fn reverse_words(s: String) -> String {
    s.split_whitespace().rev().collect::<Vec<&str>>().join(" ")
}

It has four stages:

1. Split the input based on whitespace.
2. Reverse the split-up words.
3. Collect these words as a vector of strings.
4. Join them together with one space in between them.

What is interesting about this structure is that each stage of the process has a separate type. Step 1 creates a SplitWhitespace struct. Step 2 creates a Reverse struct. Step 3 then creates a normal vector, and step 4 concludes by producing a string.

The two preliminary structures are essentially wrappers with iterators to help chain the operations together. As we’ll see, the comparable Haskell solution only uses basic lists, and this is a noteworthy difference between the languages.

Basic Haskell Solution

Our “basic” Haskell solution will follow the same outline as the basic Rust solution, but we’ll work in the opposite direction! We’ll loop through the input in forward order, and accumulate our output in reverse order.

Before we even get started though, we can make an observation from our basic Rust solution that we duplicated some code! The concept of combining the “current” word and the “result” had several edge cases to handle, so let’s write a combine function to handle these.

-- “current” is reversed and then goes in *front* of result
-- (Rust version put “current” at the back)
combine :: (String, String) -> String
combine (current, res) = if null current then res
  else reverse current <> if null res then "" else (' ' : res)

Now let’s think about our loop structure. We are going through the input, character-by-character. This means we should be able to use a fold, like we did last week! Whenever we’re using a fold, we want to think about the “state” we’re passing through each iteration. In our case, the state is the “current” word and the “result” string. This means our folding function should look like this:

loop :: (String, String) -> Char -> (String, String)
loop (current, result) c = ...

Now we just have to distinguish between the “whitespace” case and the non-whitespace case. If we encounter a space, we just combine the current word with the accumulated result. If we encounter a normal character, we append this to our current word (again, accumulating “current” in reverse).

loop :: (String, String) -> Char -> (String, String)
loop (currentWord, result) c = if isSpace c
  then ("", combine (currentWord, result))
  else (c : currentWord, result)

Now to complete the solution, we just call ‘foldl’ with our ‘loop’ and the input, and we just have to remember to combine the final “current” word with the output! Here’s our complete “basic” solution.

reverseWords :: String -> String
reverseWords input = combine $ foldl loop ("", "") input
  where
    combine :: (String, String) -> String
    combine (current, res) = if null current then res
      else reverse current <> if null res then "" else (' ' : res)

    loop :: (String, String) -> Char -> (String, String)
    loop (currentWord, result) c = if isSpace c
      then ("", combine (currentWord, result))
      else (c : currentWord, result)

Advanced Haskell Solutions

Now that we’ve seen a basic, character-by-character solution in Haskell, we can also consider more advanced solutions that incorporate library functions. The first improvement we can make is to lean on list functions like break and dropWhile.

Using break splits off the first part of a list that does not satisfy a predicate. We’ll use this to gather non-space characters. Then dropWhile allows us to drop the first series of characters in a list that satisfy a predicate. We’ll use this to get rid of whitespace as we move along!

So we’ll define this solution using a basic recursive loop rather than a fold, because each iteration will consume a variable number of characters. The “state” of this loop will be two strings: the remaining part of the input, and the accumulated result.

Since there’s no “current” word, our base case is easy. If the remaining input is empty, we return the accumulated result.

loop :: (String, String) -> String
loop ([], output) = output
...

Otherwise, we’ll follow this process:

1. Separate the first “word” using break isSpace.
2. Combine this word with the output (if it’s not null)
3. Recurse with the new output, dropping the initial whitespace from the remainder.

Here’s what it looks like:

loop :: (String, String) -> String
loop ([], output) = output
loop (cs, output) =
  -- Step 1: Separate next word from rest
  let (nextWord, rest) = L.break isSpace cs
  -- Step 2: Make new output (account for edge cases)
  -- (Can’t use ‘combine’ from above because we aren’t reversing!)
      newOutput = if null output then nextWord
                    else if null nextWord then output
                    else nextWord <> (' ' : output)
  -- Drop spaces from remainder and recurse
  in  loop (L.dropWhile isSpace rest, newOutput)

And completing the function is as simple as calling this loop with the base inputs:

reverseWords :: String -> String
reverseWords input = loop (input, “”)

The Simplest Haskell Solution

The final (and recommended) Haskell solution uses the library functions words and unwords. These do exactly what we want for this problem! We separate words based on whitespace using words, and then join them with a single space with unwords. All we have to do in between is reverse.

reverseWords :: String -> String
reverseWords = unwords . reverse . words

This has a similar elegance to the advanced Rust solution, but is much simpler to understand since there are no complex structs or iterators involved. The types of all functions involved simply relate to lists. Here are the signatures, specialized to String for this problem.

words :: String -> [String]
reverse :: [String] -> [String]
unwords :: [String] -> String

Conclusion

A simple problem will often have many solutions, but in this case, each of these solutions teaches us something new about the language we’re working with. Working character-by-character helps us understand some of the core mechanics of the language, showing us how it works under the hood. But using library functions helps us see the breadth of available options we have for simplifying future code we write.

In our Solve.hs course, you’ll go through all of these steps with Haskell. You’ll implement list library functions, data structures, and algorithms from scratch so you understand how they work under the hood. Then, you’ll know they exist and be able to apply them to efficiently solve harder problems. Take a look at the course today!

by James Bowen at May 26, 2025 08:30 AM

Mystery of the quincunx's missing quincunx

A quincunx is the X-shaped pattern of pips on the #5 face of a die.

It's so-called because the Romans had a common copper coin called an as, and it was divided (monetarily, not physically) into twelve uncia. There was a bronze coin worth five uncia called a quīncunx, which is a contraction of quīnque (“five”) + uncia, and the coin had that pattern of dots on it to indicate its value.

Uncia generally meant a twelfth of something. It was not just a twelfth of an as, but also a twelfth of a pound , which is where we get the word “ounce”, and a twelfth of a foot, which is where we get the word “inch”.

The story I always heard about the connection between the coin and the X-shaped pattern of dots was the one that is told by Wikipedia:

Its value was sometimes represented by a pattern of five dots arranged at the corners and the center of a square, like the pips of a die. So, this pattern also came to be called quincunx.

Or the Big Dictionary:

… [from a] coin of this value (occasionally marked with a pattern resembling the five spots on a dice cube),…

But today I did Google image search for qunicunxes. And while most had five dots, I found not even one that had the dots arranged in an X pattern.

(I believe the heads here are Minerva, goddess of wisdom. The owl is also associated with Minerva.)

Where's the quincunx that actually has a quincuncial arrangement of dots? Nowhere to be found, it seems. But everyone says it, so it must be true.

Addenda

• The first common use of “quincunx” as an English word was to refer to trees that were planted in a quincuncial pattern, although not necessarily in groups of exactly five, in which each square of four trees had a fifth at its center.

• Similarly, the Galton Box, has a quincuncial arrangement of little pegs. Galton himself called it a “quincunx”.

• The OED also offers this fascinating aside:

  Latin quincunx occurs earlier in an English context. Compare the following use apparently with reference to a v-shaped figure:

  1545 Decusis, tenne hole partes or ten Asses...It is also a fourme in any thynge representyng the letter, X, whiche parted in the middel, maketh an other figure called Quincunx, V.

  which shows that for someone, a quincuncial shape was a V and not an X, presumably because V is the Roman numeral for five.

  A decussis was a coin worth not ten uncia but ten asses, and it did indeed have an X on the front. A five-as coin was a quincussis and it had a V. I wonder if the author was confused?

  The source is Bibliotheca Eliotæ. The OED does not provide a page number.

• It wasn't until after I published this that I realized that today's date was the extremely quincuncial 2025-05-25. I thank the gods of chance and fortune for this little gift.

by Mark Dominus (mjd@plover.com) at May 25, 2025 11:00 PM

The fivefold symmetry of the quince

The quince is so-named because, like other fruits in the apple family, it has a natural fivefold symmetry:

This is because their fruits develop from five-petaled flowers, and the symmetry persists through development. These are pear blossoms:

You can see this in most apples if you cut them into equatorial slices:

The fivefold symmetry isn't usually apparent from the outside once the structure leaves the flowering stage. But perfect Red Delicious specimens do have five little feet:

P.S.: I was just kidding about the name of the quince, which actually has nothing to do with any of this. It is a coincidence.

by Mark Dominus (mjd@plover.com) at May 24, 2025 03:29 AM

Indexing Hackage: Glean vs. hiedb

Indexing Hackage: Glean vs. hiedb

May 22, 2025

I thought it might be fun to try to use Glean to index as much of Hackage as I could, and then do some rough comparisons against hiedb and also play around to see what interesting queries we could run against a database of all the code in Hackage.

This project was mostly just for fun: Glean is not going to replace hiedb any time soon, for reasons that will become clear. Neither are we ready (yet) to build an HLS plugin that can use Glean, but hopefully this at least demonstrates that such a thing should be possible, and Glean might offer some advantages over hiedb in performance and flexibility.

A bit of background:

• Glean is a code-indexing system that we developed at Meta. It’s used internally at Meta for a wide range of use cases, including code browsing, documentation generation and code analysis. You can read about the ways in which Glean is used at Meta in Indexing Code At Scale with Glean.

• hiedb is a code-indexing system for Haskell. It takes the .hie files that GHC produces when given the option -fwrite-ide-info and writes the information to a SQLite database in various tables. The idea is that putting the information in a DB allows certain operations that an IDE needs to do, such as go-to-definition, to be fast.

You can think of Glean as a general-purpose system that does the same job as hiedb, but for multiple languages and with a more flexible data model. The open-source version of Glean comes with indexers for ten languages or so, and moreover Glean supports SCIP which has indexers for various languages available from SourceGraph.

Since a hiedb is just a SQLite DB with a few tables, if you want you can query it directly using SQL. However, most users will access the data through either the command-line hiedb tool or through the API, which provide the higher-level operations such as go-to-definition and find-references. Glean has a similar setup: you can make raw queries using Glean’s query language (Angle) using the Glean shell or the command-line tool, while the higher-level operations that know about symbols and references are provided by a separate system called Glass which also has a command-line tool and API. In Glean the raw data is language-specific, while the Glass interface provides a language-agnostic view of the data in a way that’s useful for tools that need to navigate or search code.

An ulterior motive

In part all of this was an excuse to rewrite Glean’s Haskell indexer. We built a Haskell indexer a while ago but it’s pretty limited in what information it stores, only capturing enough information to do go-to-definition and find-references and only for a subset of identifiers. Furthermore the old indexer works by first producing a hiedb and consuming that, which is both unnecessary and limits the information we can collect. By processing the .hie files directly we have access to richer information, and we don’t have the intermediate step of creating the hiedb which can be slow.

The rest of this post

The rest of the post is organised as follows, feel free to jump around:

• Performance: a few results comparing hiedb with Glean on an index of all of Hackage

• Queries: A couple of examples of queries we can do with a Glean index of Hackage: searching by name, and finding dead code.

• Apparatus: more details on how I set everything up and how it all works.

• What’s next: some thoughts on what we still need to add to the indexer.

Performance

All of this was perfomed on a build of 2900+ packages from Hackage, for more details see Building all of Hackage below.

Indexing performance

I used this hiedb command:

hiedb index -D /tmp/hiedb . --skip-types

I’m using --skip-types because at the time of writing I haven’t implemented type indexing in Glean’s Haskell indexer, so this should hopefully give a more realistic comparison.

This was the Glean command:

glean --service localhost:1234 \
  index haskell-hie --db stackage/0 \
  --hie-indexer $(cabal list-bin hie-indexer) \
  ~/code/stackage/dist-newstyle/build/x86_64-linux/ghc-9.4.7 \
  --src '$PACKAGE'

Time to index:

• hiedb: 1021s
• Glean: 470s

I should note that in the case of Glean the only parallelism is between the indexer and the server that is writing to the DB. We didn’t try to index multiple .hie files in parallel, although that would be fairly trivial to do. I suspect hiedb is also single-threaded just going by the CPU load during indexing.

Size of the resulting DB

• hiedb: 5.2GB
• Glean: 0.8GB

It’s quite possible that hiedb is simply storing more information, but Glean does have a rather efficient storage system based on RocksDB.

Performance of find-references

Let’s look up all the references of Data.Aeson.encode:

hiedb -D /tmp/hiedb name-refs encode Data.Aeson

This is the query using Glass:

cabal run glass-democlient -- --service localhost:12345 \
  references stackage/hs/aeson/Data/Aeson/var/encode

This is the raw query using Glean:

glean --service localhost:1234 --db stackage/0 \
  '{ Refs.file, Refs.uses[..] } where Refs : hs.NameRefs; Refs.target.occ.name = "encode"; Refs.target.mod.name = "Data.Aeson"'

• hiedb: 2.3s
• glean (via Glass): 0.39s
• glean (raw query): 0.03s

(side note: hiedb found 416 references while Glean found 415. I haven’t yet checked where this discrepancy comes from.)

But these results don’t really tell the whole story.

In the case of hiedb, name-refs does a full table scan so it’s going to take time proportional to the number of refs in the DB. Glean meanwhile has indexed the references by name, so it can serve this query very efficiently. The actual query takes a few milliseconds, the main overhead is encoding and decoding the results.

The reason the Glass query takes longer than the raw Glean query is because Glass also fetches additional information about each reference, so it performs a lot more queries.

We can also do the raw hiedb query using the sqlite shell:

sqlite> select count(*) from refs where occ = "v:encode" AND mod = "Data.Aeson";
417
Run Time: real 2.038 user 1.213905 sys 0.823001

Of course hiedb could index the refs table to make this query much faster, but it’s interesting to note that Glean has already done that and it was still quicker to index and produced a smaller DB.

