diff --git a/.ghci b/.ghci deleted file mode 100644 --- a/.ghci +++ /dev/null @@ -1,1 +0,0 @@ -:set -isrc -idist/build/autogen -optP-include -optPdist/build/autogen/cabal_macros.h diff --git a/.gitignore b/.gitignore --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,5 @@ dist +dist-newstyle docs wiki TAGS @@ -13,3 +14,19 @@ *# .cabal-sandbox/ cabal.sandbox.config +.stack-work/ +cabal-dev +*.chi +*.chs.h +*.dyn_o +*.dyn_hi +.hpc +.hsenv +*.prof +*.aux +*.hp +*.eventlog +cabal.project.local +cabal.project.local~ +.HTF/ +.ghc.environment.* diff --git a/.hlint.yaml b/.hlint.yaml new file mode 100644 --- /dev/null +++ b/.hlint.yaml @@ -0,0 +1,15 @@ +- arguments: [--cpp-define=HLINT, --cpp-ansi, --cpp-include=include] + +- fixity: "infixr 5 :<" + +# This affects performance +- ignore: {name: Redundant lambda} + +# This is not valid for improve +- ignore: {name: Eta reduce} + +# DeriveDataTypable noise +- ignore: {name: Unused LANGUAGE pragma} + +# They are clearer in places +- ignore: {name: Avoid lambda} diff --git a/.travis.yml b/.travis.yml deleted file mode 100644 --- a/.travis.yml +++ /dev/null @@ -1,8 +0,0 @@ -language: haskell -notifications: - irc: - channels: - - "irc.freenode.org#haskell-lens" - skip_join: true - template: - - "\x0313free\x03/\x0306%{branch}\x03 \x0314%{commit}\x03 %{build_url} %{message}" diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown --- a/CHANGELOG.markdown +++ b/CHANGELOG.markdown @@ -1,3 +1,137 @@ +5.2 [2023.03.12] +---------------- +* Drop support for GHC 7.10 and earlier. +* Drop redundant `Monad` constraints on many functions and instances. These + constraints were only present for compatibility with pre-7.10 versions of + GHC, which `free` no longer supports. +* Add `Eq`, `Eq1`, `Ord`, `Ord1`, and `Foldable` instances for `Ap` in + `Control.Applicative.Free`. +* Switch out `bifunctors` dependency for `bifunctor-classes-compat`. + +5.1.10 [2022.11.30] +------------------- +* Add a `MonadFail` instance for `FT`. + +5.1.9 [2022.06.26] +------------------ +* Simplify the `Eq` and `Ord` instances for `FT` to avoid the use of + overlapping instances. + +5.1.8 [2022.05.07] +------------------ +* Generalize the `Monad` constraint in the type signatures for + `hoistFreeT` in `Control.Monad.Trans.Free` and `Control.Monad.Trans.Free.Ap` + to a `Functor` constraint. +* Allow building with `transformers-0.6.*` and `mtl-2.3.*`. + +5.1.7 [2021.04.30] +------------------ +* Enable `FlexibleContexts` in `Control.Monad.Trans.Free.Church` to allow + building with GHC 9.2. + +5.1.6 [2020.12.31] +------------------ +* Explicitly mark modules as `Safe`. + +5.1.5 [2020.12.16] +------------------ +* Move `indexed-traversable` (`FunctorWithIndex` etc) instances from `lens`. + +5.1.4 [2020.10.01] +------------------ +* Allow building with `template-haskell-2.17.0.0` (GHC 9.0). + +5.1.3 [2019.11.26] +------------------ +* Allow building with `template-haskell-2.16` (GHC 8.10). +* Add `Eq{1,2}`, `Ord{1,2}`, `Read{1,2}`, and `Show{1,2}` instances for + `CofreeF`. + +5.1.2 [2019.08.27] +------------------ +* Implement more performant versions of `some` and `many` in the `Alternative` + instance for the final `Alt` encoding. + +5.1.1 [2019.05.02] +------------------ +* Allow building with `base-4.13` (GHC 8.8). + +5.1 [2018.07.03] +---------------- +* Generalize the type of `_Free`. +* Allow building with `containers-0.6`. +* Avoid incurring some dependencies when using recent GHCs. + +5.0.2 [2018.04.25] +------------------ +* Add `Generic` and `Generic1` instances where possible. + +5.0.1 [2018.03.07] +------------------ +* Fix the build on old GHCs with `transformers-0.4`. + +5 [2018.01.28] +-------------- +* Add a `Semigroup` instance for `IterT`. +* Add `MonadFail` instances for `IterT` and `FreeT`. +* Add a `Comonad` instance for the free `Applicative`, `Ap`. +* Add `Control.Monad.Free.Ap` and `Control.Monad.Trans.Free.Ap` modules, based + on the "Applicative Effects in Free Monads" series of articles by Will + Fancher. +* Derive `Data` instances for `Free` and `Cofree`. +* `Control.Monad.Free.TH` now properly supports `template-haskell-2.11.0.0`. In + particular, it now supports `GadtC` and `RecGadtC`, which are new + `template-haskell` forms for representing GADTs. +* Add `telescoped_`, `shoots`, and `leaves` to `Control.Comonad.Cofree` +* Add the `Control.Applicative.Free.Fast` module, based on Dave Menendez's + article "Free Applicative Functors in Haskell" +* Add `foldFreeT` to `Control.Monad.Trans.Free` +* Improve the `foldMap` and `cutoff` functions for + `Control.Monad.Free.Church.F`, and add a `Traversable` +* Add a `MonadBase` instance for `FreeT` +* Add a performance test comparing Free and Church interpreters +* The use of `prelude-extras` has been removed. `free` now uses the + `Data.Functor.Classes` module to give `free`'s datatypes instances of `Eq1`, + `Ord1`, `Read1`, and `Show1`. Their `Eq`, `Ord`, `Read`, and `Show` instances + have also been modified to incorporate these classes. For example, what + previously existed as: + + ```haskell + instance (Eq (f (Free f a)), Eq a) => Eq (Free f a) where + ``` + + has now been changed to: + + ```haskell + instance (Eq1 f, Eq a) => Eq (Free f a) where + ``` +* Remove redundant `Functor` constraints from `Control.Alternative.Free` + +4.12.4 +------ +* Removed a number of spurious class constraints. +* Support GHC 8 + +4.12.3 +------ +* Support `comonad` 5 + +4.12.2 +------ +* Add instances for `ExceptT`: like `ErrorT`, but without an `Error` constraint. +* Support `containers` +* Support `transformers` 0.5 + + +4.12.1 +------ +* Support GHC 7.4 + +4.12 +---- +* Add instances of `MonadCatch` and `MonadThrow` from `exceptions` to `FT`, `FreeT` and `IterT`. +* `semigroupoids` 5, `profunctors` 5, and `bifunctors` 5 support. + 4.11 ----- * Pass Monad[FreeT].fail into underlying monad diff --git a/HLint.hs b/HLint.hs deleted file mode 100644 --- a/HLint.hs +++ /dev/null @@ -1,15 +0,0 @@ -import "hint" HLint.HLint - -infixr 5 :< - --- This affects performance -ignore "Redundant lambda" - --- This is not valid for improve -ignore "Eta reduce" - --- DeriveDataTypable noise -ignore "Unused LANGUAGE pragma" - --- They are clearer in places -ignore "Avoid lambda" diff --git a/README.markdown b/README.markdown --- a/README.markdown +++ b/README.markdown @@ -1,7 +1,7 @@ free ==== -[![Build Status](https://secure.travis-ci.org/ekmett/free.png?branch=master)](http://travis-ci.org/ekmett/free) +[![Hackage](https://img.shields.io/hackage/v/free.svg)](https://hackage.haskell.org/package/free) [![Build Status](https://github.com/ekmett/free/workflows/Haskell-CI/badge.svg)](https://github.com/ekmett/free/actions?query=workflow%3AHaskell-CI) This package provides a common definitions for working with free monads, free applicatives, and cofree comonads in Haskell. diff --git a/doc/proof/Control/Comonad/Trans/Cofree/instance-Applicative-CofreeT.md b/doc/proof/Control/Comonad/Trans/Cofree/instance-Applicative-CofreeT.md --- a/doc/proof/Control/Comonad/Trans/Cofree/instance-Applicative-CofreeT.md +++ b/doc/proof/Control/Comonad/Trans/Cofree/instance-Applicative-CofreeT.md @@ -200,7 +200,7 @@ . ≡ (.) ``` -By repeteadly applying the Applicative laws for the underlying functor, we +By repeatedly applying the Applicative laws for the underlying functor, we get: ```haskell @@ -288,7 +288,7 @@ $W ≡ ($ star(C w)) ``` -By repeteadly applying composition law for w, we get: +By repeatedly applying composition law for w, we get: ```haskell diff --git a/doc/proof/Control/Comonad/Trans/Cofree/instance-Monad-CofreeT.md b/doc/proof/Control/Comonad/Trans/Cofree/instance-Monad-CofreeT.md --- a/doc/proof/Control/Comonad/Trans/Cofree/instance-Monad-CofreeT.md +++ b/doc/proof/Control/Comonad/Trans/Cofree/instance-Monad-CofreeT.md @@ -20,7 +20,7 @@ This definition is equivalent to that of the Cofree module if 'w' is identity. -The tokens `CofreeT` and `runCofreeT` are abreviated as `C` and `unC`, +The tokens `CofreeT` and `runCofreeT` are abbreviated as `C` and `unC`, respectively, for readability. ## Left identity diff --git a/examples/Cabbage.lhs b/examples/Cabbage.lhs --- a/examples/Cabbage.lhs +++ b/examples/Cabbage.lhs @@ -1,7 +1,6 @@ > {-# LANGUAGE ViewPatterns #-} > module Cabbage where - -> import Control.Applicative + > import Control.Monad > import Control.Monad.State > import Control.Monad.Trans.Iter @@ -9,23 +8,23 @@ > import Data.Functor.Identity > import Data.Maybe > import Data.Tuple -> import Data.List +> import Data.List (inits, tails) Consider the following problem: -A farmer must cross a river with a wolf, a sheep and a cabbage. -He owns a boat, which can only carry himself and one other item. +A farmer must cross a river with a wolf, a sheep and a cabbage. +He owns a boat, which can only carry himself and one other item. The sheep must not be left alone with the wolf, or with the cabbage: -if that happened, one of them would eat the other. +if that happened, one of them would eat the other. > data Item = Wolf | Sheep | Cabbage | Farmer deriving (Ord, Show, Eq) -> +> > eats :: Item -> Item -> Bool > Sheep `eats` Cabbage = True > Wolf `eats` Sheep = True > _ `eats` _ = False -The problem can be represented as the set of items on each side of the river. +The problem can be represented as the set of items on each side of the river. > type Situation = ([Item],[Item]) @@ -35,7 +34,7 @@ First, some helper functions to extract single elements from lists, leaving the rest intact: -> plusTailOf :: [a] -> [a] -> (Maybe a, [a]) +> plusTailOf :: [a] -> [a] -> (Maybe a, [a]) > a `plusTailOf` b = (listToMaybe b, a ++ drop 1 b) > singleOut1 :: (a -> Bool) -> [a] -> (Maybe a,[a]) @@ -43,7 +42,7 @@ @ *Cabbage> singleOut1 (== Sheep) [Wolf, Sheep, Cabbage] -[(Just Wolf,[Sheep,Cabbage]),(Just Sheep,[Wolf,Cabbage]),(Just Cabbage,[Wolf,Sheep]),(Nothing,[Wolf,Sheep,Cabbage])] +(Just Sheep,[Wolf,Cabbage]) @ > singleOutAll :: [a] -> [(Maybe a,[a])] @@ -61,11 +60,11 @@ > move :: Situation -> [Situation] > move = move2 -> where +> where > move2 (singleOut1 (== Farmer) -> (Just Farmer,as), bs) = move1 as bs > move2 (bs, singleOut1 (== Farmer) -> (Just Farmer,as)) = map swap $ move1 as bs > move2 _ = [] -> +> > move1 as bs = [(as', [Farmer] ++ maybeToList b ++ bs) | > (b, as') <- singleOutAll as, > and [not $ x `eats` y | x <- as', y <- as']] @@ -74,15 +73,15 @@ *Cabbage> move initial [([Wolf,Cabbage],[Farmer,Sheep])] @ - + When the starting side becomes empty, the farmer succeeds. > success :: Situation -> Bool > success ([],_) = True > success _ = False -A straightforward implementation to solve the problem could use the -list monad, trying all possible solutions and +A straightforward implementation to solve the problem could use the +list monad, trying all possible solutions and > solution1 :: Situation > solution1 = head $ solutions' initial @@ -96,8 +95,8 @@ To guarantee termination, we can use the 'Iter' monad with its MonadPlus instance. As long as one of the possible execution paths finds a solution, the program -will terminate: the solution is looked for _in breadth_. - +will terminate: the solution is looked for _in breadth_. + > solution2 :: Iter Situation > solution2 = solution' initial > where diff --git a/examples/LICENSE b/examples/LICENSE new file mode 100644 --- /dev/null +++ b/examples/LICENSE @@ -0,0 +1,30 @@ +Copyright 2008-2013 Edward Kmett + +All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions +are met: + +1. Redistributions of source code must retain the above copyright + notice, this list of conditions and the following disclaimer. + +2. Redistributions in binary form must reproduce the above copyright + notice, this list of conditions and the following disclaimer in the + documentation and/or other materials provided with the distribution. + +3. Neither the name of the author nor the names of his contributors + may be used to endorse or promote products derived from this software + without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``AS IS'' AND ANY EXPRESS OR +IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED +WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE +DISCLAIMED. IN NO EVENT SHALL THE AUTHORS OR CONTRIBUTORS BE LIABLE FOR +ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, +STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN +ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +POSSIBILITY OF SUCH DAMAGE. diff --git a/examples/MandelbrotIter.lhs b/examples/MandelbrotIter.lhs --- a/examples/MandelbrotIter.lhs +++ b/examples/MandelbrotIter.lhs @@ -1,18 +1,17 @@ -Compiling to an executable file with the @-O2@ optimization level is recomended. +Compiling to an executable file with the @-O2@ optimization level is recommended. For example: @ghc -o 'mandelbrot_iter' -O2 MandelbrotIter.lhs ; ./mandelbrot_iter@ > {-# LANGUAGE PackageImports #-} +> module Main where -> import Control.Arrow +> import Control.Arrow hiding (loop) +> import Control.Monad.IO.Class (MonadIO(..)) > import Control.Monad.Trans.Iter -> import "mtl" Control.Monad.Reader -> import "mtl" Control.Monad.List -> import "mtl" Control.Monad.Identity -> import Control.Monad.IO.Class +> import "mtl" Control.Monad.Reader (ReaderT, runReaderT, asks) > import Data.Complex > import Graphics.HGL (runGraphics, Window, withPen, -> line, RGB (RGB), RedrawMode (Unbuffered, DoubleBuffered), openWindowEx, +> line, RGB (RGB), RedrawMode (DoubleBuffered), openWindowEx, > drawInWindow, mkPen, Style (Solid)) Some fractals can be defined by infinite sequences of complex numbers. For example, @@ -20,11 +19,11 @@ the following sequence is generated for each point @c@ in the complex plane: @ -z₀ = c +z₀ = c -z₁ = z₀² + c +z₁ = z₀² + c -z₂ = z₁² + c +z₂ = z₁² + c … @ @@ -96,7 +95,7 @@ Drawing a point is equivalent to drawing a line of length one. > drawPoint :: RGB -> (Int,Int) -> FractalM () -> drawPoint color p@(x,y) = do +> drawPoint color (x,y) = do > w <- asks window > let point = line (x,y) (x+1, y+1) > liftIO $ drawInWindow w $ mkPen Solid 1 color (flip withPen point) @@ -133,6 +132,6 @@ > runGraphics $ do > w <- openWindowEx "Mandelbrot" Nothing (windowWidth, windowHeight) DoubleBuffered (Just 1) > let canvas = Canvas windowWidth windowHeight w -> runFractalM' 100 canvas drawMandelbrot +> _ <- runFractalM' 100 canvas drawMandelbrot > putStrLn $ "Fin" diff --git a/examples/NewtonCoiter.lhs b/examples/NewtonCoiter.lhs --- a/examples/NewtonCoiter.lhs +++ b/examples/NewtonCoiter.lhs @@ -5,10 +5,10 @@ to find zeroes of a function is one such algorithm. > {-# LANGUAGE FlexibleInstances, MultiParamTypeClasses, UndecidableInstances #-} +> module Main where > import Control.Comonad.Trans.Coiter > import Control.Comonad.Env -> import Control.Applicative > import Data.Foldable (toList, find) > data Function = Function { @@ -62,7 +62,8 @@ > estimateError :: Solution Double -> Result > estimateError s = -> let a:a':_ = toList s in +> let (a, s') = extract $ runCoiterT s in +> let a' = extract s' in > let f = asks function s in > Result { value = a, > xerror = abs $ a - a', @@ -75,9 +76,9 @@ > estimateOutlook :: Int -> Solution Result -> Outlook > estimateOutlook sampleSize solution = > let sample = map ferror $ take sampleSize $ tail $ toList solution in -> let result = extract solution in -> Outlook { result = result, -> progress = ferror result > minimum sample } +> let result' = extract solution in +> Outlook { result = result', +> progress = ferror result' > minimum sample } To compute the square root of @c@, we solve the equation @x*x - c = 0@. We will stop whenever the accuracy of the result doesn't improve in the next 5 steps. diff --git a/examples/PerfTH.hs b/examples/PerfTH.hs new file mode 100644 --- /dev/null +++ b/examples/PerfTH.hs @@ -0,0 +1,122 @@ +{-# LANGUAGE GADTs #-} +{-# LANGUAGE TemplateHaskell #-} +{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE KindSignatures #-} +{-# LANGUAGE ScopedTypeVariables #-} +module Main where + +import System.CPUTime.Rdtsc +import System.IO.Unsafe +import Data.IORef +import Data.Word +import Control.Monad +import Control.Monad.IO.Class (MonadIO(..)) +import qualified Control.Monad.Fail as Fail (MonadFail) +import Control.Monad.Free +import Control.Monad.Free.TH +import qualified Control.Monad.Free.Church as Church +import Control.Monad.Trans.State.Strict +import Text.Printf + +-- | A data type representing basic commands for our performance-testing eDSL. +data PerfF next where + Output :: String -> next -> PerfF next + Input :: (Show a, Read a) => (a -> next) -> PerfF next + +-- | Unfortunately this Functor instance cannot yet be derived +-- automatically by GHC. +instance Functor PerfF where + fmap f (Output s x) = Output s (f x) + fmap f (Input g) = Input (f . g) + +makeFreeCon 'Output +makeFreeCon 'Input + +type PerfCnt = Word64 + +-- | Unsafe state variable: base CPU cycles +{-# NOINLINE g_base_counter #-} +g_base_counter :: IORef PerfCnt +g_base_counter = unsafePerformIO $ do + rdtsc >>= newIORef + +-- | Prints number of CPU cycles since last call +g_print_time_since_prev_call :: (MonadIO m) => m () +g_print_time_since_prev_call = liftIO $ do + cb <- readIORef g_base_counter + c <- rdtsc + writeIORef g_base_counter c + putStr $ printf "\r%-10s" (show $ c - cb) + +-- | Free-based interpreter +runPerfFree :: (MonadIO m) => [String] -> Free PerfF () -> m () +runPerfFree [] _ = return () +runPerfFree (s:ss) x = case x of + Free (Output _o next) -> do + runPerfFree (s:ss) next + Free (Input next) -> do + g_print_time_since_prev_call + runPerfFree ss (next (read s)) + Pure a -> do + return a + +-- | Church-based interpreter +runPerfF :: (Fail.MonadFail m, MonadIO m) => [String] -> Church.F PerfF () -> m () +runPerfF [] _ = return () +runPerfF ss0 f = + fst `liftM` do + flip runStateT ss0 $ Church.iterM go f where + go (Output _o next) = do + next + go (Input next) = do + g_print_time_since_prev_call + (s:ss) <- get + put ss + next (read s) + +-- | Test input is the same for all cases +test_input :: [String] +test_input = [show i | i<-([1..9999] ++ [0 :: Int])] + +-- | Tail-recursive program +test_tail :: (MonadFree PerfF m) => m () +test_tail = do + output "Enter something" + (n :: Int) <- input + output $ "Just entered: " ++ (show n) + when (n > 0) $ do + test_tail + +run_tail_free,run_tail_f :: IO () +run_tail_free = runPerfFree test_input test_tail +run_tail_f = runPerfF test_input test_tail + + +-- | Deep-recursive program +test_loop :: (MonadFree PerfF m) => m () +test_loop = do + output "Enter something" + (n :: Int) <- input + when (n > 0) $ do + test_loop + output $ "Just entered: " ++ (show n) + +run_loop_free,run_loop_f :: IO () +run_loop_free = runPerfFree test_input test_loop +run_loop_f = runPerfF test_input test_loop + +main :: IO () +main = do + putStr $ unlines [ + "Running two kinds of FreeMonad programs against two kinds of interpreters.", + "Counters represent approx. number of CPU ticks per program iteration" ] + putStrLn ">> (1/4) Tail-recursive program/Free interpreter" + run_tail_free + putStrLn "\n>> (2/4) Tail-recursive program/Church interpreter" + run_tail_f + putStrLn "\n>> (3/4) Deep-recursive program/Free interpreter (a slower one)" + run_loop_free + putStrLn "\n>> (4/4) Deep-recursive program/Church interpreter" + run_loop_f + putStrLn "\n" + diff --git a/examples/RetryTH.hs b/examples/RetryTH.hs --- a/examples/RetryTH.hs +++ b/examples/RetryTH.hs @@ -1,12 +1,15 @@ {-# LANGUAGE GADTs #-} +{-# LANGUAGE KindSignatures #-} {-# LANGUAGE TemplateHaskell #-} {-# LANGUAGE FlexibleContexts #-} module Main where import Control.Monad +import Control.Monad.Fail as Fail import Control.Monad.Free import Control.Monad.Free.TH import Control.Monad.IO.Class +import Control.Monad.Trans.Instances () import Control.Monad.Trans.Maybe import qualified Data.Foldable as F import Text.Read (readMaybe) @@ -52,10 +55,10 @@ -- retry :: MonadFree RetryF m => m a -- | We can run a retriable program in any MonadIO. -runRetry :: MonadIO m => Retry a -> m a +runRetry :: (MonadFail m, MonadIO m) => Retry a -> m a runRetry = iterM run where - run :: MonadIO m => RetryF (m a) -> m a + run :: (MonadFail m, MonadIO m) => RetryF (m a) -> m a run (Output s next) = do liftIO $ putStrLn s @@ -65,7 +68,7 @@ s <- liftIO getLine case readMaybe s of Just x -> next x - Nothing -> fail "invalid input" + Nothing -> Fail.fail "invalid input" run (WithRetry block next) = do -- Here we use @@ -75,7 +78,7 @@ Just x <- runMaybeT . F.msum $ repeat (runRetry block) next x - run Retry = fail "forced retry" + run Retry = Fail.fail "forced retry" -- | Sample program. test :: Retry () @@ -91,4 +94,3 @@ main :: IO () main = runRetry test - diff --git a/examples/Teletype.lhs b/examples/Teletype.lhs --- a/examples/Teletype.lhs +++ b/examples/Teletype.lhs @@ -1,12 +1,12 @@ > {-# LANGUAGE DeriveFunctor, TemplateHaskell, FlexibleContexts #-} -- +> module Main where +> import qualified Control.Exception as E (catch) > import Control.Monad (mfilter) > import Control.Monad.Loops (unfoldM) > import Control.Monad.Free (liftF, Free, iterM, MonadFree) > import Control.Monad.Free.TH (makeFree) -> import Control.Applicative ((<$>)) > import System.IO (isEOF) -> import Control.Exception (catch) > import System.IO.Error (ioeGetErrorString) > import System.Exit (exitSuccess) @@ -61,7 +61,7 @@ > run (ReadOrEOF eof f) = isEOF >>= \b -> if b then eof > else getChar >>= f > -> run (ReadOrError