-- | -- Module : Data.Edit -- Copyright : (c) Varun Gandhi 2018 -- License : BSD-style (see the file LICENSE) -- -- Maintainer : theindigamer15@gmail.com -- Stability : experimental -- Portability : portable -- -- This is a short (?) tutorial describing how you can use the 'Data.Edit' module -- to help you with writing dataflow analysis code for a compiler. The example -- is a bit artificial for the sake of relative conciseness -- if you have a -- better suggestion, or find any mistakes, please let me know on the Github -- <https://github.com/theindigamer/edit/issues issue tracker>. -- {-# LANGUAGE CPP #-} #ifdef TUTORIAL {-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE TupleSections #-} #endif #ifdef TUTORIAL module Data.Edit.Tutorial ( -- * TL;DR -- $tldr -- * Setup -- $setup -- * Tutorial -- -- $identexpr -- -- $ConstFold -- -- $ConstFoldTests -- -- $Substitute -- -- $SubstituteTests -- -- $StmtConstProp -- -- $ConstFoldPass -- -- $ConstPropPass -- -- $CombinedPass -- -- $CombinedTest Ident (..) , Expr (..) , constFold , substitute , Stmt , constProp , constFold' , constFoldPass , substitute' , constProp' , constPropPass , constFoldAndPropPass ) where #else module Data.Edit.Tutorial ( -- * TL;DR -- $tldr -- * Setup -- $setup -- * Tutorial -- -- $identexpr -- -- $ConstFold -- -- $ConstFoldTests -- -- $Substitute -- -- $SubstituteTests -- -- $CombinedPass -- -- $CombinedTest ) where #endif #ifdef TUTORIAL import Data.Data import Data.Edit import Data.Generics.Uniplate.Data import Data.List (unfoldr) import Data.Map (Map) import qualified Data.Map as Map #endif {- $tldr Get a fixed point from applying a sequence of transformations. > import Data.Edit (Edit, edits, polish, (>=>)) > > mkAwesome1 :: Foo -> Maybe Foo > ... > mkAwesomeN :: Foo -> Maybe Foo > > mkAwesomeAny :: Foo -> Edit Foo > mkAwesomeAny > = foldr (\f acc -> acc >=> (f `edits`)) pure > [mkAwesome1, ..., mkAwesomeN] > > mkAsAwesomeAsPossible :: Foo -> Foo > mkAsAwesomeAsPossible = polish mkAwesomeAny Transform a recursive data structure, keeping track of whether it was changed or not, and feed the result to some high-level dataflow analysis function. > import DataFlowLibrary > import PlatedLibrary > import Data.Edit (Edit, edits, toMaybe) > > instance FancyPlate Foo where ... > > mkAwesome :: Foo -> Maybe Foo > mkAwesome = ... > > mkTotallyAwesome :: Foo -> Edit Foo > mkTotallyAwesome = transformM (mkAwesome `edits`) > > dataFlowAnalysis = dataFlowLibFn (toMaybe . mkTotallyAwesome) -} -- $setup -- The examples here use the -- <https://github.com/ndmitchell/uniplate Uniplate> and -- <https://github.com/haskell/containers Containers> libraries. -- If you want to -- follow along as we proceed, you will want to supply the package flag -- @tutorial@ and maybe read the docs in your browser. -- -- If you're using @cabal@, this can be done using -- (tested using @cabal-install@ 2.0.0.1): -- -- > cabal new-configure --flags="tutorial" -- > cabal new-build -- > cabal new-haddock -- -- If you're using @stack@, the same can be done using: -- -- > stack build --flag=edit:tutorial -- > stack haddock --flag=edit:tutorial --open edit -- $identexpr -- -- Let's define a toy language @L@ with 'Int's and addition. -- -- > newtype