import Data.Either
import Data.List
+import Data.Functor
+import Data.Func
+import Data.Maybe
+import Data.Tuple
import Control.Monad
+import Control.Monad.Trans
+import Control.Monad.State
+
+import qualified Data.Map
+from Data.Map import instance Functor (Map k)
import ast
+import StdDebug
check :: [Function] -> Either [String] Expression
check fs
# dups = filter (\x->length x > 1) (groupBy (\(Function i _ _) (Function j _ _)->i == j) fs)
| length dups > 0 = Left ["Duplicate functions: ":[toString n\\[(Function n _ _):_]<-dups]]
= case partition (\a->a=:(Function ['start'] _ _)) fs of
([], _) = Left ["No start function defined"]
- ([Function _ [] e], fs) = Right (foldr (\(Function i a e)->Let i a e) e fs)
+ ([Function _ [] e], fs)
+ # e = foldr (\(Function i a e)->Let i a e) e fs
+ = case runInfer (infer 'Data.Map'.newMap e) of
+ Left e = Left e
+ Right s
+ = Left [printToString s]
([Function _ _ _], _) = Left ["Start cannot have arguments"]
-//import qualified Data.Map as DM
-//from Data.Map import instance Functor (Map k)
-//import qualified Data.Set as DS
-//import Data.Functor
-//import Data.Func
-//import Data.Either
-//import Data.List
-//import Data.Maybe
-//import Control.Applicative
-//import Control.Monad
-//import Control.Monad.Trans
-//import qualified Control.Monad.State as MS
-//import Control.Monad.State => qualified gets, put, modify
-//import Control.Monad.RWST => qualified put
-//
-//import ast
-//
-//check :: AST -> Either [String] (AST, [([Char], Scheme)])
-//check (AST fs) = pure (AST fs, [])/*case inferAST preamble fs of
-// Left e = Left e
-// Right s = Right (AST fs, 'DM'.toList s)
-//where
-// preamble = 'DM'.fromList
-// [(['if'], Forall [['a']] $ TFun TBool $ TFun (TVar ['a']) $ TFun (TVar ['a']) $ TVar ['a'])
-// ,(['eq'], Forall [] $ TFun TInt $ TFun TInt TBool)
-// ,(['mul'], Forall [] $ TFun TInt $ TFun TInt TInt)
-// ,(['div'], Forall [] $ TFun TInt $ TFun TInt TInt)
-// ,(['add'], Forall [] $ TFun TInt $ TFun TInt TInt)
-// ,(['sub'], Forall [] $ TFun TInt $ TFun TInt TInt)
-// ]
-//*/
-//
-//:: TypeEnv :== 'DM'.Map [Char] Scheme
-//:: Constraint :== (Type, Type)
-//:: Subst :== 'DM'.Map [Char] Type
-//:: Unifier :== (Subst, [Constraint])
-//:: Infer a :== RWST TypeEnv [Constraint] InferState (Either [String]) a
-//:: InferState = { count :: Int }
-//:: Scheme = Forall [[Char]] Type
-//:: Solve a :== StateT Unifier (Either [String]) a
-//
-//nullSubst :: Subst
-//nullSubst = 'DM'.newMap
-//
-//uni :: Type Type -> Infer ()
-//uni t1 t2 = tell [(t1, t2)]
-//
-//inEnv :: ([Char], Scheme) (Infer a) -> Infer a
-//inEnv (x, sc) m = local (\e->'DM'.put x sc $ 'DM'.del x e) m
-//
-//letters :: [[Char]]
-//letters = [1..] >>= flip replicateM ['a'..'z']
-//
-//fresh :: Infer Type
-//fresh = get >>= \s=:{count}->'Control.Monad.RWST'.put {s & count=count + 1} >>| pure (TVar $ letters !! count)
-//
-//class Substitutable a
-//where
-// apply :: Subst a -> a
-// ftv :: a -> [[Char]]
-//
-//instance Substitutable Type
-//where
-// apply s t=:(TVar a) = maybe t id $ 'DM'.get a s
-// apply s (TFun t1 t2) = TFun (apply s t1) (apply s t2)
-// apply _ t = t
-//
-// ftv (TVar a) = [a]
-// ftv (TFun t1 t2) = union (ftv t1) (ftv t2)
-// ftv t = []
-//
-//instance Substitutable Scheme
-//where
-// apply s (Forall as t) = Forall as $ apply (foldr 'DM'.del s as) t
-// ftv (Forall as t) = difference (ftv t) as
-//
-//instance Substitutable [a] | Substitutable a
-//where
-// apply s ls = map (apply s) ls
-// ftv t = foldr (union o ftv) [] t
-//
-//instance Substitutable TypeEnv where
-// apply s env = fmap (apply s) env
-// ftv env = ftv $ 'DM'.elems env
-//
-//instance Substitutable Constraint where
-// apply s (t1, t2) = (apply s t1, apply s t2)
-// ftv (t1, t2) = union (ftv t1) (ftv t2)