Performance of find-definition

Let’s find the definition of Data.Aeson.encode, first with hiedb:

$ hiedb -D /tmp/hiedb name-def encode Data.Aeson
Data.Aeson:181:1-181:7

Now with Glass:

$ cabal run glass-democlient -- --service localhost:12345 \
  describe stackage/hs/aeson/Data/Aeson/var/encode
stackage@aeson-2.1.2.1/src/Data/Aeson.hs:181:1-181:47

(worth noting that hiedb is giving the span of the identifier only, while Glass is giving the span of the whole definition. This is just a different choice; the .hie file contains both.)

And the raw query using Glean:

$ glean --service localhost:1234 query --db stackage/0 --recursive \
  '{ Loc.file, Loc.span } where Loc : hs.DeclarationLocation; N : hs.Name; N.occ.name = "encode"; N.mod.name = "Data.Aeson"; Loc.name = N' | jq
{
  "id": 18328391,
  "key": {
    "tuplefield0": {
      "id": 9781189,
      "key": "aeson-2.1.2.1/src/Data/Aeson.hs"
    },
    "tuplefield1": {
      "start": 4136,
      "length": 46
    }
  }
}

Times:

• hiedb: 0.18s
• Glean (via Glass): 0.05s
• Glean (raw query): 0.01s

In fact there’s a bit of overhead when using the Glean CLI, we can get a better picture of the real query time using the shell:

stackage> { Loc.file, Loc.span } where Loc : hs.DeclarationLocation; N : hs.Name; N.occ.name = "encode"; N.mod.name = "Data.Aeson"; Loc.name = N
{
  "id": 18328391,
  "key": {
    "tuplefield0": { "id": 9781189, "key": "aeson-2.1.2.1/src/Data/Aeson.hs" },
    "tuplefield1": { "start": 4136, "length": 46 }
  }
}

1 results, 2 facts, 0.89ms, 696176 bytes, 2435 compiled bytes

The query itself takes less than 1ms.

Again, the issue with hiedb is that its data is not indexed in a way that makes this query efficient: the defs table is indexed by the pair (hieFile,occ) not occ alone. Interestingly, when the module is known it ought to be possible to do a more efficient query with hiedb by first looking up the hieFile and then using that to query defs.

What other queries can we do with Glean?

I’ll look at a couple of examples here, but really the possibilities are endless. We can collect whatever data we like from the .hie file, and design the schema around whatever efficient queries we want to support.

Search by case-insensitive prefix

Let’s search for all identifiers that start with the case-insensitive prefix "withasync":

$ glass-democlient --service localhost:12345 \
  search stackage/withasync -i | wc -l
55

In less than 0.1 seconds we find 55 such identifiers in Hackage. (the output isn’t very readable so I didn’t include it here, but for example this finds results not just in async but in a bunch of packages that wrap async too).

Case-insensitive prefix search is supported by an index that Glean produces when the DB is created. It works in the same way as efficient find-references, more details on that below.

Why only prefix and not suffix or infix? What about fuzzy search? We could certainly provide a suffix search too; infix gets more tricky and it’s not clear that Glean is the best tool to use for infix or fuzzy text search: there are better data representations for that kind of thing. Still, case-insensitive prefix search is a useful thing to have.

Could we support Hoogle using Glean? Absolutely. That said, Hoogle doesn’t seem too slow. Also we need to index types in Glean before it could be used for type search.

Identify dead code

Dead code is, by definition, code that isn’t used anywhere. We have a handy way to find that: any identifier with no references isn’t used. But it’s not quite that simple: we want to ignore references in imports and exports, and from the type signature.

Admittedly finding unreferenced code within Hackage isn’t all that useful, because the libraries in Hackage are consumed by end-user code that we haven’t indexed so we can’t see all the references. But you could index your own project using Glean and use it to find dead code. In fact, I did that for Glean itself and identified one entire module that was dead, amongst a handful of other dead things.

Here’s a query to find dead code:

N where
  N = hs.Name _;
  N.sort.external?;
  hs.ModuleSource { mod = N.mod, file = F };
  !(
    hs.NameRefs { target = N, file = RefFile, uses = R };
    RefFile != F;
    coderef = (R[..]).kind
  )

Without going into all the details, here’s roughly how it works:

• N = hs.Name _; declares N to be a fact of hs.Name
• N.sort.external?; requires N to be external (i.e. exported), as opposed to a local variable
• hs.ModuleSource { mod = N.mod, file = F }; finds the file F corresponding to this name’s module
• The last part is checking to see that there are no references to this name that are (a) in a different file and (b) are in code, i.e. not import/export references. Restricting to other files isn’t exactly what we want, but it’s enough to exclude references from the type signature. Ideally we would be able to identify those more precisely (that’s on the TODO list).

You can try this on Hackage and it will find a lot of stuff. It might be useful to focus on particular modules to find things that aren’t used anywhere, for example I was interested in which identifiers in Control.Concurrent.Async aren’t used:

N where
  N = hs.Name _;
  N.mod.name = "Control.Concurrent.Async";
  N.mod.unit = "async-2.2.4-inplace";
  N.sort.external?;
  hs.ModuleSource { mod = N.mod, file = F };
  !(
    hs.NameRefs { target = N, file = RefFile, uses = R };
    RefFile != F;
    coderef = (R[..]).kind
  )

This finds 21 identifiers, which I can use to decide what to deprecate!

Apparatus

Building all of Hackage

The goal was to build as much of Hackage as possible and then to index it using both hiedb and Glean, and see how they differ.

To avoid problems with dependency resolution, I used a Stackage LTS snapshot of package versions. Using LTS-21.21 and GHC 9.4.7, I was able to build 2922 packages. About 50 failed for some reason or other.

I used this cabal.project file:

packages: */*.cabal
import: https://www.stackage.org/lts-21.21/cabal.config

package *
    ghc-options: -fwrite-ide-info

tests: False
benchmarks: False

allow-newer: *

And did a large cabal get to fetch all the packages in LTS-21.21.

Then

cabal build all --keep-going

After a few retries to install any required RPMs to get the dependency resolution phase to pass, and to delete a few packages that weren’t going to configure successfully, I went away for a few hours to let the build complete.

It’s entirely possible there’s a better way to do this that I don’t know about - please let me know!

Building Glean

The Haskell indexer I’m using is in this pull request which at the time of writing isn’t merged yet. (Since I’ve left Meta I’m just a regular open-source contributor and have to wait for my PRs to be merged just like everyone else!).

Admittedly Glean is not the easiest thing in the world to build, mainly because it has a couple of troublesome dependencies: folly (Meta’s library of highly-optimised C++ utilities) and RocksDB. Glean depends on a very up to date version of these libraries so we can’t use any distro packaged versions.

Full instructions for building Glean are here but roughly it goes like this on Linux:

• Install a bunch of dependencies with apt or yum
• Build the C++ dependencies with ./install-deps.sh and set some env vars
• make

The Makefile is needed because there are some codegen steps that would be awkward to incorporate into the Cabal setup. After the first make you can usually just switch to cabal for rebuilding stuff unless you change something (e.g. a schema) that requires re-running the codegen.

Running Glean

I’ve done everything here with a running Glean server, which was started like this:

cabal run exe:glean-server -- \
  --db-root /tmp/db \
  --port 1234 \
  --schema glean/schema/source

While it’s possible to run Glean queries directly on the DB without a server, running a server is the normal way because it avoids the latency from opening the DB each time, and it keeps an in-memory cache which significantly speeds up repeated queries.

The examples that use Glass were done using a running Glass server, started like this:

cabal run glass-server -- --service localhost:1234 --port 12345

How does it work?

The interesting part of the Haskell indexer is the schema in hs.angle. Every language that Glean indexes needs a schema, which describes the data that the indexer will store in the DB. Unlike an SQL schema, a Glean schema looks more like a set of datatype declarations, and it really does correspond to a set of (code-generated) types that you can work with when programmatically writing data, making queries, or inspecting results. For more about Glean schemas, see the documentation.

Being able to design your own schema means that you can design something that is a close match for the requirements of the language you’re indexing. In our Glean schema for Haskell, we use a Name, OccName, and Module structure that’s similar to the one GHC uses internally and is stored in the .hie files.

The indexer itself just reads the .hie files and produces Glean data using datatypes that are generated from the schema. For example, here’s a fragment of the indexer that produces Module facts, which contain a ModuleName and a UnitName:

mkModule :: Glean.NewFact m => GHC.Module -> m Hs.Module
mkModule mod = do
  modname <- Glean.makeFact @Hs.ModuleName $
    fsToText (GHC.moduleNameFS (GHC.moduleName mod))
  unitname <- Glean.makeFact @Hs.UnitName $
    fsToText (unitFS (GHC.moduleUnit mod))
  Glean.makeFact @Hs.Module $
    Hs.Module_key modname unitname

Also interesting is how we support fast find-references. This is done using a stored derived predicate in the schema:

predicate NameRefs:
  {
    target: Name,
    file: src.File,
    uses: [src.ByteSpan]
  } stored {Name, File, Uses} where
  FileXRefs {file = File, refs = Refs};
  {name = Name, spans = Uses} = Refs[..];

here NameRefs is a predicate—which you can think of as a datatype, or a table in SQL—defined in terms of another predicate, FileXRefs. The facts of the predicate NameRefs (rows of the table) are derived automatically using this definition when the DB is created. If you’re familiar with SQL, a stored derived predicate in Glean is rather like a materialized view in SQL.

What’s next?

As I mentioned earlier, the indexer doesn’t yet index types, so that would be an obvious next step. There are a handful of weird corner cases that aren’t handled correctly, particularly around record selectors, and it would be good to iron those out.

Longer term ideally the Glean data would be rich enough to produce the Haddock docs. In fact Meta’s internal code browser does produce documentation on the fly from Glean data for some languages - Hack and C++ in particular. Doing it for Haskell is a bit tricky because while I believe the .hie file does contain enough information to do this, it’s not easy to reconstruct the full ASTs for declarations. Doing it by running the compiler—perhaps using the Haddock API—would be an option, but that involves a deeper integration with Cabal so it’s somewhat more awkward to go that route.

Could HLS use Glean? Perhaps it would be useful to have a full Hackage index to be able to go-to-definition from library references? As a plugin this might make sense, but there are a lot of things to fix and polish before it’s really practical.

Longer term should we be thinking about replacing hiedb with Glean? Again, we’re some way off from that. The issue of incremental updates is an interesting one - Glean does support incremental indexing but so far it’s been aimed at speeding up whole-repository indexing rather than supporting IDE features.

May 22, 2025 12:00 AM

Comparing Code: LeetCode Problems in Rust vs. Haskell

Today will be the first in a series where we’ll be exploring some LeetCode problems and comparing different solutions from Haskell and Rust. The main idea is to demonstrate how you might translate ideas between the recursive core of Haskell, and the loop-based framing of most other languages.

If you want to learn more about problem solving in Haskell, you should take a closer look at Solve.hs! This course will give you an in-depth walkthrough of problem solving ideas in Haskell, including how concepts compare to more typical languages.

The Problem

The first problem we’ll consider is called H-Index. In academia, a person has an “H-Index” of n if they have published at least n papers that have n or more citations. So the input to our problem is a list of integers, where each integer is the number of citations of a particular paper the author wrote. Our job is to calculate the author’s H-Index.

The Algorithm

This problem is fairly straightforward if you sort the input list. Once we do this, we can look at any index i, and consider the number of remaining entries (e.g. n - i), and we’ll know that the number of papers with at least that many citations is n - i.

So we can accomplish this task with a single loop over the sorted list. Throughout this loop, we’ll be tracking the maximum “H-Index” we’ve seen so far (maxH). At each iteration, we take the following steps:

Get the number of remaining papers (rem) and the citations at this index (next) If the rem is greater than next, then update maxH to next if next is larger. Otherwise, update maxH to rem if rem is greater.

The last step is a key edge case! If we have the list [1, 1, 1, 9, 9], we’ll get to index 3, with next being 9 and rem being 2. The remainder is smaller than the index, but we would still update maxH to 2, because there are at least 2 citations remaining that are 2 or greater.

Rust Solution

Here’s our Rust solution:

pub fn h_index(citations: Vec<i32>) -> i32 {
    let mut cp = citations.clone();
    cp.sort();
    let n = cp.len();
    let mut maxH: i32 = 0;
    for i in 0..n {
        let next = cp[i];
        let rem: i32 = (n - i) as i32;
        if (rem >= next) {
            maxH = std::cmp::max(next, maxH);
        } else {
            maxH = std::cmp::max(rem, maxH);
        }
    }
    return maxH;
}

We have the first part, where we clone the input, sort it, and set up our loop variables:

pub fn h_index(citations: Vec<i32>) -> i32 {
    let mut cp = citations.clone();
    cp.sort();
    let n = cp.len();
    let mut maxH: i32 = 0;
    ...
}

Then we have the loop itself, where we have our two cases to consider:

for i in 0..n {
    let next = cp[i];
    let rem: i32 = (n - i) as i32;
    if (rem >= next) {
        // There are at least ‘next’ papers >= ‘next’
        maxH = std::cmp::max(next, maxH);
    } else {
        // ‘next’ > ‘rem’, so there are at least ‘rem’ papers >= ‘rem’
        maxH = std::cmp::max(rem, maxH);
    }
}

So this is pretty straightforward. Now how do we approach this kind of problem in Haskell?