ferror f) = catch (getChar >>= f) (ferror . ioeGetErrorString) +> run (ReadOrError ferror f) = E.catch (getChar >>= f) (ferror . ioeGetErrorString) > run (NL rest) = putChar '\n' >> rest > run (rest :\^^ str) = putStr str >> rest > run ((:%) rest format tokens) = ttFormat format tokens >> rest diff --git a/examples/ValidationForm.hs b/examples/ValidationForm.hs --- a/examples/ValidationForm.hs +++ b/examples/ValidationForm.hs @@ -1,10 +1,10 @@ module Main where -import Control.Applicative import Control.Applicative.Free -import Control.Monad.State +import Control.Monad.IO.Class (MonadIO(..)) +import Control.Monad.Trans.State -import Data.Monoid +import Data.Monoid (Sum(..)) import Text.Read (readEither) import Text.Printf @@ -66,8 +66,9 @@ -- Repeats field input until it passes validation. -- Show help message on empty input. input :: Form a -> IO a -input m = evalStateT (runAp inputField m) (1 :: Integer) +input m = evalStateT (runAp inputField m) 1 where + inputField :: Field a -> StateT Int IO a inputField f@(Field n g h) = do i <- get -- get field input with prompt diff --git a/examples/free-examples.cabal b/examples/free-examples.cabal new file mode 100644 --- /dev/null +++ b/examples/free-examples.cabal @@ -0,0 +1,109 @@ +name: free-examples +category: Control, Monads +version: 0.1 +license: BSD3 +cabal-version: 1.18 +license-file: LICENSE +author: Edward A. Kmett +maintainer: Edward A. Kmett +stability: provisional +homepage: http://github.com/ekmett/free/ +bug-reports: http://github.com/ekmett/free/issues +copyright: Copyright (C) 2008-2015 Edward A. Kmett +tested-with: GHC == 8.0.2 + , GHC == 8.2.2 + , GHC == 8.4.4 + , GHC == 8.6.5 + , GHC == 8.8.4 + , GHC == 8.10.7 + , GHC == 9.0.2 + , GHC == 9.2.6 + , GHC == 9.4.4 + , GHC == 9.6.1 +synopsis: Monads for free +description: Examples projects using @free@ +build-type: Simple + +source-repository head + type: git + location: git://github.com/ekmett/free.git + +flag mandelbrot-iter + default: True + +library + hs-source-dirs: . + default-language: Haskell2010 + exposed-modules: Cabbage + ghc-options: -Wall + build-depends: + base >= 4.9 && < 5, + free, + mtl >= 2.0.1 && < 2.4, + transformers >= 0.2 && < 0.7 + +executable free-mandelbrot-iter + if !flag(mandelbrot-iter) + buildable: False + hs-source-dirs: . + default-language: Haskell2010 + main-is: MandelbrotIter.lhs + ghc-options: -Wall + build-depends: + base >= 4.9 && < 5, + free, + HGL >= 3.2.3.2, + mtl >= 2.0.1 && < 2.4, + transformers >= 0.2 && < 0.7 + +executable free-newton-coiter + hs-source-dirs: . + default-language: Haskell2010 + main-is: NewtonCoiter.lhs + ghc-options: -Wall + build-depends: + base >= 4.9 && < 5, + comonad >= 4 && < 6, + free + +executable free-perf-th + hs-source-dirs: . + default-language: Haskell2010 + main-is: PerfTH.hs + ghc-options: -Wall + build-depends: + base >= 4.9 && < 5, + free, + rdtsc, + transformers >= 0.2 && < 0.7 + +executable free-retry-th + hs-source-dirs: . + default-language: Haskell2010 + main-is: RetryTH.hs + ghc-options: -Wall -fno-warn-orphans + build-depends: + base >= 4.9 && < 5, + free, + transformers >= 0.2 && < 0.7, + transformers-compat >= 0.6.4 && < 0.8 + +executable free-teletype + hs-source-dirs: . + default-language: Haskell2010 + main-is: Teletype.lhs + ghc-options: -Wall + build-depends: + base >= 4.9 && < 5, + free, + monad-loops + +executable free-validation-form + hs-source-dirs: . + default-language: Haskell2010 + main-is: ValidationForm.hs + ghc-options: -Wall + build-depends: + base >= 4.9 && < 5, + free, + transformers >= 0.2 && < 0.7 diff --git a/free.cabal b/free.cabal --- a/free.cabal +++ b/free.cabal @@ -1,15 +1,25 @@ name: free category: Control, Monads -version: 4.11 +version: 5.2 license: BSD3 -cabal-version: >= 1.10 +cabal-version: 1.18 license-file: LICENSE author: Edward A. Kmett maintainer: Edward A. Kmett stability: provisional homepage: http://github.com/ekmett/free/ bug-reports: http://github.com/ekmett/free/issues -copyright: Copyright (C) 2008-2013 Edward A. Kmett +copyright: Copyright (C) 2008-2015 Edward A. Kmett +tested-with: GHC == 8.0.2 + , GHC == 8.2.2 + , GHC == 8.4.4 + , GHC == 8.6.5 + , GHC == 8.8.4 + , GHC == 8.10.7 + , GHC == 9.0.2 + , GHC == 9.2.6 + , GHC == 9.4.4 + , GHC == 9.6.1 synopsis: Monads for free description: Free monads are useful for many tree-like structures and domain specific languages. @@ -28,20 +38,20 @@ . More information on free monads, including examples, can be found in the following blog posts: - - + + build-type: Simple extra-source-files: - .ghci .gitignore - .travis.yml + .hlint.yaml .vim.custom README.markdown CHANGELOG.markdown - HLint.hs doc/proof/Control/Comonad/Cofree/*.md doc/proof/Control/Comonad/Trans/Cofree/*.md + examples/free-examples.cabal + examples/LICENSE examples/*.hs examples/*.lhs extra-doc-files: @@ -56,7 +66,6 @@ hs-source-dirs: src default-language: Haskell2010 - default-extensions: CPP other-extensions: MultiParamTypeClasses FunctionalDependencies @@ -66,32 +75,52 @@ GADTs build-depends: - base == 4.*, - bifunctors == 4.*, - comonad == 4.*, - distributive >= 0.2.1, - mtl >= 2.0.1.0 && < 2.3, - prelude-extras >= 0.4 && < 1, - profunctors == 4.*, - semigroupoids == 4.*, - semigroups >= 0.8.3.1 && < 1, - transformers >= 0.2.0 && < 0.5, - template-haskell >= 2.7.0.0 && < 3 + base >= 4.9 && < 5, + comonad >= 5.0.8 && < 6, + containers >= 0.5.7.1 && < 0.7, + distributive >= 0.5.2 && < 1, + exceptions >= 0.10.4 && < 0.11, + indexed-traversable >= 0.1.1 && < 0.2, + mtl >= 2.2.2 && < 2.4, + profunctors >= 5.6.1 && < 6, + semigroupoids >= 5.3.5 && < 6, + th-abstraction >= 0.4.2.0 && < 0.6, + transformers >= 0.5 && < 0.7, + transformers-base >= 0.4.5.2 && < 0.5, + template-haskell >= 2.11 && < 2.21 + if !impl(ghc >= 8.2) + build-depends: bifunctor-classes-compat >= 0.1 && < 0.2 + exposed-modules: Control.Applicative.Free + Control.Applicative.Free.Fast + Control.Applicative.Free.Final Control.Applicative.Trans.Free Control.Alternative.Free + Control.Alternative.Free.Final Control.Comonad.Cofree Control.Comonad.Cofree.Class Control.Comonad.Trans.Cofree Control.Comonad.Trans.Coiter Control.Monad.Free + Control.Monad.Free.Ap Control.Monad.Free.Church Control.Monad.Free.Class Control.Monad.Free.TH Control.Monad.Trans.Free + Control.Monad.Trans.Free.Ap Control.Monad.Trans.Free.Church Control.Monad.Trans.Iter - ghc-options: -Wall + ghc-options: -Wall -Wcompat -Wnoncanonical-monad-instances + + if !impl(ghc >= 8.8) + ghc-options: -Wnoncanonical-monadfail-instances + + if impl(ghc >= 9.0) + -- these flags may abort compilation with GHC-8.10 + -- https://gitlab.haskell.org/ghc/ghc/-/merge_requests/3295 + ghc-options: -Winferred-safe-imports -Wmissing-safe-haskell-mode + + x-docspec-extra-packages: tagged diff --git a/src/Control/Alternative/Free.hs b/src/Control/Alternative/Free.hs --- a/src/Control/Alternative/Free.hs +++ b/src/Control/Alternative/Free.hs @@ -2,10 +2,8 @@ {-# LANGUAGE Rank2Types #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE ScopedTypeVariables #-} -#if __GLASGOW_HASKELL__ >= 707 -{-# LANGUAGE DeriveDataTypeable #-} -#endif -{-# OPTIONS_GHC -Wall #-} +{-# LANGUAGE Safe #-} + ----------------------------------------------------------------------------- -- | -- Module : Control.Alternative.Free @@ -29,31 +27,29 @@ import Control.Applicative import Data.Functor.Apply +import Data.Functor.Alt (()) +import qualified Data.Functor.Alt as Alt + +#if !(MIN_VERSION_base(4,11,0)) import Data.Semigroup -import Data.Typeable +#endif infixl 3 `Ap` data AltF f a where Ap :: f a -> Alt f (a -> b) -> AltF f b Pure :: a -> AltF f a -#if __GLASGOW_HASKELL__ >= 707 - deriving Typeable -#endif newtype Alt f a = Alt { alternatives :: [AltF f a] } -#if __GLASGOW_HASKELL__ >= 707 - deriving Typeable -#endif -instance Functor f => Functor (AltF f) where +instance Functor (AltF f) where fmap f (Pure a) = Pure $ f a fmap f (Ap x g) = x `Ap` fmap (f .) g -instance Functor f => Functor (Alt f) where +instance Functor (Alt f) where fmap f (Alt xs) = Alt $ map (fmap f) xs -instance Functor f => Applicative (AltF f) where +instance Applicative (AltF f) where pure = Pure {-# INLINE pure #-} (Pure f) <*> y = fmap f y -- fmap @@ -61,24 +57,24 @@ (Ap a f) <*> b = a `Ap` (flip <$> f <*> (Alt [b])) {-# INLINE (<*>) #-} -instance Functor f => Applicative (Alt f) where +instance Applicative (Alt f) where pure a = Alt [pure a] {-# INLINE pure #-} (Alt xs) <*> ys = Alt (xs >>= alternatives . (`ap'` ys)) where - ap' :: (Functor f) => AltF f (a -> b) -> Alt f a -> Alt f b + ap' :: AltF f (a -> b) -> Alt f a -> Alt f b Pure f `ap'` u = fmap f u (u `Ap` f) `ap'` v = Alt [u `Ap` (flip <$> f) <*> v] {-# INLINE (<*>) #-} -liftAltF :: (Functor f) => f a -> AltF f a +liftAltF :: f a -> AltF f a liftAltF x = x `Ap` pure id {-# INLINE liftAltF #-} --- | A version of 'lift' that can be used with just a 'Functor' for @f@. -liftAlt :: (Functor f) => f a -> Alt f a +-- | A version of 'lift' that can be used with any @f@. +liftAlt :: f a -> Alt f a liftAlt = Alt . (:[]) . liftAltF {-# INLINE liftAlt #-} @@ -94,24 +90,28 @@ go2 (Ap x f) = flip id <$> u x <*> go f {-# INLINABLE runAlt #-} -instance (Functor f) => Apply (Alt f) where +instance Apply (Alt f) where (<.>) = (<*>) {-# INLINE (<.>) #-} -instance (Functor f) => Alternative (Alt f) where +instance Alt.Alt (Alt f) where + () = (<|>) + {-# INLINE () #-} + +instance Alternative (Alt f) where empty = Alt [] {-# INLINE empty #-} Alt as <|> Alt bs = Alt (as ++ bs) {-# INLINE (<|>) #-} -instance (Functor f) => Semigroup (Alt f a) where +instance Semigroup (Alt f a) where (<>) = (<|>) {-# INLINE (<>) #-} -instance (Functor f) => Monoid (Alt f a) where +instance Monoid (Alt f a) where mempty = empty {-# INLINE mempty #-} - mappend = (<|>) + mappend = (<>) {-# INLINE mappend #-} mconcat as = Alt (as >>= alternatives) {-# INLINE mconcat #-} @@ -125,26 +125,3 @@ hoistAlt :: (forall a. f a -> g a) -> Alt f b -> Alt g b hoistAlt f (Alt as) = Alt (map (hoistAltF f) as) {-# INLINE hoistAlt #-} - -#if __GLASGOW_HASKELL__ < 707 -instance Typeable1 f => Typeable1 (Alt f) where - typeOf1 t = mkTyConApp altTyCon [typeOf1 (f t)] where - f :: Alt f a -> f a - f = undefined - -instance Typeable1 f => Typeable1 (AltF f) where - typeOf1 t = mkTyConApp altFTyCon [typeOf1 (f t)] where - f :: AltF f a -> f a - f = undefined - -altTyCon, altFTyCon :: TyCon -#if __GLASGOW_HASKELL__ < 704 -altTyCon = mkTyCon "Control.Alternative.Free.Alt" -altFTyCon = mkTyCon "Control.Alternative.Free.AltF" -#else -altTyCon = mkTyCon3 "free" "Control.Alternative.Free" "Alt" -altFTyCon = mkTyCon3 "free" "Control.Alternative.Free" "AltF" -#endif -{-# NOINLINE altTyCon #-} -{-# NOINLINE altFTyCon #-} -#endif diff --git a/src/Control/Alternative/Free/Final.hs b/src/Control/Alternative/Free/Final.hs new file mode 100644 --- /dev/null +++ b/src/Control/Alternative/Free/Final.hs @@ -0,0 +1,73 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE Safe #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Control.Alternative.Free.Final +-- Copyright : (C) 2012 Edward Kmett +-- License : BSD-style (see the file LICENSE) +-- +-- Maintainer : Edward Kmett +-- Stability : provisional +-- Portability : GADTs, Rank2Types +-- +-- Final encoding of free 'Alternative' functors. +---------------------------------------------------------------------------- +module Control.Alternative.Free.Final + ( Alt(..) + , runAlt + , liftAlt + , hoistAlt + ) where + +import Control.Applicative +import Data.Functor.Apply +import Data.Functor.Alt (()) +import qualified Data.Functor.Alt as Alt + +#if !(MIN_VERSION_base(4,11,0)) +import Data.Semigroup +#endif + +-- | The free 'Alternative' for any @f@. +newtype Alt f a = Alt { _runAlt :: forall g. Alternative g => (forall x. f x -> g x) -> g a } + +instance Functor (Alt f) where + fmap f (Alt g) = Alt (\k -> fmap f (g k)) + +instance Apply (Alt f) where + Alt f <.> Alt x = Alt (\k -> f k <*> x k) + +instance Applicative (Alt f) where + pure x = Alt (\_ -> pure x) + Alt f <*> Alt x = Alt (\k -> f k <*> x k) + +instance Alt.Alt (Alt f) where + Alt x Alt y = Alt (\k -> x k <|> y k) + +instance Alternative (Alt f) where + empty = Alt (\_ -> empty) + Alt x <|> Alt y = Alt (\k -> x k <|> y k) + some (Alt x) = Alt $ \k -> some (x k) + many (Alt x) = Alt $ \k -> many (x k) + +instance Semigroup (Alt f a) where + (<>) = (<|>) + +instance Monoid (Alt f a) where + mempty = empty + mappend = (<>) + +-- | A version of 'lift' that can be used with @f@. +liftAlt :: f a -> Alt f a +liftAlt f = Alt (\k -> k f) + +-- | Given a natural transformation from @f@ to @g@, this gives a canonical monoidal natural transformation from @'Alt' f@ to @g@. +runAlt :: forall f g a. Alternative g => (forall x. f x -> g x) -> Alt f a -> g a +runAlt phi g = _runAlt g phi + +-- | Given a natural transformation from @f@ to @g@ this gives a monoidal natural transformation from @Alt f@ to @Alt g@. +hoistAlt :: (forall a. f a -> g a) -> Alt f b -> Alt g b +hoistAlt phi (Alt g) = Alt (\k -> g (k . phi)) + diff --git a/src/Control/Applicative/Free.hs b/src/Control/Applicative/Free.hs --- a/src/Control/Applicative/Free.hs +++ b/src/Control/Applicative/Free.hs @@ -1,10 +1,7 @@ -{-# LANGUAGE CPP #-} {-# LANGUAGE Rank2Types #-} {-# LANGUAGE GADTs #-} -#if __GLASGOW_HASKELL__ >= 707 -{-# LANGUAGE DeriveDataTypeable #-} -#endif -{-# OPTIONS_GHC -Wall #-} +{-# LANGUAGE Safe #-} + ----------------------------------------------------------------------------- -- | -- Module : Control.Applicative.Free @@ -30,6 +27,7 @@ , runAp , runAp_ , liftAp + , iterAp , hoistAp , retractAp @@ -38,17 +36,18 @@ ) where import Control.Applicative +import Control.Comonad (Comonad(..)) import Data.Functor.Apply -import Data.Typeable -import Data.Monoid +import Data.Foldable +import Data.Semigroup.Foldable +import Data.Functor.Classes +import Prelude hiding (null) + -- | The free 'Applicative' for a 'Functor' @f@. data Ap f a where Pure :: a -> Ap f a Ap :: f a -> Ap f (a -> b) -> Ap f b -#if __GLASGOW_HASKELL__ >= 707 - deriving Typeable -#endif -- | Given a natural transformation from @f@ to @g@, this gives a canonical monoidal natural transformation from @'Ap' f@ to @g@. -- @@ -81,11 +80,237 @@ Pure f <*> y = fmap f y Ap x y <*> z = Ap x (flip <$> y <*> z) +instance Comonad f => Comonad (Ap f) where + extract (Pure a) = a + extract (Ap x y) = extract y (extract x) + duplicate (Pure a) = Pure (Pure a) + duplicate (Ap x y) = Ap (duplicate x) (extend (flip Ap) y) + +-- | @foldMap f == foldMap f . 'runAp' 'Data.Foldable.toList'@ +instance Foldable f => Foldable (Ap f) where + foldMap f (Pure a) = f a + foldMap f (Ap x y) = foldMap (\a -> foldMap (\g -> f (g a)) y) x + + null (Pure _) = False + null (Ap x y) = null x || null y + + length = go 1 + where + -- This type annotation is required to do polymorphic recursion + go :: Foldable t => Int -> Ap t a -> Int + go n (Pure _) = n + go n (Ap x y) = case n * length x of + 0 -> 0 + n' -> go n' y + +-- | @foldMap f == foldMap f . 'runAp' 'toNonEmpty'@ +instance Foldable1 f => Foldable1 (Ap f) where + foldMap1 f (Pure a) = f a + foldMap1 f (Ap x y) = foldMap1 (\a -> foldMap1 (\g -> f (g a)) y) x + + +{- $note_eq1 + +This comment section is an internal documentation, but written in proper +Haddock markup. It is to allow rendering them to ease reading this rather long document. + +=== About the definition of @Eq1 (Ap f)@ instance + +The @Eq1 (Ap f)@ instance below has a complex definition. This comment +explains why it is defined like that. + +The discussion given here also applies to @Ord1 (Ap f)@ instance with a little change. + +==== General discussion about @Eq1@ type class + +Currently, there isn't a law on the @Eq1@ type class, but the following +properties can be expected. + +* If @Eq (f ())@, and @Functor f@ holds, @Eq1 f@ satisfies + + > liftEq (\_ _ -> True) x y == (() <$ x) == (() <$ y) + +* If @Foldable f@ holds, @Eq1 f@ satisfies: + + * @boringEq x y@ implies @length (toList x) == length (toList y)@ + + * @liftEq eq x y == liftEq (\_ _ -> True) && all (\(a,b) -> eq a b)) (zip (toList x) (toList y))@ + +Let's define the commonly used function @liftEq (\\_ _ -> True)@ as @boringEq@. + +> boringEq :: Eq1 f => f a -> f b -> Bool +> boringEq = liftEq (\_ _ -> True) + +Changing the constant @True@ to the constant @False@ in the definition of +@boringEq@, let @emptyEq@ function be defined as: + +> emptyEq :: Eq1 f => f a -> f b -> Bool +> emptyEq = liftEq (\_ _ -> False) + +From the above properties expectated on a @Eq1@ instance, @emptyEq@ satisfies the following. + +> emptyEq x y = boringEq x y && null (zip (toList x) (toList y)) + +==== About @instance (Eq1 (Ap f))@ + +If we're to define @Eq1 (Ap f)@ satisfying these properties as expected, @Eq (Ap f ())@ will determine +how @liftEq@ should behave. It's not unreasonable to define equality between @Ap f ()@ as below. + +> boringEqAp (Pure _) (Pure _) = True +> boringEqAp (Ap x1 y1) (Ap x2 y2) = boringEq x1 x2 && boringEqAp y1 y2 +> {- = ((() <$ x1) == (() <$ x2)) && (y1 == y2) -} +> boringEqAp _ _ = False + +Its type can be more general than equality between @Ap f ()@: + +> boringEqAp :: Eq1 f => Ap f a -> Ap f b -> Bool + +Using @boringEqAp@, the specification of @liftEq@ will be: + +> liftEq eq x y = boringEqAp x y && and (zipWith eq (toList x) (toList y)) + +Then unfold @toList@ to remove the dependency to @Foldable@. + +> liftEq eq (Pure a1) (Pure a2) +> = boringEqAp (Pure a1) (Pure a2) && all (\(a,b) -> eq a b)) (zip (toList (Pure x)) (toList Pure y)) +> = True && all (\(a,b) -> eq a b) (zip [a1] [a2]) +> = eq a1 a2 +> liftEq eq (Ap x1 y1) (Ap x2 y2) +> = boringEqAp (Ap x1 y1) (Ap x2 y2) && all (\(b1, b2) -> eq b1 b2) (zip (toList (Ap x1 y1)) (toList (Ap x2 y2))) +> = boringEq x1 y1 && boringEqAp y1 y2 && all (\(b1, b2) -> eq b1 b2) (zip (toList x1 <**> toList y1) (toList x2 <**> toList y2)) +> = boringEq x1 y1 && boringEqAp y1 y2 && all (\(b1, b2) -> eq b1 b2) (zip (as1 <**> gs1) (as2 <**> gs2)) +> where as1 = toList x1 +> as2 = toList x2 +> gs1 = toList y1 +> gs2 = toList y2 +> = boringEq x1 y1 && boringEqAp y1 y2 && all (\(a1, a2) -> all (\(g1, g2) -> eq (g1 a1) (g2 a2)) (zip gs1 gs2)) (zip as1 as2) + +If @zip as1 as2@ is /not/ empty, the following transformation is valid. + +> (...) | not (null (zip as1 as2)) +> = boringEq x1 x2 && boringEqAp y1 y2 && all (\(a1, a2) -> all (\(g1, g2) -> eq (g1 a1) (g2 a2)) (zip gs1 gs2)) (zip as1 as2) +> = boringEq x1 x2 && all (\(a1, a2) -> boringEqAp y1 y2 && all (\(g1, g2) -> eq (g1 a1) (g2 a2)) (zip gs1 gs2)) (zip as1 as2) +> -- ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +> = boringEq x1 x2 && all (\(a1, a2) -> liftEq (\g1 g2 -> eq (g1 a1) (g2 a2)) y1 y2) (zip as1 as2) +> = liftEq (\a1 a2 -> liftEq (\g1 g2 -> eq (g1 a1) (g2 a2)) y1 y2)) x1 x2 + +Because, generally, the following transformation is valid if @xs@ is a nonempty list. + +> cond && all p xs = all (\x -> cond && p x) xs -- Only when xs is not empty! + +If @zip as1 as2@ is empty, @all (...) (zip as1 as2)@ is vacuously true, so the following transformation is valid. + +> (...) | null (zip as1 as2) +> = boringEq x1 x2 && boringEqAp y1 y2 && all (\(a1, a2) -> all (\(g1, g2) -> eq (g1 a1) (g2 a2)) (zip gs1 gs2)) (zip as1 as2) +> = boringEq x1 x2 && boringEqAp y1 y2 + +Combining two cases: + +> liftEq eq (Ap x1 y1) (Ap x2 y2) +> = null (zip as1 as2) && boringEq x1 x2 && boringEqAp y1 y2 +> || not (null (zip as1 as2)) && liftEq (\a1 a2 -> liftEq (\g1 g2 -> eq (g1 a1) (g2 a2)) y1 y2)) x1 x2 +> = null (zip as1 as2) && boringEq x1 x2 && boringEqAp y1 y2 +> || liftEq (\a1 a2 -> liftEq (\g1 g2 -> eq (g1 a1) (g2 a2)) y1 y2)) x1 x2 +> = emptyEq x1 x2 && boringEqAp y1 y2 +> || liftEq (\a1 a2 -> liftEq (\g1 g2 -> eq (g1 a1) (g2 a2)) y1 y2)) x1 x2 + +The property about @emptyEq@ is used in the last equation. + +Hence it's defined as this source code. + +-} + +-- | Specialized 'boringEq' for @Ap f@. +boringEqAp :: Eq1 f => Ap f a -> Ap f b -> Bool +boringEqAp (Pure _) (Pure _) = True +boringEqAp (Ap x1 y1) (Ap x2 y2) = boringEq x1 x2 && boringEqAp y1 y2 +boringEqAp _ _ = False + +-- | Implementaion of 'liftEq' for @Ap f@. +liftEqAp :: Eq1 f => (a -> b -> Bool) -> Ap f a -> Ap f b -> Bool +liftEqAp eq (Pure a1) (Pure a2) = eq a1 a2 +liftEqAp eq (Ap x1 y1) (Ap x2 y2) + -- This branching is necessary and not just an optimization. + -- See the above comment for more + | emptyEq x1 x2 = boringEqAp y1 y2 + | otherwise = + liftEq (\a1 a2 -> liftEqAp (\g1 g2 -> eq (g1 a1) (g2 a2)) y1 y2) x1 x2 +liftEqAp _ _ _ = False + +-- | @boringEq fa fb@ tests if @fa@ and @fb@ are equal ignoring any difference between +-- their content (the values of their last parameters @a@ and @b@.) +-- +-- It is named \'boring\' because the type parameters @a@ and @b@ are +-- treated as if they are the most boring type @()@. +boringEq :: Eq1 f => f a -> f b -> Bool +boringEq = liftEq (\_ _ -> True) + +-- | @emptyEq fa fb@ tests if @fa@ and @fb@ are equal /and/ they don't have any content +-- (the values of their last parameters @a@ and @b@.) +-- +-- It is named \'empty\' because it only tests for values without any content, +-- like an empty list or @Nothing@. +-- +-- If @f@ is also @Foldable@, @emptyEq fa fb@ would be equivalent to +-- @null fa && null fb && liftEq eq@ for any @eq :: a -> b -> Bool@. +-- +-- (It depends on each instance of @Eq1@. Since @Eq1@ does not have +-- any laws currently, this is not a hard