-//
-//instantiate :: Scheme -> Infer Type
-//instantiate (Forall as t) = mapM (const fresh) as
-// >>= \as`->let s = 'DM'.fromList $ zip2 as as` in pure $ apply s t
-//
-//generalize :: TypeEnv Type -> Scheme
-//generalize env t = Forall (difference (ftv t) (ftv env)) t
-//
-////:: Expression
-//// = Lit Value
-//// | Var [Char]
-//// | App Expression Expression
-//// | Lambda [Char] Expression
-//// | Builtin [Char] [Expression]
-//inferExpr :: TypeEnv Expression -> Either [String] Scheme
-//inferExpr env ex = case runRWST (infer ex) env {count=0} of
-// Left e = Left e
-// Right (ty, st, cs) = case runStateT solver ('DM'.newMap, cs) of
-// Left e = Left e
-// Right (s, _) = Right (closeOver (apply s ty))
-//
-//closeOver :: Type -> Scheme
-//closeOver t = normalize (generalize 'DM'.newMap t)
-//
-//normalize :: Scheme -> Scheme
-//normalize t = t
-//
-//inferAST :: TypeEnv [Function] -> Either [String] TypeEnv
-//inferAST env [] = Right env
-//inferAST env [Function name args body:rest] = case inferExpr env (foldr Lambda body args) of
-// Left e = Left e
-// Right ty = inferAST ('DM'.put name ty env) rest
-//
-//inferFunc :: [Function] -> Infer ()
-//inferFunc [] = pure ()
-//inferFunc [Function name args body:rest]
-// = ask
-// >>= \en->infer (foldr Lambda body args)
-// >>= \t1->inEnv (name, generalize en t1) (inferFunc rest)
-// >>= \_->pure ()
-//
-//infer :: Expression -> Infer Type
-//infer (Lit v) = case v of
-// Int _ = pure TInt
-// Bool _ = pure TBool
-//infer (Var s) = asks ('DM'.get s)
-// >>= maybe (liftT $ Left ["Unbound variable " +++ toString s]) instantiate
-//infer (App e1 e2)
-// = infer e1
-// >>= \t1->infer e2
-// >>= \t2->fresh
-// >>= \tv->uni t1 (TFun t2 tv)
-// >>| pure tv
-//infer (Lambda s e)
-// = fresh
-// >>= \tv->inEnv (s, Forall [] tv) (infer e)
-// >>= \t-> pure (TFun tv t)
-////infer (Let x e1 e2)
-//// = ask
-//// >>= \en->infer e1
-//// >>= \t1->inEnv (x, generalize en t1) (infer e2)
-//
-//unifies :: Type Type -> Solve Unifier
-//unifies TInt TInt = pure ('DM'.newMap, [])
-//unifies TBool TBool = pure ('DM'.newMap, [])
-//unifies (TVar a) (TVar b)
-// | a == b = pure ('DM'.newMap, [])
-//unifies (TVar v) t = tbind v t
-//unifies t (TVar v) = tbind v t
-//unifies (TFun t1 t2) (TFun t3 t4) = unifyMany [t1, t2] [t3, t4]
-//unifies t1 t2 = liftT $ Left ["Cannot unify " +++ toString t1 +++ " with " +++ toString t2]
-//
-//unifyMany :: [Type] [Type] -> Solve Unifier
-//unifyMany [] [] = pure ('DM'.newMap, [])
-//unifyMany [t1:ts1] [t2:ts2] = unifies t1 t2
-// >>= \(su1, cs1)->unifyMany (apply su1 ts1) (apply su1 ts2)
-// >>= \(su2, cs2)->pure (su2 `compose` su1, cs1 ++ cs2)
-//unifyMany t1 t2 = liftT $ Left ["Length difference in unifyMany"]
-//
-//(`compose`) infix 1 :: Subst Subst -> Subst
-//(`compose`) s1 s2 = 'DM'.union (apply s1 <$> s2) s1
-//
-//tbind :: [Char] Type -> Solve Unifier
-//tbind a (TVar b)
-// | a == b = pure ('DM'.newMap, [])
-//tbind a t
-// | occursCheck a t = liftT $ Left ["Infinite type " +++ toString a +++ toString t]
-// = pure $ ('DM'.singleton a t, [])
-//
-//occursCheck :: [Char] a -> Bool | Substitutable a
-//occursCheck a t = isMember a $ ftv t
-//
-//solver :: Solve Subst
-//solver = getState >>= \(su, cs)->case cs of
-// [] = pure su
-// [(t1, t2):cs0] = unifies t1 t2
-// >>= \(su1, cs1)->'MS'.put (su1 `compose` su, cs1 ++ (apply su1 cs0))
-// >>| solver
+import Text.GenPrint
+derive gPrint Scheme, Type
+
+//Polytypes
+:: Scheme = Forall [[Char]] Type
+:: TypeEnv :== 'Data.Map'.Map [Char] Scheme
+:: Subst :== 'Data.Map'.Map [Char] Type
+nullSubst = 'Data.Map'.newMap
+
+:: Infer a :== StateT [Int] (Either [String]) a
+runInfer :: (Infer (Subst, Type)) -> Either [String] Scheme
+runInfer i = uncurry closeOver <$> evalStateT i [0..]