Haskell Solution

Our Haskell solution will have the same structure, but instead of running a loop and indexing into a vector, we’ll use a linked list and call a recursive function. Let’s begin by getting the length and sorting our input:

import qualified Data.List as L

hIndex :: [Int] -> Int
hIndex inputs = ...
  where
    n = length inputs
    sorted = L.sort inputs

    ...

Now we need to think about our recursive loop function. At each iteration, we need access to the remaining number of values, the next citation value, and we need to pass along maxH. As with many list-based recursive functions, we’ll peel off one element of the input list each time. Ultimately we’ll return maxH from this loop when we hit our base case of an empty input list. So its type signature should look like this:

loop :: (Int, [Int], Int) -> Int

When writing a recursive function, we always handle the base case first:

loop :: (Int, [Int], Int) -> Int
loop (_, [], maxH) = maxH

Now in the recursive case, we can apply our algorithm, updating maxH if necessary:

loop :: (Int, [Int], Int) -> Int
loop (_, [], maxH) = maxH
loop (remaining, next : rest, maxH) = if remaining >= next
  then loop (remaining - 1, rest, max next maxH)
  else loop (remaining - 1, rest, max remaining maxH)

To finish up, all we need to do is call our loop function with the appropriate initial inputs (n, sorted, 0). Here’s our complete Haskell solution:

import qualified Data.List as L

hIndex :: [Int] -> Int
hIndex inputs = loop (n, sorted, 0)
  where
    n = length inputs
    sorted = L.sort inputs

    loop :: (Int, [Int], Int) -> Int
    loop (_, [], maxH) = maxH
    loop (remaining, next : rest, maxH) = if remaining >= next
      then loop (remaining - 1, rest, max next maxH)
      else loop (remaining - 1, rest, max remaining maxH)

Using a Fold

Now we can notice that our loop has a particular structure. We have one piece of accumulated state (maxH), and this changes based on each value in our list (combined with the remaining values). We can easily re-imagine this kind of loop using a fold. We just have to think of the folding function like this:

loop :: Int -> (Int, Int) -> Int
loop maxH (remaining, next) = if remaining >= next
  then max next maxH
  else max remaining maxH

This has the a -> b -> a structure of a left-fold function, where a is our accumulated maxH value, and the other values come from our list. The main benefit here is that our loop function no longer has to deal with the burden of calling a base case or passing the “shrinking” list as an argument to the next recursive call.

We can invoke this loop at the top level like so:

hIndex :: [Int] -> Int
hIndex inputs = foldl loop 0 (zip [n,n-1..1] sorted)
  where
    n = length inputs
    sorted = L.sort inputs

    loop :: Int -> (Int, Int) -> Int
    loop maxH (remaining, next) = if remaining >= next
      then max next maxH
      else max remaining maxH

We just have to zip the decreasing indices together with our sorted list. Now our recursive “loop” is more like a typical for-loop. We’re only considering one element at a time, and we’re updating the important state each time.

Conclusion

In this comparison, we saw a good comparison between a normal for-loop in Rust, and a recursive solution in Haskell. We also saw how we could simplify this recursive formulation into a “fold” structure.

If you're interested in learning more about writing recursive functions in Haskell, check out our Solve.hs course. You’ll learn how to start thinking about problems in a functional way, and you’ll learn the step-by-step processes for tackling problems with basic recursion and folds like we saw in this example.

by James Bowen at May 19, 2025 08:30 AM

Why we blog

I was the chief editor for this blog for the past 8 years or so, and I’ve just recently passed the mantle to Chris Harrison. I thought I’d take the opportunity to write a little bit about this blog, how it’s operated and what it means to us. Besides, we do like when things get meta here, so this is a blog post about the blog.

A little bit of history

One of the tenets under which Mathieu Boespflug founded Tweag was that software engineers naturally don’t write enough. Writing is an essential part of the engineering job. We write issues, pull requests, code comments, documentation of various sorts. We discuss and debate online, we have to arbitrate trade-offs. Most of this is common, in fact, to every engineering profession. And although we typically become engineers because of our taste for the technical part of our job (I certainly did, I don’t know for sure how ubiquitous it is); writing is still a big part of our job.

So Mathieu reasoned, if writing is to be such a big part of our job, but we’re technical people at heart, not writers, for the company to be at its best it needs to make it clear that precise and clear writing is important to our job. To that effect, there ought to be venues for us to write, where it was made an expectation, an actual requirement, for us to write. The blog is one of them.

At first, the blog was just there. After all, our blog was, and still is, just (part of) a Github repository. So we’d make pull requests and merge blog posts. But, of course, people seek review. When you’re posting in the name of a company, you tend to be a little more careful about what you write; besides, we’re all so used to having our PRs reviewed. This was all very ad hoc, there was no process for it.

Whatever my reason at the time (I honestly don’t remember after all this time), I ended up participating in the review of most blog posts. It’s a poorly kept, but surprisingly little discussed secret that the most common way to get a responsibility in a company is to just assume said responsibility. Do the thing, and it will become your charge. Anyway, I became editor in chief.

Why we blog

Besides being a venue to exercise our technical writing, this blog has been tremendously useful to us. Keeping a high-quality, serious, technical blog helped establish trust in our work, build bridges with community, and attract clients and employees.

It’s very rewarding for us, as individuals, to be recognised by our peers, and to work with a company which is likewise recognised. This is certainly a great motivation for us to write.

Besides, it fits very well with our open-source values, both as a company and as individuals. We strongly believe in open-source, and the value it has to the world. So we participate. And open-source software isn’t just about putting software’s sources out there. Open-source is also about sharing knowledge. Which is another important element of the company’s ethos. We do have formal and informal venues for sharing knowledge internally, all very important stuff, but it’s a topic for another time. The blog is one of our main venues for sharing knowledge with the rest of the world.

So we do share, we talk about our open-source journey, the software we build, or the software we use. But we also share what we learn through working with clients, not necessarily on open-source projects.

So this blog is something that operates at the sweet spot of any company’s activities: it’s something we do because we believe that it’s the right thing to do, and it’s also something which is valuable to the company. In fact the blog brought so many clients that it allowed Tweag to operate without a marketing team for quite a few years. Nowadays, the company’s bigger and we can’t rely on a blog alone, but it’s still a great way to connect.

How we blog

Writing a blog post is making a pull request against the Github repository for the tweag.io website. A post is a Markdown file, possibly accompanied by resources (such as images). It’s a workflow which is very familiar to software engineers. All the review process is, in fact, a Github pull request review.

The author of a blog post is first tasked with obtaining a “technical review” from their peers: people close to the topic review the blog post for accuracy and relevance. The blog post editors are all engineers (the entire process, in fact, is owned by engineers), but aren’t necessarily very familiar with the blog post’s topic, so this first round of review couldn’t be performed by the editing team, it’s also much better for scalability as technical review uses a little time from a lot of people, rather than a lot of time from a few.

When the author and technical reviewers are satisfied with the blog post, they send it to the editing team, which will do two rounds of review (which we cleverly call “first editorial review” and “second editorial review”). The editing team reviews for clarity and writing quality. Something that isn’t a concern of reviewers (or really of the process as a whole), on the other hand, is SEO. Certainly our blog posts make our website easier to find, and of course this is important to us. But this is the result, we hope, of making blog posts that you like.

We can propose edits in three different ways: we can ask question in the review thread, propose “suggestions” in the Github interface which the author is free to accept or not, or we can push directly to the blog post (in which case we try our best to preserve the author’s voice, and always leave time for the author to check that the edits are correct). The choice between the three is primarily driven by our degree of confidence in the edit. Really we do what makes sense to reduce the amount of back-and-forth.

Reviewing blog posts on Github with a team distributed all around the world is essentially a distributed process. As with any distributed process, we try to minimise the amount of synchronisation. Our target is to be able to do a review in two weeks or less (one week for each round). Sometimes it takes more though, when the blog post presents more difficult editing challenges, or when the author doesn’t have enough availability outside of their client work to respond to our reviews quickly enough. But we hit the target more often than not.

The two rounds of review are functionally identical. We just found that, in practice, having two rounds of review helps raise the quality a lot. The first reviewer often gets involved deeply in the writing of the blog post, to the point that they stop seeing the blog post as a reader. The second reviewer receives a blog post in almost publishable condition and brings fresh eyes to conduct the finishing touch.

What blogging means to us

When Tweag was a standalone company, blogging was almost our entire marketing strategy. Now that we’re part of the substantially larger Modus Create, we aren’t in a position to rely solely on technical blogging for marketing. Yet, this blog is still an important part of our strategy.

All of what I wrote above still applies, but I’d like to bring up something else. See, a company is a little bit faceless. It doesn’t have a drive, it doesn’t have a personality: people do. This is truer the larger a company is. We don’t aspire to be a faceless abstract entity, though. Modus Create is made of people, people that we believe to be interesting, and that we hope you’ll find interesting too. In fact our business is largely for clients (maybe you!) to find our people interesting and hire us. This blog is one of the ways we use to promote individuals. Who they are, what they like, what they know, what they can do. This is why our writing recommendations encourage authors to use the pronoun “I” where many of us would be tempted to say “we”.

A more collectivist consideration is communities. We take part in a number of communities (Haskell, Nix, Bazel, Typescript, …), and it’s all too easy for a company to say it’s part of a community but really meaning that they just use Haskell, Nix, Bazel, Typescript. But it’s not really what being part of a community means, does it? It also entails taking part in community life. There’s a bunch of things we do: we write libraries, contribute upstream, help with governance, sponsor and sometimes organise events, …. And we blog, which also plays its part in community life. This is why we don’t shy away from highly specialised blog posts. Sure they are addressed to a pretty narrow, sometimes quite niche audience, but they are relevant to one of our communities. Of course it helps establish our technical chops. Hopefully it also builds trust.

I should note that what I’m writing about is what works for us. It’s not a recipe that will automatically work for you. There are many excellent technical blogs out there, which, I assume, probably have different approaches to us, such as CockroachDB’s, Netflix’s, fly.io’s and Trail of Bits’s (the latter two I wasn’t aware of, by the way, they were brought to my attention by this blog post’s technical review). If you like this blog, you’ll probably like theirs, go check them out! Dan Luu shares some more general considerations. But at the end of the day, what makes a strong communication strategy is to build around and empower the people you already have. Capitalise on your strengths, don’t go against the grain just to imitate what someone else does, however successful they appear to be.

Sign-off

A paradox of the work of software engineers (and probably all engineering disciplines really) is that writing is such an integral part of our job, but most of us receive virtually no training in our studies.

I’ve never had technical writing classes, myself. The way I learned writing was in part by gleaning some of the popular wisdom taught among my peers, but mostly by co-authoring scientific articles with better technical writers than me and seeing them do their magic. Honestly, I found no better learning experience than seeing an entire paragraph of mine rewritten in a mere few words that were also more precise.

I don’t know how to teach technical writing formally. So a lot of the process we’ve converged on reflects my attempt to replicate what worked on me for the company: teaching technical writing by example. By showing how a blog post can be improved, hopefully the authors will learn to write better next time. Because the blog is this as well: a tool to teach ourselves, collectively, how to be technical writers.

This is a very soft target, it’s hard to measure the degree to which we’ve succeeded. But, because I don’t really know how to close this post without getting a touch emotional (it is, after all, no small moment for me), I’ve witnessed many of our engineers mature as writers, and I can’t help but feeling some parent-like pride at their growth.

May 15, 2025 12:00 AM

State-based testing with quickcheck-lockstep (Haskell Unfolder #44)

Today, 2025-05-14, at 1830 UTC (11:30 am PDT, 2:30 pm EDT, 7:30 pm GMT, 20:30 CET, …) we are streaming the 44th episode of the Haskell Unfolder live on YouTube.

State-based testing with quickcheck-lockstep (Haskell Unfolder #44)

Many Haskell programmers will be familiar with property based testing of pure functions (for those who are not, various episodes of the Haskell Unfolder have discussed this: #4, #21, #38 and #40). Property based testing for stateful systems (“IO code”) is however much less well-known, which is a pity as it is just as useful! In this episode we will demonstrate how we can use quickcheck-lockstep to verify the responses we get from a simple stateful API; as we will see, all of the lessons from property based testing for pure functions can be applied in this stateful setting also.

About the Haskell Unfolder

The Haskell Unfolder is a YouTube series about all things Haskell hosted by Edsko de Vries and Andres Löh, with episodes appearing approximately every two weeks. All episodes are live-streamed, and we try to respond to audience questions. All episodes are also available as recordings afterwards.

We have a GitHub repository with code samples from the episodes.

And we have a public Google calendar (also available as ICal) listing the planned schedule.

There’s now also a web shop where you can buy t-shirts and mugs (and potentially in the future other items) with the Haskell Unfolder logo.

by andres, edsko at May 14, 2025 12:00 AM

A descriptive theory of seasons in the Mid-Atlantic

[ I started thinking about this about twenty years ago, and then writing it down in 2019, but it seems to be obsolete. I am publishing it anyway. ]

The canonical division of the year into seasons in the northern temperate zone goes something like this:

• Spring: March 21 – June 21
• Summer: June 21 – September 21
• Autumn: September 21 – December 21
• Winter: December 21 – March 21

Living in the mid-Atlantic region of the northeast U.S., I have never been happy with this. It is just not a good description of the climate.

I begin by observing that the year is not equally partitioned between the four seasons. The summer and winter are longer, and spring and autumn are brief and happy interludes in between.

I have no problem with spring beginning in the middle of March. I think that is just right. March famously comes in like a lion and goes out like a lamb. The beginning of March is crappy, like February, and frequently has snowstorms and freezes. By the end of March, spring is usually skipping along, with singing birds and not just the early flowers (snowdrops, crocuses, daffodil) but many of the later ones also.