guarantee. But all instances in "base", "transformers", +-- "containers", "array", and "free" satisfy it.) +-- +-- Note that @emptyEq@ is not a equivalence relation, since it's possible @emptyEq x x == False@. +emptyEq :: Eq1 f => f a -> f b -> Bool +emptyEq = liftEq (\_ _ -> False) + +instance Eq1 f => Eq1 (Ap f) where + liftEq = liftEqAp + +instance (Eq1 f, Eq a) => Eq (Ap f a) where + (==) = eq1 + +-- | Specialized 'boringCompare' for @Ap f@. +boringCompareAp :: Ord1 f => Ap f a -> Ap f b -> Ordering +boringCompareAp (Pure _) (Pure _) = EQ +boringCompareAp (Pure _) (Ap _ _) = LT +boringCompareAp (Ap x1 y1) (Ap x2 y2) = boringCompare x1 x2 `mappend` boringCompareAp y1 y2 +boringCompareAp (Ap _ _) (Pure _) = GT + +-- | Implementation of 'liftCompare' for @Ap f@ +liftCompareAp :: Ord1 f => (a -> b -> Ordering) -> Ap f a -> Ap f b -> Ordering +liftCompareAp cmp (Pure a1) (Pure a2) = cmp a1 a2 +liftCompareAp _ (Pure _) (Ap _ _) = LT +liftCompareAp cmp (Ap x1 y1) (Ap x2 y2) + -- This branching is necessary and not just an optimization. + -- See the above comment for more + | emptyEq x1 x2 = boringCompareAp y1 y2 + | otherwise = liftCompare (\a1 a2 -> liftCompareAp (\g1 g2 -> cmp (g1 a1) (g2 a2)) y1 y2) x1 x2 +liftCompareAp _ (Ap _ _) (Pure _) = GT + +-- | @boringCompare fa fb@ compares @fa@ and @fb@ ignoring any difference between +-- their content (the values of their last parameters @a@ and @b@.) +-- +-- It is named \'boring\' because the type parameters @a@ and @b@ are +-- treated as if they are the most boring type @()@. +boringCompare :: Ord1 f => f a -> f b -> Ordering +boringCompare = liftCompare (\_ _ -> EQ) + +instance Ord1 f => Ord1 (Ap f) where + liftCompare = liftCompareAp + +instance (Ord1 f, Ord a) => Ord (Ap f a) where + compare = compare1 + -- | A version of 'lift' that can be used with just a 'Functor' for @f@. liftAp :: f a -> Ap f a liftAp x = Ap x (Pure id) {-# INLINE liftAp #-} +-- | Tear down a free 'Applicative' using iteration. +iterAp :: Functor g => (g a -> a) -> Ap g a -> a +iterAp algebra = go + where go (Pure a) = a + go (Ap underlying apply) = algebra (go . (apply <*>) . pure <$> underlying) + -- | Given a natural transformation from @f@ to @g@ this gives a monoidal natural transformation from @Ap f@ to @Ap g@. hoistAp :: (forall a. f a -> g a) -> Ap f b -> Ap g b hoistAp _ (Pure a) = Pure a @@ -98,22 +323,6 @@ retractAp :: Applicative f => Ap f a -> f a retractAp (Pure a) = pure a retractAp (Ap x y) = x <**> retractAp y - -#if __GLASGOW_HASKELL__ < 707 -instance Typeable1 f => Typeable1 (Ap f) where - typeOf1 t = mkTyConApp apTyCon [typeOf1 (f t)] where - f :: Ap f a -> f a - f = undefined - -apTyCon :: TyCon -#if __GLASGOW_HASKELL__ < 704 -apTyCon = mkTyCon "Control.Applicative.Free.Ap" -#else -apTyCon = mkTyCon3 "free" "Control.Applicative.Free" "Ap" -#endif -{-# NOINLINE apTyCon #-} - -#endif {- $examples diff --git a/src/Control/Applicative/Free/Fast.hs b/src/Control/Applicative/Free/Fast.hs new file mode 100644 --- /dev/null +++ b/src/Control/Applicative/Free/Fast.hs @@ -0,0 +1,121 @@ +{-# LANGUAGE GADTs #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE Safe #-} + +-------------------------------------------------------------------------------- +-- | +-- A faster free applicative. +-- Based on . +-------------------------------------------------------------------------------- +module Control.Applicative.Free.Fast + ( + -- * The Sequence of Effects + ASeq(..) + , reduceASeq + , hoistASeq + , traverseASeq + , rebaseASeq + -- * The Faster Free Applicative + , Ap(..) + , liftAp + , retractAp + , runAp + , runAp_ + , hoistAp + ) where + +import Control.Applicative +import Data.Functor.Apply + +-- | The free applicative is composed of a sequence of effects, +-- and a pure function to apply that sequence to. +-- The fast free applicative separates these from each other, +-- so that the sequence may be built up independently, +-- and so that 'fmap' can run in constant time by having immediate access to the pure function. +data ASeq f a where + ANil :: ASeq f () + ACons :: f a -> ASeq f u -> ASeq f (a,u) + +-- | Interprets the sequence of effects using the semantics for +-- `pure` and `<*>` given by the Applicative instance for 'f'. +reduceASeq :: Applicative f => ASeq f u -> f u +reduceASeq ANil = pure () +reduceASeq (ACons x xs) = (,) <$> x <*> reduceASeq xs + +-- | Given a natural transformation from @f@ to @g@ this gives a natural transformation from @ASeq f@ to @ASeq g@. +hoistASeq :: (forall x. f x -> g x) -> ASeq f a -> ASeq g a +hoistASeq _ ANil = ANil +hoistASeq u (ACons x xs) = ACons (u x) (u `hoistASeq` xs) + +-- | Traverse a sequence with resepect to its interpretation type 'f'. +traverseASeq :: Applicative h => (forall x. f x -> h (g x)) -> ASeq f a -> h (ASeq g a) +traverseASeq _ ANil = pure ANil +traverseASeq f (ACons x xs) = ACons <$> f x <*> traverseASeq f xs + +-- | It may not be obvious, but this essentially acts like ++, +-- traversing the first sequence and creating a new one by appending the second sequence. +-- The difference is that this also has to modify the return functions and that the return type depends on the input types. +-- +-- See the source of 'hoistAp' as an example usage. +rebaseASeq :: ASeq f u -> (forall x. (x -> y) -> ASeq f x -> z) -> + (v -> u -> y) -> ASeq f v -> z +rebaseASeq ANil k f = k (\v -> f v ()) +rebaseASeq (ACons x xs) k f = + rebaseASeq xs (\g s -> k (\(a,u) -> g u a) (ACons x s)) + (\v u a -> f v (a,u)) + + +-- | The faster free 'Applicative'. +newtype Ap f a = Ap + { unAp :: forall u y z. + (forall x. (x -> y) -> ASeq f x -> z) -> + (u -> a -> y) -> ASeq f u -> z } + +-- | Given a natural transformation from @f@ to @g@, this gives a canonical monoidal natural transformation from @'Ap' f@ to @g@. +-- +-- prop> runAp t == retractApp . hoistApp t +runAp :: Applicative g => (forall x. f x -> g x) -> Ap f a -> g a +runAp u = retractAp . hoistAp u + +-- | Perform a monoidal analysis over free applicative value. +-- +-- Example: +-- +-- @ +-- count :: Ap f a -> Int +-- count = getSum . runAp_ (\\_ -> Sum 1) +-- @ +runAp_ :: Monoid m => (forall a. f a -> m) -> Ap f b -> m +runAp_ f = getConst . runAp (Const . f) + +instance Functor (Ap f) where + fmap g x = Ap (\k f -> unAp x k (\s -> f s . g)) + +instance Apply (Ap f) where + (<.>) = (<*>) + +instance Applicative (Ap f) where + pure a = Ap (\k f -> k (`f` a)) + x <*> y = Ap (\k f -> unAp y (unAp x k) (\s a g -> f s (g a))) + +-- | A version of 'lift' that can be used with just a 'Functor' for @f@. +liftAp :: f a -> Ap f a +liftAp a = Ap (\k f s -> k (\(a',s') -> f s' a') (ACons a s)) +{-# INLINE liftAp #-} + +-- | Given a natural transformation from @f@ to @g@ this gives a monoidal natural transformation from @Ap f@ to @Ap g@. +hoistAp :: (forall x. f x -> g x) -> Ap f a -> Ap g a +hoistAp g x = Ap (\k f s -> + unAp x + (\f' s' -> + rebaseASeq (hoistASeq g s') k + (\v u -> f v (f' u)) s) + (const id) + ANil) + +-- | Interprets the free applicative functor over f using the semantics for +-- `pure` and `<*>` given by the Applicative instance for f. +-- +-- prop> retractApp == runAp id +retractAp :: Applicative f => Ap f a -> f a +retractAp x = unAp x (\f s -> f <$> reduceASeq s) (\() -> id) ANil diff --git a/src/Control/Applicative/Free/Final.hs b/src/Control/Applicative/Free/Final.hs new file mode 100644 --- /dev/null +++ b/src/Control/Applicative/Free/Final.hs @@ -0,0 +1,85 @@ +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE Safe #-} + +----------------------------------------------------------------------------- +-- | +-- Module : Control.Applicative.Free.Final +-- Copyright : (C) 2012-2013 Edward Kmett +-- License : BSD-style (see the file LICENSE) +-- +-- Maintainer : Edward Kmett +-- Stability : provisional +-- Portability : GADTs, Rank2Types +-- +-- Final encoding of free 'Applicative' functors. +---------------------------------------------------------------------------- +module Control.Applicative.Free.Final + ( + -- | Compared to the free monad, they are less expressive. However, they are also more + -- flexible to inspect and interpret, as the number of ways in which + -- the values can be nested is more limited. + + Ap(..) + , runAp + , runAp_ + , liftAp + , hoistAp + , retractAp + + -- * Examples + -- $examples + ) where + +import Control.Applicative +import Data.Functor.Apply + +-- | The free 'Applicative' for a 'Functor' @f@. +newtype Ap f a = Ap { _runAp :: forall g. Applicative g => (forall x. f x -> g x) -> g a } + +-- | Given a natural transformation from @f@ to @g@, this gives a canonical monoidal natural transformation from @'Ap' f@ to @g@. +-- +-- prop> runAp t == retractApp . hoistApp t +runAp :: Applicative g => (forall x. f x -> g x) -> Ap f a -> g a +runAp phi m = _runAp m phi + +-- | Perform a monoidal analysis over free applicative value. +-- +-- Example: +-- +-- @ +-- count :: Ap f a -> Int +-- count = getSum . runAp_ (\\_ -> Sum 1) +-- @ +runAp_ :: Monoid m => (forall a. f a -> m) -> Ap f b -> m +runAp_ f = getConst . runAp (Const . f) + +instance Functor (Ap f) where + fmap f (Ap g) = Ap (\k -> fmap f (g k)) + +instance Apply (Ap f) where + Ap f <.> Ap x = Ap (\k -> f k <*> x k) + +instance Applicative (Ap f) where + pure x = Ap (\_ -> pure x) + Ap f <*> Ap x = Ap (\k -> f k <*> x k) + +-- | A version of 'lift' that can be used with just a 'Functor' for @f@. +liftAp :: f a -> Ap f a +liftAp x = Ap (\k -> k x) + +-- | Given a natural transformation from @f@ to @g@ this gives a monoidal natural transformation from @Ap f@ to @Ap g@. +hoistAp :: (forall a. f a -> g a) -> Ap f b -> Ap g b +hoistAp f (Ap g) = Ap (\k -> g (k . f)) + +-- | Interprets the free applicative functor over f using the semantics for +-- `pure` and `<*>` given by the Applicative instance for f. +-- +-- prop> retractApp == runAp id +retractAp :: Applicative f => Ap f a -> f a +retractAp (Ap g) = g id + +{- $examples + + + +-} diff --git a/src/Control/Applicative/Trans/Free.hs b/src/Control/Applicative/Trans/Free.hs --- a/src/Control/Applicative/Trans/Free.hs +++ b/src/Control/Applicative/Trans/Free.hs @@ -1,10 +1,7 @@ -{-# LANGUAGE CPP #-} {-# LANGUAGE Rank2Types #-} {-# LANGUAGE GADTs #-} -#if __GLASGOW_HASKELL__ >= 707 -{-# LANGUAGE DeriveDataTypeable #-} -#endif -{-# OPTIONS_GHC -Wall #-} +{-# LANGUAGE Safe #-} + ----------------------------------------------------------------------------- -- | -- Module : Control.Applicative.Trans.Free @@ -36,6 +33,7 @@ , hoistApF , transApT , transApF + , joinApT -- * Free Applicative , Ap , runAp @@ -47,28 +45,18 @@ ) where import Control.Applicative +import Control.Monad (liftM) import Data.Functor.Apply import Data.Functor.Identity -import Data.Typeable -#if !(MIN_VERSION_base(4,8,0)) -import Data.Monoid (Monoid) -#endif -import qualified Data.Foldable as F -- | The free 'Applicative' for a 'Functor' @f@. data ApF f g a where Pure :: a -> ApF f g a Ap :: f a -> ApT f g (a -> b) -> ApF f g b -#if __GLASGOW_HASKELL__ >= 707 - deriving Typeable -#endif -- | The free 'Applicative' transformer for a 'Functor' @f@ over -- 'Applicative' @g@. newtype ApT f g a = ApT { getApT :: g (ApF f g a) } -#if __GLASGOW_HASKELL__ >= 707 - deriving Typeable -#endif instance Functor g => Functor (ApF f g) where fmap f (Pure a) = Pure (f a) @@ -129,13 +117,13 @@ -- Examples: -- -- @ --- height :: ('Functor' g, 'F.Foldable' g) => 'ApT' f g a -> 'Int' --- height = 'getSum' . runApT_ (\_ -> 'Sum' 1) 'F.maximum' +-- height :: ('Functor' g, 'Foldable' g) => 'ApT' f g a -> 'Int' +-- height = 'getSum' . runApT_ (\_ -> 'Sum' 1) 'maximum' -- @ -- -- @ --- size :: ('Functor' g, 'F.Foldable' g) => 'ApT' f g a -> 'Int' --- size = 'getSum' . runApT_ (\_ -> 'Sum' 1) 'F.fold' +-- size :: ('Functor' g, 'Foldable' g) => 'ApT' f g a -> 'Int' +-- size = 'getSum' . runApT_ (\_ -> 'Sum' 1) 'fold' -- @ runApT_ :: (Functor g, Monoid m) => (forall a. f a -> m) -> (g m -> m) -> ApT f g b -> m runApT_ f g = getConst . runApT (Const . f) (Const . g . fmap getConst) @@ -158,6 +146,13 @@ transApT :: Functor g => (forall a. g a -> g' a) -> ApT f g b -> ApT f g' b transApT f (ApT g) = ApT $ f (transApF f <$> g) +-- | Pull out and join @m@ layers of @'ApT' f m a@. +joinApT :: Monad m => ApT f m a -> m (Ap f a) +joinApT (ApT m) = m >>= joinApF + where + joinApF (Pure x) = return (pure x) + joinApF (Ap x y) = (liftApT x <**>) `liftM` joinApT y + -- | The free 'Applicative' for a 'Functor' @f@. type Ap f = ApT f Identity @@ -189,31 +184,8 @@ type Alt f = ApT f [] -- | Given a natural transformation from @f@ to @g@, this gives a canonical monoidal natural transformation from @'Alt' f@ to @g@. -runAlt :: (Alternative g, F.Foldable t) => (forall x. f x -> g x) -> ApT f t a -> g a -runAlt f (ApT xs) = F.foldr (\x acc -> h x <|> acc) empty xs +runAlt :: (Alternative g, Foldable t) => (forall x. f x -> g x) -> ApT f t a -> g a +runAlt f (ApT xs) = foldr (\x acc -> h x <|> acc) empty xs where h (Pure x) = pure x h (Ap x g) = f x <**> runAlt f g - -#if __GLASGOW_HASKELL__ < 707 -instance (Typeable1 f, Typeable1 g) => Typeable1 (ApT f g) where - typeOf1 t = mkTyConApp apTTyCon [typeOf1 (f t)] where - f :: ApT f g a -> g (f a) - f = undefined - -instance (Typeable1 f, Typeable1 g) => Typeable1 (ApF f g) where - typeOf1 t = mkTyConApp apFTyCon [typeOf1 (f t)] where - f :: ApF f g a -> g (f a) - f = undefined - -apTTyCon, apFTyCon :: TyCon -#if __GLASGOW_HASKELL__ < 704 -apTTyCon = mkTyCon "Control.Applicative.Trans.Free.ApT" -apFTyCon = mkTyCon "Control.Applicative.Trans.Free.ApF" -#else -apTTyCon = mkTyCon3 "free" "Control.Applicative.Trans.Free" "ApT" -apFTyCon = mkTyCon3 "free" "Control.Applicative.Trans.Free" "ApF" -#endif -{-# NOINLINE apTTyCon #-} -{-# NOINLINE apFTyCon #-} -#endif diff --git a/src/Control/Comonad/Cofree.hs b/src/Control/Comonad/Cofree.hs --- a/src/Control/Comonad/Cofree.hs +++ b/src/Control/Comonad/Cofree.hs @@ -1,12 +1,12 @@ -{-# LANGUAGE CPP #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE Rank2Types #-} -{-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} -#if __GLASGOW_HASKELL__ >= 707 -{-# LANGUAGE DeriveDataTypeable #-} -#endif +{-# LANGUAGE Safe #-} +{-# LANGUAGE StandaloneDeriving #-} + ----------------------------------------------------------------------------- -- | -- Module : Control.Comonad.Cofree @@ -25,12 +25,17 @@ , ComonadCofree(..) , section , coiter + , coiterW , unfold + , unfoldM , hoistCofree -- * Lenses into cofree comonads , _extract , _unwrap , telescoped + , telescoped_ + , shoots + , leaves ) where import Control.Applicative @@ -40,20 +45,25 @@ import Control.Comonad.Env.Class import Control.Comonad.Store.Class as Class import Control.Comonad.Traced.Class +import Control.Comonad.Hoist.Class import Control.Category -import Control.Monad(ap) +import Control.Monad(ap, (>=>), liftM) import Control.Monad.Zip import Data.Functor.Bind +import Data.Functor.Classes import Data.Functor.Extend +import Data.Functor.WithIndex import Data.Data import Data.Distributive import Data.Foldable +import Data.Foldable.WithIndex import Data.Semigroup import Data.Traversable +import Data.Traversable.WithIndex import Data.Semigroup.Foldable import Data.Semigroup.Traversable +import GHC.Generics hiding (Infix, Prefix) import Prelude hiding (id,(.)) -import Prelude.Extras infixr 5 :< @@ -63,7 +73,7 @@ -- /Formally/ -- -- A 'Comonad' @v@ is a cofree 'Comonad' for @f@ if every comonad homomorphism --- another comonad @w@ to @v@ is equivalent to a natural transformation +-- from another comonad @w@ to @v@ is equivalent to a natural transformation -- from @w@ to @f@. -- -- A 'cofree' functor is right adjoint to a forgetful functor. @@ -80,7 +90,7 @@ -- -- For instance, -- --- * @'Cofree' 'Maybe'@ forms the a comonad for a non-empty list. +-- * @'Cofree' 'Maybe'@ forms the comonad for a non-empty list. -- -- * @'Cofree' ('Const' b)@ is a product. -- @@ -96,24 +106,32 @@ -- -- In particular, if @f a ≡ [a]@, the -- resulting data structure is a . --- For a practical application, check --- by Neil Ghani et al. +-- For a practical application, check +-- by Neil Ghani et al. data Cofree f a = a :< f (Cofree f a) -#if __GLASGOW_HASKELL__ >= 707 - deriving (Typeable) -#endif + deriving (Generic, Generic1) +deriving instance (Typeable f, Data (f (Cofree f a)), Data a) => Data (Cofree f a) + -- | Use coiteration to generate a cofree comonad from a seed. -- -- @'coiter' f = 'unfold' ('id' 'Control.Arrow.&&&' f)@ coiter :: Functor f => (a -> f a) -> a -> Cofree f a coiter psi a = a :< (coiter psi <$> psi a) +-- | Like coiter for comonadic values. +coiterW :: (Comonad w, Functor f) => (w a -> f (w a)) -> w a -> Cofree f a +coiterW psi a = extract a :< (coiterW psi <$> psi a) + -- | Unfold a cofree comonad from a seed. unfold :: Functor f => (b -> (a, f b)) -> b -> Cofree f a unfold f c = case f c of (x, d) -> x :< fmap (unfold f) d +-- | Unfold a cofree comonad from a seed, monadically. +unfoldM :: (Traversable f, Monad m) => (b -> m (a, f b)) -> b -> m (Cofree f a) +unfoldM f = f >=> \ (x, t) -> (x :<) `liftM` Data.Traversable.mapM (unfoldM f) t + hoistCofree :: Functor f => (forall x . f x -> g x) -> Cofree f a -> Cofree g a hoistCofree f (x :< y) = x :< f (hoistCofree f <$> y) @@ -146,7 +164,7 @@ {-# INLINE lower #-} instance Alternative f => Monad (Cofree f) where - return x = x :< empty + return = pure {-# INLINE return #-} (a :< m) >>= k = case k a of b :< n -> b :< (n <|> fmap (>>= k) m) @@ -177,59 +195,56 @@ {-# INLINE (@>) #-} instance Alternative f => Applicative (Cofree f) where - pure = return + pure x = x :< empty {-# INLINE pure #-} (<*>) = ap {-# INLINE (<*>) #-} -instance (Functor f, Show1 f) => Show1 (Cofree f) where - showsPrec1 d (a :< as) = showParen (d > 5) $ - showsPrec 6 a . showString " :< " . showsPrec1 5 (fmap Lift1 as) +instance (Show1 f) => Show1 (Cofree f) where + liftShowsPrec sp sl = go + where + goList = liftShowList sp sl + go d (a :< as) = showParen (d > 5) $ + sp 6 a . showString " :< " . liftShowsPrec go goList 5 as -instance (Show (f (Cofree f a)), Show a) => Show (Cofree f a) where - showsPrec d (a :< as) = showParen (d > 5) $ - showsPrec 6 a . showString " :< " . showsPrec 5 as +instance (Show1 f, Show a) => Show (Cofree f a) where + showsPrec = showsPrec1 -instance (Functor f, Read1 f) => Read1 (Cofree f) where - readsPrec1 d r = readParen (d > 5) - (\r' -> [(u :< fmap lower1 v,w) | - (u, s) <- readsPrec 6 r', - (":<", t) <- lex s, - (v, w) <- readsPrec1 5 t]) r +instance (Read1 f) => Read1 (Cofree f) where + liftReadsPrec rp rl = go + where + goList = liftReadList rp rl + go d r = readParen (d > 5) + (\r' -> [(u :< v, w) | + (u, s) <- rp 6 r', + (":<", t) <- lex s, + (v, w) <- liftReadsPrec go goList 5 t]) r -instance (Read (f (Cofree f a)), Read a) => Read (Cofree f a) where - readsPrec d r = readParen (d > 5) - (\r' -> [(u :< v,w) | - (u, s) <- readsPrec 6 r', - (":<", t) <- lex s, - (v, w) <- readsPrec 5 t]) r +instance (Read1 f, Read a) => Read (Cofree f a) where + readsPrec = readsPrec1 -instance (Eq (f (Cofree f a)), Eq a) => Eq (Cofree f a) where -#ifndef HLINT - a :< as == b :< bs = a == b && as == bs -#endif +instance (Eq1 f, Eq a) => Eq (Cofree f a) where + (==) = eq1 -instance (Functor f, Eq1 f) => Eq1 (Cofree f) where -#ifndef HLINT - a :< as ==# b :< bs = a == b && fmap Lift1 as ==# fmap Lift1 bs -#endif +instance (Eq1 f) => Eq1 (Cofree f) where + liftEq eq = go + where + go (a :< as) (b :< bs) = eq a b && liftEq go as bs -instance (Ord (f (Cofree f a)), Ord a) => Ord (Cofree f a) where - compare (a :< as) (b :< bs) = case compare a b of - LT -> LT - EQ -> compare as bs - GT -> GT +instance (Ord1 f, Ord a) => Ord (Cofree f a) where + compare = compare1 -instance (Functor f, Ord1 f) => Ord1 (Cofree f) where - compare1 (a :< as) (b :< bs) = case compare a b of - LT -> LT - EQ -> compare1 (fmap Lift1 as) (fmap Lift1 bs) - GT -> GT +instance (Ord1 f) => Ord1 (Cofree f) where + liftCompare cmp = go + where + go (a :< as) (b :< bs) = cmp a b `mappend` liftCompare go as bs instance Foldable f => Foldable (Cofree f) where foldMap f = go where go (a :< as) = f a `mappend` foldMap go as {-# INLINE foldMap #-} + length = go 0 where + go s (_ :< as) = foldl' go (s + 1) as instance Foldable1 f => Foldable1 (Cofree f) where foldMap1 f = go where @@ -246,45 +261,20 @@ go (a :< as) = (:<) <$> f a <.