implementation module check
import StdEnv
+
+import Control.Monad => qualified join
+import Control.Monad.State
+import Control.Monad.Trans
+import Control.Monad.Writer
import Data.Either
-import Data.List
-import Data.Functor
import Data.Func
+import Data.List
+import Data.Tuple
+import Data.Map => qualified put, union, difference, find, updateAt
import Data.Maybe
-import Data.Monoid
-import Control.Applicative
-import Control.Monad
-import Control.Monad.Trans
-import Control.Monad.RWST
-import qualified Data.Map as DM
-from Data.Map import instance Functor (Map k)
-
-import ast
-
-check :: AST -> Either [String] AST
-check (AST fs) = case find (\f->f=:(Function ['start'] [] _)) fs of
- Nothing = Left ["No start function defined"]
- Just _ = Right (AST fs)
-
-:: Type
- = TVar [Char]
- | TInt
- | TBool
- | TChar
- | TFun Type Type
-instance == Type where
- (==) (TVar a) (TVar b) = a == b
- (==) TInt TInt = True
- (==) TBool TBool = True
- (==) TChar TChar = True
- (==) (TFun a1 a2) (TFun b1 b2) = a1 == b1 && a2 == b2
- (==) _ _ = False
-instance toString Type where
- toString (TVar s) = toString s
- toString TInt = "Int"
- toString TBool = "Bool"
- toString TChar = "Char"
- toString (TFun t1 t2) = toString t1 +++ " -> " +++ toString t2
-:: Scheme = Scheme [[Char]] Type
-class Types a where
- ftv :: a -> [[Char]]
+import Text
+
+import ast, scc
+
+import StdDebug
+
+check :: ![Either TypeDef Function] -> Either [String] (Expression, [([Char], Scheme)])
+check tdfs
+ # dups = filter (\x->length x > 1) (groupBy (\(Function i _ _) (Function j _ _)->i == j) functions)
+ | length dups > 0 = Left ["Duplicate functions: ":[toString n\\[(Function n _ _):_]<-dups]]
+ = case partition (\a->a=:(Function ['start'] _ _)) functions of
+ ([], _) = Left ["No start function defined"]
+ ([Function _ [] e:_], fs)
+ # e = makeExpression fs e
+ = tuple e <$> runInfer (infer (fromList (conses ++ builtin)) e)
+ ([Function _ _ _:_], _) = Left ["Start cannot have arguments"]
+where
+ functions = rights tdfs
+ conses = flatten $ map (\(TypeDef n t cs)->
+ let cons = Forall t o foldr (-->) (foldl TApp (TVar n) (map TVar t))
+ in map (appSnd cons) cs) $ lefts tdfs
+ builtin =
+ [(['_if'], Forall [['a']] $ TBool --> TVar ['a'] --> TVar ['a'] --> TVar ['a'])
+ ,(['_eq'], Forall [] $ TInt --> TInt --> TBool)
+ ,(['_mul'], Forall [] $ TInt --> TInt --> TInt)
+ ,(['_add'], Forall [] $ TInt --> TInt --> TInt)
+ ,(['_sub'], Forall [] $ TInt --> TInt --> TInt)
+ ,(['_div'], Forall [] $ TInt --> TInt --> TInt)
+ ]
+
+makeExpression :: [Function] Expression -> Expression
+makeExpression fs start = foldr mkExpr start $ scc $ map (appSnd vars) nicefuns
+where
+ mkExpr :: [[Char]] -> (Expression -> Expression)
+ mkExpr scc = Let [(l, e)\\(l, e)<-nicefuns, s<-scc | s == l]
+
+ nicefuns :: [([Char], Expression)]
+ nicefuns = [(l, foldr ((o) o Lambda) id i e)\\(Function l i e)<-fs]
+
+ vars :: Expression -> [[Char]]
+ vars (Var v) = [v]
+ vars (App l r) = vars l ++ vars r
+ vars (Lambda l e) = flt l e
+ vars (Let ns e) = flatten [[v\\v<-vars e | not (isMember v (map fst ns))]:map (uncurry flt) ns]
+ vars _ = []
+
+ flt i e = [v\\v<-vars e | v <> i]
+
+instance toString Scheme where
+ toString (Forall [] t) = toString t
+ toString (Forall as t) = concat ["A.", join " " (map toString as), ": ", toString t]
+
+:: TypeEnv :== Map [Char] Scheme
+:: Subst :== Map [Char] Type
+