+where
+ closeOver :: Subst Type -> Scheme
+ closeOver sub ty = normalize (generalize 'Data.Map'.newMap (apply sub ty))
+
+ normalize :: Scheme -> Scheme
+ normalize i = i
+// normalize (Forall ts body) = Forall (snd <$> ord) (normtype body)
+// where
+// ord = zip2 (removeDup $ fv body) (fmap letters)
+//
+// fv (TVar a) = [a]
+// fv (TFun a b) = fv a ++ fv b
+// fv _ = []
+//
+// normtype (TFun a b) = TFun (normtype a) (normtype b)
+// normtype (TCon a) = TCon a
+// normtype (TVar a) =
+// case lookup a ord of
+// Just x = TVar x
+// Nothing = Left ["type variable not in signature"]
+
+fresh :: Infer Type
+fresh = getState >>= \[s:ss]->put ss >>| pure (TVar (['v':[c\\c<-:toString s]]))
+
+compose :: Subst Subst -> Subst
+compose s1 s2 = 'Data.Map'.union (apply s1 <$> s2) s1
+
+class Substitutable a where
+ apply :: Subst a -> a
+ ftv :: a -> [[Char]]
+
+instance Substitutable Type where
+ apply s t=:(TVar v) = 'Data.Map'.findWithDefault t v s
+ apply s (TFun t1 t2) = on TFun (apply s) t1 t2
+ apply _ x = x
+
+ ftv (TVar v) = [v]
+ ftv (TFun t1 t2) = on union ftv t1 t2
+ ftv _ = []
+
+instance Substitutable Scheme where
+ apply s (Forall as t) = Forall as $ apply (foldr 'Data.Map'.del s as) t
+ ftv (Forall as t) = difference (ftv t) (removeDup as)
+
+instance Substitutable TypeEnv where
+ apply s env = apply s <$> env
+ ftv env = ftv ('Data.Map'.elems env)
+
+instance Substitutable [a] | Substitutable a where
+ apply s l = apply s <$> l
+ ftv t = foldr (union o ftv) [] t
+
+occursCheck :: [Char] -> (a -> Bool) | Substitutable a
+occursCheck a = isMember a o ftv
+
+unify :: Type Type -> Infer Subst
+unify (TFun l r) (TFun l` r`)
+ = unify l l`
+ >>= \s1->on unify (apply s1) r r`
+ >>= \s2->pure (compose s1 s2)
+unify (TVar a) t = bind a t
+unify t (TVar a) = bind a t
+unify TInt TInt = pure nullSubst
+unify TBool TBool = pure nullSubst
+unify t1 t2 = liftT (Left ["Cannot unify: ", toString t1, " with ", toString t2])
+
+bind :: [Char] Type -> Infer Subst
+bind a (TVar t) | a == t = pure nullSubst
+bind a t
+ | occursCheck a t = liftT (Left ["Infinite type: ", toString a, " and ", toString t])
+ = pure ('Data.Map'.singleton a t)
+
+instantiate :: Scheme -> Infer Type
+instantiate (Forall as t)
+ = sequence [fresh\\_<-as]
+ >>= \as`->pure (apply ('Data.Map'.fromList $ zip2 as as`) t)
+
+generalize :: TypeEnv Type -> Scheme
+generalize env t = Forall (difference (ftv t) (ftv env)) t
+
+infer :: TypeEnv Expression -> Infer (Subst, Type)
+infer env (Lit (Int _)) = pure (nullSubst, TInt)
+infer env (Lit (Bool _)) = pure (nullSubst, TBool)
+infer env (Var x) = case 'Data.Map'.get x env of
+ Nothing = liftT (Left ["Unbound variable: ", toString x])
+ Just s = tuple nullSubst <$> instantiate s
+infer env (App e1 e2)
+ = fresh
+ >>= \tv-> infer env e1
+ >>= \(s1, t1)->infer (apply s1 env) e2
+ >>= \(s2, t2)->unify (apply s2 t1) (TFun t2 tv)
+ >>= \s3-> pure (compose (compose s3 s2) s1, apply s3 tv)
+infer env (Lambda x b)
+ = fresh
+ >>= \tv-> infer ('Data.Map'.put x (Forall [] tv) env) b
+ >>= \(s1, t1)->pure (s1, TFun (apply s1 tv) t1)
+infer env (Builtin c a) = undef
+infer env (Let i args e b) = undef
repositories / minfp.git / commitdiff