> traverse1 go as {-# INLINE traverse1 #-} -#if __GLASGOW_HASKELL__ < 707 -instance (Typeable1 f) => Typeable1 (Cofree f) where - typeOf1 dfa = mkTyConApp cofreeTyCon [typeOf1 (f dfa)] - where - f :: Cofree f a -> f a - f = undefined - -instance (Typeable1 f, Typeable a) => Typeable (Cofree f a) where - typeOf = typeOfDefault - -cofreeTyCon :: TyCon -#if __GLASGOW_HASKELL__ < 704 -cofreeTyCon = mkTyCon "Control.Comonad.Cofree.Cofree" -#else -cofreeTyCon = mkTyCon3 "free" "Control.Comonad.Cofree" "Cofree" -#endif -{-# NOINLINE cofreeTyCon #-} +instance FunctorWithIndex i f => FunctorWithIndex [i] (Cofree f) where + imap f (a :< as) = f [] a :< imap (\i -> imap (f . (:) i)) as + {-# INLINE imap #-} -instance - ( Typeable1 f - , Data (f (Cofree f a)) - , Data a - ) => Data (Cofree f a) where - gfoldl f z (a :< as) = z (:<) `f` a `f` as - toConstr _ = cofreeConstr - gunfold k z c = case constrIndex c of - 1 -> k (k (z (:<))) - _ -> error "gunfold" - dataTypeOf _ = cofreeDataType - dataCast1 f = gcast1 f +instance FoldableWithIndex i f => FoldableWithIndex [i] (Cofree f) where + ifoldMap f (a :< as) = f [] a `mappend` ifoldMap (\i -> ifoldMap (f . (:) i)) as + {-# INLINE ifoldMap #-} -cofreeConstr :: Constr -cofreeConstr = mkConstr cofreeDataType ":<" [] Infix -{-# NOINLINE cofreeConstr #-} +instance TraversableWithIndex i f => TraversableWithIndex [i] (Cofree f) where + itraverse f (a :< as) = (:<) <$> f [] a <*> itraverse (\i -> itraverse (f . (:) i)) as + {-# INLINE itraverse #-} -cofreeDataType :: DataType -cofreeDataType = mkDataType "Control.Comonad.Cofree.Cofree" [cofreeConstr] -{-# NOINLINE cofreeDataType #-} -#endif +instance ComonadHoist Cofree where + cohoist = hoistCofree instance ComonadEnv e w => ComonadEnv e (Cofree w) where ask = ask . lower @@ -326,13 +316,85 @@ _unwrap f (a :< as) = (a :<) <$> f as {-# INLINE _unwrap #-} --- | Construct a @Lens@ into a @'Cofree' f@ given a list of lenses into the base functor. +-- | Construct an @Lens@ into a @'Cofree' g@ given a list of lenses into the base functor. +-- When the input list is empty, this is equivalent to '_extract'. +-- When the input list is non-empty, this composes the input lenses +-- with '_unwrap' to walk through the @'Cofree' g@ before using +-- '_extract' to get the element at the final location. -- -- For more on lenses see the 'lens' package on hackage. -- --- @telescoped :: 'Functor' g => [Lens' ('Cofree' g a) (g ('Cofree' g a))] -> Lens' ('Cofree' g a) a@ -telescoped :: (Functor f, Functor g) => +-- @telescoped :: [Lens' (g ('Cofree' g a)) ('Cofree' g a)] -> Lens' ('Cofree' g a) a@ +-- +-- @telescoped :: [Traversal' (g ('Cofree' g a)) ('Cofree' g a)] -> Traversal' ('Cofree' g a) a@ +-- +-- @telescoped :: [Getter (g ('Cofree' g a)) ('Cofree' g a)] -> Getter ('Cofree' g a) a@ +-- +-- @telescoped :: [Fold (g ('Cofree' g a)) ('Cofree' g a)] -> Fold ('Cofree' g a) a@ +-- +-- @telescoped :: [Setter' (g ('Cofree' g a)) ('Cofree' g a)] -> Setter' ('Cofree' g a) a@ +telescoped :: Functor f => [(Cofree g a -> f (Cofree g a)) -> g (Cofree g a) -> f (g (Cofree g a))] -> (a -> f a) -> Cofree g a -> f (Cofree g a) telescoped = Prelude.foldr (\l r -> _unwrap . l . r) _extract {-# INLINE telescoped #-} + +-- not actually named 'eats' +-- | Construct an @Lens@ into a @'Cofree' g@ given a list of lenses into the base functor. +-- The only difference between this and 'telescoped' is that 'telescoped' focuses on a single value, but this focuses on the entire remaining subtree. +-- When the input list is empty, this is equivalent to 'id'. +-- When the input list is non-empty, this composes the input lenses +-- with '_unwrap' to walk through the @'Cofree' g@. +-- +-- For more on lenses see the 'lens' package on hackage. +-- +-- @telescoped :: [Lens' (g ('Cofree' g a)) ('Cofree' g a)] -> Lens' ('Cofree' g a) ('Cofree' g a)@ +-- +-- @telescoped :: [Traversal' (g ('Cofree' g a)) ('Cofree' g a)] -> Traversal' ('Cofree' g a) ('Cofree' g a)@ +-- +-- @telescoped :: [Getter (g ('Cofree' g a)) ('Cofree' g a)] -> Getter ('Cofree' g a) ('Cofree' g a)@ +-- +-- @telescoped :: [Fold (g ('Cofree' g a)) ('Cofree' g a)] -> Fold ('Cofree' g a) ('Cofree' g a)@ +-- +-- @telescoped :: [Setter' (g ('Cofree' g a)) ('Cofree' g a)] -> Setter' ('Cofree' g a) ('Cofree' g a)@ +telescoped_ :: Functor f => + [(Cofree g a -> f (Cofree g a)) -> g (Cofree g a) -> f (g (Cofree g a))] -> + (Cofree g a -> f (Cofree g a)) -> Cofree g a -> f (Cofree g a) +telescoped_ = Prelude.foldr (\l r -> _unwrap . l . r) id +{-# INLINE telescoped_ #-} + +-- | A @Traversal'@ that gives access to all non-leaf @a@ elements of a +-- @'Cofree' g@ a, where non-leaf is defined as @x@ from @(x :< xs)@ where +-- @null xs@ is @False@. +-- +-- Because this doesn't give access to all values in the @'Cofree' g@, +-- it cannot be used to change types. +-- +-- @shoots :: Traversable g => Traversal' (Cofree g a) a@ +-- +-- N.B. On GHC < 7.9, this is slightly less flexible, as it has to +-- use @null (toList xs)@ instead. +shoots :: (Applicative f, Traversable g) => (a -> f a) -> Cofree g a -> f (Cofree g a) +shoots f = go + where + go xxs@(x :< xs) | null xs = pure xxs + | otherwise = (:<) <$> f x <*> traverse go xs +{-# INLINE shoots #-} + +-- | A @Traversal'@ that gives access to all leaf @a@ elements of a +-- @'Cofree' g@ a, where leaf is defined as @x@ from @(x :< xs)@ where +-- @null xs@ is @True@. +-- +-- Because this doesn't give access to all values in the @'Cofree' g@, +-- it cannot be used to change types. +-- +-- @shoots :: Traversable g => Traversal' (Cofree g a) a@ +-- +-- N.B. On GHC < 7.9, this is slightly less flexible, as it has to +-- use @null (toList xs)@ instead. +leaves :: (Applicative f, Traversable g) => (a -> f a) -> Cofree g a -> f (Cofree g a) +leaves f = go + where + go (x :< xs) | null xs = (:< xs) <$> f x + | otherwise = (x :<) <$> traverse go xs +{-# INLINE leaves #-} diff --git a/src/Control/Comonad/Cofree/Class.hs b/src/Control/Comonad/Cofree/Class.hs --- a/src/Control/Comonad/Cofree/Class.hs +++ b/src/Control/Comonad/Cofree/Class.hs @@ -1,7 +1,9 @@ {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE FunctionalDependencies #-} {-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE Safe #-} {-# LANGUAGE UndecidableInstances #-} + ----------------------------------------------------------------------------- -- | -- Module : Control.Comonad.Cofree.Class @@ -22,8 +24,8 @@ import Control.Comonad.Trans.Store import Control.Comonad.Trans.Traced import Control.Comonad.Trans.Identity -import Data.List.NonEmpty -import Data.Semigroup +import Data.List.NonEmpty (NonEmpty(..)) +import Data.Tree -- | Allows you to peel a layer off a cofree comonad. class (Functor f, Comonad w) => ComonadCofree f w | w -> f where @@ -34,6 +36,9 @@ unwrap (_ :| []) = Nothing unwrap (_ :| (a : as)) = Just (a :| as) +instance ComonadCofree [] Tree where + unwrap = subForest + instance ComonadCofree (Const b) ((,) b) where unwrap = Const . fst @@ -46,5 +51,5 @@ instance ComonadCofree f w => ComonadCofree f (StoreT s w) where unwrap (StoreT wsa s) = flip StoreT s <$> unwrap wsa -instance (ComonadCofree f w, Semigroup m, Monoid m) => ComonadCofree f (TracedT m w) where +instance (ComonadCofree f w, Monoid m) => ComonadCofree f (TracedT m w) where unwrap (TracedT wma) = TracedT <$> unwrap wma diff --git a/src/Control/Comonad/Trans/Cofree.hs b/src/Control/Comonad/Trans/Cofree.hs --- a/src/Control/Comonad/Trans/Cofree.hs +++ b/src/Control/Comonad/Trans/Cofree.hs @@ -1,11 +1,11 @@ -{-# LANGUAGE CPP #-} -{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} -#if __GLASGOW_HASKELL__ >= 707 -{-# LANGUAGE DeriveDataTypeable #-} -#endif +{-# LANGUAGE Rank2Types #-} +{-# LANGUAGE Safe #-} +{-# LANGUAGE StandaloneDeriving #-} ----------------------------------------------------------------------------- -- | @@ -26,6 +26,7 @@ , ComonadCofree(..) , headF , tailF + , transCofreeT , coiterT ) where @@ -33,30 +34,65 @@ import Control.Comonad import Control.Comonad.Trans.Class import Control.Comonad.Cofree.Class +import Control.Comonad.Env.Class +import Control.Comonad.Hoist.Class import Control.Category import Data.Bifunctor import Data.Bifoldable import Data.Bitraversable import Data.Foldable +import Data.Functor.Classes import Data.Functor.Identity -import Data.Semigroup import Data.Traversable import Control.Monad (liftM) import Control.Monad.Trans import Control.Monad.Zip import Prelude hiding (id,(.)) import Data.Data +import GHC.Generics hiding (Infix, Prefix) infixr 5 :< -- | This is the base functor of the cofree comonad transformer. data CofreeF f a b = a :< f b - deriving (Eq,Ord,Show,Read -#if __GLASGOW_HASKELL__ >= 707 - ,Typeable -#endif - ) + deriving (Eq,Ord,Show,Read,Generic,Generic1) +instance Show1 f => Show2 (CofreeF f) where + liftShowsPrec2 spa _sla spb slb d (a :< fb) = + showParen (d > 5) $ + spa 6 a . showString " :< " . liftShowsPrec spb slb 6 fb + +instance (Show1 f, Show a) => Show1 (CofreeF f a) where + liftShowsPrec = liftShowsPrec2 showsPrec showList + +instance Read1 f => Read2 (CofreeF f) where + liftReadsPrec2 rpa _rla rpb rlb d = + readParen (d > 5) $ + (\r' -> [ (u :< v, w) + | (u, s) <- rpa 6 r' + , (":<", t) <- lex s + , (v, w) <- liftReadsPrec rpb rlb 6 t + ]) + +instance (Read1 f, Read a) => Read1 (CofreeF f a) where + liftReadsPrec = liftReadsPrec2 readsPrec readList + +instance Eq1 f => Eq2 (CofreeF f) where + liftEq2 eqa eqfb (a :< fb) (a' :< fb') = eqa a a' && liftEq eqfb fb fb' + +instance (Eq1 f, Eq a) => Eq1 (CofreeF f a) where + liftEq = liftEq2 (==) + +instance Ord1 f => Ord2 (CofreeF f) where + liftCompare2 cmpa cmpfb (a :< fb) (a' :< fb') = + case cmpa a a' of + LT -> LT + EQ -> liftCompare cmpfb fb fb' + GT -> GT + +instance (Ord1 f, Ord a) => Ord1 (CofreeF f a) where + liftCompare = liftCompare2 compare + -- | Extract the head of the base functor headF :: CofreeF f a b -> a headF (a :< _) = a @@ -83,11 +119,12 @@ instance Traversable f => Bitraversable (CofreeF f) where bitraverse f g (a :< as) = (:<) <$> f a <*> traverse g as +transCofreeF :: (forall x. f x -> g x) -> CofreeF f a b -> CofreeF g a b +transCofreeF t (a :< fb) = a :< t fb +{-# INLINE transCofreeF #-} + -- | This is a cofree comonad of some functor @f@, with a comonad @w@ threaded through it at each level. newtype CofreeT f w a = CofreeT { runCofreeT :: w (CofreeF f a (CofreeT f w a)) } -#if __GLASGOW_HASKELL__ >= 707 - deriving Typeable -#endif -- | The cofree `Comonad` of a functor @f@. type Cofree f = CofreeT f Identity @@ -132,12 +169,19 @@ instance (Traversable f, Traversable w) => Traversable (CofreeT f w) where traverse f = fmap CofreeT . traverse (bitraverse f (traverse f)) . runCofreeT -instance Functor f => ComonadTrans (CofreeT f) where +instance ComonadTrans (CofreeT f) where lower = fmap headF . runCofreeT instance (Functor f, Comonad w) => ComonadCofree f (CofreeT f w) where unwrap = tailF . extract . runCofreeT +instance (Functor f, ComonadEnv e w) => ComonadEnv e (CofreeT f w) where + ask = ask . lower + {-# INLINE ask #-} + +instance Functor f => ComonadHoist (CofreeT f) where + cohoist g = CofreeT . fmap (second (cohoist g)) . g . runCofreeT + instance Show (w (CofreeF f a (CofreeT f w a))) => Show (CofreeT f w a) where showsPrec d (CofreeT w) = showParen (d > 10) $ showString "CofreeT " . showsPrec 11 w @@ -153,8 +197,6 @@ compare (CofreeT a) (CofreeT b) = compare a b instance (Alternative f, Monad w) => Monad (CofreeT f w) where - return = CofreeT . return . (:< empty) - {-# INLINE return #-} CofreeT cx >>= f = CofreeT $ do a :< m <- cx b :< n <- runCofreeT $ f a @@ -177,75 +219,24 @@ (a :< fa, b :< fb) <- mzip ma mb return $ (a, b) :< (uncurry mzip <$> mzip fa fb) +-- | Lift a natural transformation from @f@ to @g@ into a comonad homomorphism from @'CofreeT' f w@ to @'CofreeT' g w@ +transCofreeT :: (Functor g, Comonad w) => (forall x. f x -> g x) -> CofreeT f w a -> CofreeT g w a +transCofreeT t = CofreeT . liftW (fmap (transCofreeT t) . transCofreeF t) . runCofreeT + -- | Unfold a @CofreeT@ comonad transformer from a coalgebra and an initial comonad. coiterT :: (Functor f, Comonad w) => (w a -> f (w a)) -> w a -> CofreeT f w a coiterT psi = CofreeT . extend (\w -> extract w :< fmap (coiterT psi) (psi w)) -#if __GLASGOW_HASKELL__ < 707 - -instance Typeable1 f => Typeable2 (CofreeF f) where - typeOf2 t = mkTyConApp cofreeFTyCon [typeOf1 (f t)] where - f :: CofreeF f a b -> f a - f = undefined - -instance (Typeable1 f, Typeable1 w) => Typeable1 (CofreeT f w) where - typeOf1 t = mkTyConApp cofreeTTyCon [typeOf1 (f t), typeOf1 (w t)] where - f :: CofreeT f w a -> f a - f = undefined - w :: CofreeT f w a -> w a - w = undefined - -cofreeFTyCon, cofreeTTyCon :: TyCon -#if __GLASGOW_HASKELL__ < 704 -cofreeTTyCon = mkTyCon "Control.Comonad.Trans.Cofree.CofreeT" -cofreeFTyCon = mkTyCon "Control.Comonad.Trans.Cofree.CofreeF" -#else -cofreeTTyCon = mkTyCon3 "free" "Control.Comonad.Trans.Cofree" "CofreeT" -cofreeFTyCon = mkTyCon3 "free" "Control.Comonad.Trans.Cofree" "CofreeF" -#endif -{-# NOINLINE cofreeTTyCon #-} -{-# NOINLINE cofreeFTyCon #-} - -#else -#define Typeable1 Typeable -#endif - -instance - ( Typeable1 f, Typeable a, Typeable b +deriving instance + ( Typeable f , Data a, Data (f b), Data b - ) => Data (CofreeF f a b) where - gfoldl f z (a :< as) = z (:<) `f` a `f` as - toConstr _ = cofreeFConstr - gunfold k z c = case constrIndex c of - 1 -> k (k (z (:<))) - _ -> error "gunfold" - dataTypeOf _ = cofreeFDataType - dataCast1 f = gcast1 f + ) => Data (CofreeF f a b) -instance - ( Typeable1 f, Typeable1 w, Typeable a +deriving instance + ( Typeable f, Typeable w , Data (w (CofreeF f a (CofreeT f w a))) , Data a - ) => Data (CofreeT f w a) where - gfoldl f z (CofreeT w) = z CofreeT `f` w - toConstr _ = cofreeTConstr - gunfold k z c = case constrIndex c of - 1 -> k (z CofreeT) - _ -> error "gunfold" - dataTypeOf _ = cofreeTDataType - dataCast1 f = gcast1 f - -cofreeFConstr, cofreeTConstr :: Constr -cofreeFConstr = mkConstr cofreeFDataType ":<" [] Infix -cofreeTConstr = mkConstr cofreeTDataType "CofreeT" [] Prefix -{-# NOINLINE cofreeFConstr #-} -{-# NOINLINE cofreeTConstr #-} - -cofreeFDataType, cofreeTDataType :: DataType -cofreeFDataType = mkDataType "Control.Comonad.Trans.Cofree.CofreeF" [cofreeFConstr] -cofreeTDataType = mkDataType "Control.Comonad.Trans.Cofree.CofreeT" [cofreeTConstr] -{-# NOINLINE cofreeFDataType #-} -{-# NOINLINE cofreeTDataType #-} + ) => Data (CofreeT f w a) -- lowerF :: (Functor f, Comonad w) => CofreeT f w a -> f a -- lowerF = fmap extract . unwrap diff --git a/src/Control/Comonad/Trans/Coiter.hs b/src/Control/Comonad/Trans/Coiter.hs --- a/src/Control/Comonad/Trans/Coiter.hs +++ b/src/Control/Comonad/Trans/Coiter.hs @@ -1,11 +1,9 @@ -{-# LANGUAGE CPP #-} -{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} -#if __GLASGOW_HASKELL__ >= 707 -{-# LANGUAGE DeriveDataTypeable #-} -#endif +{-# LANGUAGE Safe #-} +{-# LANGUAGE StandaloneDeriving #-} ----------------------------------------------------------------------------- -- | @@ -27,7 +25,7 @@ -- They are the dual notion of iterative monads. While iterative computations -- produce no values or eventually terminate with one, coiterative -- computations constantly produce values and they never terminate. - -- + -- -- It's simpler form, 'Coiter', is an infinite stream of data. 'CoiterT' -- extends this so that each step of the computation can be performed in -- a comonadic context. @@ -58,31 +56,39 @@ import Data.Bitraversable import Data.Data import Data.Foldable -import Data.Function (on) +import Data.Functor.Classes import Data.Functor.Identity import Data.Traversable import Prelude hiding (id,(.)) -import Prelude.Extras -- | This is the coiterative comonad generated by a comonad newtype CoiterT w a = CoiterT { runCoiterT :: w (a, CoiterT w a) } -#if __GLASGOW_HASKELL__ >= 707 - deriving Typeable -#endif -instance (Functor w, Eq1 w) => Eq1 (CoiterT w) where - (==#) = on (==#) (fmap (fmap Lift1) . runCoiterT) +instance (Eq1 w) => Eq1 (CoiterT w) where + liftEq eq = go + where + go (CoiterT x) (CoiterT y) = liftEq (liftEq2 eq go) x y -instance (Functor w, Ord1 w) => Ord1 (CoiterT w) where - compare1 = on compare1 (fmap (fmap Lift1) . runCoiterT) +instance (Ord1 w) => Ord1 (CoiterT w) where + liftCompare cmp = go + where + go (CoiterT x) (CoiterT y) = liftCompare (liftCompare2 cmp go) x y -instance (Functor w, Show1 w) => Show1 (CoiterT w) where - showsPrec1 d (CoiterT as) = showParen (d > 10) $ - showString "CoiterT " . showsPrec1 11 (fmap (fmap Lift1) as) +instance (Show1 w) => Show1 (CoiterT w) where + liftShowsPrec sp sl = go + where + goList = liftShowList sp sl + go d (CoiterT x) = showsUnaryWith + (liftShowsPrec (liftShowsPrec2 sp sl go goList) (liftShowList2 sp sl go goList)) + "CoiterT" d x -instance (Functor w, Read1 w) => Read1 (CoiterT w) where - readsPrec1 d = readParen (d > 10) $ \r -> - [ (CoiterT (fmap (fmap lower1) m),t) | ("CoiterT",s) <- lex r, (m,t) <- readsPrec1 11 s] +instance (Read1 w) => Read1 (CoiterT w) where + liftReadsPrec rp rl = go + where + goList = liftReadList rp rl + go = readsData $ readsUnaryWith + (liftReadsPrec (liftReadsPrec2 rp rl go goList) (liftReadList2 rp rl go goList)) + "CoiterT" CoiterT -- | The coiterative comonad type Coiter = CoiterT Identity @@ -121,11 +127,11 @@ instance Comonad w => ComonadCofree Identity (CoiterT w) where unwrap = Identity . snd . extract . runCoiterT {-# INLINE unwrap #-} - + instance ComonadEnv e w => ComonadEnv e (CoiterT w) where ask = ask . lower {-# INLINE ask #-} - + instance ComonadHoist CoiterT where cohoist g = CoiterT . fmap (second (cohoist g)) . g . runCoiterT @@ -147,65 +153,29 @@ {-# INLINE seeks #-} {-# INLINE experiment #-} -instance Show (w (a, CoiterT w a)) => Show (CoiterT w a) where - showsPrec d w = showParen (d > 10) $ - showString "CoiterT " . showsPrec 11 w +instance (Show1 w, Show a) => Show (CoiterT w a) where + showsPrec = showsPrec1 -instance Read (w (a, CoiterT w a)) => Read (CoiterT w a) where - readsPrec d = readParen (d > 10) $ \r -> - [(CoiterT w, t) | ("CoiterT", s) <- lex r, (w, t) <- readsPrec 11 s] +instance (Read1 w, Read a) => Read (CoiterT w a) where + readsPrec = readsPrec1 -instance Eq (w (a, CoiterT w a)) => Eq (CoiterT w a) where - CoiterT a == CoiterT b = a == b +instance (Eq1 w, Eq a) => Eq (CoiterT w a) where + (==) = eq1 {-# INLINE (==) #-} -instance Ord (w (a, CoiterT w a)) => Ord (CoiterT w a) where - compare (CoiterT a) (CoiterT b) = compare a b +instance (Ord1 w, Ord a) => Ord (CoiterT w a) where + compare = compare1 {-# INLINE compare #-} -- | Unfold a @CoiterT@ comonad transformer from a cokleisli arrow and an initial comonadic seed. unfold :: Comonad w => (w a -> a) -> w a -> CoiterT w a unfold psi = CoiterT . extend (extract &&& unfold psi . extend psi) -#if __GLASGOW_HASKELL__ < 707 - -instance Typeable1 w => Typeable1 (CoiterT w) where - typeOf1 t = mkTyConApp coiterTTyCon [typeOf1 (w t)] where - w :: CoiterT w a -> w a - w = undefined - -coiterTTyCon :: TyCon -#if __GLASGOW_HASKELL__ < 704 -coiterTTyCon = mkTyCon "Control.Comonad.Trans.Coiter.CoiterT" -#else -coiterTTyCon = mkTyCon3 "free" "Control.Comonad.Trans.Coiter" "CoiterT" -#endif -{-# NOINLINE coiterTTyCon #-} - -#else -#define Typeable1 Typeable -#endif - -instance - ( Typeable1 w, Typeable a +deriving instance + ( Typeable w , Data (w (a, CoiterT w a)) , Data a - ) => Data (CoiterT w a) where - gfoldl f z (CoiterT w) = z CoiterT `f` w - toConstr _ = coiterTConstr - gunfold k z c = case constrIndex c of - 1 -> k (z CoiterT) - _ -> error "gunfold" - dataTypeOf _ = coiterTDataType - dataCast1 f = gcast1 f - -coiterTConstr :: Constr -coiterTConstr = mkConstr coiterTDataType "CoiterT" [] Prefix -{-# NOINLINE coiterTConstr #-} - -coiterTDataType :: DataType -coiterTDataType = mkDataType "Control.Comonad.Trans.Coiter.CoiterT" [coiterTConstr] -{-# NOINLINE coiterTDataType #-} + ) => Data (CoiterT w a) {- $example diff --git a/src/Control/Monad/Free.hs b/src/Control/Monad/Free.hs --- a/src/Control/Monad/Free.hs +++ b/src/Control/Monad/Free.hs @@ -1,15 +1,12 @@ -{-# LANGUAGE CPP #-} -{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE Rank2Types #-} -#if __GLASGOW_HASKELL__ >= 707 -{-# LANGUAGE DeriveDataTypeable #-} -#endif -#ifndef MIN_VERSION_base -#define MIN_VERSION_base(x,y,z) 1 -#endif +{-# LANGUAGE StandaloneDeriving #-} +{-# LANGUAGE Safe #-} + ----------------------------------------------------------------------------- -- | -- Module : Control.Monad.Free @@ -28,16 +25,20 @@ , retract , liftF , iter + , iterA , iterM , hoistFree , foldFree , toFreeT , cutoff + , unfold + , unfoldM , _Pure, _Free ) where import Control.Applicative -import Control.Monad (liftM, MonadPlus(..)) +import Control.Arrow ((>>>)) +import Control.Monad (liftM, MonadPlus(..), (>=>)) import Control.Monad.Fix import Control.Monad.Trans.Class import qualified Control.Monad.Trans.Free as FreeT @@ -48,15 +49,27 @@ import Control.Monad.Error.Class import Control.Monad.Cont.Class import Data.Functor.Bind +import Data.Functor.Classes +import Data.Functor.WithIndex import Data.Foldable +import Data.Foldable.WithIndex import Data.Profunctor import Data.Traversable +import Data.Traversable.WithIndex import Data.Semigroup.Foldable import Data.Semigroup.Traversable import Data.Data +import GHC.Generics import Prelude hiding (foldr) -import Prelude.Extras +-- $setup +-- >>> import Control.Applicative (Const (..)) +-- >>> import Data.Functor.Identity (Identity (..)) +-- >>> import Data.Monoid (First (..)) +-- >>> import Data.Tagged (Tagged (..)) +-- >>> let preview l x = getFirst (getConst (l (Const . First . Just) x)) +-- >>> let review l x = runIdentity (unTagged (l (Tagged (Identity x)))) + -- | The 'Free' 'Monad' for a 'Functor' @f@. -- -- /Formally/ @@ -76,7 +89,7 @@ -- -- then 'Free' is the left adjoint to @U@. -- --- Being 'Free' being left adjoint to @U@ means that there is an isomorphism between +-- 'Free' being left adjoint to @U@ means that there is an isomorphism between -- -- @'Free' f -> m@ in the category of monads and @f -> U m@ in the category of functors. -- @@ -102,64 +115,50 @@ -- -- * @'Free' 'Maybe'@ can be used to model a partiality monad where each layer represents running the computation for a while longer. data Free f a = Pure a | Free (f (Free f a)) -#if __GLASGOW_HASKELL__ >= 707 - deriving (Typeable) -#endif + deriving (Generic, Generic1) -instance (Functor f, Eq1 f) => Eq1 (Free f) where - Pure a ==# Pure b = a == b - Free fa ==# Free fb = fmap