+:: Infer a :== StateT [Int] (WriterT [([Char], Scheme)] (Either [String])) a
+
+runInfer :: (Infer (Subst, Type)) -> Either [String] [([Char], Scheme)]
+runInfer i = case runWriterT (evalStateT i [0..]) of
+ Left e = Left e
+ Right ((s, t), w) = pure [(['start'], generalize newMap (apply s t)):w]
+
+fresh :: Infer Type
+fresh = getState >>= \[s:ss]->put ss >>| pure (TVar (['v':[c\\c<-:toString s]]))
+
+(oo) infixl 9 :: Subst Subst -> Subst
+(oo) s1 s2 = 'Data.Map'.union (apply s1 <$> s2) s1
+
+class Substitutable a where
apply :: Subst a -> a
-instance Types Type where
- ftv (TVar n) = [n]
- ftv TInt = []
- ftv TBool = []
- ftv TChar = []
- ftv (TFun t1 t2) = union (ftv t1) (ftv t2)
-
- apply s (TVar n) = case 'DM'.get n s of
- Nothing = TVar n
- Just t = t
- apply s (TFun t1 t2) = TFun (apply s t1) (apply s t2)
- apply s t = t
-instance Types Scheme where
- ftv (Scheme vars t) = difference (ftv t) vars
- apply s (Scheme vars t) = Scheme vars (apply (foldr 'DM'.del s vars) t)
-instance Types [a] | Types a where
- ftv l = foldr union [] (map ftv l)
- apply s l = map (apply s) l
-
-:: Subst :== 'DM'.Map [Char] Type
-composeSubst s1 s2 = 'DM'.union ((apply s1) <$> s2) s1
-
-:: TypeEnv = TypeEnv ('DM'.Map [Char] Scheme)
-remove :: TypeEnv [Char] -> TypeEnv
-remove (TypeEnv env) var = TypeEnv ('DM'.del var env)
-
-instance Types TypeEnv where
- ftv (TypeEnv env) = ftv ('DM'.elems env)
- apply s (TypeEnv env) = TypeEnv (apply s <$> env)
+ ftv :: a -> [[Char]]
+
+instance Substitutable Type where
+ apply s t=:(TVar v) = fromMaybe t (get v s)
+ apply s (t1 --> t2) = apply s t1 --> apply s t2
+ apply s (TApp t1 t2) = TApp (apply s t1) (apply s t2)
+ apply _ x = x
+
+ ftv (TVar v) = [v]
+ ftv (t1 --> t2) = on union ftv t1 t2
+ ftv (TApp t1 t2) = on union ftv t1 t2
+ ftv _ = []
+
+instance Substitutable Scheme where
+ apply s (Forall as t) = Forall as $ apply (foldr del s as) t
+ ftv (Forall as t) = difference (ftv t) (removeDup as)
+
+instance Substitutable TypeEnv where
+ apply s env = apply s <$> env
+ ftv env = ftv (elems env)
+
+instance Substitutable [a] | Substitutable a where
+ apply s l = apply s <$> l
+ ftv t = foldr (union o ftv) [] t
+
+occursCheck :: [Char] -> (a -> Bool) | Substitutable a
+occursCheck a = isMember a o ftv
+
+err :: [String] -> Infer a
+err e = liftT (liftT (Left e))
+
+unify :: Type Type -> Infer Subst
+unify (l --> r) (l` --> r`)
+ = unify l l`
+ >>= \s1->on unify (apply s1) r r`
+ >>= \s2->pure (s1 oo s2)
+unify (TVar a) (TVar t)
+ | a == t = pure newMap
+unify (TVar a) t
+ | occursCheck a t = err ["Infinite type: ", toString a, " to ", toString t]
+ = pure (singleton a t)
+unify t (TVar a) = unify (TVar a) t
+unify TInt TInt = pure newMap
+unify TBool TBool = pure newMap
+unify (TApp l r) (TApp l` r`)
+ = unify l l`
+ >>= \s1->on unify (apply s1) r r`
+ >>= \s2->pure (s1 oo s2)
+unify t1 t2 = err ["Cannot unify: ", toString t1, " with ", toString t2]
+
+unifyl :: [Type] -> Infer Subst
+unifyl [t1,t2:ts] = unify t1 t2 >>= \s->unifyl (map (apply s) [t2:ts])
+unifyl _ = pure newMap
+
+instantiate :: Scheme -> Infer Type
+instantiate (Forall as t)
+ = sequence [fresh\\_<-as]
+ >>= \as`->pure (apply (fromList $ zip2 as as`) t)
generalize :: TypeEnv Type -> Scheme
-generalize env t = Scheme (difference (ftv t) (ftv env)) t
-
-:: TI a :== RWST TIEnv () TIState (Either [String]) a
-:: TIState = {tiSupply :: Int, tiSubst :: Subst}
-:: TIEnv :== [Int]
-