By the middle of May the spring flowers are over and the weather is getting warm, often uncomfortably so. Summer continues through the beginning of September, which is still good for swimming and lightweight clothes. In late September it finally gives way to autumn.

Autumn is jacket weather but not overcoat weather. Its last gasp is in the middle of November. By this time all the leaves have changed, and the ones that are going to fall off the trees have done so. The cool autumn mist has become a chilly winter mist. The cold winter rains begin at the end of November.

So my first cut would look something like this:

Months

Seasons

January

February

March

April

May

June

July

August

September

October

November

December

Winter

Spring

Summer

Autumn

Winter

Note that this puts Thanksgiving where it belongs at the boundary between autumn (harvest season) and winter (did we harvest enough to survive?). Also, it puts the winter solstice (December 21) about one quarter of the way through the winter. This is correct. By the solstice the days have gotten short, and after that the cold starts to kick in. (“As the days begin to lengthen, the cold begins to strengthen”.) The conventional division takes the solstice as the beginning of winter, which I just find perplexing. December 1 is not the very coldest part of winter, but it certainly isn't autumn.

There is something to be said for it though. I think I can distinguish several subseasons — ten in fact:

Dominus Seasonal Calendar

Months

Seasons

Sub-seasons

January

February

March

April

May

June

July

August

September

October

November

December

Winter

Spring

Summer

Autumn

Winter

Midwinter

Late Winter

Early spring

Late spring

Early Summer

Midsummer

Late Summer

Early autumn

Late autumn

Early winter

Midwinter

Midwinter, beginning around the solstice, is when the really crappy weather arrives, day after day of bitter cold. In contrast, early and late winter are typically much milder. By late February the snow is usually starting to melt. (March, of course, is always unpredictable, and usually has one nasty practical joke hiding up its sleeve. Often, March is pleasant and springy in the second week, and then mocks you by turning back into January for the third week. This takes people by surprise almost every year and I wonder why they never seem to catch on.)

Similarly, the really hot weather is mostly confined to midsummer. Early and late summer may be warm but you do not get blazing sun and you have to fry your eggs indoors, not on the pavement.

Why the seasons seem to turn in the middle of each month, and not at the beginning, I can't say. Someone messed up, but who? Probably the Romans. I hear that the Persians and the Baha’i start their year on the vernal equinox. Smart!

Weather in other places is very different, even in the temperate zones. For example, in southern California they don't have any of the traditional seasons. They have a period of cooler damp weather in the winter months, and then instead of summer they have a period of gloomy haze from June through August.

However

I may have waited too long to publish this article, as climate change seems to have rendered it obsolete. In recent years, we have barely had midwinter, and instead of the usual two to three annual snows we have zero. Midsummer has grown from two to four months, and summer now lasts into October.

by Mark Dominus (mjd@plover.com) at May 08, 2025 10:39 PM

The Haskell Unfolder Episode 43: monomorphism restriction and defaulting

Today, 2025-05-07, at 1830 UTC (11:30 am PDT, 2:30 pm EDT, 7:30 pm GMT, 20:30 CET, …) we are streaming the 43th episode of the Haskell Unfolder live on YouTube.

The Haskell Unfolder Episode 43: monomorphism restriction and defaulting

In this episode, we are going to look at two interacting “features” of the Haskell language (the monomorphism restriction and defaulting) that can be somewhat surprising, in particular to newcomers: there are situations where Haskell’s type inference algorithm deliberately refuses to infer the most general type. We are going to look at a number of examples, explain what exactly is going on, and why.

About the Haskell Unfolder

The Haskell Unfolder is a YouTube series about all things Haskell hosted by Edsko de Vries and Andres Löh, with episodes appearing approximately every two weeks. All episodes are live-streamed, and we try to respond to audience questions. All episodes are also available as recordings afterwards.

We have a GitHub repository with code samples from the episodes.

And we have a public Google calendar (also available as ICal) listing the planned schedule.

There’s now also a web shop where you can buy t-shirts and mugs (and potentially in the future other items) with the Haskell Unfolder logo.

by andres, edsko at May 07, 2025 12:00 AM

Payslips and tax: calculating your own

In the UK, it’s very common that your employer pays you once a month. When this happens, they give you a document called a payslip, that has some numbers on it, such as how much your salary is, how much they paid you this month, how much went to HMRC in tax, how much went to your pension, and a few other numbers. But they never show any workings, so you really have no way to check whether any of these numbers are correct. There are plenty of online take-home-pay calculators, but these all focus on the full year; they have no facility to calculate your next payslip.

About half way through April 2024, I stopped working for one company. Everything was wrapped up – I received my final payslip from them, along with my P45. I then had a few months off, and started a new job in July 2024. When you start a new job it always takes a while for money things to get sorted out, for example pension enrolment and sorting out pension contributions, so it’s really worthwhile to keep a close eye on your payslips particularly for these first few months. Mine were arriving and some numbers looked right, but other numbers, such as the amount of tax I was paying, were changing dramatically, month to month. I had no idea why; whether they should be changing like that; whether they were going to keep changing or would eventually settle down. I had no way to check any of these numbers. Was I going to get in trouble with HMRC and get investigated?

I was also a little on edge because this was the first job where my pension contributions were using a thing called Qualifying Earnings. In all my previous jobs, if I chose for 10% of my salary to go into my pension, then that’s what would happen. But now there was this thing called Qualifying Earnings, which is (numbers correct at time of writing) a band from £6240 to £50,270. If you’re earning, say £30k, then your x% contribution is actually x% of £30,000-£6240. If you’re earning above £50,270, then any further increase to your salary will not result in any extra contributions to your pension because you’re above the band. The 2008 Pensions Act, which created the legal requirement for all employees to have workplace pensions and for automatic enrolment (with a minimum 8% combined contribution from the employer and employee), also created this concept of Qualifying Earnings. I consider this is a pretty scummy way of reducing employer pension contributions for large firms. It complicates the maths and no doubt adds confusion for people trying to check their own payslips. Given that 74% of the population have pensions that are too small to retire on, this whole concept of Qualifying Earnings seems amoral at best.

These days, a lot of smaller companies outsource their payroll processing. In my case, I was officially working for an international Employer of Record and they were then outsourcing payroll processing to local firms with country-specific expertise. So when I started asking questions, there was no ability to go and sit with someone and work through it. Or have a call. It was all messages passed across multiple different systems, and partial answers at best would come back several days later. Even if your payroll is done in-house, I strongly suspect that a lot of the time, some software package will be being used that does all the calculations and quite likely no one will actually understand or be able to explain the maths that’s going on.

After a while of getting no-where, and after uncovering some substantial mistakes that had been made that affected me, I decided to spend some weekends actually figuring out how PAYE works, and writing some code that can calculate my next payslip. This library is available for anyone to use. There’s a README that hopefully explains the basic principles of how the calculations are done. This only works if your tax-code ends in an L, and it only works if you’re in National Insurance category A. All the code can do is use some details you provide to predict your next payslips. Also, I’m not a trained accountant or financial adviser, and even for my own payslips, every month, the numbers don’t quite match up (but they’re within £1). So please treat this as a toy, rather than the basis for building a payroll processor!

Getting started

The library is written in Go so you’ll need Go installed. Then, in a terminal do:

$ mkdir payslips
$ cd payslips
$ go mod init mypayslips
$ go get wellquite.org/tax@latest

Now we need to write a tiny amount of code. In your new payslips directory, create a main.go file, and open it in your editor. You want something like this:

package main

import (
   "fmt"
   "wellquite.org/tax"
)

func main() {
   payslips := tax.Payslips{
      {
         Year:                            2024,
         TaxCode:                         "1257L",
         Salary:                          tax.Yearly(50000),
         PensionType:                     tax.Salary,
         EmployeePensionContributionRate: 0.05,
         EmployerPensionContributionRate: 0.03,
      },
      {
         Salary:                          tax.Yearly(50000),
         PensionType:                     tax.Salary,
         EmployeePensionContributionRate: 0.05,
         EmployerPensionContributionRate: 0.03,
      },
      {},
      {
         Salary:                          tax.Yearly(60000),
         PensionType:                     tax.QualifyingEarnings,
         EmployeePensionContributionRate: 0.05,
         EmployerPensionContributionRate: 0.03,
      },
      {
         Salary:                          tax.Yearly(60000),
         PensionType:                     tax.QualifyingEarnings,
         EmployeePensionContributionRate: 0.15,
         EmployerPensionContributionRate: 0.03,
      },
      {
         Salary:                          tax.Yearly(60000),
         PensionType:                     tax.QualifyingEarnings,
         Expenses:                        116.08,
         EmployeePensionContributionRate: 0.15,
         EmployerPensionContributionRate: 0.03,
      },
   }

   payslips.Complete()
   fmt.Println(payslips)
}

We create a list of Payslips. The first payslip must specify a year, and your tax-code. These details are automatically applied to the payslips that follow, if not explicitly provided. Many of the calculations rely on year-to-date totals, and so we must have a complete record of your payslips from the start of the tax year. So that means the first payslip is month 1 (in this example, April 2024), then month 2 (May 2024) and so on. If you have no income for a month then you can just put in an empty payslip ({}). The above example describes being paid in April and May 2024, then nothing in June, and then being paid (with a higher salary) in July, August and September.

Save this main.go file. Then, back in your terminal, in your payslips directory, just do:

go run main.go

You should get some output showing all sorts of calculations, including income tax, and personal allowance. With a little luck, if you change the numbers to match your own salary and other details, the numbers produced should match quite closely your own payslips, provided nothing you’re doing is too exotic.

There is documentation for all the different fields that you can provide in each payslip. In general, the code will try to fill in missing values. It should be able to cope with things like salary-sacrifice, or, if you change job within a month and have several payslips for the same month, this should work too. Everything is run locally on your computer: please feel free to check the source – there are no 3rd party libraries at all, and nothing imports the net package. It’ll work just the same if you yank out your network cable or disable your WiFi.

Note however, this code is lightly tested. Whilst it works for me (and one or two friends), I make no claims that it correctly models the entirety of PAYE, so it may very well not work for you. Feedback, contributions, corrections, and patches are all very welcome!

May 05, 2025 02:30 PM

Analyzing API Design via Algebraic Laws

The other day, someone asked:

Why doesn’t [the Data.Map function] unionWith :: (a -> a -> a) -> Map k a -> Map k a -> Map k a allow for different value types the way intersectionWith :: (a -> b -> c) -> Map k a -> Map k b -> Map k c does?

This is a very reasonable question, and it lead down an interesting rabbit hole of at the intersection of API design and efficient implementation.

To answer the original question, what would the type of a different value type of unionWith look like? It would be something in the flavor of:

unionWith :: (Maybe a -> Maybe b -> c) -> Map k a -> Map k b -> Map k c

But this new Maybe a -> Maybe b -> c parameter is somewhat lossy, in that it gives the impression that it could be called with Nothing Nothing as parameters, which doesn’t fit into the vibe of being a “union.”

So instead we could restrict that possibility by using These a b:

data These a b = This a | That b | These a b

unionWith :: (These a b -> c) -> Map k a -> Map k b -> Map k c

which seems reasonable enough.

---

But let’s take reasonableness out of the picture and start again from first principles. Instead let’s ask ourselves the deep philsophical question of what even IS a map?

A Map k v is a particularly efficient implementation of functions with type k -> Maybe v. But why is this Maybe here? It’s really only to encode the “default” value of performing a lookup. Nothing goes wrong if we generalize this to be Monoid v => k -> v. In fact, it helps us make sense of the right bias present in Data.Map, where we see:

lookup k (singleton k v1 <> singleton k v2) = Just v2

This equality is hard to justify under the normal understanding of Map k v being an encoding of a function k -> Maybe v. But under the general monoid interpretation, we get a nice semigroup homomorphism:

lookup k (m1 <> m2) = lookup k m1 <> lookup k m2

where the monoid in question has been specialized to be Last.

Of course, we also have a monoid homomorphism:

lookup k mempty = mempty

Let’s re-evaluate the original question in terms of this newly-generalized Map. Now that we’ve removed all of the unnecessary baggage of Maybe, we can again think about the desired type of unionWith:

unionWith
    :: (a -> b -> c)
    -> Map k a
    -> Map k b
    -> Map k c

which looks awfully familiar. This new type signature automatically resolves our original concerns about “what should we do if the key isn’t present?”—just call the function with mempty as a parameter!

We can give some semantics as to what unionWith ought to do again by relating it to the observation lookup. The relevant law here seems like it ought to be:

lookup k (unionWith f m n) = f (lookup k m) (lookup k n)

By choosing a degenerate function f, say, \_ _ -> nontrivial, where nontrivial is some value that is not mempty, we can see the beginnings of a problem:

  lookup k (unionWith f m n)
=
  f (lookup k m) (lookup k n)
= <let f = \_ _ -> nontrivial>
  nontrivial

Regardless of the key we lookup in our unionWithed Map, we need to get back nontrivial. How can we implement such a thing? I see only two ways:

1. explicitly associate every key in the map with nontrivial, or
2. keep nontrivial around as a default value in the map

#1 is clearly a non-starter, given that we want our Maps to be efficient encodings of functions, which leaves us with only #2. This is actually a pretty common construction, which stems immediately from the fact that a pair of monoids is itself a monoid. The construction would look something like this:

data Map k v = Map
  { defaultValue :: v
  , implementation :: Data.Map.Map k v
  }
  deriving stock Generic
  deriving (Semigroup, Monoid) via (Generically (Map k v))

unionWith
    :: (a -> b -> c)
    -> Map k a
    -> Map k b
    -> Map k c
unionWith f (Map def1 imp1) (Map def2 imp2) =
  Map (f def1 def2) (liftA2 f imp1 imp2)

Seems fine, right? The nail in the coffin comes from when we reintroduce our semigroup homomorphism:

lookup k (m1 <> m2) = lookup k m1 <> lookup k m2

Without loss of generalization, take m2 = pure nontrivial (where pure is just unionWith with a constant function.) This gives us:

lookup k (m1 <> pure nontrivial) = lookup k m1 <> nontrivial

Making this thing efficient is a further complication! We again have two options:

1. modify the value at every key by multiplying in nontrivial, or
2. finding a way of suspending this computation

#1 clearly requires \(O(n)\) work, which again forces us to look at #2. But #2 seems very challenging, because the monoidal values we need to suspend need not span the entire Map. For example, consider a Map constructed a la:

((pure prefix1 <> ((pure prefix2 <> m) <> n)) <> (p <> pure suffix)

Representing this thing efficiently certainly isn’t impossible, but you’re not going to be able to do it on the balanced binary search trees that underlie the implementation of Data.Map.Map.