Lift1 fa ==# fmap Lift1 fb - _ ==# _ = False +deriving instance (Typeable f, Data (f (Free f a)), Data a) => Data (Free f a) -instance (Eq (f (Free f a)), Eq a) => Eq (Free f a) where - Pure a == Pure b = a == b - Free fa == Free fb = fa == fb - _ == _ = False +instance Eq1 f => Eq1 (Free f) where + liftEq eq = go + where + go (Pure a) (Pure b) = eq a b + go (Free fa) (Free fb) = liftEq go fa fb + go _ _ = False -instance (Functor f, Ord1 f) => Ord1 (Free f) where - Pure a `compare1` Pure b = a `compare` b - Pure _ `compare1` Free _ = LT - Free _ `compare1` Pure _ = GT - Free fa `compare1` Free fb = fmap Lift1 fa `compare1` fmap Lift1 fb +instance (Eq1 f, Eq a) => Eq (Free f a) where + (==) = eq1 -instance (Ord (f (Free f a)), Ord a) => Ord (Free f a) where - Pure a `compare` Pure b = a `compare` b - Pure _ `compare` Free _ = LT - Free _ `compare` Pure _ = GT - Free fa `compare` Free fb = fa `compare` fb +instance Ord1 f => Ord1 (Free f) where + liftCompare cmp = go + where + go (Pure a) (Pure b) = cmp a b + go (Pure _) (Free _) = LT + go (Free _) (Pure _) = GT + go (Free fa) (Free fb) = liftCompare go fa fb -instance (Functor f, Show1 f) => Show1 (Free f) where - showsPrec1 d (Pure a) = showParen (d > 10) $ - showString "Pure " . showsPrec 11 a - showsPrec1 d (Free m) = showParen (d > 10) $ - showString "Free " . showsPrec1 11 (fmap Lift1 m) +instance (Ord1 f, Ord a) => Ord (Free f a) where + compare = compare1 -instance (Show (f (Free f a)), Show a) => Show (Free f a) where - showsPrec d (Pure a) = showParen (d > 10) $ - showString "Pure " . showsPrec 11 a - showsPrec d (Free m) = showParen (d > 10) $ - showString "Free " . showsPrec 11 m +instance Show1 f => Show1 (Free f) where + liftShowsPrec sp sl = go + where + go d (Pure a) = showsUnaryWith sp "Pure" d a + go d (Free fa) = showsUnaryWith (liftShowsPrec go (liftShowList sp sl)) "Free" d fa -instance (Functor f, Read1 f) => Read1 (Free f) where - readsPrec1 d r = readParen (d > 10) - (\r' -> [ (Pure m, t) - | ("Pure", s) <- lex r' - , (m, t) <- readsPrec 11 s]) r - ++ readParen (d > 10) - (\r' -> [ (Free (fmap lower1 m), t) - | ("Free", s) <- lex r' - , (m, t) <- readsPrec1 11 s]) r +instance (Show1 f, Show a) => Show (Free f a) where + showsPrec = showsPrec1 -instance (Read (f (Free f a)), Read a) => Read (Free f a) where - readsPrec d r = readParen (d > 10) - (\r' -> [ (Pure m, t) - | ("Pure", s) <- lex r' - , (m, t) <- readsPrec 11 s]) r - ++ readParen (d > 10) - (\r' -> [ (Free m, t) - | ("Free", s) <- lex r' - , (m, t) <- readsPrec 11 s]) r +instance Read1 f => Read1 (Free f) where + liftReadsPrec rp rl = go + where + go = readsData $ + readsUnaryWith rp "Pure" Pure `mappend` + readsUnaryWith (liftReadsPrec go (liftReadList rp rl)) "Free" Free +instance (Read1 f, Read a) => Read (Free f a) where + readsPrec = readsPrec1 + instance Functor f => Functor (Free f) where fmap f = go where go (Pure a) = Pure (f a) @@ -183,7 +182,7 @@ Free m >>- f = Free ((>>- f) <$> m) instance Functor f => Monad (Free f) where - return = Pure + return = pure {-# INLINE return #-} Pure a >>= f = f a Free m >>= f = Free ((>>= f) <$> m) @@ -199,7 +198,7 @@ {-# INLINE (<|>) #-} -- | This violates the MonadPlus laws, handle with care. -instance (Functor v, MonadPlus v) => MonadPlus (Free v) where +instance MonadPlus v => MonadPlus (Free v) where mzero = Free mzero {-# INLINE mzero #-} a `mplus` b = Free (return a `mplus` return b) @@ -223,14 +222,12 @@ Free fa -> foldr (flip go) r fa {-# INLINE foldr #-} -#if MIN_VERSION_base(4,6,0) foldl' f = go where go r free = case free of Pure a -> f r a Free fa -> foldl' go r fa {-# INLINE foldl' #-} -#endif instance Foldable1 f => Foldable1 (Free f) where foldMap1 f = go where @@ -250,7 +247,22 @@ go (Free fa) = Free <$> traverse1 go fa {-# INLINE traverse1 #-} -instance (Functor m, MonadWriter e m) => MonadWriter e (Free m) where +instance FunctorWithIndex i f => FunctorWithIndex [i] (Free f) where + imap f (Pure a) = Pure $ f [] a + imap f (Free s) = Free $ imap (\i -> imap (f . (:) i)) s + {-# INLINE imap #-} + +instance FoldableWithIndex i f => FoldableWithIndex [i] (Free f) where + ifoldMap f (Pure a) = f [] a + ifoldMap f (Free s) = ifoldMap (\i -> ifoldMap (f . (:) i)) s + {-# INLINE ifoldMap #-} + +instance TraversableWithIndex i f => TraversableWithIndex [i] (Free f) where + itraverse f (Pure a) = Pure <$> f [] a + itraverse f (Free s) = Free <$> itraverse (\i -> itraverse (f . (:) i)) s + {-# INLINE itraverse #-} + +instance MonadWriter e m => MonadWriter e (Free m) where tell = lift . tell {-# INLINE tell #-} listen = lift . listen . retract @@ -258,25 +270,25 @@ pass = lift . pass . retract {-# INLINE pass #-} -instance (Functor m, MonadReader e m) => MonadReader e (Free m) where +instance MonadReader e m => MonadReader e (Free m) where ask = lift ask {-# INLINE ask #-} local f = lift . local f . retract {-# INLINE local #-} -instance (Functor m, MonadState s m) => MonadState s (Free m) where +instance MonadState s m => MonadState s (Free m) where get = lift get {-# INLINE get #-} put s = lift (put s) {-# INLINE put #-} -instance (Functor m, MonadError e m) => MonadError e (Free m) where +instance MonadError e m => MonadError e (Free m) where throwError = lift . throwError {-# INLINE throwError #-} catchError as f = lift (catchError (retract as) (retract . f)) {-# INLINE catchError #-} -instance (Functor m, MonadCont m) => MonadCont (Free m) where +instance MonadCont m => MonadCont (Free m) where callCC f = lift (callCC (retract . f . liftM lift)) {-# INLINE callCC #-} @@ -300,18 +312,23 @@ iter _ (Pure a) = a iter phi (Free m) = phi (iter phi <$> m) --- | Like iter for monadic values. +-- | Like 'iter' for applicative values. +iterA :: (Applicative p, Functor f) => (f (p a) -> p a) -> Free f a -> p a +iterA _ (Pure x) = pure x +iterA phi (Free f) = phi (iterA phi <$> f) + +-- | Like 'iter' for monadic values. iterM :: (Monad m, Functor f) => (f (m a) -> m a) -> Free f a -> m a iterM _ (Pure x) = return x -iterM phi (Free f) = phi $ fmap (iterM phi) f +iterM phi (Free f) = phi (iterM phi <$> f) --- | Lift a natural transformation from @f@ to @g@ into a natural transformation from @'FreeT' f@ to @'FreeT' g@. +-- | Lift a natural transformation from @f@ to @g@ into a natural transformation from @'Free' f@ to @'Free' g@. hoistFree :: Functor g => (forall a. f a -> g a) -> Free f b -> Free g b hoistFree _ (Pure a) = Pure a hoistFree f (Free as) = Free (hoistFree f <$> f as) --- | The very definition of a free monoid is that given a natural transformation you get a monoid homomorphism. -foldFree :: (Functor m, Monad m) => (forall x . f x -> m x) -> Free f a -> m a +-- | The very definition of a free monad is that given a natural transformation you get a monad homomorphism. +foldFree :: Monad m => (forall x . f x -> m x) -> Free f a -> m a foldFree _ (Pure a) = return a foldFree f (Free as) = f as >>= foldFree f @@ -332,13 +349,21 @@ -- prop> cutoff (n+1) . lift == lift . liftM Just -- prop> cutoff (n+1) . wrap == wrap . fmap (cutoff n) -- --- Calling 'retract . cutoff n' is always terminating, provided each of the +-- Calling @'retract' '.' 'cutoff' n@ is always terminating, provided each of the -- steps in the iteration is terminating. cutoff :: (Functor f) => Integer -> Free f a -> Free f (Maybe a) cutoff n _ | n <= 0 = return Nothing cutoff n (Free f) = Free $ fmap (cutoff (n - 1)) f cutoff _ m = Just <$> m +-- | Unfold a free monad from a seed. +unfold :: Functor f => (b -> Either a (f b)) -> b -> Free f a +unfold f = f >>> either Pure (Free . fmap (unfold f)) + +-- | Unfold a free monad from a seed, monadically. +unfoldM :: (Traversable f, Monad m) => (b -> m (Either a (f b))) -> b -> m (Free f a) +unfoldM f = f >=> either (pure . pure) (fmap Free . traverse (unfoldM f)) + -- | This is @Prism' (Free f a) a@ in disguise -- -- >>> preview _Pure (Pure 3) @@ -355,60 +380,18 @@ {-# INLINE impure #-} {-# INLINE _Pure #-} --- | This is @Prism' (Free f a) (f (Free f a))@ in disguise +-- | This is @Prism (Free f a) (Free g a) (f (Free f a)) (g (Free g a))@ in disguise -- -- >>> preview _Free (review _Free (Just (Pure 3))) -- Just (Just (Pure 3)) -- -- >>> review _Free (Just (Pure 3)) -- Free (Just (Pure 3)) -_Free :: forall f m a p. (Choice p, Applicative m) - => p (f (Free f a)) (m (f (Free f a))) -> p (Free f a) (m (Free f a)) +_Free :: forall f g m a p. (Choice p, Applicative m) + => p (f (Free f a)) (m (g (Free g a))) -> p (Free f a) (m (Free g a)) _Free = dimap unfree (either pure (fmap Free)) . right' where unfree (Free x) = Right x - unfree x = Left x + unfree (Pure x) = Left (Pure x) {-# INLINE unfree #-} {-# INLINE _Free #-} - - -#if __GLASGOW_HASKELL__ < 707 -instance Typeable1 f => Typeable1 (Free f) where - typeOf1 t = mkTyConApp freeTyCon [typeOf1 (f t)] where - f :: Free f a -> f a - f = undefined - -freeTyCon :: TyCon -#if __GLASGOW_HASKELL__ < 704 -freeTyCon = mkTyCon "Control.Monad.Free.Free" -#else -freeTyCon = mkTyCon3 "free" "Control.Monad.Free" "Free" -#endif -{-# NOINLINE freeTyCon #-} - -instance - ( Typeable1 f, Typeable a - , Data a, Data (f (Free f a)) - ) => Data (Free f a) where - gfoldl f z (Pure a) = z Pure `f` a - gfoldl f z (Free as) = z Free `f` as - toConstr Pure{} = pureConstr - toConstr Free{} = freeConstr - gunfold k z c = case constrIndex c of - 1 -> k (z Pure) - 2 -> k (z Free) - _ -> error "gunfold" - dataTypeOf _ = freeDataType - dataCast1 f = gcast1 f - -pureConstr, freeConstr :: Constr -pureConstr = mkConstr freeDataType "Pure" [] Prefix -freeConstr = mkConstr freeDataType "Free" [] Prefix -{-# NOINLINE pureConstr #-} -{-# NOINLINE freeConstr #-} - -freeDataType :: DataType -freeDataType = mkDataType "Control.Monad.Free.FreeF" [pureConstr, freeConstr] -{-# NOINLINE freeDataType #-} - -#endif diff --git a/src/Control/Monad/Free/Ap.hs b/src/Control/Monad/Free/Ap.hs new file mode 100644 --- /dev/null +++ b/src/Control/Monad/Free/Ap.hs @@ -0,0 +1,349 @@ +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE Rank2Types #-} +{-# LANGUAGE Safe #-} +{-# LANGUAGE StandaloneDeriving #-} + +-------------------------------------------------------------------------------- +-- | +-- \"Applicative Effects in Free Monads\" +-- +-- Often times, the '(\<*\>)' operator can be more efficient than 'ap'. +-- Conventional free monads don't provide any means of modeling this. +-- The free monad can be modified to make use of an underlying applicative. +-- But it does require some laws, or else the '(\<*\>)' = 'ap' law is broken. +-- When interpreting this free monad with 'foldFree', +-- the natural transformation must be an applicative homomorphism. +-- An applicative homomorphism @hm :: (Applicative f, Applicative g) => f x -> g x@ +-- will satisfy these laws. +-- +-- * @hm (pure a) = pure a@ +-- * @hm (f \<*\> a) = hm f \<*\> hm a@ +-- +-- This is based on the \"Applicative Effects in Free Monads\" series of articles by Will Fancher +-- +-- * +-- +-- * +-------------------------------------------------------------------------------- +module Control.Monad.Free.Ap + ( MonadFree(..) + , Free(..) + , retract + , liftF + , iter + , iterA + , iterM + , hoistFree + , foldFree + , toFreeT + , cutoff + , unfold + , unfoldM + , _Pure, _Free + ) where + +import Control.Applicative +import Control.Arrow ((>>>)) +import Control.Monad (liftM, MonadPlus(..), (>=>)) +import Control.Monad.Fix +import Control.Monad.Trans.Class +import qualified Control.Monad.Trans.Free.Ap as FreeT +import Control.Monad.Free.Class +import Control.Monad.Reader.Class +import Control.Monad.Writer.Class +import Control.Monad.State.Class +import Control.Monad.Error.Class +import Control.Monad.Cont.Class +import Data.Functor.Bind +import Data.Functor.Classes +import Data.Foldable +import Data.Profunctor +import Data.Traversable +import Data.Semigroup.Foldable +import Data.Semigroup.Traversable +import Data.Data +import GHC.Generics +import Prelude hiding (foldr) + +-- $setup +-- >>> import Control.Applicative (Const (..)) +-- >>> import Data.Functor.Identity (Identity (..)) +-- >>> import Data.Monoid (First (..)) +-- >>> import Data.Tagged (Tagged (..)) +-- >>> let preview l x = getFirst (getConst (l (Const . First . Just) x)) +-- >>> let review l x = runIdentity (unTagged (l (Tagged (Identity x)))) + +-- | A free monad given an applicative +data Free f a = Pure a | Free (f (Free f a)) + deriving (Generic, Generic1) + +deriving instance + ( Typeable f + , Data a, Data (f (Free f a)) + ) => Data (Free f a) + +instance Eq1 f => Eq1 (Free f) where + liftEq eq = go + where + go (Pure a) (Pure b) = eq a b + go (Free fa) (Free fb) = liftEq go fa fb + go _ _ = False + +instance (Eq1 f, Eq a) => Eq (Free f a) where + (==) = eq1 + +instance Ord1 f => Ord1 (Free f) where + liftCompare cmp = go + where + go (Pure a) (Pure b) = cmp a b + go (Pure _) (Free _) = LT + go (Free _) (Pure _) = GT + go (Free fa) (Free fb) = liftCompare go fa fb + +instance (Ord1 f, Ord a) => Ord (Free f a) where + compare = compare1 + +instance Show1 f => Show1 (Free f) where + liftShowsPrec sp sl = go + where + go d (Pure a) = showsUnaryWith sp "Pure" d a + go d (Free fa) = showsUnaryWith (liftShowsPrec go (liftShowList sp sl)) "Free" d fa + +instance (Show1 f, Show a) => Show (Free f a) where + showsPrec = showsPrec1 + +instance Read1 f => Read1 (Free f) where + liftReadsPrec rp rl = go + where + go = readsData $ + readsUnaryWith rp "Pure" Pure `mappend` + readsUnaryWith (liftReadsPrec go (liftReadList rp rl)) "Free" Free + +instance (Read1 f, Read a) => Read (Free f a) where + readsPrec = readsPrec1 + +instance Functor f => Functor (Free f) where + fmap f = go where + go (Pure a) = Pure (f a) + go (Free fa) = Free (go <$> fa) + {-# INLINE fmap #-} + +instance Apply f => Apply (Free f) where + Pure a <.> Pure b = Pure (a b) + Pure a <.> Free fb = Free $ fmap a <$> fb + Free fa <.> Pure b = Free $ fmap ($ b) <$> fa + Free fa <.> Free fb = Free $ fmap (<.>) fa <.> fb + +instance Applicative f => Applicative (Free f) where + pure = Pure + {-# INLINE pure #-} + Pure a <*> Pure b = Pure $ a b + Pure a <*> Free mb = Free $ fmap a <$> mb + Free ma <*> Pure b = Free $ fmap ($ b) <$> ma + Free ma <*> Free mb = Free $ fmap (<*>) ma <*> mb + +instance Apply f => Bind (Free f) where + Pure a >>- f = f a + Free m >>- f = Free ((>>- f) <$> m) + +instance Applicative f => Monad (Free f) where + return = pure + {-# INLINE return #-} + Pure a >>= f = f a + Free m >>= f = Free ((>>= f) <$> m) + +instance Applicative f => MonadFix (Free f) where + mfix f = a where a = f (impure a); impure (Pure x) = x; impure (Free _) = error "mfix (Free f): Free" + +-- | This violates the Alternative laws, handle with care. +instance Alternative v => Alternative (Free v) where + empty = Free empty + {-# INLINE empty #-} + a <|> b = Free (pure a <|> pure b) + {-# INLINE (<|>) #-} + +-- | This violates the MonadPlus laws, handle with care. +instance MonadPlus v => MonadPlus (Free v) where + mzero = Free mzero + {-# INLINE mzero #-} + a `mplus` b = Free (return a `mplus` return b) + {-# INLINE mplus #-} + +-- | This is not a true monad transformer. It is only a monad transformer \"up to 'retract'\". +instance MonadTrans Free where + lift = Free . liftM Pure + {-# INLINE lift #-} + +instance Foldable f => Foldable (Free f) where + foldMap f = go where + go (Pure a) = f a + go (Free fa) = foldMap go fa + {-# INLINE foldMap #-} + + foldr f = go where + go r free = + case free of + Pure a -> f a r + Free fa -> foldr (flip go) r fa + {-# INLINE foldr #-} + + foldl' f = go where + go r free = + case free of + Pure a -> f r a + Free fa -> foldl' go r fa + {-# INLINE foldl' #-} + +instance Foldable1 f => Foldable1 (Free f) where + foldMap1 f = go where + go (Pure a) = f a + go (Free fa) = foldMap1 go fa + {-# INLINE foldMap1 #-} + +instance Traversable f => Traversable (Free f) where + traverse f = go where + go (Pure a) = Pure <$> f a + go (Free fa) = Free <$> traverse go fa + {-# INLINE traverse #-} + +instance Traversable1 f => Traversable1 (Free f) where + traverse1 f = go where + go (Pure a) = Pure <$> f a + go (Free fa) = Free <$> traverse1 go fa + {-# INLINE traverse1 #-} + +instance MonadWriter e m => MonadWriter e (Free m) where + tell = lift . tell + {-# INLINE tell #-} + listen = lift . listen . retract + {-# INLINE listen #-} + pass = lift . pass . retract + {-# INLINE pass #-} + +instance MonadReader e m => MonadReader e (Free m) where + ask = lift ask + {-# INLINE ask #-} + local f = lift . local f . retract + {-# INLINE local #-} + +instance MonadState s m => MonadState s (Free m) where + get = lift get + {-# INLINE get #-} + put s = lift (put s) + {-# INLINE put #-} + +instance MonadError e m => MonadError e (Free m) where + throwError = lift . throwError + {-# INLINE throwError #-} + catchError as f = lift (catchError (retract as) (retract . f)) + {-# INLINE catchError #-} + +instance MonadCont m => MonadCont (Free m) where + callCC f = lift (callCC (retract . f . liftM lift)) + {-# INLINE callCC #-} + +instance Applicative f => MonadFree f (Free f) where + wrap = Free + {-# INLINE wrap #-} + +-- | +-- 'retract' is the left inverse of 'lift' and 'liftF' +-- +-- @ +-- 'retract' . 'lift' = 'id' +-- 'retract' . 'liftF' = 'id' +-- @ +retract :: Monad f => Free f a -> f a +retract = foldFree id + +-- | Given an applicative homomorphism from @f@ to 'Identity', tear down a 'Free' 'Monad' using iteration. +iter :: Applicative f => (f a -> a) -> Free f a -> a +iter _ (Pure a) = a +iter phi (Free m) = phi (iter phi <$> m) + +-- | Like 'iter' for applicative values. +iterA :: (Applicative p, Applicative f) => (f (p a) -> p a) -> Free f a -> p a +iterA _ (Pure x) = pure x +iterA phi (Free f) = phi (iterA phi <$> f) + +-- | Like 'iter' for monadic values. +iterM :: (Monad m, Applicative f) => (f (m a) -> m a) -> Free f a -> m a +iterM _ (Pure x) = return x +iterM phi (Free f) = phi (iterM phi <$> f) + +-- | Lift an applicative homomorphism from @f@ to @g@ into a monad homomorphism from @'Free' f@ to @'Free' g@. +hoistFree :: (Applicative f, Applicative g) => (forall a. f a -> g a) -> Free f b -> Free g b +hoistFree f = foldFree (liftF . f) + +-- | Given an applicative homomorphism, you get a monad homomorphism. +foldFree :: (Applicative f, Monad m) => (forall x . f x -> m x) -> Free f a -> m a +foldFree _ (Pure a) = return a +foldFree f (Free as) = f as >>= foldFree f + +-- | Convert a 'Free' monad from "Control.Monad.Free.Ap" to a 'FreeT.FreeT' monad +-- from "Control.Monad.Trans.Free.Ap". +-- WARNING: This assumes that 'liftF' is an applicative homomorphism. +toFreeT :: (Applicative f, Monad m) => Free f a -> FreeT.FreeT f m a +toFreeT = foldFree liftF + +-- | Cuts off a tree of computations at a given depth. +-- If the depth is 0 or less, no computation nor +-- monadic effects will take place. +-- +-- Some examples (n ≥ 0): +-- +-- prop> cutoff 0 _ == return Nothing +-- prop> cutoff (n+1) . return == return . Just +-- prop> cutoff (n+1) . lift == lift . liftM Just +-- prop> cutoff (n+1) . wrap == wrap . fmap (cutoff n) +-- +-- Calling 'retract . cutoff n' is always terminating, provided each of the +-- steps in the iteration is terminating. +cutoff :: (Applicative f) => Integer -> Free f a -> Free f (Maybe a) +cutoff n _ | n <= 0 = return Nothing +cutoff n (Free f) = Free $ fmap (cutoff (n - 1)) f +cutoff _ m = Just <$> m + +-- | Unfold a free monad from a seed. +unfold :: Applicative f => (b -> Either a (f b)) -> b -> Free f a +unfold f = f >>> either Pure (Free . fmap (unfold f)) + +-- | Unfold a free monad from a seed, monadically. +unfoldM :: (Applicative f, Traversable f, Monad m) => (b -> m (Either a (f b))) -> b -> m (Free f a) +unfoldM f = f >=> either (pure . pure) (fmap Free . traverse (unfoldM f)) + +-- | This is @Prism' (Free f a) a@ in disguise +-- +-- >>> preview _Pure (Pure 3) +-- Just 3 +-- +-- >>> review _Pure 3 :: Free Maybe Int +-- Pure 3 +_Pure :: forall f m a p. (Choice p, Applicative m) + => p a (m a) -> p (Free f a) (m (Free f a)) +_Pure = dimap impure (either pure (fmap Pure)) . right' + where + impure (Pure x) = Right x + impure x = Left x + {-# INLINE impure #-} +{-# INLINE _Pure #-} + +-- | This is @Prism' (Free f a) (f (Free f a))@ in disguise +-- +-- >>> preview _Free (review _Free (Just (Pure 3))) +-- Just (Just (Pure 3)) +-- +-- >>> review _Free (Just (Pure 3)) +-- Free (Just (Pure 3)) +_Free :: forall f m a p. (Choice p, Applicative m) + => p (f (Free f a)) (m (f (Free f a))) -> p (Free f a) (m (Free f a)) +_Free = dimap unfree (either pure (fmap Free)) . right' + where + unfree (Free x) = Right x + unfree x = Left x + {-# INLINE unfree #-} +{-# INLINE _Free #-} diff --git a/src/Control/Monad/Free/Church.hs b/src/Control/Monad/Free/Church.hs --- a/src/Control/Monad/Free/Church.hs +++ b/src/Control/Monad/Free/Church.hs @@ -1,12 +1,10 @@ {-# LANGUAGE BangPatterns #-} -{-# LANGUAGE CPP #-} {-# LANGUAGE Rank2Types #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} -#ifndef MIN_VERSION_base -#define MIN_VERSION_base(x,y,z) 1 -#endif +{-# LANGUAGE Safe #-} + ----------------------------------------------------------------------------- -- | -- Module : Control.Monad.Free.Church @@ -48,14 +46,15 @@ -- -- This is based on the \"Free Monads for Less\" series of articles by Edward Kmett: -- --- * +-- * -- --- * +-- * ---------------------------------------------------------------------------- module Control.Monad.Free.Church ( F(..) , improve , fromF + , iter , iterM , toF , retract @@ -69,26 +68,32 @@ import Control.Applicative import Control.Monad as Monad import Control.Monad.Fix -import Control.Monad.Free hiding (retract, iterM, cutoff) -import qualified Control.Monad.Free as Free +import Control.Monad.Free hiding (retract, iter, iterM, cutoff) import Control.Monad.Reader.Class import Control.Monad.Writer.Class import Control.Monad.Cont.Class import Control.Monad.Trans.Class import Control.Monad.State.Class import Data.Foldable +import Data.Traversable import Data.Functor.Bind +import Data.Semigroup.Foldable +import Data.Semigroup.Traversable import Prelude hiding (foldr) -- | The Church-encoded free monad for a functor @f@. -- -- It is /asymptotically/ more efficient to use ('>>=') for 'F' than it is to ('>>=') with 'Free'. -- --- +-- newtype F f a = F { runF :: forall r. (a -> r) -> (f r -> r) -> r } +-- | Tear down a 'Free' 'Monad' using iteration. +iter :: (f a -> a) -> F f a -> a +iter phi xs = runF xs id phi + -- | Like iter for monadic values. -iterM :: (Monad m, Functor f) => (f (m a) -> m a) -> F f a -> m a +iterM :: Monad m => (f (m a) -> m a) -> F f a -> m a iterM phi xs = runF xs return phi instance Functor (F f) where @@ -110,7 +115,7 @@ (>>-) = (>>=) instance Monad (F f) where - return a = F (\kp _ -> kp a) + return = pure F m >>= f = F (\kp kf -> m (\a -> runF (f a) kp kf) kf) instance MonadFix (F f) where @@ -118,15 +123,26 @@ a = f (impure a) impure (F x) = x id (error "MonadFix (F f): wrap") -instance (Foldable f, Functor f) => Foldable (F f) where +instance Foldable f => Foldable (F f) where + foldMap f xs = runF xs f fold + {-# INLINE foldMap #-} + foldr f r xs = runF xs f (foldr (.) id) r {-# INLINE foldr #-} -#if MIN_VERSION_base(4,6,0) foldl' f z xs = runF xs (\a !r -> f r a) (flip $ foldl' $ \r g -> g r) z {-# INLINE foldl' #-} -#endif +instance Traversable f => Traversable (F f) where + traverse f m = runF m (fmap return . f) (fmap wrap . sequenceA) + {-# INLINE traverse #-} + +instance Foldable1 f => Foldable1 (F f) where + foldMap1 f m = runF m f fold1 + +instance Traversable1 f => Traversable1 (F f) where + traverse1 f m = runF m (fmap return . f) (fmap wrap . sequence1) + -- | This violates the MonadPlus laws, handle with care. instance MonadPlus f => MonadPlus (F f) where mzero = F (\_ kf -> kf mzero) @@ -169,7 +185,7 @@ hoistF :: (forall x. f x -> g x) -> F f a -> F g a hoistF t (F m) = F (\p f -> m p (f . t)) --- | The very definition of a free monoid is that given a natural transformation you get a monoid homomorphism. +-- | The very definition of a free monad is that given a natural transformation you get a monad homomorphism. foldF :: Monad m => (forall x. f x -> m x) -> F f a -> m a foldF f (F m) = m return (Monad.join . f) @@ -188,9 +204,9 @@ -- -- This is based on the \"Free Monads for Less\" series of articles by Edward Kmett: -- --- * +-- * -- --- * +-- * -- -- and by Janis Voightländer. improve :: Functor f => (forall m. MonadFree f m => m a) -> Free f a @@ -211,6 +227,23 @@ -- -- Calling @'retract' . 