-mgu :: Type Type -> TI Subst
-mgu (TFun l r) (TFun l` r`) = composeSubst <$> mgu l l` <*> mgu r r`
-mgu (TVar u) t = varBind u t
-mgu t (TVar u) = varBind u t
-mgu TInt TInt = pure 'DM'.newMap
-mgu TBool TBool = pure 'DM'.newMap
-mgu TChar TChar = pure 'DM'.newMap
-mgu t1 t2 = liftT (Left ["cannot unify: " +++ toString t1 +++ " with " +++ toString t2])
-
-varBind :: [Char] Type -> TI Subst
-varBind u t
- | t == TVar u = pure 'DM'.newMap
- | isMember u (ftv t) = liftT (Left ["occur check fails: " +++ toString u +++ " vs. " +++ toString t])
- = pure ('DM'.singleton u t)
-
-newTyVar :: [Char] -> TI Type
-newTyVar prefix
- = get
- >>= \t->put {t & tiSupply=t.tiSupply+1}
- >>| pure (TVar (prefix ++ fromString (toString t.tiSupply)))
-
-instantiate :: Scheme -> TI Type
-instantiate (Scheme vars t)
- = mapM (\_->newTyVar ['a']) vars
- >>= \nvars->pure (apply ('DM'.fromList (zip2 vars nvars)) t)
-
-class infer a :: TypeEnv a -> TI (Subst, Type)
-instance infer Value where
- infer _ (Int _) = pure ('DM'.newMap, TInt)
- infer _ (Bool _) = pure ('DM'.newMap, TBool)
- infer _ (Char _) = pure ('DM'.newMap, TChar)
-instance infer Expression where
- infer e (Lit a) = infer e a
- infer (TypeEnv env) (Var v) = case 'DM'.get v env of
- Nothing = liftT (Left ["unbound variable: " +++ toString v])
- Just s = instantiate s >>= \t->pure ('DM'.newMap, t)
- infer env (App e1 e2)
- = newTyVar ['a']
- >>= \tv ->infer env e1
- >>= \(s1, t1)->infer (apply s1 env) e2
- >>= \(s2, t2)->mgu (apply s2 t1) (TFun t2 tv)
- >>= \s3->pure (composeSubst s3 (composeSubst s2 s1), apply s3 tv)
- //infer env (Lambda s e)
- // = newTyVar ['l']
- // >>= \tv->pure undef//inEnv (s, Forall [] tv) (infer e)
- // >>= \t-> pure (TFun tv t)
+generalize env t = Forall (difference (ftv t) (ftv env)) t
+
+infer :: TypeEnv Expression -> Infer (Subst, Type)
+infer env (Lit (Int _)) = pure (newMap, TInt)
+infer env (Lit (Bool _)) = pure (newMap, TBool)
+infer env (Var x) = maybe (err ["Unbound variable: ", toString x])
+ (\s->tuple newMap <$> instantiate s) $ get x env
+infer env (App e1 e2)
+ = fresh
+ >>= \tv-> infer env e1
+ >>= \(s1, t1)->infer (apply s1 env) e2
+ >>= \(s2, t2)->unify (apply s2 t1) (t2 --> tv)
+ >>= \s3-> pure (s3 oo s2 oo s1, apply s3 tv)
+infer env (Lambda x b)
+ = fresh
+ >>= \tv-> infer ('Data.Map'.put x (Forall [] tv) env) b
+ >>= \(s1, t1)->pure (s1, apply s1 tv --> t1)
+//Non recursion
+//infer env (Let [(x, e1)] e2)
+// = infer env e1
+// >>= \(s1, t1)->infer ('Data.Map'.put x (generalize (apply s1 env) t1) env) e2
+// >>= \(s2, t2)->liftT (tell [(x, Forall [] t1)])
+// >>| pure (s1 oo s2, t2)
+//Single recursion
+//infer env (Let [(x, e1)] e2)
+// = fresh
+// >>= \tv-> let env` = 'Data.Map'.put x (Forall [] tv) env
+// in infer env` e1
+// >>= \(s1,t1)-> infer ('Data.Map'.put x (generalize (apply s1 env`) t1) env`) e2
+// >>= \(s2, t2)->pure (s1 oo s2, t2)
+//Multiple recursion
+infer env (Let xs e2)
+ # (ns, bs) = unzip xs
+ = sequence [fresh\\_<-ns]
+ >>= \tvs-> let env` = foldr (\(k, v)->'Data.Map'.put k (Forall [] v)) env (zip2 ns tvs)
+ in unzip <$> sequence (map (infer env`) bs)
+ >>= \(ss,ts)-> unifyl ts
+ >>= \s-> liftT (tell [(n, generalize (apply s env`) t)\\t<-ts & n<-ns])
+ >>| let env`` = foldr (\(n, s, t) m->'Data.Map'.put n (generalize (apply s env`) t) m) env` (zip3 ns ss ts)
+ in infer env`` e2
+ >>= \(s2, t2)->pure (s oo s2, t2)
repositories / minfp.git / blobdiff