---

I find this quite an interesting result. I always assumed that Data.Map.Map (or at least, Data.Map.Monoidal.MonoidalMap) didn’t have an Applicative instance because it would require a Monoid constraint on its output—but that’s not the sort of thing we can express in Haskell.

But the analysis above says that’s not actually the reason! It’s that there can be no efficient implementation of Applicative, even if we could constrain the result.

What I find so cool about this style of analysis is that we didn’t actually write any code, nor did we peek into the implementation of Data.Map (except to know that it’s implemented as a balanced BST.) All we did was look at the obvious laws, instantiate them with degenerate inputs, and think about what would be required to to efficiently get the right answer.

May 05, 2025 07:33 AM

Using Obscure Graph Theory to solve PL Problems

Usually I write about solutions to problems I’ve worked out, but I’ve found myself increasingly becoming interesting in where solutions come from. Maybe it’s because I’ve been reading Boorstin’s excellent The Discoverers, which I’d strongly recommend.

Regardless of why, I thought I’d switch up the usual dance step today, and discuss what solving my most-recent-big-problem actually looked like, in terms of what I tried, where I looked, and what the timeline was.

The Problem

The problem is to serialize a program graph into a series of let-bindings. For example, given the following graph:

      +
    /   \
  f ---> g
  |     / \
  a     \ /
      expensive

which represents the program:

f a (g expensive expensive) + g expensive expensive

Unfortunately, this is a naive representation of the program, since it duplicates the work required to compute expensive four times, and g expensive expensive twice. Instead, we would prefer to generate the equivalent-but-more-efficient program:

let $0 = expensive
    $1 = g $0 $0
 in f a $1 + $1

This transformation is affectionately known as sharing, since it shares the computed answer whenever there is repeated work to be done.

So this is what we’re trying to do. Given the original graph, determine the best place to insert these let-bindings, for some reasonable definition of “best.” We can assume there are no side effects involved, so any place that an expression is well-scoped is an acceptable solution.

In order to understand some of my attempted solutions, it’s worth noting that our final solution should build something of type Expr, and the original graph is represented as a IntMap (ExprF Int). ExprF is the Base functor of Expr, with all of its self-references replaced by some type variable, in this case Int. Thus, the graph above looks much more like:

_ : IntMap (ExprF Int)
_ = IM.fromList
  [ (0, Apply "+" [1, 3])
  , (1, Apply "f" [2, 3]
  , (2, ...)  -- a
  , (3, Apply "g" [4, 4])
  , (4, ...)  -- expensive
  ]

The Original Solution

I spent over a year trying to solve this problem, with various mostly-working solutions during that time. My strategy here was to think really hard, write up some algorithm that seemed plausible, and then run it against our (small) battery of integration tests to make sure it got the same answer as before.

Why not property test it? I tried, but found it very challenging to implement well-typed generators that would reliably introduce shared thunks. But maybe there’s a different lesson to be learned here about writing good generators.

Anyway. For eight months, one of these think-really-hard algorithms fit the bill and didn’t give us any problems. It was a weird, bespoke solution to the problem that independetly kept track of all of the free variables in every graph fragment, and tried to let-bind a fragment as soon as we landed in a context where all of the free variables were in scope. It seemed to work, but it was extremely messy and unmaintainable.

At the time of writing, this sharing algorithm was the only source of let-binds in our entire language, which meant that it didn’t need to account for let-binds in the program.

Of course, that invariant eventually changed. We added a way in the source langauge to introduce lets, which meant my algorithm was wrong. And I had written it sufficiently long ago that I no longer remembered exactly why it worked. Which meant the theory of my program was lost, and thus that we ought to rewrite it.

Unfolding a Solution

I went back to the problem statement, and stared at it for a long time (back to the think-really-hard algorithm!) Upon staring at the problem, I realized that what I was really trying to do was determine where diamond patterns arose in the propgram graph.

Recall our original graph:

      +
    /   \
  f ---> g
  |     / \
  a     \ /
      expensive

If we redraw it such that g is on a different rank than f, then the two diamond patterns become much clearer:

      +
    /  \
  f     |
  | \   |
  a  \ /
      g
     / \
     \ /
   expensive

The insight I came up with is that if a node n is the source of a diamond, then we must let-bind the sink of the diamond immediately before inlining the definition of n.

This gives rise to the question of “how do we identify a diamond?” What we can do is give a mapping from each node to its reachable set of nodes. For example, in the above, we’d compute the map:

+         -> {+, f, a, g, expensive}
f         -> {f, a, g, expensive}
a         -> {a}
g         -> {g, expensive}
expensive -> {expensive}

Then when we go to inline a node, say, +, we can look for any nodes that are reachable via more than one of its immediate subterms. Since the immediate subterms of + are f and g, we can take the intersections of their reachable sets:

{f, a, g, expensive} union {g, expensive}

giving us

{g, expensive}

which is exactly the set of nodes that we need to perform sharing on. If you topologically sort this set, it gives you the order that you should perform your let bindings.

EXCEPT there’s a kink in the whole thing. What happens if one of the terms in this diamond contains free variables? In particular, we might have something like this:

      +
    /  \
  f     |
  | \   |
  a  \ /
      λx
     / \
     \ /
   expensive
      |
      x

This gives us an analogous set of reachable nodes when we look at +, but we obviously can’t lift expensive x above the lambda.

Resolving this problem required giving up on the notion of memoizing the entire reachable set of nodes, and to instead crawl the graph ensuring that everything is well-scoped.

Performance Woes

My algorithm looked fine, and, importantly, got the right answer in a reasonable amount of time on our (small) battery of integration tests. So I shipped it, commended myself on a job well done, and thought nothing more about it. For about a week, until a bug report came in saying that our compiler now seemed to hang on big programs.

Which was something I hadn’t noticed, since we didn’t have any big programs in our integration tests.

Damn!

Upon digging in to what exactly was so slow, I noticed that my algorithm was accidentally quadratic. I needed to fold over every node in the graph, and that required looking at the entire reachable set underneath it. I had put in some of the obvious safeguards, hoping that they would prune the search tree early, but it wasn’t enough sacrifice for the Great God of Asymptotes.

Did I mention that at this point in the story, having this algorithm working fast was on the critical path of the company? Everybody else was blocked on me figuring this out. Talk about pressure!

Anyway. You’ll notice above that in my description of the algorithm, everything sounds fine. But the juice is in the details, as the common saying goes. Computing reachability isn’t quite the right thing to be using here, as it gave us the wrong answer for the lambda example above. Which is unfortunate because reachability is something we can do in linear time.

And then when reachability didn’t work, I just threw away the fast performance and hoped my bespoke algorithm would do the job. My only redemption comes from the fact that at least it got the right answer, even if it did so very slowly.

Finding the Kernel

Back to the drawing board.

Whenever I have graph theory problems, I call up my boy Vikrem. He’s good at nerd stuff like this.

We rubberducked the problem, and tried to reframe the problem in the language of graph theory. We had a Merkiv–Maguire moment where we indepdently realized that the goal was somehow related to finding the lowest common ancestor (LCA) of a node.

Which is to say, roughly, that we are looking for forks in the diamond diagram. Which we already knew, but it was nice to have some language for.

Our new problem is that LCA is defined only over trees. There are some extensions to DAGs, but none of them seem to be particularly well founded. However, searching for exactly that brought me to this stackoverflow question, where nestled in the comments is someone suggesting that the poster isn’t looking for LCA, but instead for a related notion the lowest single common ancestor. LSCA is defined in a 2010 paper New common ancestor problems in trees and directed acyclic graphs.

The standard definition of LCA(x, y) = l is that “l is an ancestor of x and of y, and that no descendent of l has this property.”

But the definition of LSCA(x, y) = l is that “l lies on all root-to-x paths, and that l lies on all root-to-y paths, and that no descendent of l has this property.”

The distinction between the two is easily seen in the following graph:

  0
 / \
1   2
| X |
3   4

Under the standard definition, LCA is not uniquely defined for DAGs. That is, LCA(3, 4) = {1, 2}. But neither 1 nor 2 lies on all paths from the root. Under LSCA therefore we get LSCA(3, 4) = 0, which is the obviously-correct place to let-bind 3 and 4.

The paper gives a preprocessing scheme for computing LSCA by building a “lowest single ancestor” (LSA) tree. The LSA of a node is the LSCA of all of its in-edges. This definition cashes out to mean “the most immediate diamond above any node.” Finally! This is exactly what we’re looking for, since this is where we must insert our let-bindings! Even better, the paper gives us an algorithm for computing the LSA tree in linear time!

The First Implementer

Of course, I’m lazy and would prefer not to implement this thing. So instead I searched on hackage for lsca, and found nothing. But then I searched for lca and found that, like always, Ed Kmett was 13 years ahead of me.

The lca package implements an \(O(log n)\) algorithm for computing the LCA of any two nodes in a graph. Which is very convenient for me, since the LSCA algorithm requires being able to do this.

Time to roll up the sleeves and get cracking I suppose.

The paper was surprisingly straightforward, and my first attempt implemented the (imperative) algorithms as given (imperatively.) The first step is to do a topological sort on the DAG in order to know in which order one ought to unfold the LSA tree.

But as is so often the case, this topological sort isn’t actually relevant to the algorithm; it’s just an encoding detail of expressing the algorithm imperatively. But you don’t need that when you’ve got laziness on your side! Instead you can just tie the know and do something cool like this:

lsaTree :: Ord v => Map v (Set v) -> Map v (Path v)
lsaTree input = fix $ \result -> M.fromList $ do
  (node, parents) <- M.toList input
  let parentResults = fmap (result M.!) parents
  ...

Notice how we use fix to bind the eventual result of the final computation. Then we can chase pointers by looking them up in result—even though it’s not yet “computed.” Who cares what order the computer does it in. Why is that a thing I should need to specify?

Anyway. The exact details of implementing LSA are not particularly important for the remainder of this blog post. If you’re interested, you can peep the PR, which is delightfully small.

Tying It All Back Together

Equipped with my LSA tree, I was now ready to go back and solve the original problem of figuring out where to stick let-bindings. It’s easy now. Given the original program graph, find the LSA for each node. The LSA is the place you should insert the let binding.

So given the map of nodes to their LSAs, invert that map and get back a map of nodes to descendents who have this node as an LSA. Now when you go to inline a node, just look up everything in this map and inline it first.

It turns out to be a very elegant solution. It’s one third of the length of my horrible ad-hoc implementations, and it runs in linear time of the number of nodes in the graph. All in all, very good.

More often than I’m comfortable about, people will ask me how I can have so many good ideas. And what I like about this story is that it’s pretty typical of how I actually “have” “good” ideas. I’m reminded of the fact that luck favors the prepared mind. Attentive readers will notice that none of this process was due to brilliance on my part. I happened to know Vikrem who’s a genius. Together we pulled at some ancient graph theory strings and remembered a fact that someone else had thought important to teach us. That wasn’t actually the right path, but it lead us to stackoverflow where someone had linked to a relevant paper. I implemented the paper using a library that someone else had done the heavy lifting on, and simplified the implementation using this knot-tying trick I picked up somewhere along the way.

Also, I’m just really pleased that the solution came from trying to reverse engineer the relevant graph-theory search terms. Maybe that’s the actual takeaway here.

May 04, 2025 08:05 AM

Claude and I write a utility program

Then I had two problems…

A few days ago I got angry at xargs for the hundredth time, because for me xargs is one of those "then he had two problems" technologies. It never does what I want by default and I can never remember how to use it. This time what I wanted wasn't complicated: I had a bunch of PDF documents in /tmp and I wanted to use GPG to encrypt some of them, something like this:

    gpg -ac $(ls *.pdf | menupick)

menupick is a lovely little utility that reads lines from standard input, presents a menu, prompts on the terminal for a selection from the items, and then prints the selection to standard output. Anyway, this didn't work because some of the filenames I wanted had spaces in them, and the shell sucks. Also because gpg probably only does one file at a time.

I could have done it this way:

    ls *.pdf | menupick | while read f; do gpg -ac "$f"; done

but that's a lot to type. I thought “aha, I'll use xargs.” Then I had two problems.

    ls *.pdf | menupick | xargs gpg -ac

This doesn't work because xargs wants to batch up the inputs to run as few instances of gpg as possible, and gpg only does one file at a time. I glanced at the xargs manual looking for the "one at a time please" option (which should have been the default) but I didn't see it amongst the forest of other options.

I think now that I needed -n 1 but I didn't find it immediately, and I was tired of looking it up every time when it was what I wanted every time. After many years of not remembering how to get xargs to do what I wanted, I decided the time had come to write a stripped-down replacement that just did what I wanted and nothing else.