Ident = Ident String -- > deriving (Show, Eq) -- > -- > data Expr -- > = Val Int -- > | Var Ident -- > | Add Expr Expr -- > deriving (Show, Eq) #ifdef TUTORIAL newtype Ident = Ident String deriving (Eq, Ord, Show, Typeable, Data) data Expr = Val Int | Add Expr Expr | Var Ident deriving (Show, Eq, Typeable, Data) #endif -- $ConstFold -- Q. How would you implement constant folding for the 'Expr' type? -- -- (1) Write the recursion by hand. While this is easy enough to do since -- 'Expr' only has a few constructors, this isn't very practical when you have -- lots of constructors. The exact point where you recognize that this is a -- recursive descent into unmaintainability depends on your personal boilerplate -- threshold. -- -- (2) Use recursion schemes and get lost in the unfathomable type errors -- (I'm half-joking). While this is a reasonable approach, we're not going to -- follow this here. -- -- (3) Use a generics library. For simplicity, we'll be using Uniplate here. -- The particular functions that are relevant at the moment are 'rewrite' and -- 'transform'. Let's use 'rewrite'. -- -- @ -- __\{-\# LANGUAGE DeriveDataTypeable \#-\}__ -- -- __import Data.Data__ -- __import Data.Generics.Uniplate.Data__ -- -- newtype Ident = Ident String -- deriving (Show, Eq__, Typeable, Data__) -- -- data Expr -- = Val Int -- | Var Ident -- | Add Expr Expr -- deriving (Show, Eq__, Typeable, Data__) -- -- __constFold :: Expr -> Expr__ -- __constFold e = rewrite go e__ -- __where__ -- __go (Add (Val i) (Val j)) = Just (Val (i + j))__ -- __go _ = Nothing__ -- @ #ifdef TUTORIAL constFold :: Expr -> Expr constFold = rewrite go where go (Add (Val i) (Val j)) = Just (Val (i + j)) go _ = Nothing #endif -- $ConstFoldTests -- Test that the implementation works as expected. -- -- >>> two = Add (Val 1) (Val 1) -- >>> four = Add (Val 2) (Val 2) -- >>> constFold (Add two four) -- Val 6 -- >>> constFold (Add (Var "x") two) -- Add (Var "x") (Val 2) -- $Substitute -- Let's say we add assignment statements to the language and write a function -- to do constant propagation. First we add a @substitute@ function. -- -- @ -- __import Data.Map (Map)__ -- __import qualified Data.Map as Map__ -- -- newtype Ident = Ident String -- deriving (Eq, __Ord,__ Show, Typeable, Data) -- -- __substitute :: Map Ident Int -> Expr -> Expr__ -- __substitute m e = rewrite go e__ -- __where__ -- __go (Var x) = Val \<$\> Map.lookup x m__ -- __go _ = Nothing__ -- @ #ifdef TUTORIAL substitute :: Map Ident Int -> Expr -> Expr substitute m = rewrite go where go (Var x) = Val <$> Map.lookup x m go _ = Nothing #endif -- $SubstituteTests -- Let's test this out. -- -- >>> x = Var (Ident "x") -- >>> quadrupleX = Add x (Add x (Add x x)) -- >>> m1 = Map.fromList [(Ident "x", 5)] -- >>> substitute m1 quadrupleX -- Add (Val 5) (Add (Val 5) (Add (Val 5) (Val 5))) -- $StmtConstProp -- Finally add in statements and a constant propagation function. -- -- @ -- __infix 9 :=__ -- __data Stmt = Ident := Expr__ -- __deriving (Show)__ -- -- __constProp :: Map Ident Int -> Stmt -> (Map Ident Int, Stmt)__ -- __constProp map_ (var := expr) = (f map_, var := expr')__ -- __where__ -- __expr' = substitute map_ expr__ -- __f = case expr' of__ -- __Val x -> Map.insert