'cutoff' n@ is always terminating, provided each of the -- steps in the iteration is terminating. +{-# INLINE cutoff #-} cutoff :: (Functor f) => Integer -> F f a -> F f (Maybe a) -cutoff n = toF . Free.cutoff n . fromF +cutoff n m + | n <= 0 = return Nothing + | n <= toInteger (maxBound :: Int) = cutoffI (fromInteger n :: Int) m + | otherwise = cutoffI n m +{-# SPECIALIZE cutoffI :: (Functor f) => Int -> F f a -> F f (Maybe a) #-} +{-# SPECIALIZE cutoffI :: (Functor f) => Integer -> F f a -> F f (Maybe a) #-} +cutoffI :: (Functor f, Integral n) => n -> F f a -> F f (Maybe a) +cutoffI n m = F m' where + m' kp kf = runF m kpn kfn n where + kpn a i + | i <= 0 = kp Nothing + | otherwise = kp (Just a) + kfn fr i + | i <= 0 = kp Nothing + | otherwise = let + i' = i - 1 + in i' `seq` kf (fmap ($ i') fr) diff --git a/src/Control/Monad/Free/Class.hs b/src/Control/Monad/Free/Class.hs --- a/src/Control/Monad/Free/Class.hs +++ b/src/Control/Monad/Free/Class.hs @@ -1,12 +1,16 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE DefaultSignatures #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE FunctionalDependencies #-} {-# LANGUAGE FlexibleInstances #-} -{-# LANGUAGE UndecidableInstances #-} -#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 704 -{-# LANGUAGE DefaultSignatures #-} +{-# LANGUAGE Safe #-} {-# LANGUAGE TypeFamilies #-} +{-# LANGUAGE TypeOperators #-} +{-# LANGUAGE UndecidableInstances #-} +#if !(MIN_VERSION_transformers(0,6,0)) +{-# OPTIONS_GHC -Wno-deprecations #-} #endif -{-# OPTIONS_GHC -fno-warn-deprecations #-} + ----------------------------------------------------------------------------- -- | -- Module : Control.Monad.Free.Class @@ -25,7 +29,6 @@ , wrapT ) where -import Control.Applicative import Control.Monad import Control.Monad.Trans.Class import Control.Monad.Trans.Reader @@ -37,12 +40,14 @@ import qualified Control.Monad.Trans.RWS.Lazy as Lazy import Control.Monad.Trans.Cont import Control.Monad.Trans.Maybe -import Control.Monad.Trans.List -import Control.Monad.Trans.Error +import Control.Monad.Trans.Except import Control.Monad.Trans.Identity --- import Control.Monad.Trans.Either -import Data.Monoid +#if !(MIN_VERSION_transformers(0,6,0)) +import Control.Monad.Trans.Error +import Control.Monad.Trans.List +#endif + -- | -- Monads provide substitution ('fmap') and renormalization ('Control.Monad.join'): -- @@ -96,10 +101,8 @@ -- wrap (fmap f x) ≡ wrap (fmap return x) >>= f -- @ wrap :: f (m a) -> m a -#if defined(__GLASGOW_HASKELL__) && __GLASGOW_HASKELL__ >= 704 default wrap :: (m ~ t n, MonadTrans t, MonadFree f n, Functor f) => f (m a) -> m a wrap = join . lift . wrap . fmap return -#endif instance (Functor f, MonadFree f m) => MonadFree f (ReaderT e m) where wrap fm = ReaderT $ \e -> wrap $ flip runReaderT e <$> fm @@ -131,14 +134,19 @@ instance (Functor f, MonadFree f m) => MonadFree f (IdentityT m) where wrap = IdentityT . wrap . fmap runIdentityT -instance (Functor f, MonadFree f m) => MonadFree f (ListT m) where - wrap = ListT . wrap . fmap runListT +instance (Functor f, MonadFree f m) => MonadFree f (ExceptT e m) where + wrap = ExceptT . wrap . fmap runExceptT +-- instance (Functor f, MonadFree f m) => MonadFree f (EitherT e m) where +-- wrap = EitherT . wrap . fmap runEitherT + +#if !(MIN_VERSION_transformers(0,6,0)) instance (Functor f, MonadFree f m, Error e) => MonadFree f (ErrorT e m) where wrap = ErrorT . wrap . fmap runErrorT --- instance (Functor f, MonadFree f m) => MonadFree f (EitherT e m) where --- wrap = EitherT . wrap . fmap runEitherT +instance (Functor f, MonadFree f m) => MonadFree f (ListT m) where + wrap = ListT . wrap . fmap runListT +#endif -- | A version of lift that can be used with just a Functor for f. liftF :: (Functor f, MonadFree f m) => f a -> m a diff --git a/src/Control/Monad/Free/TH.hs b/src/Control/Monad/Free/TH.hs --- a/src/Control/Monad/Free/TH.hs +++ b/src/Control/Monad/Free/TH.hs @@ -1,3 +1,10 @@ +{-# LANGUAGE CPP #-} +#if MIN_VERSION_template_haskell(2,12,0) +{-# LANGUAGE Safe #-} +#else +{-# LANGUAGE Trustworthy #-} +#endif + ----------------------------------------------------------------------------- -- | -- Module : Control.Monad.Trans.TH @@ -27,10 +34,12 @@ ) where import Control.Arrow -import Control.Applicative import Control.Monad import Data.Char (toLower) -import Language.Haskell.TH +import Data.List ((\\), nub) +import Language.Haskell.TH.Datatype.TyVarBndr +import Language.Haskell.TH.Ppr (pprint) +import Language.Haskell.TH.Syntax data Arg = Captured Type Exp @@ -52,10 +61,6 @@ zipExprs ps (c:cs) (Captured _ _ : as) = c : zipExprs ps cs as zipExprs _ _ _ = [] -tyVarBndrName :: TyVarBndr -> Name -tyVarBndrName (PlainTV name) = name -tyVarBndrName (KindedTV name _) = name - findTypeOrFail :: String -> Q Name findTypeOrFail s = lookupTypeName s >>= maybe (fail $ s ++ " is not in scope") return @@ -68,19 +73,19 @@ mkOpName :: String -> Q String mkOpName (':':name) = return name mkOpName ( c :name) = return $ toLower c : name -mkOpName _ = fail "null constructor name" +mkOpName _ = fail "impossible happened: empty (null) constructor name" -- | Check if parameter is used in type. usesTV :: Name -> Type -> Bool usesTV n (VarT name) = n == name usesTV n (AppT t1 t2) = any (usesTV n) [t1, t2] usesTV n (SigT t _ ) = usesTV n t -usesTV n (ForallT bs _ t) = usesTV n t && n `notElem` map tyVarBndrName bs +usesTV n (ForallT bs _ t) = usesTV n t && n `notElem` map tvName bs usesTV _ _ = False -- | Analyze constructor argument. -mkArg :: Name -> Type -> Q Arg -mkArg n t +mkArg :: Type -> Type -> Q Arg +mkArg (VarT n) t | usesTV n t = case t of -- if parameter is used as is, the return type should be () @@ -91,19 +96,50 @@ -- expression is an N-tuple secion (,...,). AppT (AppT ArrowT _) _ -> do (ts, name) <- arrowsToTuple t - when (name /= n) $ fail "return type is not the parameter" - let tup = foldl AppT (TupleT $ length ts) ts + when (any (usesTV n) ts) $ fail $ unlines + [ "type variable " ++ pprint n ++ " is forbidden" + , "in a type like (a1 -> ... -> aN -> " ++ pprint n ++ ")" + , "in a constructor's argument type: " ++ pprint t ] + when (name /= n) $ fail $ unlines + [ "expected final return type `" ++ pprint n ++ "'" + , "but got `" ++ pprint name ++ "'" + , "in a constructor's argument type: `" ++ pprint t ++ "'" ] + let tup = nonUnaryTupleT ts xs <- mapM (const $ newName "x") ts - return $ Captured tup (LamE (map VarP xs) (TupE (map VarE xs))) - _ -> fail "don't know how to make Arg" + return $ Captured tup (LamE (map VarP xs) (nonUnaryTupE $ map VarE xs)) + _ -> fail $ unlines + [ "expected a type variable `" ++ pprint n ++ "'" + , "or a type like (a1 -> ... -> aN -> " ++ pprint n ++ ")" + , "but got `" ++ pprint t ++ "'" + , "in a constructor's argument" ] | otherwise = return $ Param t where - arrowsToTuple (AppT (AppT ArrowT t1) (VarT name)) = return ([t1], name) arrowsToTuple (AppT (AppT ArrowT t1) t2) = do (ts, name) <- arrowsToTuple t2 return (t1:ts, name) - arrowsToTuple _ = fail "return type is not a variable" + arrowsToTuple (VarT name) = return ([], name) + arrowsToTuple rt = fail $ unlines + [ "expected final return type `" ++ pprint n ++ "'" + , "but got `" ++ pprint rt ++ "'" + , "in a constructor's argument type: `" ++ pprint t ++ "'" ] + nonUnaryTupleT :: [Type] -> Type + nonUnaryTupleT [t'] = t' + nonUnaryTupleT ts = foldl AppT (TupleT $ length ts) ts + + nonUnaryTupE :: [Exp] -> Exp + nonUnaryTupE [e] = e + nonUnaryTupE es = TupE $ +#if MIN_VERSION_template_haskell(2,16,0) + map Just +#endif + es + +mkArg n _ = fail $ unlines + [ "expected a type variable" + , "but got `" ++ pprint n ++ "'" + , "as the last parameter of the type constructor" ] + -- | Apply transformation to the return value independently of how many -- parameters does @e@ have. -- E.g. @mapRet Just (\x y z -> x + y * z)@ goes to @@ -135,9 +171,23 @@ unifyCaptured a [] = return (VarT a, []) unifyCaptured _ [(t, e)] = return (t, [e]) unifyCaptured _ [x, y] = unifyT x y -unifyCaptured _ _ = fail "can't unify more than 2 arguments that use type parameter" +unifyCaptured _ xs = fail $ unlines + [ "can't unify more than 2 return types" + , "that use type parameter" + , "when unifying return types: " + , unlines (map (pprint . fst) xs) ] -liftCon' :: Bool -> [TyVarBndr] -> Cxt -> Type -> Name -> [Name] -> Name -> [Type] -> Q [Dec] +extractVars :: Type -> [Name] +extractVars (ForallT bs _ t) = extractVars t \\ map tvName bs +extractVars (VarT n) = [n] +extractVars (AppT x y) = extractVars x ++ extractVars y +extractVars (SigT x k) = extractVars x ++ extractVars k +extractVars (InfixT x _ y) = extractVars x ++ extractVars y +extractVars (UInfixT x _ y) = extractVars x ++ extractVars y +extractVars (ParensT x) = extractVars x +extractVars _ = [] + +liftCon' :: Bool -> [TyVarBndrSpec] -> Cxt -> Type -> Type -> [Type] -> Name -> [Type] -> Q [Dec] liftCon' typeSig tvbs cx f n ns cn ts = do -- prepare some names opName <- mkName <$> mkOpName (nameBase cn) @@ -159,51 +209,83 @@ let pat = map VarP xs -- this is LHS exprs = zipExprs (map VarE xs) es args -- this is what ctor would be applied to fval = foldl AppE (ConE cn) exprs -- this is RHS without liftF - q = tvbs ++ map PlainTV (qa ++ m : ns) + ns' = nub (concatMap extractVars ns) + q = filter nonNext tvbs ++ map plainTVSpecified (qa ++ m : ns') qa = case retType of VarT b | a == b -> [a]; _ -> [] - f' = foldl AppT f (map VarT ns) + f' = foldl AppT f ns return $ concat [ if typeSig -#if MIN_VERSION_template_haskell(2,10,0) then [ SigD opName (ForallT q (cx ++ [ConT monadFree `AppT` f' `AppT` VarT m]) opType) ] -#else - then [ SigD opName (ForallT q (cx ++ [ClassP monadFree [f', VarT m]]) opType) ] -#endif else [] , [ FunD opName [ Clause pat (NormalB $ AppE (VarE liftF) fval) [] ] ] ] + where + nonNext tv = VarT (tvName tv) /= n -- | Provide free monadic actions for a single value constructor. -liftCon :: Bool -> [TyVarBndr] -> Cxt -> Type -> Name -> [Name] -> Con -> Q [Dec] -liftCon typeSig ts cx f n ns con = - case con of - NormalC cName fields -> liftCon' typeSig ts cx f n ns cName $ map snd fields - RecC cName fields -> liftCon' typeSig ts cx f n ns cName $ map (\(_, _, ty) -> ty) fields - InfixC (_,t1) cName (_,t2) -> liftCon' typeSig ts cx f n ns cName [t1, t2] - ForallC ts' cx' con' -> liftCon typeSig (ts ++ ts') (cx ++ cx') f n ns con' +liftCon :: Bool -> [TyVarBndrSpec] -> Cxt -> Type -> Type -> [Type] -> Maybe [Name] -> Con -> Q [Dec] +liftCon typeSig ts cx f n ns onlyCons con + | not (any (`melem` onlyCons) (constructorNames con)) = return [] + | otherwise = case con of + NormalC cName fields -> liftCon' typeSig ts cx f n ns cName $ map snd fields + RecC cName fields -> liftCon' typeSig ts cx f n ns cName $ map (\(_, _, ty) -> ty) fields + InfixC (_,t1) cName (_,t2) -> liftCon' typeSig ts cx f n ns cName [t1, t2] + ForallC ts' cx' con' -> liftCon typeSig (ts ++ ts') (cx ++ cx') f n ns onlyCons con' + GadtC cNames fields resType -> do + decs <- forM (filter (`melem` onlyCons) cNames) $ \cName -> + liftGadtC cName fields resType typeSig ts cx f + return (concat decs) + RecGadtC cNames fields resType -> do + let fields' = map (\(_, x, y) -> (x, y)) fields + decs <- forM (filter (`melem` onlyCons) cNames) $ \cName -> + liftGadtC cName fields' resType typeSig ts cx f + return (concat decs) +splitAppT :: Type -> (Type, [Type]) +splitAppT ty = go ty ty [] + where + go :: Type -> Type -> [Type] -> (Type, [Type]) + go _ (AppT ty1 ty2) args = go ty1 ty1 (ty2:args) + go origTy (SigT ty' _) args = go origTy ty' args + go origTy (InfixT ty1 n ty2) args = go origTy (ConT n `AppT` ty1 `AppT` ty2) args + go origTy (ParensT ty') args = go origTy ty' args + go origTy _ args = (origTy, args) + +liftGadtC :: Name -> [BangType] -> Type -> Bool -> [TyVarBndrSpec] -> Cxt -> Type -> Q [Dec] +liftGadtC cName fields resType typeSig ts cx f = + liftCon typeSig ts cx f nextTy (init tys) Nothing (NormalC cName fields) + where + (_f, tys) = splitAppT resType + nextTy = last tys + +melem :: Eq a => a -> Maybe [a] -> Bool +melem _ Nothing = True +melem x (Just xs) = x `elem` xs + +-- | Get construstor name(s). +constructorNames :: Con -> [Name] +constructorNames (NormalC name _) = [name] +constructorNames (RecC name _) = [name] +constructorNames (InfixC _ name _) = [name] +constructorNames (ForallC _ _ c) = constructorNames c +constructorNames (GadtC names _ _) = names +constructorNames (RecGadtC names _ _) = names + -- | Provide free monadic actions for a type declaration. liftDec :: Bool -- ^ Include type signature? -> Maybe [Name] -- ^ Include only mentioned constructor names. Use all constructors when @Nothing@. -> Dec -- ^ Data type declaration. -> Q [Dec] -liftDec typeSig onlyCons (DataD _ tyName tyVarBndrs cons _) - | null tyVarBndrs = fail $ "Type " ++ show tyName ++ " needs at least one free variable" - | otherwise = concat <$> mapM (liftCon typeSig [] [] con nextTyName (init tyNames)) cons' +liftDec typeSig onlyCons (DataD _ tyName tyVarBndrs _ cons _) + | null tyVarBndrs = fail $ "Type constructor " ++ pprint tyName ++ " needs at least one type parameter" + | otherwise = concat <$> mapM (liftCon typeSig [] [] con nextTy (init tys) onlyCons) cons where - cons' = case onlyCons of - Nothing -> cons - Just ns -> filter (\c -> constructorName c `elem` ns) cons - tyNames = map tyVarBndrName tyVarBndrs - nextTyName = last tyNames + tys = map (VarT . tvName) tyVarBndrs + nextTy = last tys con = ConT tyName -liftDec _ _ dec = fail $ "liftDec: Don't know how to lift " ++ show dec - --- | Get construstor name. -constructorName :: Con -> Name -constructorName (NormalC name _) = name -constructorName (RecC name _) = name -constructorName (InfixC _ name _) = name -constructorName (ForallC _ _ c) = constructorName c +liftDec _ _ dec = fail $ unlines + [ "failed to derive makeFree operations:" + , "expected a data type constructor" + , "but got " ++ pprint dec ] -- | Generate monadic actions for a data type. genFree :: Bool -- ^ Include type signature? @@ -223,15 +305,17 @@ genFreeCon typeSig cname = do info <- reify cname case info of - DataConI _ _ tname _ -> genFree typeSig (Just [cname]) tname - _ -> fail "makeFreeCon expects a data constructor" + DataConI _ _ tname -> genFree typeSig (Just [cname]) tname + _ -> fail $ unlines + [ "expected a data constructor" + , "but got " ++ pprint info ] -- | @$('makeFree' ''T)@ provides free monadic actions for the -- constructors of the given data type @T@. makeFree :: Name -> Q [Dec] makeFree = genFree True Nothing --- | Like 'makeFreeCon', but does not provide type signatures. +-- | Like 'makeFree', but does not provide type signatures. -- This can be used to attach Haddock comments to individual arguments -- for each generated function. -- diff --git a/src/Control/Monad/Trans/Free.hs b/src/Control/Monad/Trans/Free.hs --- a/src/Control/Monad/Trans/Free.hs +++ b/src/Control/Monad/Trans/Free.hs @@ -1,17 +1,13 @@ {-# LANGUAGE CPP #-} -{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE StandaloneDeriving #-} {-# LANGUAGE Rank2Types #-} -#if __GLASGOW_HASKELL__ >= 707 -{-# LANGUAGE DeriveDataTypeable #-} -#endif +{-# LANGUAGE Safe #-} -#ifndef MIN_VERSION_mtl -#define MIN_VERSION_mtl(x,y,z) 1 -#endif ----------------------------------------------------------------------------- -- | -- Module : Control.Monad.Trans.Free @@ -38,7 +34,9 @@ , iterT , iterTM , hoistFreeT + , foldFreeT , transFreeT + , joinFreeT , cutoff , partialIterT , intersperseT @@ -54,8 +52,11 @@ import Control.Applicative import Control.Monad (liftM, MonadPlus(..), ap, join) +import Control.Monad.Base (MonadBase(..)) +import Control.Monad.Catch (MonadThrow(..), MonadCatch(..)) import Control.Monad.Trans.Class import Control.Monad.Free.Class +import qualified Control.Monad.Fail as Fail import Control.Monad.IO.Class import Control.Monad.Reader.Class import Control.Monad.Writer.Class @@ -63,61 +64,52 @@ import Control.Monad.Error.Class import Control.Monad.Cont.Class import Data.Functor.Bind hiding (join) -import Data.Monoid -import Data.Foldable -import Data.Function (on) +import Data.Functor.Classes import Data.Functor.Identity import Data.Traversable import Data.Bifunctor import Data.Bifoldable import Data.Bitraversable import Data.Data -import Prelude.Extras +import GHC.Generics -- | The base functor for a free monad. data FreeF f a b = Pure a | Free (f b) - deriving (Eq,Ord,Show,Read -#if __GLASGOW_HASKELL__ >= 707 - ,Typeable -#endif - ) + deriving (Eq,Ord,Show,Read,Generic,Generic1,Data) instance Show1 f => Show2 (FreeF f) where - showsPrec2 d (Pure a) = showParen (d > 10) $ showString "Pure " . showsPrec 11 a - showsPrec2 d (Free as) = showParen (d > 10) $ showString "Free " . showsPrec1 11 as + liftShowsPrec2 spa _sla _spb _slb d (Pure a) = + showsUnaryWith spa "Pure" d a + liftShowsPrec2 _spa _sla spb slb d (Free as) = + showsUnaryWith (liftShowsPrec spb slb) "Free" d as instance (Show1 f, Show a) => Show1 (FreeF f a) where - showsPrec1 = showsPrec2 + liftShowsPrec = liftShowsPrec2 showsPrec showList instance Read1 f => Read2 (FreeF f) where - readsPrec2 d r = readParen (d > 10) - (\r' -> [ (Pure m, t) - | ("Pure", s) <- lex r' - , (m, t) <- readsPrec 11 s]) r - ++ readParen (d > 10) - (\r' -> [ (Free m, t) - | ("Free", s) <- lex r' - , (m, t) <- readsPrec1 11 s]) r + liftReadsPrec2 rpa _rla rpb rlb = readsData $ + readsUnaryWith rpa "Pure" Pure `mappend` + readsUnaryWith (liftReadsPrec rpb rlb) "Free" Free instance (Read1 f, Read a) => Read1 (FreeF f a) where - readsPrec1 = readsPrec2 + liftReadsPrec = liftReadsPrec2 readsPrec readList instance Eq1 f => Eq2 (FreeF f) where - Pure a ==## Pure b = a == b - Free as ==## Free bs = as ==# bs - _ ==## _ = False + liftEq2 eq _ (Pure a) (Pure b) = eq a b + liftEq2 _ eq (Free as) (Free bs) = liftEq eq as bs + liftEq2 _ _ _ _ = False instance (Eq1 f, Eq a) => Eq1 (FreeF f a) where - (==#) = (==##) + liftEq = liftEq2 (==) instance Ord1 f => Ord2 (FreeF f) where - Pure a `compare2` Pure b = a `compare` b - Pure _ `compare2` Free _ = LT - Free _ `compare2` Pure _ = GT - Free fa `compare2` Free fb = fa `compare1` fb + liftCompare2 cmp _ (Pure a) (Pure b) = cmp a b + liftCompare2 _ _ (Pure _) (Free _) = LT + liftCompare2 _ _ (Free _) (Pure _) = GT + liftCompare2 _ cmp (Free fa) (Free fb) = liftCompare cmp fa fb instance (Ord1 f, Ord a) => Ord1 (FreeF f a) where - compare1 = compare2 + liftCompare = liftCompare2 compare instance Functor f => Functor (FreeF f a) where fmap _ (Pure a) = Pure a @@ -170,34 +162,46 @@ free = FreeT . Identity {-# INLINE free #-} -deriving instance Eq (m (FreeF f a (FreeT f m a))) => Eq (FreeT f m a) +instance (Eq1 f, Eq1 m, Eq a) => Eq (FreeT f m a) where + (==) = eq1 -instance (Functor f, Eq1 f, Functor m, Eq1 m) => Eq1 (FreeT f m) where - (==#) = on (==#) (fmap (Lift1 . fmap Lift1) . runFreeT) +instance (Eq1 f, Eq1 m) => Eq1 (FreeT f m) where + liftEq eq = go + where + go (FreeT x) (FreeT y) = liftEq (liftEq2 eq go) x y -deriving instance Ord (m (FreeF f a (FreeT f m a))) => Ord (FreeT f m a) +instance (Ord1 f, Ord1 m, Ord a) => Ord (FreeT f m a) where + compare = compare1 -instance (Functor f, Ord1 f, Functor m, Ord1 m) => Ord1 (FreeT f m) where - compare1 = on compare1 (fmap (Lift1 . fmap Lift1) . runFreeT) +instance (Ord1 f, Ord1 m) => Ord1 (FreeT f m) where + liftCompare cmp = go + where + go (FreeT x) (FreeT y) = liftCompare (liftCompare2 cmp go) x y -instance (Functor f, Show1 f, Functor m, Show1 m) => Show1 (FreeT f m) where - showsPrec1 d (FreeT m) = showParen (d > 10) $ - showString "FreeT " . showsPrec1 11 (Lift1 . fmap Lift1 <$> m) +instance (Show1 f, Show1 m) => Show1 (FreeT f m) where + liftShowsPrec sp sl = go + where + goList = liftShowList sp sl + go d (FreeT x) = showsUnaryWith + (liftShowsPrec (liftShowsPrec2 sp sl go goList) (liftShowList2 sp sl go goList)) + "FreeT" d x -instance Show (m (FreeF f a (FreeT f m a))) => Show (FreeT f m a) where - showsPrec d (FreeT m) = showParen (d > 10) $ - showString "FreeT " . showsPrec 11 m +instance (Show1 f, Show1 m, Show a) => Show (FreeT f m a) where + showsPrec = showsPrec1 -instance (Functor f, Read1 f, Functor m, Read1 m) => Read1 (FreeT f m) where - readsPrec1 d = readParen (d > 10) $ \r -> - [ (FreeT (fmap lower1 . lower1 <$> m),t) | ("FreeT",s) <- lex r, (m,t) <- readsPrec1 11 s] +instance (Read1 f, Read1 m) => Read1 (FreeT f m) where + liftReadsPrec rp rl = go + where + goList = liftReadList rp rl + go = readsData $ readsUnaryWith + (liftReadsPrec (liftReadsPrec2 rp rl go goList) (liftReadList2 rp rl go goList)) + "FreeT" FreeT -instance Read (m (FreeF f a (FreeT f m a))) => Read (FreeT f m a) where - readsPrec d = readParen (d > 10) $ \r -> - [ (FreeT m,t) | ("FreeT",s) <- lex r, (m,t) <- readsPrec 11 s] +instance (Read1 f, Read1 m, Read a) => Read (FreeT f m a) where + readsPrec = readsPrec1 -instance (Functor f, Monad m) => Functor (FreeT f m) where - fmap f (FreeT m) = FreeT (liftM f' m) where +instance (Functor f, Functor m) => Functor (FreeT f m) where + fmap f (FreeT m) = FreeT (fmap f' m) where f' (Pure a) = Pure (f a) f' (Free as) = Free (fmap (fmap f) as) @@ -214,14 +218,20 @@ (>>-) = (>>=) instance (Functor f, Monad m) => Monad (FreeT f m) where - fail e = FreeT (fail e) - return a = FreeT (return (Pure a)) + return = pure {-# INLINE return #-} FreeT m >>= f = FreeT $ m >>= \v -> case v of Pure a -> runFreeT (f a) Free w -> return (Free (fmap (>>= f) w)) -instance MonadTrans (FreeT f) where +#if !MIN_VERSION_base(4,13,0) + fail e = FreeT (fail e) +#endif + +instance (Functor f, Fail.MonadFail m) => Fail.MonadFail (FreeT f m) where + fail e = FreeT (Fail.fail e) + +instance Functor f => MonadTrans (FreeT f) where lift = FreeT . liftM Pure {-# INLINE lift #-} @@ -229,6 +239,10 @@ liftIO = lift . liftIO {-# INLINE liftIO #-} +instance (Functor f, MonadBase b m) => MonadBase b (FreeT f m) where + liftBase = lift . liftBase + {-# INLINE liftBase #-} + instance (Functor f, MonadReader r m) => MonadReader r (FreeT f m) where ask = lift ask {-# INLINE ask #-} @@ -241,27 +255,23 @@ listen (FreeT m) = FreeT $ liftM concat' $ listen (fmap listen `liftM` m) where concat' (Pure x, w) = Pure (x, w) - concat' (Free y, w) = Free $ fmap (second (w <>)) <$> y + concat' (Free y, w) = Free $ fmap (second (w `mappend`)) <$> y pass m = FreeT . pass' . runFreeT . hoistFreeT clean $ listen m where clean = pass . liftM (\x -> (x, const mempty)) pass' = join . liftM g g (Pure ((x, f), w)) = tell (f w) >> return (Pure x) g (Free f) = return . Free . fmap (FreeT . pass' . runFreeT) $ f -#if MIN_VERSION_mtl(2,1,1) writer w = lift (writer w) {-# INLINE writer #-} -#endif instance (Functor f, MonadState s m) => MonadState s (FreeT f m) where get = lift get {-# INLINE get #-} put = lift . put {-# INLINE put #-} -#if MIN_VERSION_mtl(2,1,1) state f = lift (state f) {-# INLINE state #-} -#endif instance (Functor f, MonadError e m) => MonadError e (FreeT f m) where throwError = lift . throwError @@ -286,6 +296,15 @@ wrap = FreeT . return . Free {-# INLINE wrap #-} +instance (Functor f, MonadThrow m) => MonadThrow (FreeT f m) where + throwM = lift . throwM + {-# INLINE throwM #-} + +instance (Functor f, MonadCatch m) => MonadCatch (FreeT f m) where + FreeT m `catch` f = FreeT $ liftM (fmap (`Control.Monad.Catch.catch` f)) m + `Control.Monad.Catch.catch` (runFreeT . f) + {-# INLINE catch #-} + -- | Tear down a free monad transformer using iteration. iterT :: (Functor f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a iterT f (FreeT m) = do @@ -310,14 +329,30 @@ -- | Lift a monad homomorphism from @m@ to @n@ into a monad homomorphism from @'FreeT' f m@ to @'FreeT' f n@ -- --- @'hoistFreeT' :: ('Monad' m, 'Functor' f) => (m ~> n) -> 'FreeT' f m ~> 'FreeT' f n@ -hoistFreeT :: (Monad m, Functor f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b -hoistFreeT mh = FreeT . mh . liftM (fmap (hoistFreeT mh)) . runFreeT +-- @'hoistFreeT' :: ('Functor' m, 'Functor' f) => (m ~> n) -> 'FreeT' f m ~> 'FreeT' f n@ +hoistFreeT :: (Functor m, Functor f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b +hoistFreeT mh = FreeT . mh . fmap (fmap (hoistFreeT mh)) . runFreeT --- | Lift a natural transformation from @f@ to @g@ into a monad homomorphism from @'FreeT' f m@ to @'FreeT' g n@ +-- | The very definition of a free monad transformer is that given a natural +-- transformation you get a monad transformer homomorphism. +foldFreeT :: (MonadTrans t, Monad (t m), Monad m) + => (forall n x. Monad n => f x -> t n x) -> FreeT f m a -> t m a +foldFreeT f (FreeT m) = lift m >>= foldFreeF + where + foldFreeF (Pure a) = return a + foldFreeF (Free as) = f as >>= foldFreeT f + +-- | Lift a natural transformation from @f@ to @g@ into a monad homomorphism from @'FreeT' f m@ to @'FreeT' g m@ transFreeT :: (Monad m, Functor g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b transFreeT nt = FreeT . liftM (fmap (transFreeT nt) . transFreeF nt) . runFreeT +-- | Pull out and join @m@ layers of @'FreeT' f m a@. +joinFreeT :: (Monad m, Traversable f) => FreeT f m a -> m (Free f a) +joinFreeT (FreeT m) = m >>= joinFreeF + where + joinFreeF (Pure x) = return (return x) + joinFreeF (Free f) = wrap `liftM` Data.Traversable.mapM joinFreeT f + -- | -- 'retract' is the left inverse of 'liftF' -- @@ -406,77 +441,9 @@ -- @ -- 'intercalateT' f ≡ 'retractT' . 'intersperseT' f -- @ -intercalateT :: (Monad m, MonadTrans t, Monad (t m), Functor (t m)) => t m a -> FreeT (t m) m b -> t m b +intercalateT :: (Monad m, MonadTrans t, Monad (t m)) => t m a -> FreeT (t m) m b -> t m b intercalateT f (FreeT m) = do val <- lift m case val of Pure x -> return x Free y -> y >>= iterTM (\x -> f >> join x) - -#if __GLASGOW_HASKELL__ < 707 -instance Typeable1 f => Typeable2 (FreeF f) where - typeOf2 t = mkTyConApp freeFTyCon [typeOf1 (f t)] where - f :: FreeF f a b -> f a - f = undefined - -instance (Typeable1 f, Typeable1 w) => Typeable1 (FreeT f w) where - typeOf1 t = mkTyConApp freeTTyCon [typeOf1 (f t), typeOf1 (w t)] where - f :: FreeT f w a -> f a - f = undefined - w :: FreeT f w a -> w a - w = undefined - -freeFTyCon, freeTTyCon :: TyCon -#if __GLASGOW_HASKELL__ < 704 -freeTTyCon = mkTyCon "Control.Monad.Trans.Free.FreeT" -freeFTyCon = mkTyCon "Control.Monad.Trans.Free.FreeF" -#else -freeTTyCon = mkTyCon3 "free" "Control.Monad.Trans.Free" "FreeT" -freeFTyCon = mkTyCon3 "free" "Control.Monad.Trans.Free" "FreeF" -#endif -{-# NOINLINE freeTTyCon #-} -{-# NOINLINE freeFTyCon #-} - -instance - ( Typeable1 f, Typeable a, Typeable b - , Data a, Data (f b), Data b - ) => Data (FreeF f a b) where - gfoldl f z (Pure a) = z Pure `f` a - gfoldl f z (Free as) = z Free `f` as - toConstr Pure{} = pureConstr - toConstr Free{} = freeConstr - gunfold k z c = case constrIndex c of - 1 -> k (z Pure) - 2 -> k (z Free) - _ -> error "gunfold" - dataTypeOf _ = freeFDataType - dataCast1 f = gcast1 f - -instance - ( Typeable1 f, Typeable1 w, Typeable a - , Data (w (FreeF f a (FreeT f w a))) - , Data a - ) => Data (FreeT f w a) where - gfoldl f z (FreeT w) = z FreeT `f` w - toConstr _ = freeTConstr - gunfold k z c = case constrIndex c of - 1 -> k (z FreeT) - _ -> error "gunfold" - dataTypeOf _ = freeTDataType - dataCast1 f = gcast1 f - -pureConstr, freeConstr, freeTConstr :: Constr -pureConstr = mkConstr freeFDataType "Pure" [] Prefix -freeConstr = mkConstr freeFDataType "Free" [] Prefix -freeTConstr = mkConstr freeTDataType "FreeT" [] Prefix -{-# NOINLINE pureConstr #-} -{-# NOINLINE freeConstr #-} -{-# NOINLINE freeTConstr #-} - -freeFDataType, freeTDataType :: DataType -freeFDataType = mkDataType "Control.Monad.Trans.Free.FreeF" [pureConstr, freeConstr] -freeTDataType = mkDataType "Control.Monad.Trans.Free.FreeT" [freeTConstr] -{-# NOINLINE freeFDataType #-} -{-# NOINLINE freeTDataType #-} -#endif - diff --git a/src/Control/Monad/Trans/Free/Ap.hs b/src/Control/Monad/Trans/Free/Ap.hs new file mode 100644 --- /dev/null +++ b/src/Control/Monad/Trans/Free/Ap.hs @@ -0,0 +1,443 @@ +{-# LANGUAGE CPP #-} +{-# LANGUAGE DeriveDataTypeable #-} +{-# LANGUAGE DeriveGeneric #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE StandaloneDeriving #-} +{-# LANGUAGE Rank2Types #-} +{-# LANGUAGE Safe #-} + +-------------------------------------------------------------------------------- +-- | +-- Given an applicative, the free monad transformer. +-------------------------------------------------------------------------------- + +module Control.Monad.Trans.Free.Ap + ( + -- * The base functor + FreeF(..) + -- * The free monad transformer + , FreeT(..) + -- * The free monad + , Free, free, runFree + -- * Operations + , liftF + , iterT + , iterTM + , hoistFreeT + , transFreeT + , joinFreeT + , cutoff + , partialIterT + , intersperseT + , intercalateT + , retractT + -- * Operations of free monad + , retract + , iter + , iterM + -- * Free Monads With Class + , MonadFree(..) + ) where + +import Control.Applicative +import Control.Monad (liftM, MonadPlus(..), join) +import Control.Monad.Catch (MonadThrow(..), MonadCatch(..)) +import Control.Monad.Trans.Class +import qualified Control.Monad.Fail as Fail +import Control.Monad.Free.Class +import Control.Monad.IO.Class +import Control.Monad.Reader.Class +import Control.Monad.Writer.Class +import Control.Monad.State.Class +import Control.Monad.Error.Class +import Control.Monad.Cont.Class +import Data.Functor.Bind hiding (join) +import Data.Functor.Classes +import Data.Functor.Identity +import Data.Traversable +import Data.Bifunctor +import Data.Bifoldable +import Data.Bitraversable +import Data.Data +import GHC.Generics + +-- | The base functor for a free monad. +data FreeF f a b = Pure a | Free (f b) + deriving (Eq,Ord,Show,Read,Data,Generic,Generic1) + +instance Show1 f => Show2 (FreeF f) where + liftShowsPrec2 spa _sla _spb _slb d (Pure a) = + showsUnaryWith spa "Pure" d a + liftShowsPrec2 _spa _sla spb slb d (Free as) = + showsUnaryWith (liftShowsPrec spb slb) "Free" d as + +instance (Show1 f, Show a) => Show1 (FreeF f a) where + liftShowsPrec = liftShowsPrec2 showsPrec showList + +instance Read1 f => Read2 (FreeF f) where + liftReadsPrec2 rpa _rla rpb rlb = readsData $ + readsUnaryWith rpa "Pure" Pure `mappend` + readsUnaryWith (liftReadsPrec rpb rlb) "Free" Free + +instance (Read1 f, Read a) => Read1 (FreeF f a) where + liftReadsPrec = liftReadsPrec2 readsPrec readList + +instance Eq1 f => Eq2 (FreeF f) where + liftEq2 eq _ (Pure a) (Pure b) = eq a b + liftEq2 _ eq (Free as) (Free bs) = liftEq eq as bs + liftEq2 _ _ _ _ = False + +instance (Eq1 f, Eq a) => Eq1 (FreeF f a) where + liftEq = liftEq2 (==) + +instance Ord1 f => Ord2 (FreeF f) where + liftCompare2 cmp _ (Pure a) (Pure b) = cmp a b + liftCompare2 _ _ (Pure _) (Free _) = LT + liftCompare2 _ _ (Free _) (Pure _) = GT + liftCompare2 _ cmp (Free fa) (Free fb) = liftCompare cmp fa fb + +instance (Ord1 f, Ord a) => Ord1 (FreeF f a) where + liftCompare = liftCompare2 compare + +instance Functor f => Functor (FreeF f a) where + fmap _ (Pure a) = Pure a + fmap f (Free as) = Free (fmap f as) + {-# INLINE fmap #-} + +instance Foldable f => Foldable (FreeF f a) where + foldMap f (Free as) = foldMap f as + foldMap _ _ = mempty + {-# INLINE foldMap #-} + +instance Traversable f => Traversable (FreeF f a) where + traverse _ (Pure a) = pure (Pure a) + traverse f (Free as) = Free <$> traverse f as + {-# INLINE traverse #-} + +instance Functor f => Bifunctor (FreeF f) where + bimap f _ (Pure a) = Pure (f a) + bimap _ g (Free as) = Free (fmap g as) + {-# INLINE bimap #-} + +instance Foldable f => Bifoldable (FreeF f) where + bifoldMap f _ (Pure a) = f a + bifoldMap _ g (Free as) = foldMap g as + {-# INLINE bifoldMap #-} + +instance Traversable f => Bitraversable (FreeF f) where + bitraverse f _ (Pure a) = Pure <$> f a + bitraverse _ g (Free as) = Free <$> traverse g as + {-# INLINE bitraverse #-} + +transFreeF :: (forall x. f x -> g x) -> FreeF f a b -> FreeF g a b +transFreeF _ (Pure a) = Pure a +transFreeF t (Free as) = Free (t as) +{-# INLINE transFreeF #-} + +-- | The \"free monad transformer\" for an applicative @f@ +newtype FreeT f m a = FreeT { runFreeT :: m (FreeF f a (FreeT f m a)) } + +-- | The \"free monad\" for an applicative @f@. +type Free f = FreeT f Identity + +-- | Evaluates the first layer out of a free monad value. +runFree :: Free f a -> FreeF f a (Free f a) +runFree = runIdentity . runFreeT +{-# INLINE runFree #-} + +-- | Pushes a layer into a free monad value. +free :: FreeF f a (Free f a) -> Free f a +free = FreeT . Identity +{-# INLINE free #-} + +deriving instance + ( Typeable f, Typeable m + , Data (m (FreeF f a (FreeT f m a))) + , Data a + ) => Data (FreeT f m a) + +instance (Eq1 f, Eq1 m, Eq a) => Eq (FreeT f m a) where + (==) = eq1 + +instance (Eq1 f, Eq1 m) => Eq1 (FreeT f m) where + liftEq eq = go + where + go (FreeT x) (FreeT y) = liftEq (liftEq2 eq go) x y + +instance (Ord1 f, Ord1 m, Ord a) => Ord (FreeT f m a) where + compare = compare1 + +instance (Ord1 f, Ord1 m) => Ord1 (FreeT f m) where + liftCompare cmp = go + where + go (FreeT x) (FreeT y) = liftCompare (liftCompare2 cmp go) x y + +instance (Show1 f, Show1 m) => Show1 (FreeT f m) where + liftShowsPrec sp sl = go + where + goList = liftShowList sp sl + go d (FreeT x) = showsUnaryWith + (liftShowsPrec (liftShowsPrec2 sp sl go goList) (liftShowList2 sp sl go goList)) + "FreeT" d x + +instance (Show1 f, Show1 m, Show a) => Show (FreeT f m a) where + showsPrec = showsPrec1 + +instance (Read1 f, Read1 m) => Read1 (FreeT f m) where + liftReadsPrec rp rl = go + where + goList = liftReadList rp rl + go = readsData $ readsUnaryWith + (liftReadsPrec (liftReadsPrec2 rp rl go goList) (liftReadList2 rp rl go goList)) + "FreeT" FreeT + +instance (Read1 f, Read1 m, Read a) => Read (FreeT f m a) where + readsPrec = readsPrec1 + +instance (Functor f, Functor m) => Functor (FreeT f m) where + fmap f (FreeT m) = FreeT (fmap f' m) where + f' (Pure a) = Pure (f a) + f' (Free as) = Free (fmap (fmap f) as) + +instance (Applicative f, Applicative m) => Applicative (FreeT f m) where + pure a = FreeT (pure (Pure a)) + {-# INLINE pure #-} + FreeT f <*> FreeT a = FreeT $ g <$> f <*> a where + g (Pure f') (Pure a') = Pure (f' a') + g (Pure f') (Free as) = Free $ fmap f' <$> as + g (Free fs) (Pure a') = Free $ fmap ($ a') <$> fs + g (Free fs) (Free as) = Free $ (<*>) <$> fs <*> as + {-# INLINE (<*>) #-} + +instance (Apply f, Apply m) => Apply (FreeT f m) where + FreeT f <.> FreeT a = FreeT $ g <$> f <.> a where + g (Pure f') (Pure a') = Pure (f' a') + g (Pure f') (Free as) = Free $ fmap f' <$> as + g (Free fs) (Pure a') = Free $ fmap ($ a') <$> fs + g (Free fs) (Free as) = Free $ (<.>) <$> fs <.> as + +instance (Apply f, Apply m, Monad m) => Bind (FreeT f m) where + FreeT m >>- f = FreeT $ m >>= \v -> case v of + Pure a -> runFreeT (f a) + Free w -> return (Free (fmap (>>- f) w)) + +instance (Applicative f, Monad m) => Monad (FreeT f m) where + return = pure + {-# INLINE return #-} + FreeT m >>= f = FreeT $ m >>= \v -> case v of + Pure a -> runFreeT (f a) + Free w -> return (Free (fmap (>>= f) w)) +#if !MIN_VERSION_base(4,13,0) + fail e = FreeT (fail e) +#endif + +instance (Applicative f, Fail.MonadFail m) => Fail.MonadFail (FreeT f m) where + fail e = FreeT (Fail.fail e) + +instance Applicative f => MonadTrans (FreeT f) where + lift = FreeT . liftM Pure + {-# INLINE lift #-} + +instance (Applicative f, MonadIO m) => MonadIO (FreeT f m) where + liftIO = lift . liftIO + {-# INLINE liftIO #-} + +instance (Applicative f, MonadReader r m) => MonadReader r (FreeT f m) where + ask = lift ask + {-# INLINE ask #-} + local f = hoistFreeT (local f) + {-# INLINE local #-} + +instance (Applicative f, MonadWriter w m) => MonadWriter w (FreeT f m) where + tell = lift . tell + {-# INLINE tell #-} + listen (FreeT m) = FreeT $ liftM concat' $ listen (fmap listen `liftM` m) + where + concat' (Pure x, w) = Pure (x, w) + concat' (Free y, w) = Free $ fmap (second (w `mappend`)) <$> y + pass m = FreeT . pass' . runFreeT . hoistFreeT clean $ listen m + where + clean = pass . liftM (\x -> (x, const mempty)) + pass' = join . liftM g + g (Pure ((x, f), w)) = tell (f w) >> return (Pure x) + g (Free f) = return . Free . fmap (FreeT . pass' . runFreeT) $ f + writer w = lift (writer w) + {-# INLINE writer #-} + +instance (Applicative f, MonadState s m) => MonadState s (FreeT f m) where + get = lift get + {-# INLINE get #-} + put = lift . put + {-# INLINE put #-} + state f = lift (state f) + {-# INLINE state #-} + +instance (Applicative f, MonadError e m) => MonadError e (FreeT f m) where + throwError = lift . throwError + {-# INLINE throwError #-} + FreeT m `catchError` f = FreeT $ liftM (fmap (`catchError` f)) m `catchError` (runFreeT . f) + +instance (Applicative f, MonadCont m) => MonadCont (FreeT f m) where + callCC f = FreeT $ callCC (\k -> runFreeT $ f (lift . k . Pure)) + +instance (Applicative f, MonadPlus m) => Alternative (FreeT f m) where + empty = FreeT mzero + FreeT ma <|> FreeT mb = FreeT (mplus ma mb) + {-# INLINE (<|>) #-} + +instance (Applicative f, MonadPlus m) => MonadPlus (FreeT f m) where + mzero = FreeT mzero + {-# INLINE mzero #-} + mplus (FreeT ma) (FreeT mb) = FreeT (mplus ma mb) + {-# INLINE mplus #-} + +instance (Applicative f, Monad m) => MonadFree f (FreeT f m) where + wrap = FreeT . return . Free + {-# INLINE wrap #-} + +instance (Applicative f, MonadThrow m) => MonadThrow (FreeT f m) where + throwM = lift . throwM + {-# INLINE throwM #-} + +instance (Applicative f, MonadCatch m) => MonadCatch (FreeT f m) where + FreeT m `catch` f = FreeT $ liftM (fmap (`Control.Monad.Catch.catch` f)) m + `Control.Monad.Catch.catch` (runFreeT . f) + {-# INLINE catch #-} + +-- | Given an applicative homomorphism from @f (m a)@ to @m a@, +-- tear down a free monad transformer using iteration. +iterT :: (Applicative f, Monad m) => (f (m a) -> m a) -> FreeT f m a -> m a +iterT f (FreeT m) = do + val <- m + case fmap (iterT f) val of + Pure x -> return x + Free y -> f y + +-- | Given an applicative homomorphism from @f (t m a)@ to @t m a@, +-- tear down a free monad transformer using iteration over a transformer. +iterTM :: (Applicative f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> FreeT f m a -> t m a +iterTM f (FreeT m) = do + val <- lift m + case fmap (iterTM f) val of + Pure x -> return x + Free y -> f y + +instance (Foldable m, Foldable f) => Foldable (FreeT f m) where + foldMap f (FreeT m) = foldMap (bifoldMap f (foldMap f)) m + +instance (Monad m, Traversable m, Traversable f) => Traversable (FreeT f m) where + traverse f (FreeT m) = FreeT <$> traverse (bitraverse f (traverse f)) m + +-- | Lift a monad homomorphism from @m@ to @n@ into a monad homomorphism from @'FreeT' f m@ to @'FreeT' f n@ +-- +-- @'hoistFreeT' :: ('Functor' m, 'Applicative' f) => (m ~> n) -> 'FreeT' f m ~> 'FreeT' f n@ +hoistFreeT :: (Functor m, Applicative f) => (forall a. m a -> n a) -> FreeT f m b -> FreeT f n b +hoistFreeT mh = FreeT . mh . fmap (fmap (hoistFreeT mh)) . runFreeT + +-- | Lift an applicative homomorphism from @f@ to @g@ into a monad homomorphism from @'FreeT' f m@ to @'FreeT' g m@ +transFreeT :: (Monad m, Applicative g) => (forall a. f a -> g a) -> FreeT f m b -> FreeT g m b +transFreeT nt = FreeT . liftM (fmap (transFreeT nt) . transFreeF nt) . runFreeT + +-- | Pull out and join @m@ layers of @'FreeT' f m a@. +joinFreeT :: (Monad m, Traversable f, Applicative f) => FreeT f m a -> m (Free f a) +joinFreeT (FreeT m) = m >>= joinFreeF + where + joinFreeF (Pure x) = return (return x) + joinFreeF (Free f) = wrap `liftM` Data.Traversable.mapM joinFreeT f + +-- | +-- 'retract' is the left inverse of 'liftF' +-- +-- @ +-- 'retract' . 