(In hindsight I should perhaps have looked to see if gpg's --multifile option did what I wanted, but it's okay that I didn't, this solution is more general and I will use it over and over in coming years.)

xar is a worse version of xargs, but worse is better (for me)

First I wrote a comment that specified the scope of the project:

    # Version of xargs that will be easier to use
    #
    # 1. Replace each % with the filename, if there are any
    # 2. Otherwise put the filename at the end of the line
    # 3. Run one command per argument unless there is (some flag)
    # 4. On error, continue anyway
    # 5. Need -0 flag to allow NUL-termination

There! It will do one thing well, as Brian and Rob commanded us in the Beginning Times.

I wrote a draft implementation that did not even do all those things, just items 2 and 4, then I fleshed it out with item 1. I decided that I would postpone 3 and 5 until I needed them. (5 at least isn't a YAGNI, because I know I have needed it in the past.)

The result was this:

    import subprocess
    import sys

    def command_has_percent(command):
        for word in command:
            if "%" in word:
                return True
        return False

    def substitute_percents(target, replacement):
        return [ s.replace("%", replacement) for s in target ]

    def run_command_with_filename(command_template, filename):
        command = command_template.copy()
        if not command_has_percent(command):
            command.append("%")

        res = subprocess.run(substitute_percents(command, filename), check=False)
        return res.returncode == 0

    if __name__ == '__main__':
        template = sys.argv[1:]
        ok = True
        for line in sys.stdin:
            if line.endswith("\n"):
                line = line[:-1]
            if not run_command_with_filename(template, line):
                ok = False
        exit(0 if ok else 1)

Short, clean, simple, easy to use. I called it xar, ran

    ls *.pdf | menupick | xar gpg -ac

and was content.

Now again, with Claude

The following day I thought this would be the perfect opportunity to try getting some LLM help with programming. I already had a baseline version of xar working, and had thought through the problem specification. Now I could do it over with the LLM and compare the two results. The program I wanted was small and self-contained. If the LLM sabotaged me somehow, I would probably notice, and if I didn't, it wouldn't matter, because I had a working version already.

So I asked Claude about it. I knew Claude was not the right choice, because Claude is not really designed for this task, and has no integration with the coding editor, but Claude is what I am familiar with so I thought I'd give it a shot.

On the whole it went extremely well. The complete transcript is here. I imagine this was pretty much a maximally good experience, that all the terrible problems of LLM coding arise in larger, more complicated systems. But this program is small and self-contained, with no subtleties, so the LLM could be at its best.

Phase 1

First I just told Claude what I wanted and let it write the program from scratch.

Let's write a program in Python called xar. It will be a stripped-down version of the standard Unix xargs utility, but it will do less and be simpler to use.

It will get command-line arguments that specify a command template. Then it will read lines from stdin. Each line will be appended to the command template to produce a command. The program will run the resulting command, one command for each line of input.

Any questions?

Default Claude is very chatty and I am going to omit most of its chatty comments, which make me impatient.

The program it wrote it was not what I would have written, but it was good enough. If I had just used it right off the bat, instead of writing my own, it would have been enough, and it would have taken somewhere between 2% and 10% as long to produce.

So the one-line summary of this article is: I should stop writing simple command-line utilities, and just have Claude write them instead, because Claude's are good enough, and definitely better than yak-shaving.

Here's Claude's initial version:

    #!/usr/bin/env python3

    import sys
    import subprocess
    import shlex

    def main():
        if len(sys.argv) < 2:
            print("Usage: xar command [args...]", file=sys.stderr)
            sys.exit(1)

        command_template = sys.argv[1:]

        for line in sys.stdin:
            line = line.rstrip('\n')

            full_command = command_template + [line]

            try:
                result = subprocess.run(full_command, check=True)
            except subprocess.CalledProcessError as e:
                print(f"Command failed with exit code {e.returncode}: {' '.join(full_command)}", 
                      file=sys.stderr)
            except FileNotFoundError:
                print(f"Command not found: {full_command[0]}", file=sys.stderr)
                sys.exit(1)

    if __name__ == "__main__":
        main()

Claude's version had numerous comments, which I have omitted. I later told it to stop putting in comments, which it did.

Claude's use of check here was not what I wanted, because that makes subprocess.run raise an exception when the subcommand fails, and then the exception has to be immediately caught and handled. My original control flow had been simpler:

        res = subprocess.run(substitute_percents(command, filename), check=False)
        return res.returncode == 0

        …

        if not run_command_with_filename(template, line):
            ok = False

Claude's program pulled in shlex without noticing that it was unused. But Claude did teach me about str.rstrip('\n') which I had not known about before (or maybe had forgotten), so that was one small win already.

Argument parsing

The next step was a big win. Python's library for command-line argument handling is called argparse and it is really nice. If I were still writing programs in Perl, I would implement a Perl version of argparse because Perl has 29 available argument parsing libraries and they are all loathsome. The one problem with argparse is I never remember off the top of my head how to use it. I think the module is called argparse but it provides a class called Argparser but I often get these backward and try to use argparser and Argparse.

Instead of figuring it out every time I usually dig up some previous Python program and then copy-paste the argument parser from there, amending it to suit the purpose.

But this time I didn't have to do that. Instead, I just said to Claude:

This is good, now please add code at the top to handle argument parsing with the standard Argparse library, even though there are no options yet.

Claude handed me back pretty much the same program, but with the argument parser at the top:

    def parse_arguments():
        """Parse command-line arguments using argparse."""
        parser = argparse.ArgumentParser(
            description="A simplified version of xargs that appends each line from stdin to a command template.",
            prog="xar"
        )

        # Store all positional arguments as the command to execute
        parser.add_argument(
            "command", 
            nargs="+", 
            help="The command template to execute for each input line"
        )

        return parser.parse_args()

Let's pause for a moment. Maybe you kids are unimpressed by this. But if someone had sent this interaction back in time and showed it to me even as late as five years ago, I would have been stunned. It would have been completely science-fictional. The code that it produced is not so impressive, maybe, but that I was able to get it in response to an unstructured request in plain English is like seeing a nuclear-powered jetpack in action.

I make some changes

It bothered me that the command-line arguments were being taken implicitly from sys.argv; that makes the program hard to test. A better way to do this is to have the list of command-line arguments be a function to the main function, and then for the runtime to call main(sys.argv[1:]) instead of just main(). That way you can test the program without having to fake up sys.argv. So I changed that, and while I was making changes I got rid of Claude's comments and the unnecessary exception handling. I pasted the result back at Claude, saying:

Good so far. I have adjusted your source code in several ways:

1. I removed the comments.
2. I removed the exception handling for the subcommand. If one of the subcommands fails, that no longer terminates the main loop
3. Command-line arguments are passed to the main() function rather than being accessed directly

Here is the code. Tell me if you see any problems or if you have any questions about it

I had also sabotaged the code with at least one likely error. Python's subprocess.run returns a “result” structure that includes the subcommand's output and exit status, and I can never remember the name of the component that records the exit status. I either look it up or get it by trial-and-error. This time I didn't bother to either, I just guessed that it was result.exitcode, which I handed off to Claude even though I thought was probably wrong.

Claude's reply said:

Here are a couple of issues I noticed:

There's an error in the error handling code - you're using result.exitcode but in the subprocess.run() function, the attribute is called returncode not exitcode

Awesome, now I don't have to remember that name of that component.

Claude continued:

The parse_arguments() function definition is missing in the pasted code, but it would need to be updated to accept the argv parameter

I had passed sys.argv[1:] to main, and then had main call parse_arguments(argv). But I hadn't changed parse_arguments to expect an argument list. (I hadn't included it in my paste at all, in fact.) Claude was exactly right, and continued with the corrected version:

    #!/usr/bin/env python3

    import sys
    import subprocess
    import argparse

    def parse_arguments(argv):
        …
        return parser.parse_args(argv)

    def main(argv):
        # Parse command-line arguments
        args = parse_arguments(argv)
        …

    if __name__ == "__main__":
        ok = main(sys.argv[1:])
        exit(0 if ok else 1)

Handling NUL-separated values

I said

It's great, thanks for catching those errors. Now let's add a -0 command-line option that tells the program to split the input on "\0" characters instead of at line breaks.

Recall that my handwritten xar did not do this yet; I had left that feature for another day. Claude just added it for me, adding

    parser.add_argument(
        "-0", "--null",
        action="store_true",
        help="Input items are terminated by a null character instead of by newline"
    )

to the argument parser and changing the main loop to:

    # Split input based on the delimiter option
    if args.null:
        # Split on null characters
        items = stdin_data.split('\0')
    else:
        # Split on newlines
        items = stdin_data.splitlines()

    for item in items:
        if not item:
            continue

        …

I was tired of Claude's comments, so I said

Give me the same thing, with no comments

which it did, so I said

From now on leave out the comments. I'm a Python expert and I don't need them. If there is something I don't understand I will ask you.

Claude complied. If I were going to do use Claude again in the future I would include that in the canned instructions that Claude is given up front. Instead I will probably use a tool better-suited to programming, and do whatever the analogous thing is.

Template filling

Now I told Claude to add the % feature:

I changed if not item to if item == "". Now let's make the following change:

• If the command template includes any % characters, each of these should be replaced with the input item.
• Otherwise, if there were no % characters, the input item should be appended to the end of the command as in the current version

Claude did this. It used an explicit loop instead of the list comprehension that I had used (and preferred), but it did do it correctly:

    for arg in command_template:
        if '%' in arg:
            has_placeholder = True
            full_command.append(arg.replace('%', item))
        else:
            full_command.append(arg)

    if not has_placeholder:
        full_command.append(item)

Even without the list comprehension, I would have factored out the common code:

    for arg in command_template:
        if '%' in arg:
            has_placeholder = True
        full_command.append(arg.replace('%', item))

    if not has_placeholder:
        full_command.append(item)

But I am not going to complain, my code is simpler but is doing unnecessary work.

Claude also took my hint to change item == "" even though I didn't explicitly tell it to change that.

At this point the main loop of the main function was 15 lines long, because Claude had stuck all the %-processing inline. So I said:

Good, let's extract the command template processing into a subroutine.

It did this right, understanding correctly what code I was referring to and extracting it into a subroutine called process_command_template. More science fiction: I can say "command template processing" and it guesses what I had in mind!

This cut the main loop to 7 lines. That worked so well I tried it again:

Good, now let's extract the part of main that processes stdin into a subroutine that returns the items array

It pulled the correct code into a function called process_stdin. It did not make the novice mistake of passing the entire args structure to this function. In the caller it had process_stdin(args.null) and inside of process_stdin this parameter was named use_null_delimiter,

YAGNI?

At this point I was satisfied but I thought I might as well ask if it should do something else before we concluded:

Can you think of any features I left out that would be useful enough to warrant inclusion? Remember this program is supposed to be small and easy to use, in contrast to the existing xargs which is very complicated.

Claude had four suggestions:

1. A -p or --parallel option to run commands in parallel

2. A -n or --max-args option to specify the maximum number of items to pass per command

3. A simple -v or --verbose flag to show commands as they're executed

4. A way to replace the command's standard input with the item instead of adding it as an argument

All reasonable suggestions, nothing stupid. (It also supplied code for #3, which I had not asked for and did not want, but as I said before, default Claude is very chatty.)

Parallelization

I didn't want any of these, and I knew that #2–4 would be easy to add if I did want any of them later. But #1 was harder. I've done code like this in the past, where the program has a worker pool and runs a new process whenever the worker pool isn't at capacity. It's not even that hard. In Perl you can play a cute trick and use something like

    $workers{spawn()} = 1 while delete $workers{wait()};

where the workers hash maps process IDs to dummy values. A child exits, wait() awakens and returns the process ID of the completed child, which is then deleted from the map, and the loop starts another worker.

I wanted to see how Claude would do it, and the result was an even bigger win than I had had previously, because Claude wrote this:

   with concurrent.futures.ProcessPoolExecutor(max_workers=args.parallel) as executor:
        futures = [executor.submit(execute_command, cmd, args.verbose) for cmd in commands]

        for future in concurrent.futures.as_completed(futures):
            success = future.result()
            if not success:
                ok = False

What's so great about this? What's great is that I hadn't known about concurrent.futures or ProcessPoolExecutor. And while I might have suspected that something like them existed, I didn't know what they were called. But now I do know about them.

If someone had asked me to write the --parallel option, I would have had to have this conversation with myself:

Python probably has something like this already. But how long will it take me to track it down? And once I do, will the API documentation be any good, or will it be spotty and incorrect? And will there be only one module, or will there be three and I will have to pick the right one? And having picked module F6, will I find out an hour later that F6 is old and unmaintained and that people will tell me “Oh, you should have used A1, it is the new hotness, everyone knows that.”

When I put all that uncertainty on a balance, and weigh it against the known costs of doing it myself, which one wins?

The right choice is: I should do the research, find the good module (A1, not F6), and figure out how to use it.

But one of my biggest weaknesses as a programmer is that I too often make the wrong choice in this situation. I think “oh, I've done this before, it will be quicker to just do it myself”, and then I do and it is.

Let me repeat, it is quicker to do it myself. But that is still the wrong choice.

Maybe the thing I wrote would be sooner or smaller or faster or more technically suitable to the project than the canned module would have been. But it would only have been more be technically suitable today. If it needed a new feature in the future it might have to be changed by someone who had never seen it before, whereas the canned module could well already have the needed feature ready to go, already documented, and perhaps already familiar to whoever had to make the change. My bespoke version would certainly be unfamiliar to every other programmer on the project — including perhaps myself six months later — so would be the wrong thing to use.

I'm really good at hacking this stuff up. Which is a problem. It makes me want to hack stuff up, even when I shouldn't.