var x__ -- ___ -> Map.delete var__ -- delete old entry if var is re-defined -- @ -- -- >>> x = Var (Ident "x") -- >>> m1 = Map.fromList [(Ident "x", 5)] -- >>> constProp m1 (Ident "y" := Var (Ident "x")) -- (fromList [(Ident "x",5),(Ident "y",5)],Ident "y":=Val 5) #ifdef TUTORIAL infix 9 := data Stmt = Ident := Expr deriving (Show) constProp :: Map Ident Int -> Stmt -> (Map Ident Int, Stmt) constProp map_ (var := expr) = (f map_, var := expr') where expr' = substitute map_ expr f = case expr' of Val x -> Map.insert var x _ -> id #endif -- $ConstFoldPass -- Now let's say we want to write two passes -- one for constant folding, one -- for constant propagation, and then iterate until no more optimization can be -- done (yes, this isn't an optimal strategy, but then this tutorial would be -- even longer :O). -- -- However, the 'constFold' function, as it stands, doesn't save the -- "information" whether it changed something or not. Consequently, we won't -- be able to tell if we hit the fixed point or not unless we do an equality -- check (which could be expensive if the expression trees are big). Time to -- finally use the 'Edit' monad! -- -- We can use the 'edits' function, which converts a function @f: a -> Maybe a@ -- to a function @f' : a -> Edit a@. -- -- @ -- __import Data.Edit__ -- -- -- We don't have to alter the core logic here, neat! -- constFold__'__ :: Expr -> __Edit__ Expr -- constFold__'__ = __transformM__ (go __\`edits\`__) -- where -- go (Add (Val i) (Val j)) = Just (Val (i + j)) -- go _ = Nothing -- -- __constFoldPass :: [Stmt] -> Edit [Stmt]__ -- __constFoldPass ss = traverse (\\(v := e) -> (v :=) \<$\> constFold' e) ss__ -- @ -- #ifdef TUTORIAL constFold' :: Expr -> Edit Expr constFold' = transformM (go `edits`) where go (Add (Val i) (Val j)) = Just (Val (i + j)) go _ = Nothing constFoldPass :: [Stmt] -> Edit [Stmt] constFoldPass = traverse (\(v := e) -> (v :=) <$> constFold' e) #endif -- $ConstPropPass -- We also need slightly different versions of 'substitute' and 'constProp'. -- Here we use the 'extract' function; it has the signature @Edit a -> a@. -- It is fine to throw away the 'Clean'/'Dirty' information when we are updating -- the map, because we are only interested in changes to the @Stmt@ and don't -- care if the @Map@ gets changed or not. -- -- @ -- substitute__'__ :: Map Ident Int -> Expr -> __Edit__ Expr -- substitute__'__ m e = __transformM__ (go __\`edits\`__) e -- where -- go (Var x) = Val \<$\> Map.lookup x m -- go _ = Nothing -- -- constProp__'__ :: Map Ident Int -> Stmt -> (Map Ident Int, __Edit__ Stmt) -- constProp__'__ map_ (var := expr) = (f map_, (var :=) __\<$\>__ expr') -- where -- expr' = substitute__'__ map_ expr -- f = case __extract__ expr' of -- Val x -> Map.insert var x -- _ -> id -- @ -- -- Let's add a top-level function similar to 'constFoldPass'. -- -- Note: If you're unfamiliar with 'unfoldr', you can think of it as the -- opposite of 'foldr'. 