'liftF' = 'id' +-- @ +retract :: Monad f => Free f a -> f a +retract m = + case runIdentity (runFreeT m) of + Pure a -> return a + Free as -> as >>= retract + +-- | Given an applicative homomorphism from @f@ to 'Identity', tear down a 'Free' 'Monad' using iteration. +iter :: Applicative f => (f a -> a) -> Free f a -> a +iter phi = runIdentity . iterT (Identity . phi . fmap runIdentity) + +-- | Like 'iter' for monadic values. +iterM :: (Applicative f, Monad m) => (f (m a) -> m a) -> Free f a -> m a +iterM phi = iterT phi . hoistFreeT (return . runIdentity) + +-- | Cuts off a tree of computations at a given depth. +-- If the depth is @0@ or less, no computation nor +-- monadic effects will take place. +-- +-- Some examples (@n ≥ 0@): +-- +-- @ +-- 'cutoff' 0 _ ≡ 'return' 'Nothing' +-- 'cutoff' (n+1) '.' 'return' ≡ 'return' '.' 'Just' +-- 'cutoff' (n+1) '.' 'lift' ≡ 'lift' '.' 'liftM' 'Just' +-- 'cutoff' (n+1) '.' 'wrap' ≡ 'wrap' '.' 'fmap' ('cutoff' n) +-- @ +-- +-- Calling @'retract' '.' 'cutoff' n@ is always terminating, provided each of the +-- steps in the iteration is terminating. +cutoff :: (Applicative f, Monad m) => Integer -> FreeT f m a -> FreeT f m (Maybe a) +cutoff n _ | n <= 0 = return Nothing +cutoff n (FreeT m) = FreeT $ bimap Just (cutoff (n - 1)) `liftM` m + +-- | @partialIterT n phi m@ interprets first @n@ layers of @m@ using @phi@. +-- This is sort of the opposite for @'cutoff'@. +-- +-- Some examples (@n ≥ 0@): +-- +-- @ +-- 'partialIterT' 0 _ m ≡ m +-- 'partialIterT' (n+1) phi '.' 'return' ≡ 'return' +-- 'partialIterT' (n+1) phi '.' 'lift' ≡ 'lift' +-- 'partialIterT' (n+1) phi '.' 'wrap' ≡ 'join' . 'lift' . phi +-- @ +partialIterT :: Monad m => Integer -> (forall a. f a -> m a) -> FreeT f m b -> FreeT f m b +partialIterT n phi m + | n <= 0 = m + | otherwise = FreeT $ do + val <- runFreeT m + case val of + Pure a -> return (Pure a) + Free f -> phi f >>= runFreeT . partialIterT (n - 1) phi + +-- | @intersperseT f m@ inserts a layer @f@ between every two layers in +-- @m@. +-- +-- @ +-- 'intersperseT' f '.' 'return' ≡ 'return' +-- 'intersperseT' f '.' 'lift' ≡ 'lift' +-- 'intersperseT' f '.' 'wrap' ≡ 'wrap' '.' 'fmap' ('iterTM' ('wrap' '.' ('<$' f) '.' 'wrap')) +-- @ +intersperseT :: (Monad m, Applicative f) => f a -> FreeT f m b -> FreeT f m b +intersperseT f (FreeT m) = FreeT $ do + val <- m + case val of + Pure x -> return $ Pure x + Free y -> return . Free $ fmap (iterTM (wrap . (<$ f) . wrap)) y + +-- | Tear down a free monad transformer using Monad instance for @t m@. +retractT :: (MonadTrans t, Monad (t m), Monad m) => FreeT (t m) m a -> t m a +retractT (FreeT m) = do + val <- lift m + case val of + Pure x -> return x + Free y -> y >>= retractT + +-- | @intercalateT f m@ inserts a layer @f@ between every two layers in +-- @m@ and then retracts the result. +-- +-- @ +-- 'intercalateT' f ≡ 'retractT' . 'intersperseT' f +-- @ +intercalateT :: (Monad m, MonadTrans t, Monad (t m)) => t m a -> FreeT (t m) m b -> t m b +intercalateT f (FreeT m) = do + val <- lift m + case val of + Pure x -> return x + Free y -> y >>= iterTM (\x -> f >> join x) diff --git a/src/Control/Monad/Trans/Free/Church.hs b/src/Control/Monad/Trans/Free/Church.hs --- a/src/Control/Monad/Trans/Free/Church.hs +++ b/src/Control/Monad/Trans/Free/Church.hs @@ -1,13 +1,9 @@ -{-# LANGUAGE CPP #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} -{-# LANGUAGE Rank2Types #-} +{-# LANGUAGE RankNTypes #-} +{-# LANGUAGE Safe #-} {-# LANGUAGE UndecidableInstances #-} -#ifndef MIN_VERSION_mtl -#define MIN_VERSION_mtl(x,y,z) 1 -#endif - ----------------------------------------------------------------------------- -- | -- Module : Control.Monad.Trans.Free.Church @@ -17,7 +13,7 @@ -- Maintainer : Edward Kmett -- Stability : provisional -- Portability : non-portable (rank-2 polymorphism, MTPCs) --- +-- -- Church-encoded free monad transformer. -- ----------------------------------------------------------------------------- @@ -28,11 +24,13 @@ -- * The free monad , F, free, runF -- * Operations + , improveT , toFT, fromFT , iterT , iterTM , hoistFT , transFT + , joinFT , cutoff -- * Operations of free monad , improve @@ -49,6 +47,8 @@ import Control.Applicative import Control.Category ((<<<), (>>>)) import Control.Monad +import Control.Monad.Catch (MonadCatch(..), MonadThrow(..)) +import qualified Control.Monad.Fail as Fail import Control.Monad.Identity import Control.Monad.Trans.Class import Control.Monad.IO.Class @@ -60,22 +60,26 @@ import Control.Monad.Free.Class import Control.Monad.Trans.Free (FreeT(..), FreeF(..), Free) import qualified Control.Monad.Trans.Free as FreeT -import Data.Foldable (Foldable) import qualified Data.Foldable as F -import Data.Traversable (Traversable) import qualified Data.Traversable as T import Data.Functor.Bind hiding (join) -import Data.Function +import Data.Functor.Classes -- | The \"free monad transformer\" for a functor @f@ -newtype FT f m a = FT {runFT :: forall r. (a -> m r) -> (f (m r) -> m r) -> m r} +newtype FT f m a = FT { runFT :: forall r. (a -> m r) -> (forall x. (x -> m r) -> f x -> m r) -> m r } -instance (Functor f, Monad m, Eq (FreeT f m a)) => Eq (FT f m a) where - (==) = (==) `on` fromFT +instance (Functor f, Monad m, Eq1 f, Eq1 m) => Eq1 (FT f m) where + liftEq eq x y = liftEq eq (fromFT x) (fromFT y) -instance (Functor f, Monad m, Ord (FreeT f m a)) => Ord (FT f m a) where - compare = compare `on` fromFT +instance (Functor f, Monad m, Ord1 f, Ord1 m) => Ord1 (FT f m) where + liftCompare cmp x y= liftCompare cmp (fromFT x) (fromFT y) +instance (Functor f, Monad m, Eq1 f, Eq1 m, Eq a) => Eq (FT f m a) where + (==) = eq1 + +instance (Functor f, Monad m, Ord1 f, Ord1 m, Ord a) => Ord (FT f m a) where + compare = compare1 + instance Functor (FT f m) where fmap f (FT k) = FT $ \a fr -> k (a . f) fr @@ -93,9 +97,13 @@ return = pure FT fk >>= f = FT $ \b fr -> fk (\d -> runFT (f d) b fr) fr -instance (Functor f) => MonadFree f (FT f m) where - wrap f = FT (\kp kf -> kf (fmap (\(FT m) -> m kp kf) f)) +instance Fail.MonadFail m => Fail.MonadFail (FT f m) where + fail = lift . Fail.fail + {-# INLINE fail #-} +instance MonadFree f (FT f m) where + wrap f = FT (\kp kf -> kf (\ft -> runFT ft kp kf) f) + instance MonadTrans (FT f) where lift m = FT (\a _ -> m >>= a) @@ -110,22 +118,20 @@ instance (Foldable f, Foldable m, Monad m) => Foldable (FT f m) where foldr f r xs = F.foldr (<<<) id inner r where - inner = runFT xs (return . f) (F.foldr (liftM2 (<<<)) (return id)) + inner = runFT xs (return . f) (\xg xf -> F.foldr (liftM2 (<<<) . xg) (return id) xf) {-# INLINE foldr #-} -#if MIN_VERSION_base(4,6,0) foldl' f z xs = F.foldl' (!>>>) id inner z where (!>>>) h g = \r -> g $! h r - inner = runFT xs (return . flip f) (F.foldr (liftM2 (>>>)) (return id)) + inner = runFT xs (return . flip f) (\xg xf -> F.foldr (liftM2 (>>>) . xg) (return id) xf) {-# INLINE foldl' #-} -#endif instance (Monad m, Traversable m, Traversable f) => Traversable (FT f m) where traverse f (FT k) = fmap (join . lift) . T.sequenceA $ k traversePure traverseFree where traversePure = return . fmap return . f - traverseFree = return . fmap (wrap . fmap (join . lift)) . T.sequenceA . fmap T.sequenceA + traverseFree xg = return . fmap (wrap . fmap (join . lift)) . T.traverse (T.sequenceA . xg) instance (MonadIO m) => MonadIO (FT f m) where liftIO = lift . liftIO @@ -136,10 +142,10 @@ {-# INLINE throwError #-} m `catchError` f = toFT $ fromFT m `catchError` (fromFT . f) -instance (MonadCont m) => MonadCont (FT f m) where +instance MonadCont m => MonadCont (FT f m) where callCC f = join . lift $ callCC (\k -> return $ f (lift . k . return)) -instance (Functor f, MonadReader r m) => MonadReader r (FT f m) where +instance MonadReader r m => MonadReader r (FT f m) where ask = lift ask {-# INLINE ask #-} local f = hoistFT (local f) @@ -150,64 +156,72 @@ {-# INLINE tell #-} listen = toFT . listen . fromFT pass = toFT . pass . fromFT -#if MIN_VERSION_mtl(2,1,1) writer w = lift (writer w) {-# INLINE writer #-} -#endif -instance (Functor f, MonadState s m) => MonadState s (FT f m) where +instance MonadState s m => MonadState s (FT f m) where get = lift get {-# INLINE get #-} put = lift . put {-# INLINE put #-} -#if MIN_VERSION_mtl(2,1,1) state f = lift (state f) {-# INLINE state #-} -#endif +instance MonadThrow m => MonadThrow (FT f m) where + throwM = lift . throwM + {-# INLINE throwM #-} + +instance (Functor f, MonadCatch m) => MonadCatch (FT f m) where + catch m f = toFT $ fromFT m `Control.Monad.Catch.catch` (fromFT . f) + {-# INLINE catch #-} + -- | Generate a Church-encoded free monad transformer from a 'FreeT' monad -- transformer. -toFT :: (Monad m, Functor f) => FreeT f m a -> FT f m a +toFT :: Monad m => FreeT f m a -> FT f m a toFT (FreeT f) = FT $ \ka kfr -> do freef <- f case freef of Pure a -> ka a - Free fb -> kfr $ fmap (($ kfr) . ($ ka) . runFT . toFT) fb + Free fb -> kfr (\x -> runFT (toFT x) ka kfr) fb -- | Convert to a 'FreeT' free monad representation. fromFT :: (Monad m, Functor f) => FT f m a -> FreeT f m a -fromFT (FT k) = FreeT $ k (return . Pure) (runFreeT . wrap . fmap FreeT) +fromFT (FT k) = FreeT $ k (return . Pure) (\xg -> runFreeT . wrap . fmap (FreeT . xg)) -- | The \"free monad\" for a functor @f@. type F f = FT f Identity -- | Unwrap the 'Free' monad to obtain it's Church-encoded representation. runF :: Functor f => F f a -> (forall r. (a -> r) -> (f r -> r) -> r) -runF (FT m) = \kp kf -> runIdentity $ m (return . kp) (return . kf . fmap runIdentity) +runF (FT m) = \kp kf -> runIdentity $ m (return . kp) (\xg -> return . kf . fmap (runIdentity . xg)) -- | Wrap a Church-encoding of a \"free monad\" as the free monad for a functor. -free :: Functor f => (forall r. (a -> r) -> (f r -> r) -> r) -> F f a -free f = FT (\kp kf -> return $ f (runIdentity . kp) (runIdentity . kf . fmap return)) +free :: (forall r. (a -> r) -> (f r -> r) -> r) -> F f a +free f = FT (\kp kf -> return $ f (runIdentity . kp) (runIdentity . kf return)) -- | Tear down a free monad transformer using iteration. iterT :: (Functor f, Monad m) => (f (m a) -> m a) -> FT f m a -> m a -iterT phi (FT m) = m return phi +iterT phi (FT m) = m return (\xg -> phi . fmap xg) {-# INLINE iterT #-} -- | Tear down a free monad transformer using iteration over a transformer. iterTM :: (Functor f, Monad m, MonadTrans t, Monad (t m)) => (f (t m a) -> t m a) -> FT f m a -> t m a -iterTM f (FT m) = join . lift $ m (return . return) (return . f . fmap (join .lift)) +iterTM f (FT m) = join . lift $ m (return . return) (\xg -> return . f . fmap (join . lift . xg)) -- | Lift a monad homomorphism from @m@ to @n@ into a monad homomorphism from @'FT' f m@ to @'FT' f n@ -- -- @'hoistFT' :: ('Monad' m, 'Monad' n, 'Functor' f) => (m ~> n) -> 'FT' f m ~> 'FT' f n@ -hoistFT :: (Monad m, Monad n, Functor f) => (forall a. m a -> n a) -> FT f m b -> FT f n b -hoistFT phi (FT m) = FT (\kp kf -> join . phi $ m (return . kp) (return . kf . fmap (join . phi))) +hoistFT :: (Monad m, Monad n) => (forall a. m a -> n a) -> FT f m b -> FT f n b +hoistFT phi (FT m) = FT (\kp kf -> join . phi $ m (return . kp) (\xg -> return . kf (join . phi . xg))) -- | Lift a natural transformation from @f@ to @g@ into a monad homomorphism from @'FT' f m@ to @'FT' g n@ -transFT :: (Monad m, Functor g) => (forall a. f a -> g a) -> FT f m b -> FT g m b -transFT phi (FT m) = FT (\kp kf -> m kp (kf . phi)) +transFT :: (forall a. f a -> g a) -> FT f m b -> FT g m b +transFT phi (FT m) = FT (\kp kf -> m kp (\xg -> kf xg . phi)) +-- | Pull out and join @m@ layers of @'FreeT' f m a@. +joinFT :: (Monad m, Traversable f) => FT f m a -> m (F f a) +joinFT (FT m) = m (return . return) (\xg -> liftM wrap . T.mapM xg) + -- | Cuts off a tree of computations at a given depth. -- If the depth is 0 or less, no computation nor -- monadic effects will take place. @@ -230,13 +244,13 @@ -- @ -- 'retract' . 'liftF' = 'id' -- @ -retract :: (Functor f, Monad f) => F f a -> f a +retract :: Monad f => F f a -> f a retract m = runF m return join {-# INLINE retract #-} -- | Tear down a free monad transformer using iteration over a transformer. retractT :: (MonadTrans t, Monad (t m), Monad m) => FT (t m) m a -> t m a -retractT (FT m) = join . lift $ m (return . return) $ \x -> return $ x >>= join . lift +retractT (FT m) = join . lift $ m (return . return) (\xg xf -> return $ xf >>= join . lift . xg) -- | Tear down an 'F' 'Monad' using iteration. iter :: Functor f => (f a -> a) -> F f a -> a @@ -253,7 +267,7 @@ {-# INLINE fromF #-} -- | Generate a Church-encoded free monad from a 'Free' monad. -toF :: (Functor f) => Free f a -> F f a +toF :: Free f a -> F f a toF = toFT {-# INLINE toF #-} @@ -261,8 +275,8 @@ -- -- This is based on the \"Free Monads for Less\" series of articles by Edward Kmett: -- --- --- +-- +-- -- -- and \"Asymptotic Improvement of Computations over Free Monads\" by Janis Voightländer: -- @@ -270,4 +284,12 @@ improve :: Functor f => (forall m. MonadFree f m => m a) -> Free f a improve m = fromF m {-# INLINE improve #-} + +-- | Improve the asymptotic performance of code that builds a free monad transformer +-- with only binds and returns by using 'FT' behind the scenes. +-- +-- Similar to 'improve'. +improveT :: (Functor f, Monad m) => (forall t. MonadFree f (t m) => t m a) -> FreeT f m a +improveT m = fromFT m +{-# INLINE improveT #-} diff --git a/src/Control/Monad/Trans/Iter.hs b/src/Control/Monad/Trans/Iter.hs --- a/src/Control/Monad/Trans/Iter.hs +++ b/src/Control/Monad/Trans/Iter.hs @@ -1,14 +1,11 @@ {-# LANGUAGE CPP #-} -{-# LANGUAGE FlexibleContexts #-} +{-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE UndecidableInstances #-} {-# LANGUAGE MultiParamTypeClasses #-} {-# LANGUAGE Rank2Types #-} -{-# LANGUAGE DeriveDataTypeable #-} - -#ifndef MIN_VERSION_mtl -#define MIN_VERSION_mtl(x,y,z) 1 -#endif +{-# LANGUAGE Safe #-} +{-# LANGUAGE StandaloneDeriving #-} ----------------------------------------------------------------------------- -- | @@ -73,9 +70,11 @@ ) where import Control.Applicative +import Control.Monad.Catch (MonadCatch(..), MonadThrow(..)) import Control.Monad (ap, liftM, MonadPlus(..), join) import Control.Monad.Fix import Control.Monad.Trans.Class +import qualified Control.Monad.Fail as Fail import Control.Monad.Free.Class import Control.Monad.State.Class import Control.Monad.Error.Class @@ -87,26 +86,23 @@ import Data.Bitraversable import Data.Either import Data.Functor.Bind hiding (join) +import Data.Functor.Classes import Data.Functor.Identity -import Data.Foldable hiding (fold) -import Data.Function (on) -import Data.Traversable hiding (mapM) -import Data.Monoid import Data.Semigroup.Foldable import Data.Semigroup.Traversable import Data.Typeable import Data.Data -import Prelude.Extras +#if !(MIN_VERSION_base(4,11,0)) +import Data.Semigroup +#endif + -- | The monad supporting iteration based over a base monad @m@. -- -- @ -- 'IterT' ~ 'FreeT' 'Identity' -- @ newtype IterT m a = IterT { runIterT :: m (Either a (IterT m a)) } -#if __GLASGOW_HASKELL__ >= 707 - deriving (Typeable) -#endif -- | Plain iterative computations. type Iter = IterT Identity @@ -125,33 +121,43 @@ runIter = runIdentity . runIterT {-# INLINE runIter #-} -instance (Functor m, Eq1 m) => Eq1 (IterT m) where - (==#) = on (==#) (fmap (fmap Lift1) . runIterT) +instance (Eq1 m) => Eq1 (IterT m) where + liftEq eq = go + where + go (IterT x) (IterT y) = liftEq (liftEq2 eq go) x y -instance Eq (m (Either a (IterT m a))) => Eq (IterT m a) where - IterT m == IterT n = m == n +instance (Eq1 m, Eq a) => Eq (IterT m a) where + (==) = eq1 -instance (Functor m, Ord1 m) => Ord1 (IterT m) where - compare1 = on compare1 (fmap (fmap Lift1) . runIterT) +instance (Ord1 m) => Ord1 (IterT m) where + liftCompare cmp = go + where + go (IterT x) (IterT y) = liftCompare (liftCompare2 cmp go) x y -instance Ord (m (Either a (IterT m a))) => Ord (IterT m a) where - compare (IterT m) (IterT n) = compare m n +instance (Ord1 m, Ord a) => Ord (IterT m a) where + compare = compare1 -instance (Functor m, Show1 m) => Show1 (IterT m) where - showsPrec1 d (IterT m) = showParen (d > 10) $ - showString "IterT " . showsPrec1 11 (fmap (fmap Lift1) m) +instance (Show1 m) => Show1 (IterT m) where + liftShowsPrec sp sl = go + where + goList = liftShowList sp sl + go d (IterT x) = showsUnaryWith + (liftShowsPrec (liftShowsPrec2 sp sl go goList) (liftShowList2 sp sl go goList)) + "IterT" d x -instance Show (m (Either a (IterT m a))) => Show (IterT m a) where - showsPrec d (IterT m) = showParen (d > 10) $ - showString "IterT " . showsPrec 11 m +instance (Show1 m, Show a) => Show (IterT m a) where + showsPrec = showsPrec1 -instance (Functor m, Read1 m) => Read1 (IterT m) where - readsPrec1 d = readParen (d > 10) $ \r -> - [ (IterT (fmap (fmap lower1) m),t) | ("IterT",s) <- lex r, (m,t) <- readsPrec1 11 s] +instance (Read1 m) => Read1 (IterT m) where + liftReadsPrec rp rl = go + where + goList = liftReadList rp rl + go = readsData $ readsUnaryWith + (liftReadsPrec (liftReadsPrec2 rp rl go goList) (liftReadList2 rp rl go goList)) + "IterT" IterT -instance Read (m (Either a (IterT m a))) => Read (IterT m a) where - readsPrec d = readParen (d > 10) $ \r -> - [ (IterT m,t) | ("IterT",s) <- lex r, (m,t) <- readsPrec 11 s] +instance (Read1 m, Read a) => Read (IterT m a) where + readsPrec = readsPrec1 instance Monad m => Functor (IterT m) where fmap f = IterT . liftM (bimap f (fmap f)) . runIterT @@ -164,10 +170,16 @@ {-# INLINE (<*>) #-} instance Monad m => Monad (IterT m) where - return = IterT . return . Left + return = pure {-# INLINE return #-} IterT m >>= k = IterT $ m >>= either (runIterT . k) (return . Right . (>>= k)) {-# INLINE (>>=) #-} +#if !MIN_VERSION_base(4,13,0) + fail = Fail.fail + {-# INLINE fail #-} +#endif + +instance Monad m => Fail.MonadFail (IterT m) where fail _ = never {-# INLINE fail #-} @@ -232,27 +244,23 @@ listen (IterT m) = IterT $ liftM concat' $ listen (fmap listen `liftM` m) where concat' (Left x, w) = Left (x, w) - concat' (Right y, w) = Right $ second (w <>) <$> y + concat' (Right y, w) = Right $ second (w `mappend`) <$> y pass m = IterT . pass' . runIterT . hoistIterT clean $ listen m where clean = pass . liftM (\x -> (x, const mempty)) pass' = join . liftM g g (Left ((x, f), w)) = tell (f w) >> return (Left x) g (Right f) = return . Right . IterT . pass' . runIterT $ f -#if MIN_VERSION_mtl(2,1,1) writer w = lift (writer w) {-# INLINE writer #-} -#endif instance MonadState s m => MonadState s (IterT m) where get = lift get {-# INLINE get #-} put s = lift (put s) {-# INLINE put #-} -#if MIN_VERSION_mtl(2,1,1) state f = lift (state f) {-# INLINE state #-} -#endif instance MonadError e m => MonadError e (IterT m) where throwError = lift . throwError @@ -269,6 +277,14 @@ wrap = IterT . return . Right . runIdentity {-# INLINE wrap #-} +instance MonadThrow m => MonadThrow (IterT m) where + throwM = lift . throwM + {-# INLINE throwM #-} + +instance MonadCatch m => MonadCatch (IterT m) where + catch (IterT m) f = IterT $ liftM (fmap (`Control.Monad.Catch.catch` f)) m `Control.Monad.Catch.catch` (runIterT . f) + {-# INLINE catch #-} + -- | Adds an extra layer to a free monad value. -- -- In particular, for the iterative monad 'Iter', this makes the @@ -372,17 +388,9 @@ interleave_ xs = IterT $ liftM (Right . interleave_ . rights) $ mapM runIterT xs {-# INLINE interleave_ #-} -instance (Monad m, Monoid a) => Monoid (IterT m a) where +instance (Monad m, Semigroup a, Monoid a) => Monoid (IterT m a) where mempty = return mempty - x `mappend` y = IterT $ do - x' <- runIterT x - y' <- runIterT y - case (x', y') of - ( Left a, Left b) -> return . Left $ a `mappend` b - ( Left a, Right b) -> return . Right $ liftM (a `mappend`) b - (Right a, Left b) -> return . Right $ liftM (`mappend` b) a - (Right a, Right b) -> return . Right $ a `mappend` b - + mappend = (<>) mconcat = mconcat' . map Right where mconcat' :: (Monad m, Monoid a) => [Either a (IterT m a)] -> IterT m a @@ -400,46 +408,23 @@ compact' a [] = [Left a] compact' a (r@(Right _):xs) = (Left a):(r:(compact xs)) - compact' a ( (Left a'):xs) = compact' (a <> a') xs - -#if __GLASGOW_HASKELL__ < 707 -instance Typeable1 m => Typeable1 (IterT m) where - typeOf1 t = mkTyConApp freeTyCon [typeOf1 (f t)] where - f :: IterT m a -> m a - f = undefined - -freeTyCon :: TyCon -#if __GLASGOW_HASKELL__ < 704 -freeTyCon = mkTyCon "Control.Monad.Iter.IterT" -#else -freeTyCon = mkTyCon3 "free" "Control.Monad.Iter" "IterT" -#endif -{-# NOINLINE freeTyCon #-} + compact' a ( (Left a'):xs) = compact' (a `mappend` a') xs -#else -#define Typeable1 Typeable -#endif +instance (Monad m, Semigroup a) => Semigroup (IterT m a) where + x <> y = IterT $ do + x' <- runIterT x + y' <- runIterT y + case (x', y') of + ( Left a, Left b) -> return . Left $ a <> b + ( Left a, Right b) -> return . Right $ liftM (a <>) b + (Right a, Left b) -> return . Right $ liftM (<> b) a + (Right a, Right b) -> return . Right $ a <> b -instance - ( Typeable1 m, Typeable a +deriving instance + ( Typeable m , Data (m (Either a (IterT m a))) , Data a - ) => Data (IterT m a) where - gfoldl f z (IterT as) = z IterT `f` as - toConstr IterT{} = iterConstr - gunfold k z c = case constrIndex c of - 1 -> k (z IterT) - _ -> error "gunfold" - dataTypeOf _ = iterDataType - dataCast1 f = gcast1 f - -iterConstr :: Constr -iterConstr = mkConstr iterDataType "IterT" [] Prefix -{-# NOINLINE iterConstr #-} - -iterDataType :: DataType -iterDataType = mkDataType "Control.Monad.Iter.IterT" [iterConstr] -{-# NOINLINE iterDataType #-} + ) => Data (IterT m a) {- $examples