Claude tips the balance strongly toward the correct side, which is that I should use the prepackaged module that someone else wrote and not hack something up.

And now I know about concurrent.futures.ProcessPoolExecutor! The world is full of manuals, how can I decide which ones I should read? One way is to read them all, which used to work back when I was younger, but now I have more responsibilities and I don't have time to read the entire Python library reference including all the useless bits I will never use. But here's Claude pointing out to me that this is something I need to know about, now, today, and I should read this one. That is valuable knowledge.

Claude flubs

While testing the program I did

    xar --parallel=2 bash -c '...'

which didn't work because the argparse library tried to parse the -c as a flag to xar, when I wanted it to be a flag to bash. This was my fault, and there is a standard way around it, which is that I should have said

    xar --parallel=2 -- bash -c '...'

which tells argparse to drop the -- and take everything after it literally with no interpretation.

I thought I'd see what Claude had to say about this, and it dropped the ball in a very LLM sort of way.

I asked:

When I did xar --parallel=2 bash -c '...' it misunderstood the arguments. It thought I was trying to pass -c to xar and failed with unrecognized arguments. What should I do about that?

Claude replied:

There are two main approaches to handle this:

1. Use the -- separator to indicate the end of arguments for xar: …
2. Modify your code to handle this case specifically by looking for a command terminator in the argument parser.

Here's how you could modify your code to implement the first approach:

And then it followed with the same, unmodified code…

Which was correct, because -- is already handled by argparse, so no change was actually required to implement the first approach! But Claude's characterization of it as a modification was misleading, wrong, and potentially very confusing.

I said:

I don't see what the difference is in that argument parsing code as compared to what I had before.

and Claude got into the LLM tail-chasing mode where it got more and more confused:

You're right, I apologize for the confusion. There's no difference in the argument parsing code I provided compared to what you had before. The issue is with how argparse handles arguments by default.

To fix the issue with xar --parallel=2 bash -c '...', you need to actually implement support for the -- separator in your code…

   # Find the index of '--' if it exists
   try:
       separator_index = argv.index('--')
       xar_args = argv[:separator_index]
       command_args = argv[separator_index+1:]
   except ValueError: …

Ugh, all wrong in the worst way. The code probably works, but it is completely unnecessary. Claude's claim that “you need to actually implement support for the -- separator” is flat wrong. I pointed this out and Claude got more confused. Oh well, nobody is perfect!

Lessons learned

A long time ago, when syntax-coloring editors were still new, I tried one and didn't like it, then tried again a few years later and discovered that I liked it better than I had before, and not for the reasons that anyone had predicted or that I would have been able to predict. (I wrote an article about the surprising reasons to use the syntax coloring.)

This time also. As usual, an actual experiment produced unexpected results, because the world is complicated and interesting. Some of the results were unsurprising, but some were not anything I would have thought of beforehand.

Claude's code is good enough, but it is not a magic oracle

Getting Claude to write most of the code was a lot faster and easier than writing it myself. This is good! But I was dangerously tempted to just take Claude's code at face value instead of checking it carefully. I quickly got used to flying along at great speed, and it was tough to force myself to slow down and be methodical, looking over everything as carefully as I would if Claude were a real junior programmer. It would be easy for me to lapse into bad habits, especially if I were tired or ill. I will have to be wary.

Fortunately there is already a part of my brain trained to deal with bright kids who lack experience, and I think perhaps that part of my brain will be able to deal effectively with Claude.

I did not notice any mistakes on Claude's part — at least this time.

At one point my testing turned up what appeared to be a bug, but it was not. The testing was still time well-spent.

Claude remembers the manual better than I do

Having Claude remember stuff for me, instead of rummaging the manual, is great. Having Claude stub out an argument parser, instead of copying one from somewhere else, was pure win.

Partway along I was writing a test script and I wanted to use that Bash flag that tells Bash to quit early if any of the subcommands fails. I can never remember what that flag is called. Normally I would have hunted for it in one of my own shell scripts, or groveled over the 378 options in the bash manual. This time I just asked in plain English “What's the bash option that tells the script to abort if a command fails?” Claude told me, and we went back to what we were doing.

Claude can talk about code with me, at least small pieces

Claude easily does simple refactors. At least at this scale, it got them right. I was not expecting this to work as well as it did.

When I told Claude to stop commenting every line, it did. I wonder, if I had told it to use if not expr only for Boolean expressions, would it have complied? Perhaps, at least for a while.

When Claude wrote code I wasn't sure about, I asked it what it was doing and at least once it explained correctly. Claude had written

     parser.add_argument(
        "-p", "--parallel",
        nargs="?",
        const=5,
        type=int,
        default=1,
        help="Run up to N commands in parallel (default: 5)"
    )

Wait, I said, I know what the const=5 is doing, that's so that if you have --parallel with no number it defaults to 5. But what is the --default doing here? I just asked Claude and it told me: that's used if there is no --parallel flag at all.

This was much easier than it would have been for me to pick over the argparse manual to figure out how to do this in the first place.

More thoughts

On a different project, Claude might have done much worse. It might have given wrong explanations, or written wrong code. I think that's okay though. When I work with human programmers, they give wrong explanations and write wrong code all the time. I'm used to it.

I don't know how well it will work for larger systems. Possibly pretty well if I can keep the project sufficiently modular that it doesn't get confused about cross-module interactions. But if the criticism is “that LLM stuff doesn't work unless you keep the code extremely modular” that's not much of a criticism. We all need more encouragement to keep the code modular.

Programmers often write closely-coupled modules knowing that it is bad and it will cause maintenance headaches down the line, knowing that the problems will most likely be someone else's to deal with. But what if writing closely-coupled modules had an immediate cost today, the cost being that the LLM would be less helpful and more likely to mess up today's code? Maybe programmers would be more careful about letting that happen!

Will my programming skill atrophy?

Folks at Recurse Center were discussing this question.

I don't think it will. It will only atrophy if I let it. And I have a pretty good track record of not letting it. The essence of engineering is to pay attention to what I am doing and why, to try to produce a solid product that satisifes complex constraints, to try to spot problems and correct them. I am not going to stop doing this. Perhaps the problems will be different ones than they were before. That is all right.

Starting decades ago I have repeatedly told people

You cannot just paste code with no understanding of what is going on and expect it to work.

That was true then without Claude and it is true now with Claude. Why would I change my mind about this? How could Claude change it?

Will I lose anything from having Claude write that complex parser.add_argument call for me? Perhaps if I had figured it out on my own, on future occasions I would have remembered the const=5 and default=1 specifications and how they interacted. Perhaps.

But I suspect that I have figured it out on my own in the past, more than once, and it didn't stick. I am happy with how it went this time. After I got Claude's explanation, I checked its claimed behavior pretty carefully with a stub program, as if I had been reviewing a colleague's code that I wasn't sure about.

The biggest win Claude gave me was that I didn't know about this ProcessPoolExecutor thing before, and now I do. That is going to make me a better programmer. Now I know something about useful that I didn't know before, and I have a pointer to documentation I know I should study.

My skill at writing ad-hoc process pool managers might atrophy, but if it does, that is good. I have already written too many ad-hoc process pool managers. It was a bad habit, I should have stopped long ago, and this will help me stop.

Conclusion

This works.

Perfectly? No, it's technology, technology never works perfectly. Have you ever used a computer?

Will it introduce new problems? Probably, it's new technology, and new technology always introduces new problems.

But is it better than what we had before? Definitely.

I still see some programmers turning up their noses at this technology as if they were sure it was a silly fad that would burn itself out once people came to their senses and saw what a terrible idea it was.

I think that is not going to happen, and those nose-turning-up people, like the people who pointed out all the drawbacks and unknown-unknowns of automobiles as compared to horse-drawn wagons, are going to look increasingly foolish.

Because it works.

by Mark Dominus (mjd@plover.com) at May 03, 2025 04:46 PM

A puzzle about balancing test tubes in a centrifuge

Suppose a centrifuge has slots, arranged in a circle around the center, and we have test tubes we wish to place into the slots. If the tubes are not arranged symmetrically around the center, the centrifuge will explode.

(By "arranged symmetrically around the center, I mean that if the center is at , then the sum of the positions of the tubes must also be at .)

Let's consider the example of . Clearly we can arrange , , , or tubes symmetrically:

Equally clearly we can't arrange only . Also it's easy to see we can do tubes if and only if we can also do tubes, which rules out .

From now on I will write to mean the problem of balancing tubes in a centrifuge with slots. So and are possible, and and are not. And is solvable if and only if is.

It's perhaps a little surprising that is possible. If you just ask this to someone out of nowhere they might have a happy inspiration: “Oh, I'll just combine the solutions for and , easy.” But that doesn't work because two groups of the form and always overlap.

For example, if your group of is the slots then you can't also have your group of be , because slot already has a tube in it.

The other balanced groups of are blocked in the same way. You cannot solve the puzzle with ; you have to do as below left. The best way to approach this is to do , as below right. This is easy, since the triangle only blocks three of the six symmetric pairs. Then you replace the holes with tubes and the tubes with holes to turn into .

Given and , how can we decide whether the centrifuge can be safely packed?

Clearly you can solve when is a multiple of , but the example of (or ) shows this isn't a necessary condition.

A generalization of this is that is always solvable if since you can easily balance tubes at positions , then do another tubes one position over, and so on. For example, to do you just put first four tubes in slots and the next four one position over, in slots .

An interesting counterexample is that the strategy for , where we did , cannot be extended to . One would want to do , but there is no way to arrange the tubes so that the group of doesn't conflict with the group of , which blocks one slot from every pair.

But we can see that this must be true without even considering the geometry. is the reverse of , which impossible: the only nontrivial divisors of are and , so must be a sum of s and s, and is not.

You can't fit tubes when , but again the reason is a bit tricky. When I looked at directly, I did a case analysis to make sure that the -group and the -group would always conflict. But again there was an easier was to see this: and clearly won't work, as is not a sum of s and s. I wonder if there's an example where both and are not obvious?

For , every works except and the always-impossible .

What's the answer in general? I don't know.

Addenda

20250502

Now I am amusing myself thinking about the perversity of a centrifuge with a prime number of slots, say . If you use it at all, you must fill every slot. I hope you like explosions!

While I did not explode any centrifuges in university chemistry, I did once explode an expensive Liebig condenser.

Condenser setup by Mario Link from an original image by Arlen on Flickr. Licensed cc-by-2.0, provided via Wikimedia Commons.

20250503

• Michael Lugo informs me that a complete solution may be found on Matt Baker's math blog. I have not yet looked at this myself.

• Omar Antolín points out an important consideration I missed: it may be necessary to subtract polygons. Consider . This is obviously possible since . But there is a more interesting solution. We can add the pentagon to the digons and to obtain the solution $${0,5,6,10,12,18, 20, 24, 25}.$$

  Then from this we can subtract the triangle to obtain $${5, 6, 12, 18, 24, 25},$$ a solution to which is not a sum of regular polygons:

  

• Thanks to Dave Long for pointing out a small but significant error, which I have corrected.

20250505

• Robin Houston points out this video, The centrifuge Problem with Holly Krieger, on the Numberphile channel.

by Mark Dominus (mjd@plover.com) at May 03, 2025 03:25 PM

GHC 9.10.2 is now available

GHC 9.10.2 is now available

Zubin Duggal - 2025-05-03

The GHC developers are very pleased to announce the availability of the final release for GHC 9.10.2. Binary distributions, source distributions, and documentation are available at downloads.haskell.org and via GHCup.

GHC 9.10.2 is a bug-fix release fixing over 50 issues of a variety of severities and scopes, including:

• Significantly improved performance when dynamically loading Haskell symbols (#23415).
• Fixing a bug where the simplifier sometimes destroyed join points during float out, which could impact performance (#24768).
• Reduced memory fragmentation in the non-moving GC’s segment allocator, improving resident set size by up to 26% for some applications (#24150).
• Added new flags to control speculative evaluation (-fspec-eval and -fspec-eval-dictfun) to work around performance regressions (#25606).
• Fixed several platform-specific issues, including segfaults with FFI on PowerPC (#23034) and improved code generation for AArch64 with multiway branches now using jump tables (#19912)
• And many more!

A full accounting of these fixes can be found in the release notes. As always, GHC’s release status, including planned future releases, can be found on the GHC Wiki status.

We would like to thank Well-Typed, Tweag I/O, Juspay, QBayLogic, Channable, Serokell, SimSpace, the Haskell Foundation, and other anonymous contributors whose on-going financial and in-kind support has facilitated GHC maintenance and release management over the years. Finally, this release would not have been possible without the hundreds of open-source contributors whose work comprise this release.

As always, do give this release a try and open a ticket if you see anything amiss.

by ghc-devs at May 03, 2025 12:00 AM

Prompt chaining reimagined with type inference

Prompt chaining reimagined with type inference

At work I’ve been researching how to improve the ergonomics of prompt engineering and I wanted to share and open source some of what I’ve done. This initial post is about how I’ve been experimenting with using bidirectional type inference to streamline prompt chaining.

