diff --git a/CHANGELOG.md b/CHANGELOG.md new file mode 100644 --- /dev/null +++ b/CHANGELOG.md @@ -0,0 +1,5 @@ +# Revision history for comonad-coactions + +## 0.1.0.0 -- 2026-02-08 + +* First version. Released on an unsuspecting world. diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,661 @@ + GNU AFFERO GENERAL PUBLIC LICENSE + Version 3, 19 November 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU Affero General Public License is a free, copyleft license for +software and other kinds of works, specifically designed to ensure +cooperation with the community in the case of network server software. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. 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There are many ways you could offer source, and different +solutions will be better for different programs; see section 13 for the +specific requirements. + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU AGPL, see +. diff --git a/comonad-coactions.cabal b/comonad-coactions.cabal new file mode 100644 --- /dev/null +++ b/comonad-coactions.cabal @@ -0,0 +1,114 @@ +cabal-version: 3.4 +name: comonad-coactions + +-- The package version. +-- See the Haskell package versioning policy (PVP) for standards +-- guiding when and how versions should be incremented. +-- https://pvp.haskell.org +-- PVP summary: +-+------- breaking API changes +-- | | +----- non-breaking API additions +-- | | | +--- code changes with no API change +version: 0.1.0.0 + +synopsis: Coactions of comonads on functors + +description: + This package defines classes for left and right coactions of + comonads on functors. + +license: AGPL-3.0-or-later +license-file: LICENSE +author: noiioiu +maintainer: noiioiu@cocaine.ninja + +homepage: https://codeberg.org/noiioiu/comonad-coactions + +category: Control, + Comonads +build-type: Simple + +extra-doc-files: CHANGELOG.md + +common warnings + ghc-options: -Wall + +source-repository head + type: git + location: ssh://git@codeberg.org/noiioiu/comonad-coactions.git + +library + import: warnings + exposed-modules: Control.Comonad.Coaction, + Control.Comonad.TransformerStack, + Control.Comonad.Coaction.Left, + Control.Comonad.Coaction.Right, + other-modules: Control.Comonad.Coaction.TH + build-depends: base >= 4.20.2 && < 4.21, + comonad >= 5.0.10 && < 5.1, + kan-extensions >= 5.2.8 && < 5.3, + free >= 5.2 && < 5.3, + template-haskell >= 2.22.0 && < 2.23, + adjunctions >= 4.4.4 && < 4.5, + + hs-source-dirs: src + default-language: GHC2021 + +flag examples + description: Build examples + default: False + manual: True + +executable ca + import: warnings + if !flag(examples) + buildable: False + default-language: GHC2021 + hs-source-dirs: examples + main-is: ElementaryCA.hs + build-depends: + comonad-coactions, + base >= 4.20.2 && < 4.21, + comonad >= 5.0.10 && < 5.1, + finite-typelits >= 0.2.1 && < 0.3, + random >= 1.3.1 && < 1.4, + terminal-size >= 0.3.4 && < 0.4, + vector-sized >= 1.6.1 && < 1.7, + +executable life + import: warnings + if !flag(examples) + buildable: False + default-language: GHC2021 + hs-source-dirs: examples + main-is: Life.hs + ghc-options: -threaded -rtsopts -fplugin GHC.TypeLits.KnownNat.Solver + build-depends: + comonad-coactions, + adjunctions >= 4.4.4 && < 4.5, + base >= 4.20.2 && < 4.21, + clock >= 0.8.4 && < 0.9, + comonad >= 5.0.10 && < 5.1, + constraints >= 0.14.4 && < 0.15, + distributive >= 0.6.3 && < 0.7, + finite-typelits >= 0.2.1 && < 0.3, + ghc-typelits-knownnat >= 0.8.2 && < 0.9, + ki >= 1.0.1 && < 1.1, + random >= 1.3.1 && < 1.4, + termbox-tea >= 1.0.0 && < 1.1, + vector-sized >= 1.6.1 && < 1.7, + +test-suite comonad-coactions-test + import: warnings + default-language: GHC2021 + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Main.hs + build-depends: + base, + comonad, + comonad-coactions, + containers, + QuickCheck, + checkers, + tasty, + tasty-quickcheck diff --git a/examples/ElementaryCA.hs b/examples/ElementaryCA.hs new file mode 100644 --- /dev/null +++ b/examples/ElementaryCA.hs @@ -0,0 +1,70 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE LambdaCase #-} +{-# LANGUAGE PatternSynonyms #-} + +module Main where + +import Control.Comonad.Coaction +import Control.Comonad.Identity +import Control.Comonad.Store +import Control.Concurrent +import Control.Monad +import Data.Bits +import Data.Finite +import Data.Vector.Sized qualified as V +import GHC.TypeLits +import System.Console.Terminal.Size +import System.IO +import System.Random + +type Cell = Bool + +pattern Off :: Cell +pattern Off = False + +pattern On :: Cell +pattern On = True + +{-# COMPLETE On, Off #-} + +cellToChar :: Cell -> Char +cellToChar = \case + Off -> ' ' + On -> '█' + +cellsToString :: (Foldable f) => f Cell -> String +cellsToString = foldr ((:) . cellToChar) "" + +pattern Store :: (s -> a) -> s -> Store s a +pattern Store a b = StoreT (Identity a) b + +{-# COMPLETE Store #-} + +rule :: (KnownNat n) => Int -> V.Vector n Cell -> V.Vector n Cell +rule rn = + rextend $ \(Store f i) -> + let i' = getFinite i + nbhd = foldl ((+) . (* 2)) 0 $ fromEnum . f . modulo . (+ i') <$> [-1, 0, 1] + in testBit rn nbhd + +mainLoop :: forall n. Maybe (SNat n) -> Int -> IO () +mainLoop (Just sn) rn = withKnownNat sn $ + do + x <- sequence . V.replicate @n $ randomIO + forever $ go x + where + go x = do + putStrLn $ cellsToString x + threadDelay 25000 + go $ rule rn x +mainLoop Nothing _ = pure () + +main :: IO () +main = do + putStr "Enter rule number: " + hFlush stdout + ruleNumber <- readLn + Just Window {width} <- size + let loop = withSomeSNat width mainLoop + loop ruleNumber diff --git a/examples/Life.hs b/examples/Life.hs new file mode 100644 --- /dev/null +++ b/examples/Life.hs @@ -0,0 +1,186 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE DataKinds #-} +{-# LANGUAGE LambdaCase #-} +{-# LANGUAGE PatternSynonyms #-} +{-# LANGUAGE QualifiedDo #-} +{-# LANGUAGE RecordWildCards #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE ViewPatterns #-} +{-# LANGUAGE NoStarIsType #-} +{-# OPTIONS_GHC -fplugin GHC.TypeLits.KnownNat.Solver -threaded -rtsopts #-} + +module Main (main) where + +import Control.Comonad.Coaction +import Control.Comonad.Coaction.Right qualified as R +import Control.Comonad.Identity hiding ((<@>)) +import Control.Comonad.Store hiding (pos, (<@>)) +import Control.Concurrent +import Control.Monad +import Data.Bifunctor +import Data.Constraint +import Data.Distributive +import Data.Finite +import Data.Foldable +import Data.Functor.Rep +import Data.Vector.Sized qualified as V +import GHC.TypeLits +import Ki qualified +import System.Clock +import System.IO +import System.Random hiding (Finite) +import Termbox.Tea qualified as TB +import Prelude hiding (replicate) + +newtype Array2D (m :: Nat) (n :: Nat) a = Array2D {getArray2D :: V.Vector (m * n) a} + deriving + ( Eq, + Ord, + Show, + Functor, + Foldable, + Traversable + ) + +instance (KnownNat (m * n)) => Distributive (Array2D m n) where + distribute = Array2D . distribute . fmap getArray2D + +instance (KnownNat m, KnownNat n) => Representable (Array2D m n) where + type Rep (Array2D m n) = (Finite m, Finite n) + index Array2D {getArray2D} = index getArray2D . combineProduct + tabulate f = Array2D . tabulate $ f . separateProduct + +replicate :: (KnownNat (m * n)) => a -> Array2D m n a +replicate = Array2D . V.replicate + +imap :: (KnownNat m) => ((Finite m, Finite n) -> a -> b) -> Array2D m n a -> Array2D m n b +imap f = Array2D . V.imap (f . separateProduct) . getArray2D + +type Cell = Bool + +pattern Off :: Cell +pattern Off = False + +pattern On :: Cell +pattern On = True + +{-# COMPLETE On, Off #-} + +cellArray :: (KnownNat m) => Array2D m n Cell -> TB.Image +cellArray = + fold + . imap + ( \(i, j) c -> + if c + then + TB.atRow (fromInteger $ getFinite i) + . TB.atCol (fromInteger $ 2 * getFinite j) + . ap mappend (TB.atCol 1) + $ TB.char '█' + else mempty + ) + +pattern Store :: (s -> a) -> s -> Store s a +pattern Store a b = StoreT (Identity a) b + +{-# COMPLETE Store #-} + +life :: (KnownNat m, KnownNat n, KnownNat (m * n)) => Array2D m n Cell -> Array2D m n Cell +life = rextend $ \(Store grid (i, j)) -> + let s = + sum . fmap (fromEnum . grid . bimap modulo modulo) $ + (,) + <$> fmap (getFinite i +) [-1, 0, 1] + <*> fmap (getFinite j +) [-1, 0, 1] + in s == 3 || (s == 4 && grid (i, j)) + +data SomeBoard where SomeBoard :: (KnownNat m, KnownNat n) => SNat m -> SNat n -> Array2D m n Cell -> SomeBoard + +data LifeState = LifeState + { board :: !SomeBoard, + running :: !Bool, + time :: !TimeSpec, + done :: !Bool, + delay :: !TimeSpec, + drawing :: !(Maybe Cell), + steps :: !Int + } + +snatDict :: SNat n -> Dict (KnownNat n) +snatDict sn = withKnownNat sn Dict + +initialize :: TimeSpec -> TB.Size -> LifeState +initialize time = \TB.Size {width, height} -> + withSomeSNat (fromIntegral $ width `div` 2) $ + withSomeSNat (fromIntegral height) $ + \case + Nothing -> error "Unknown nat" + Just sm -> \case + Nothing -> error "Unknown nat" + Just sn -> case (snatDict sm, snatDict sn) of + (Dict, Dict) -> + LifeState + { board = SomeBoard sm sn $ replicate Off, + running = True, + time, + done = False, + delay = TimeSpec {sec = 0, nsec = 100_000_000}, + drawing = Nothing, + steps = 0 + } + +pollEvent :: MVar TimeSpec -> Maybe (IO TimeSpec) +pollEvent m = Just $ takeMVar m + +handleEvent :: LifeState -> TB.Event TimeSpec -> IO LifeState +handleEvent s@(LifeState {board = SomeBoard (sm :: SNat m) (sn :: SNat n) b, ..}) = + \case + TB.EventKey (TB.KeyChar 'r') -> + do + randomBoard <- sequence $ replicate randomIO + pure $ s {board = SomeBoard sm sn randomBoard, steps = 0} + TB.EventKey (TB.KeyChar 'c') -> pure $ s {board = SomeBoard sm sn $ replicate Off, steps = 0} + TB.EventKey (TB.KeyChar 'q') -> pure $ s {done = True} + TB.EventKey (TB.KeyChar '+') -> pure $ s {delay = max 0 $ delay - TimeSpec {sec = 0, nsec = 20_000_000}} + TB.EventKey (TB.KeyChar '-') -> pure $ s {delay = delay + TimeSpec {sec = 0, nsec = 20_000_000}} + TB.EventKey TB.KeySpace -> pure $ s {running = not running} + TB.EventMouse TB.Mouse {button = TB.LeftClick, pos = TB.Pos {..}} -> + let r = modulo $ fromIntegral row + c = modulo $ fromIntegral $ col `div` 2 + in case drawing of + Nothing -> + let b' = b R.=>> \(Store grid (i, j)) -> if (i, j) == (r, c) then not $ grid (i, j) else grid (i, j) + in pure s {board = SomeBoard sm sn b', drawing = Just $ index b' (r, c)} + Just cell -> + let b' = b R.=>> \(Store grid (i, j)) -> if (i, j) == (r, c) then cell else grid (i, j) + in pure s {board = SomeBoard sm sn b'} + TB.EventMouse TB.Mouse {button = TB.ReleaseClick} -> pure s {drawing = Nothing} + TB.EventUser t -> if t - time >= delay && running then pure s {board = SomeBoard sm sn $ life b, time = t, steps = steps + 1} else pure s + _ -> pure s + +render :: LifeState -> TB.Scene +render = TB.image . (\(SomeBoard _ _ b) -> cellArray b) . board + +main :: IO () +main = do + t0 <- getTime Monotonic + result <- + Ki.scoped $ \scope -> do + timeVar <- newEmptyMVar + Ki.fork_ scope + . forever + $ threadDelay 1000 + >> getTime Monotonic + >>= putMVar timeVar + TB.run + TB.Program + { initialize = initialize t0, + pollEvent = pollEvent timeVar, + handleEvent, + render, + finished = done + } + case result of + Left err -> hPutStrLn stderr $ "Failed to initialize: " ++ show err + Right LifeState {steps} -> putStrLn $ "Ran for " ++ show steps ++ " steps" diff --git a/src/Control/Comonad/Coaction.hs b/src/Control/Comonad/Coaction.hs new file mode 100644 --- /dev/null +++ b/src/Control/Comonad/Coaction.hs @@ -0,0 +1,176 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE LambdaCase #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE UndecidableInstances #-} + +-- | Given a comonad \(W\) on a category \(\mathcal{D}\) with counit \(\varepsilon\) and +-- comultiplication \(\Delta\) and a functor \(F\) from \(\mathcal{C}\) to \(\mathcal{D}\), +-- a left (or outer) comonad coaction of \(W\) on \(F\) is a natural transformation +-- \(\Sigma: F \to W \circ F\) such that the following two laws hold: +-- +-- * \((\varepsilon \circ F) \cdot \Sigma = \mathrm{id}_F\) +-- * \((\Delta \circ F) \cdot \Sigma = (W \circ \Sigma) \cdot \Sigma\) +-- +-- We also say that \(F\) is a left comodule over \(W\). In the case +-- \(\mathcal{C} = \mathcal{D}\), a left comonad comodule is a left comonoid comodule +-- object in the category of endofunctors on \(\mathcal{C}\). +-- +-- Right (or inner) comonad coactions are defined similarly. +module Control.Comonad.Coaction + ( LeftComodule (..), + RightComodule (..), + BiComodule (..), + ComonadTransStack (..), + ) +where + +import Control.Comonad (Comonad (..)) +import Control.Comonad.Density (Density (..)) +import Control.Comonad.Env.Class (ComonadEnv (..)) +import Control.Comonad.Identity (Identity (..)) +import Control.Comonad.Store.Class (ComonadStore (..)) +import Control.Comonad.Traced.Class (ComonadTraced (..)) +import Control.Comonad.Trans.Store (Store, store) +import Control.Comonad.Trans.Traced (Traced, traced) +import Control.Comonad.TransformerStack (ComonadTransStack (..)) +import Control.Monad (liftM2) +import Data.Functor.Compose (Compose (..)) +import Data.Functor.Rep (Representable (..)) +import Data.Functor.Sum (Sum (..)) + +-- | Instances must satisfy the following laws: +-- +-- * @'duplicate' '.' 'lduplicate' = 'fmap' 'lduplicate' '.' 'lduplicate'@ +-- +-- * @'extract' '.' 'lduplicate' = 'id'@ +class (Comonad w, Functor f) => LeftComodule w f where + lduplicate :: + f a -> + -- | left comonad coaction + w (f a) + lduplicate = lextend id + lextend :: (f a -> b) -> f a -> w b + lextend f = fmap f . lduplicate + {-# MINIMAL lduplicate | lextend #-} + +-- | Instances must satisfy the following laws: +-- +-- * @'fmap' 'duplicate' '.' 'rduplicate' = 'rduplicate' '.' 'rduplicate'@ +-- +-- * @'fmap' 'extract' '.' 'lduplicate' = 'id'@ +class (Comonad w, Functor f) => RightComodule w f where + rduplicate :: + f a -> + -- | right comonad coaction + f (w a) + rduplicate = rextend id + rextend :: (w a -> b) -> f a -> f b + rextend f = fmap f . rduplicate + {-# MINIMAL rduplicate | rextend #-} + +-- | Given two comonads r and s, an (r, s) bicomodule is a functor that is a left comodule over r and a right comodule over s, where the two coactions are compatible. +-- Instances must satisfy the following law in addition to the laws for @'LeftComodule'@ and @'RightComodule'@: +-- +-- * @'lduplicate' '.' 'rduplicate' = 'fmap' 'rduplicate' '.' 'lduplicate' = 'biduplicate'@ +class (LeftComodule r f, RightComodule s f) => BiComodule r s f where + biduplicate :: + f a -> + -- | two-sided comonad coaction + r (f (s a)) + biduplicate = lduplicate . rduplicate + +instance {-# INCOHERENT #-} (Comonad w) => LeftComodule Identity w where + lduplicate = Identity + +instance {-# INCOHERENT #-} (Comonad w) => RightComodule Identity w where + rduplicate = fmap Identity + +instance {-# INCOHERENT #-} (Comonad w) => BiComodule Identity Identity w where + biduplicate = Identity . fmap Identity + +instance {-# INCOHERENT #-} (Comonad w, Functor f, LeftComodule