'foldr' takes a list and a starting value and -- collapses it to a single value; 'unfoldr' takes a starting value (often -- called a seed) and generates a list out of it. -- -- @ -- __import Data.List (unfoldr)__ -- -- __constPropPass :: [Stmt] -> Edit [Stmt]__ -- __constPropPass ss = sequence $ unfoldr go (Map.empty, ss)__ -- __where__ -- __go (_, []) = Nothing__ -- __go (m, x:xs) = let (m', ex) = constProp' m x in Just (ex, (m', xs))__ -- @ #ifdef TUTORIAL substitute' :: Map Ident Int -> Expr -> Edit Expr substitute' m e = transformM (go `edits`) e where go (Var x) = Val <$> Map.lookup x m go _ = Nothing constProp' :: Map Ident Int -> Stmt -> (Map Ident Int, Edit Stmt) constProp' map_ (var := expr) = (f map_, (var :=) <$> expr') where expr' = substitute' map_ expr f = case extract expr' of Val x -> Map.insert var x _ -> Map.delete var constPropPass :: [Stmt] -> Edit [Stmt] constPropPass ss = sequence $ unfoldr go (Map.empty, ss) where go (_, []) = Nothing go (m, x:xs) = let (m', ex) = constProp' m x in Just (ex, (m', xs)) #endif -- $CombinedPass -- Finally putting all the pieces together. We can use the 'polish' function -- to find the fixed point, which (in this case) is a fancy way of saying that -- we keep iterating until we have a 'Clean' (unchanged) value. -- -- @ -- __constFoldAndPropPass :: [Stmt] -> [Stmt]__ -- __constFoldAndPropPass = polish (constFoldPass >=> constPropPass)__ -- @ #ifdef TUTORIAL constFoldAndPropPass :: [Stmt] -> [Stmt] constFoldAndPropPass = polish (constFoldPass >=> constPropPass) #endif -- $CombinedTest -- We're not done yet though! We still need to check that this works :P. -- -- >>> [w, x, y] = map Ident ["w", "x", "y"] -- >>> s1 = w := Add (Val 1) (Val 2) -- >>> s2 = x := Add (Var w) (Var w) -- >>> s3 = y := Add (Var w) (Add (Val 1) (Var x)) -- >>> s4 = x := Add (Var y) (Var y) -- >>> s5 = y := Add (Var w) (Var x) -- >>> constFoldAndPropPass [s1, s2, s3, s4, s5] -- [Ident "w" := Val 3,Ident "x" := Val 6,Ident "y" := Val 10,Ident "x" := Val 20,Ident "y" := Val 23] -- -- Yup, it works! For fun, let's see the transformation process in action. -- We can do this using the 'iterations' function. -- -- >>> pprint = putStr . unlines . map (unlines . map show) -- >>> pprint $ iterations (constFoldPass >=> constPropPass) [s1, s2, s3, s4, s5] -- -- The output shows the full history, with the final result that we obtained -- earlier at the end. -- -- @ -- Ident "w" := Add (Val 1) (Val 2) -- Ident "x" := Add (Var (Ident "w")) (Var (Ident "w")) -- Ident "y" := Add (Var (Ident "w")) (Add (Val 1) (Var (Ident "x"))) -- Ident "x" := Add (Var (Ident "y")) (Var (Ident "y")) -- Ident "y" := Add (Var (Ident "w")) (Var (Ident "x")) -- -- Ident "w" := Val 3 -- Ident "x" := Add (Val 3) (Val 3) -- Ident "y" := Add (Val 3) (Add (Val 1) (Var (Ident "x"))) -- Ident "x" := Add (Var (Ident "y")) (Var (Ident "y")) -- Ident "y" := Add (Val 3) (Var (Ident "x")) -- -- Ident "w" := Val 3 -- Ident "x" := Val 6 -- Ident "y" := Add (Val 3) (Add (Val 1) (Val 6)) -- Ident "x" := Add (Var (Ident "y")) (Var (Ident "y")) -- Ident "y" := Add (Val 3) (Var (Ident "x")) -- -- Ident "w" := Val 3 -- Ident "x" := Val 6 -- Ident "y" := Val 10 -- Ident "x" := Add (Val 10) (Val 10) -- Ident "y" := Add (Val 3) (Var (Ident "x")) -- -- Ident "w" := Val 3 -- Ident "x" := Val 6 -- Ident "y" := Val 10 -- Ident "x" := Val 20 -- Ident "y" := Add (Val 3) (Val 20) -- -- Ident "w" := Val 3 -- Ident "x" := Val 6 -- Ident "y" := Val 10 -- Ident "x" := Val 20 -- Ident "y" := Val 23 -- @ -- -- Fin.