“Prompt chaining” is a prompt engineering technique that splits a larger task/prompt into multiple smaller tasks/prompts which are chained together using code. For example, instead of prompting a model to generate a poem in one prompt like this:

Write a poem based off this idea:

${idea}

… by following this process:

• First think through the form, stanza count, lines per stanza, and rhyme scheme
• Then choose a poetic style (tone, voice, and literary devices) based on the poem’s form
• Then write a complete poem based on that plan

… you can split it into smaller prompts, like this:

structure prompt:

Plan the structure of a new poem based on this idea

${idea}

Describe its form, stanza count, lines per stanza, and rhyme scheme

style prompt:

Given this poem structure:

• Form: ${structure.form}
• Stanzas: ${structure.stanzaCount}
• Lines per stanza: ${structure.linesPerStanza}
• Rhyme scheme: ${structure.rhymeScheme}

Choose a poetic style: tone, voice, and literary devices to emphasize

poem prompt:

Write a complete poem based on this idea:

${idea}

Structure:

• Form: ${structure.form}
• Stanzas: ${structure.stanzaCount}
• Lines per stanza: ${structure.linesPerStanza}
• Rhyme scheme: ${structure.rhymeScheme}

Style:

• Tone: ${style.stone}
• Voice: ${style.voice}
• Literary Devices: ${style.literaryDevices}

Why might you want to do this?

• to improve the quality of the results

  Models perform better when working on more constrained subproblems. Splitting a larger prompt into smaller prompts helps the model stay focused at each step.

• to introspect intermediate results

  This comes in handy when you want to log, validate, or correct intermediate results.

• to perform actions in between prompts

  You might want to take the output of one prompt, use that to call some tool, then use the output of that tool to decide what the next prompt should be, which you can’t do with a single prompt.

In other words, prompt chaining unlocks greater accuracy, control, and flexibility for prompt engineering.

The problem

The main issue with prompt chaining is that it is a huge pain in the ass; if you start do anything a little bit complicated you need to start using structured outputs (i.e. JSON), which adds a whole lot of boilerplate to the process:

• you have to define the schema for each intermediate step of the process

  You typically do this by defining your data model in your host programming language (e.g. a Pydantic model in Python) or directly defining your JSON schema

• You have to instruct the model to produce JSON and explain the shape of the expected output

• (Depending on the framework) you have to decode the JSON into your data model

For small prompt chaining pipelines this isn’t too hard, but it starts to get annoying to define all these schemas when you scale this up to more sophisticated prompt chaining pipelines.

So as a thought experiment I wanted to create a research prototype that handled all of that for you so that you didn’t need to specify any schemas at all. In other words I wanted to build a programming language that harnessed bidirectional type inference to perform schema inference for prompts with structured JSON outputs.

Example

I’ll cut to the case by showing the above prompt chain written as a program in this language:

let concatSep =
      https://raw.githubusercontent.com/Gabriella439/grace/refs/heads/main/prelude/text/concatSep.ffg

let lines = concatSep "\n"

let generatePoem idea =
        let structure = prompt
                { model: "gpt-4o"
                , text: lines
                    [ "Plan the structure of a new poem based on this idea:"
                    , ""
                    , idea
                    , ""
                    , "Describe its form, stanza count, lines per stanza, and rhyme scheme."
                    ]
                }

        let renderedStructure = lines
                [ "- Form: " + structure.form
                , "- Stanzas: " + Real/show (structure.stanzaCount : Integer)
                , "- Lines per stanza: " + Real/show (structure.linesPerStanza : Integer)
                , "- Rhyme scheme: " + structure.rhymeScheme
                ]

        let style = prompt
                { model: "gpt-4o"
                , text: lines
                    [ "Given this poem structure:"
                    , renderedStructure
                    , ""
                    , "Choose a poetic style: tone, voice, and literary devices to emphasize."
                    ]
                }

        let renderedStyle = lines
                [ "- Tone: " + style.tone
                , "- Voice: " + style.voice
                , "- Literary Devices: " + concatSep ", " style.literaryDevices
                ]

        let poem : Text = prompt
                { model: "gpt-4o"
                , text: lines
                    [ "Write a complete poem based on this idea:"
                    , ""
                    , idea
                    , ""
                    , "Structure:"
                    , renderedStructure
                    , ""
                    , "Style:"
                    , renderedStyle
                    ]
                }

        in { structure: structure, style: style, poem: poem }

in  generatePoem "The stillness of early morning"

The above prompt chain is a real program in a research programming language named Fall-from-Grace (or “Grace” for short). Specifically, this is implemented in a branch of the language that adds a magic prompt keyword that works like in the above example.

If you run the above example, you might get an output like this:

{
  "structure": {
    "form": "Free verse with a sprinkle of rhyme",
    "linesPerStanza": 4,
    "rhymeScheme": "ABCB",
    "stanzaCount": 5
  },
  "style": {
    "literaryDevices": [
      "imagery",
      "alliteration",
      "personification",
      "enjambment"
    ],
    "tone": "nostalgic",
    "voice": "reflective"
  },
  "poem": "### The Stillness of Early Morning\n\n**I**  \nIn the gentle rise of dawn's embrace,  \nA whisper of winds through sleepy skies,  \nThe world lies suspended in an echo  \nOf yesterday's dreams, reluctantly saying goodbye.\n\n**II**  \nSoft orange light graces fields of dew,  \nCradling tenacious tendrils of the past.  \nMorning breathes upon the waiting world  \nWith promises that this serenity will last.\n\n**III**  \nWaves of silence surge across the meadow,  \nNature's symphony gently cradles rest.  \nA chorus of leaves sings its soft refrain,  \nComforted by morning's tender caress.\n\n**IV**  \nThe silence dips to caress weary trees,  \nWhose branches waltz to whispers soft and slow.  \nEach tendril holds close the morning's intention,  \nBefore the day's demands, the chaos, start to show.\n\n**V**  \nEarly rays dance upon a tranquil sea,  \nA canvas painted through a dreamy haze.  \nTime sits by, savoring the gentle hush,  \nAs the world awakens, stirs, and finally plays."
}

… and if you’re curious what the formatted poem looks like:

The Stillness of Early Morning

I
In the gentle rise of dawn’s embrace,
A whisper of winds through sleepy skies,
The world lies suspended in an echo
Of yesterday’s dreams, reluctantly saying goodbye.

II
Soft orange light graces fields of dew,
Cradling tenacious tendrils of the past.
Morning breathes upon the waiting world
With promises that this serenity will last.

III
Waves of silence surge across the meadow,
Nature’s symphony gently cradles rest.
A chorus of leaves sings its soft refrain,
Comforted by morning’s tender caress.

IV
The silence dips to caress weary trees,
Whose branches waltz to whispers soft and slow.
Each tendril holds close the morning’s intention,
Before the day’s demands, the chaos, start to show.

V
Early rays dance upon a tranquil sea,
A canvas painted through a dreamy haze.
Time sits by, savoring the gentle hush,
As the world awakens, stirs, and finally plays.

Type inference

The sample Grace program hardly specifies any types (mainly the final expected type for the poem: Text). The reason this works is because Grace supports bidirectional type inference, which means that Grace can work backwards from how intermediate results are used to infer their schemas.

I’ll illustrate this with a contrived Grace example:

let numbers = prompt{ text: "Give me two numbers" }

in  { x: numbers.x
    , y: numbers.y
    , sum: numbers.x + numbers.y : Integer
    }

… which might produce an output like this:

$ grace interpret ./numbers.ffg

{ "x": 7, "y": 14, "sum": 21 }

When Grace analyzes this program the type checker works backwards from this expression:

numbers.x + numbers.y : Integer

… and reasons about it like this:

• the addition produces an Integer, therefore numbers.x and numbers.y must also be Integers

• therefore numbers is a record with two fields, x and y, both of which are Integers

  … or using Grace syntax, the inferred type of numbers is: { x: Integer, y: Integer }

• therefore the output of the prompt command must have the same type

… and then Grace generates a JSON schema for the prompt which looks like this:

{ "type": "object",
  "properties": {
    "x": { "type": "integer" },
    "y": { "type": "integer" }
  },
  "required": [ "x", "y" ],
  "additionalProperties": false
}

Of course, you can specify types if you want (and they’re more lightweight than schemas in traditional prompt chaining frameworks). For example:

$ grace repl
>>> prompt{ text: "Give me a first and last name" } : { first: Text, last: Text }
{ "first": "Emily", "last": "Johnson" }
>>> prompt{ text: "Give me a list of names" } : List Text
[ "Alice"
, "Bob"
, "Charlie"
, "Diana"
, "Ethan"
, "Fiona"
, "George"
, "Hannah"
, "Isaac"
, "Jack"
]

However in our original example we don’t need to specify intermediate types because when the type-checker sees this code:

let structure = prompt
        { model: "gpt-4o"
        , text: lines
            [ "Plan the structure of a new poem based on this idea:"
            , ""
            , idea
            , ""
            , "Describe its form, stanza count, lines per stanza, and rhyme scheme."
            ]
        }

let renderedStructure = lines
        [ "- Form: " + structure.form
        , "- Stanzas: " + Real/show (structure.stanzaCount : Integer)
        , "- Lines per stanza: " + Real/show (structure.linesPerStanza : Integer)
        , "- Rhyme scheme: " + structure.rhymeScheme
        ]

… the compiler can reason backwards from how the structure value is used to infer that the JSON schema for the prompt needs to be:

{ "type": "object",
  "properties": {
    "form": { "type": "string" },
    "stanzaCount": { "type": "integer" },
    "linesPerStanza": { "type": "integer" },
    "rhymeScheme": { "type": "string" }
  },
  "required": [
    "form",
    "stanzaCount",
    "linesPerStanza",
    "rhymeScheme"
    ],
  "additionalProperties": false
}

Tool use

Grace also supports generating sum types (a.k.a. tagged unions), and you can imagine using this to subsume traditional tool use frameworks.

For example, consider this Grace program:

let concatSep = https://raw.githubusercontent.com/Gabriella439/grace/refs/heads/main/prelude/text/concatSep.ffg

let call = merge
      { HttpRequest: \x -> "curl " + x.url
      , ShellCommand: \x -> concatSep " " ([ x.executable ] + x.arguments)
      }

in  List/map call (prompt{ text: "Call some tools" })

This doesn’t actually run any tools (I haven’t added any callable tools to my work-in-progress branch yet), but just renders the tool use as a string for now:

$ grace interpret ./tools.ffg

[ "curl https://api.example.com/data", "ls -l -a" ]

However, the idea is that you can model a tool as a sum type with one constructor per callable tool, and in the above example the type checker infers that the sum type representing one tool call is:

< HttpRequest: { url: Text }
| ShellCommand: { executable: Text, arguments: List Text }
>

… so the inferred type of call is:

call : < HttpRequest: …, ShellCommand: … > -> Text

… but since we List/map the call function over the output of the prompt the type checker infers that the prompt needs to generate a List of tool calls:

prompt{ text: "Call some tools" } : List < HttpRequest: …, ShellCommand: … >

… and then Grace does some magic under the hood to convert that type to the equivalent JSON schema.

What’s particularly neat about this example is that the prompt is so incredibly bare (“Call some tools”) because all the information the model needs is present in the schema.

Schema-driven prompting

We can explore this idea of using the schema to drive the prompt instead of prose using an example like this:

prompt{ text: "Generate some characters for a story", model: "gpt-4o" }
  : List
    { "The character's name": Text
    , "The most memorable thing about the character": Text
    , "The character's personal arc": Text
    }

[ { "The character's name": "Aveline Thatcher"
  , "The character's personal arc":
      "Aveline starts as a skeptical journalist who doubts the stories of mythical creatures. Over time, she becomes a firm believer, risking her career to uncover the truth and protect these creatures."
  , "The most memorable thing about the character":
      "The intricate tattoo of a phoenix on her forearm that seems to glow when she discovers hidden truths."
  }
, { "The character's name": "Kelan Frost"
  , "The character's personal arc":
      "A former rogue alchemist who turns hero after he inadvertently creates a dangerous substance. Driven by guilt, Kelan seeks redemption by finding an antidote and saving his village."
  , "The most memorable thing about the character":
      "His iridescent blue eyes that seem to see into one's soul, a side effect of his alchemical experiments."
  }
, { "The character's name": "Luciana Blair"
  , "The character's personal arc":
      "Luciana is a reclusive artist who initially fears the world outside her home. After a mysterious vision rejuvenates her, she sets out on a journey of self-discovery, ultimately finding both her voice and courage."
  , "The most memorable thing about the character":
      "Her ability to paint scenes before they happen, which she attributes to the visions she sees in her dreams."
  }
, { "The character's name": "Ezra Hartman"
  , "The character's personal arc":
      "Once a charismatic but self-centered lawyer, Ezra is confronted with a moral crisis that forces him to reevaluate his values. He chooses a path of integrity, becoming an advocate for justice."
  , "The most memorable thing about the character":
      "His perfectly tailored suits that slowly become more casual, symbolizing his transformation and shifting priorities."
  }
, { "The character's name": "Seraphine Mora"
  , "The character's personal arc":
      "Seraphine is a young music prodigy who loses her hearing after an accident. Battling despair, she learns to embrace a new way of 'hearing' music through vibrations and her other senses."
  , "The most memorable thing about the character":
      "The ethereal way she 'dances' with the music, using her entire body to express each note's emotion."
  }
]

Grace is a superset of JSON and since JSON supports arbitrary field names so does Grace! Field names in Grace support arbitrary capitalization, punctuation, and whitespace as long as you quote them, and we can use the field names to “smuggle” the description of each field into the schema.

Conclusion

Hopefully this gives you some idea of why I’ve begun to think of prompt chaining as a programming languages problem. Type inference is just the beginning and I think it is possible to use a domain-specific programming language not just to simplify the code but to ultimately unlock greater reasoning power.

I’m going to continue to use Grace as a research vehicle for prompt chaining but my LLM-enabled branch of Grace (like Grace itself) is not really intended to be used in production and I created it mainly as a proof-of-concept for where I’d like prompt chaining frameworks to go. If I do end up eventually productionizing this research I will create a proper fork with its own name and the whole works.

by Gabriella Gonzalez (noreply@blogger.com) at May 02, 2025 05:56 PM