w v) => LeftComodule w (Compose v f) where + lduplicate = fmap Compose . lduplicate . getCompose + lextend f = lextend (f . Compose) . getCompose + +instance {-# INCOHERENT #-} (Comonad w, Functor f, RightComodule w v) => RightComodule w (Compose f v) where + rduplicate = Compose . fmap rduplicate . getCompose + rextend f = Compose . fmap (rextend f) . getCompose + +instance {-# INCOHERENT #-} (Comonad s, Comonad t, Functor f, LeftComodule s u, RightComodule t v) => BiComodule s t (Compose u (Compose f v)) + +-- | Proof that @f@ is always a left comodule over @t'Density' f@: +-- +-- * @ 'duplicate' ('lduplicate' w) +-- = 'duplicate' ('Density' 'id' w) +-- = 'Density' ('Density' 'id') w +-- = 'Density' 'lduplicate' w +-- = 'fmap' 'lduplicate' ('Density' 'id' w) +-- = 'fmap' 'lduplicate' ('lduplicate' w)@ +-- +-- * @'extract' ('lduplicate' w) = 'extract' ('Density' 'id' w) = w@ +instance (Functor f) => LeftComodule (Density f) f where + lduplicate = Density id + +instance {-# OVERLAPS #-} (Comonad q, Comonad w, ComonadTransStack w q) => LeftComodule w q where + lduplicate = lowerStack . duplicate + lextend f = lowerStack . extend f + +instance {-# OVERLAPS #-} (Comonad q, Comonad w, ComonadTransStack w q) => RightComodule w q where + rduplicate = lextend lowerStack + rextend f = extend $ f . lowerStack + +instance {-# OVERLAPS #-} (Comonad q, Comonad w, ComonadTransStack w q) => BiComodule w w q + +instance {-# INCOHERENT #-} (ComonadStore s w) => LeftComodule (Store s) w where + lduplicate = liftM2 store (flip peek) pos . duplicate + lextend f = liftM2 store (flip peek) pos . extend f + +-- instance {-# INCOHERENT #-} (ComonadStore s w) => RightComodule (Store s) w where +-- rduplicate = extend $ liftM2 store (flip peek) pos +-- rextend f = extend $ f . liftM2 store (flip peek) pos + +-- instance {-# INCOHERENT #-} (ComonadStore s w) => BiComodule (Store s) (Store s) w + +instance {-# INCOHERENT #-} (ComonadEnv e w) => LeftComodule ((,) e) w where + lduplicate = liftM2 (,) ask extract . duplicate + lextend f = liftM2 (,) ask extract . extend f + +instance {-# INCOHERENT #-} (ComonadEnv e w) => RightComodule ((,) e) w where + rduplicate = extend $ liftM2 (,) ask extract + rextend f = extend $ f . liftM2 (,) ask extract + +instance {-# INCOHERENT #-} (ComonadEnv e w) => BiComodule ((,) e) ((,) e) w + +instance {-# INCOHERENT #-} (ComonadTraced m w, Monoid m) => LeftComodule (Traced m) w where + lduplicate = traced . flip trace . duplicate + lextend f = traced . flip trace . extend f + +instance {-# INCOHERENT #-} (ComonadTraced m w, Monoid m) => RightComodule (Traced m) w where + rduplicate = extend $ traced . flip trace + rextend f = extend $ f . traced . flip trace + +instance {-# INCOHERENT #-} (ComonadTraced m w, Monoid m) => BiComodule (Traced m) (Traced m) w + +instance {-# INCOHERENT #-} (LeftComodule w f, LeftComodule w g) => LeftComodule w (Sum f g) where + lduplicate = \case + InL x -> InL <$> lduplicate x + InR x -> InR <$> lduplicate x + lextend f = \case + InL x -> lextend @w (f . InL) x + InR x -> lextend @w (f . InR) x + +instance {-# INCOHERENT #-} (RightComodule w f, RightComodule w g) => RightComodule w (Sum f g) where + rduplicate = \case + InL x -> InL $ rduplicate x + InR x -> InR $ rduplicate x + rextend f = \case + InL x -> InL $ rextend @w f x + InR x -> InR $ rextend @w f x + +instance {-# INCOHERENT #-} (BiComodule w q f, BiComodule w q g) => BiComodule w q (Sum f g) where + biduplicate = \case + InL x -> InL <$> biduplicate x + InR x -> InR <$> biduplicate x + +instance (Representable f, Rep f ~ s) => RightComodule (Store s) f where + rduplicate = tabulate . store . index diff --git a/src/Control/Comonad/Coaction/Left.hs b/src/Control/Comonad/Coaction/Left.hs new file mode 100644 --- /dev/null +++ b/src/Control/Comonad/Coaction/Left.hs @@ -0,0 +1,35 @@ +-- | Operators for left comonad coactions. +-- This module should be imported qualified. +module Control.Comonad.Coaction.Left + ( (<<=), + (=>>), + (=>=), + (=<=), + ) +where + +import Control.Comonad.Coaction + +infixl 1 =>> + +infixr 1 <<=, =<=, =>= + +-- | @'lextend'@ in operator form. +(<<=) :: (LeftComodule w f) => (f a -> b) -> f a -> w b +(<<=) = lextend +{-# INLINE (<<=) #-} + +-- | @'lextend'@ with arguments swapped. +(=>>) :: (LeftComodule w f) => f a -> (f a -> b) -> w b +(=>>) = flip lextend +{-# INLINE (=>>) #-} + +-- | Left to right Cokleisli arrow scalar multiplication induced by a left comonad coaction. +(=>=) :: (LeftComodule w f) => (f a -> b) -> (w b -> c) -> f a -> c +f =>= g = g . lextend f +{-# INLINE (=>=) #-} + +-- | Right to left Cokleisli arrow scalar multiplication induced by a left comonad coaction. +(=<=) :: (LeftComodule w f) => (w b -> c) -> (f a -> b) -> f a -> c +f =<= g = f . lextend g +{-# INLINE (=<=) #-} diff --git a/src/Control/Comonad/Coaction/Right.hs b/src/Control/Comonad/Coaction/Right.hs new file mode 100644 --- /dev/null +++ b/src/Control/Comonad/Coaction/Right.hs @@ -0,0 +1,37 @@ +{-# LANGUAGE MonoLocalBinds #-} + +-- | Operators for left comonad coactions. +-- This module should be imported qualified. +module Control.Comonad.Coaction.Right + ( (<<=), + (=>>), + (=>=), + (=<=), + ) +where + +import Control.Comonad.Coaction + +infixl 1 =>> + +infixr 1 <<=, =<=, =>= + +-- | @'rextend'@ in operator form. +(<<=) :: (RightComodule w f) => (w a -> b) -> f a -> f b +(<<=) = rextend +{-# INLINE (<<=) #-} + +-- | @'rextend'@ with arguments swapped. +(=>>) :: (RightComodule w f) => f a -> (w a -> b) -> f b +(=>>) = flip rextend +{-# INLINE (=>>) #-} + +-- | Left to right Cokleisli arrow scalar multiplication induced by a right comonad coaction. +(=>=) :: (RightComodule w f) => (w a -> b) -> (f b -> c) -> f a -> c +f =>= g = g . rextend f +{-# INLINE (=>=) #-} + +-- | Right to left Cokleisli arrow scalar multiplication induced by a right comonad coaction. +(=<=) :: (RightComodule w f) => (f b -> c) -> (w a -> b) -> f a -> c +f =<= g = f . rextend g +{-# INLINE (=<=) #-} diff --git a/src/Control/Comonad/Coaction/TH.hs b/src/Control/Comonad/Coaction/TH.hs new file mode 100644 --- /dev/null +++ b/src/Control/Comonad/Coaction/TH.hs @@ -0,0 +1,75 @@ +{-# LANGUAGE LambdaCase #-} +{-# LANGUAGE TemplateHaskellQuotes #-} +{-# LANGUAGE TypeData #-} + +module Control.Comonad.Coaction.TH (mkLowerBy) where + +import Control.Comonad +import Control.Comonad.Trans.Class (ComonadTrans (..)) +import Data.Kind qualified as K +import Language.Haskell.TH + +infixl 5 # + +(#) :: Type -> Type -> Type +(#) = AppT + +(|->|) :: Type -> Type -> Type +a |->| b = ArrowT # a # b + +mkLowerBy :: Q [Dec] +mkLowerBy = + reify ''ComonadTrans + >>= \case + ClassI _ instances -> + do + decs <- + [d| + type data Nat = Z | S Nat + + class (Comonad w, Comonad q) => LowerBy (k :: Nat) (w :: K.Type -> K.Type) (q :: K.Type -> K.Type) | k q -> w where + lowerBy :: q a -> w a + + instance (Comonad w) => LowerBy Z w w where + lowerBy = id + |] + let famName = mkName "Steps" + w <- newName "w" + q <- newName "q" + k <- newName "k" + let famDec = + ClosedTypeFamilyD + ( TypeFamilyHead + famName + [ KindedTV w BndrReq (StarT |->| StarT), + KindedTV q BndrReq (StarT |->| StarT) + ] + (KindSig . ConT $ mkName "Nat") + Nothing + ) + $ TySynEqn Nothing (ConT famName # VarT w # VarT w) (ConT $ mkName "Z") + : ( instances >>= \case + InstanceD _ _ (AppT (ConT _) t) _ -> + [ TySynEqn + Nothing + (ConT famName # VarT w # (t # VarT q)) + (ConT (mkName "S") # (ConT famName # VarT w # VarT q)) + ] + _ -> [] + ) + let inductiveInstances = + instances >>= \case + InstanceD ov ct (AppT (ConT _) t) _ -> + pure $ + InstanceD + ov + (ct ++ [ConT (mkName "LowerBy") # VarT k # VarT w # VarT q, ConT ''Comonad # (t # VarT q)]) + (ConT (mkName "LowerBy") # (ConT (mkName "S") # VarT k) # VarT w # (t # VarT q)) + [ ValD + (VarP $ mkName "lowerBy") + (NormalB $ UInfixE (AppTypeE (VarE $ mkName "lowerBy") (VarT k)) (VarE '(.)) (VarE 'lower)) + [] + ] + _ -> [] + pure $ decs ++ famDec : inductiveInstances + _ -> pure [] diff --git a/src/Control/Comonad/TransformerStack.hs b/src/Control/Comonad/TransformerStack.hs new file mode 100644 --- /dev/null +++ b/src/Control/Comonad/TransformerStack.hs @@ -0,0 +1,36 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE FunctionalDependencies #-} +{-# LANGUAGE TemplateHaskell #-} +{-# LANGUAGE TypeData #-} +{-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE UndecidableInstances #-} + +module Control.Comonad.TransformerStack (ComonadTransStack (..)) where + +import Control.Comonad.Coaction.TH +import Control.Comonad.Trans.Cofree () +import Control.Comonad.Trans.Env () +import Control.Comonad.Trans.Identity () +import Control.Comonad.Trans.Store () +import Control.Comonad.Trans.Traced () + +$mkLowerBy + +-- | All @'ComonadTransStack'@ instances are defined inductively using @'Control.Comonad.Trans.Class.ComonadTrans'@ instances. +-- +-- No laws are given in the documentation for @'Control.Comonad.Trans.Class.ComonadTrans'@, +-- but all instances should satisfy the following laws, dual to the laws for +-- @'Control.Monad.Trans.Class.MonadTrans'@, which state that @'Control.Comonad.Trans.Class.lower'@ is a comonad homomorphism: +-- +-- * @'Control.Comonad.extract' '.' 'Control.Comonad.Trans.Class.lower' = 'Control.Comonad.extract'@ +-- +-- * @'Control.Comonad.duplicate' '.' 'Control.Comonad.Trans.Class.lower' = 'Control.Comonad.Trans.Class.lower' '.' 'fmap' 'Control.Comonad.Trans.Class.lower' . 'Control.Comonad.duplicate'@ +-- +-- It follows by induction that @'lowerStack'@ is a comonad homomorphism. +-- The proofs of the comodule laws may be obtained by looking at the corresponding +-- proofs of the module laws in a mirror. +class (LowerBy (Steps w q) w q) => ComonadTransStack w q where + lowerStack :: forall a. q a -> w a + +instance (LowerBy (Steps w q) w q) => ComonadTransStack w q where + lowerStack = lowerBy @(Steps w q) diff --git a/test/Main.hs b/test/Main.hs new file mode 100644 --- /dev/null +++ b/test/Main.hs @@ -0,0 +1,203 @@ +{-# LANGUAGE AllowAmbiguousTypes #-} +{-# LANGUAGE MonoLocalBinds #-} +{-# LANGUAGE ScopedTypeVariables #-} +{-# OPTIONS_GHC -Wno-orphans #-} +{-# OPTIONS_GHC -Wno-unrecognised-pragmas #-} +{-# OPTIONS_GHC -Wno-unused-top-binds #-} + +module Main (main) where + +import Control.Comonad +import Control.Comonad.Coaction +import Control.Comonad.Store +import Control.Comonad.Traced (TracedT (..)) +import Data.Functor.Compose +import Data.List.NonEmpty qualified as NE +import Data.Monoid (Sum) +import Data.Tree +import Test.QuickCheck +import Test.QuickCheck.Checkers +import Test.Tasty +import Test.Tasty.QuickCheck + +leftcomodule :: + forall w f a. + ( LeftComodule w f, + Arbitrary (f a), + Show (f a), + EqProp (f a), + EqProp (w (w (f a))) + ) => + TestBatch +leftcomodule = + ( "left comodule laws", + [ ("left coidentity", property leftP), + ("coassociativity", property coassocP) + ] + ) + where + leftP :: f a -> Property + coassocP :: f a -> Property + + leftP a = extract (lduplicate @w a) =-= a + coassocP a = duplicate @w (lduplicate a) =-= fmap lduplicate (lduplicate a) + +leftcomodulestore :: + forall w s a. + ( Comonad w, + Arbitrary s, + Arbitrary (w (Fun s a)), + Show s, + EqProp s, + EqProp (w a), + Show (w (Fun s a)), + EqProp (w (w (w a, s))), + ComonadTransStack w (StoreT s w) + ) => + TestBatch +leftcomodulestore = + ( "left comodule laws for StoreT", + [ ("right coidentity", property leftP), + ("associativity", property coassocP) + ] + ) + where + leftP :: w (Fun s a) -> s -> s -> Property + coassocP :: w (Fun s a) -> s -> s -> Property + + leftP a s t = + let x@(StoreT f1 s1) = StoreT (applyFun <$> a) s + StoreT f2 s2 = extract (lduplicate @w x) + in (($ t) <$> f1, s1) =-= (($ t) <$> f2, s2) + coassocP a s t = + let x = StoreT (applyFun <$> a) s + w1 = fmap (\(StoreT f u) -> (($ t) <$> f, u)) <$> duplicate @w (lduplicate x) + w2 = fmap (\(StoreT f u) -> (($ t) <$> f, u)) <$> fmap lduplicate (lduplicate x) + in w1 =-= w2 + +leftcomoduletraced :: + forall w m a. + ( Comonad w, + Arbitrary m, + Arbitrary a, + Monoid m, + EqProp (w a), + Arbitrary (w (Fun m a)), + Show m, + Show (w (Fun m a)), + EqProp (w (w (w a))), + ComonadTransStack w (TracedT m w) + ) => + TestBatch +leftcomoduletraced = + ( "left comodule laws for TracedT", + [ ("right coidentity", property leftP), + ("associativity", property coassocP) + ] + ) + where + leftP :: w (Fun m a) -> m -> Property + coassocP :: w (Fun m a) -> m -> Property + + leftP a t = + let x@(TracedT f1) = TracedT (applyFun <$> a) + TracedT f2 = extract (lduplicate @w x) + in (($ t) <$> f1) =-= (($ t) <$> f2) + coassocP a t = + let x = TracedT (applyFun <$> a) + w1 = fmap (\(TracedT f) -> ($ t) <$> f) <$> duplicate @w (lduplicate x) + w2 = fmap (\(TracedT f) -> ($ t) <$> f) <$> fmap lduplicate (lduplicate x) + in w1 =-= w2 + +rightcomodule :: + forall w f a. + ( RightComodule w f, + EqProp (f a), + EqProp (f (w (w a))), + Arbitrary (f a), + Show (f a) + ) => + TestBatch +rightcomodule = + ( "right comodule laws", + [ ("right coidentity", property rightP), + ("coassociativity", property coassocP) + ] + ) + where + rightP :: f a -> Property + coassocP :: f a -> Property + + rightP a = fmap extract (rduplicate @w a) =-= a + coassocP a = fmap duplicate (rduplicate @w a) =-= fmap rduplicate (rduplicate a) + +rightcomodulestore :: + forall w s a. + ( Comonad w, + Arbitrary s, + Arbitrary (w (Fun s a)), + Show s, + Show (w (Fun s a)), + EqProp s, + EqProp (w a), + EqProp (w (w (w a))), + ComonadTransStack w (StoreT s w) + ) => + TestBatch +rightcomodulestore = + ( "right comodule laws for StoreT", + [ ("right coidentity", property rightP), + ("associativity", property coassocP) + ] + ) + where + rightP :: w (Fun s a) -> s -> s -> Property + coassocP :: w (Fun s a) -> s -> s -> Property + + rightP a s t = + let x@(StoreT f1 s1) = StoreT (applyFun <$> a) s + StoreT f2 s2 = fmap extract (rduplicate @w x) + in (($ t) <$> f1, s1) =-= (($ t) <$> f2, s2) + coassocP a s t = + let x = StoreT (applyFun <$> a) s + StoreT f1 s1 = fmap duplicate (rduplicate @w x) + StoreT f2 s2 = fmap rduplicate (rduplicate x) + in (($ t) <$> f1, s1) =-= (($ t) <$> f2, s2) + +bicomodule :: + forall s t f a. + ( BiComodule s t f, + Arbitrary a, + EqProp (s (f (t a))), + Arbitrary (f a), + Show (f a) + ) => + TestBatch +bicomodule = + ( "bicomodule laws", + [ ("coassociativity 1", property assoc1P), + ("coassociativity 2", property assoc2P) + ] + ) + where + assoc1P :: f a -> Property + assoc2P :: f a -> Property + + assoc1P a = biduplicate @s @t a =-= lduplicate (rduplicate a) + assoc2P a = biduplicate @s @t a =-= fmap rduplicate (lduplicate a) + +instance (EqProp a) => EqProp (Tree a) + +main :: IO () +main = + defaultMain + ( testGroup "monad action laws" $ + uncurry testProperties + <$> [ leftcomodule @NE.NonEmpty @(Compose NE.NonEmpty Maybe) @Int, + rightcomodule @NE.NonEmpty @(Compose Maybe NE.NonEmpty) @Int, + rightcomodulestore @NE.NonEmpty @Bool @Int, + rightcomodulestore @Tree @Char @Int, + leftcomodulestore @Tree @Char @Char, + leftcomoduletraced @Tree @(Sum Int) @Char + ] + )