- toString (ParseError p e) = concat [
- toString p,"SemError: ParseError: ", e]
- toString (Error e) = "SemError: " +++ e
- toString (UnifyError p t1 t2) = concat [
- toString p,
- "SemError: Cannot unify types. Expected: ",
- toString t1, ". Given: ", toString t2]
-
-sem :: AST -> SemOutput
-sem (AST vd fd)
-# (eithervds, gamma) = runState (mapM semVarDecl vd) 'Map'.newMap
-# (eitherfds, gamma) = runState (mapM semFunDecl fd) gamma
-= case splitEithers eithervds of
- (Left errs) = Left $ errs ++ [x\\(Left x)<-eitherfds]
- (Right vds) = case splitEithers eitherfds of
- (Left errs) = Left errs
- (Right fds) = Right $ AST vds fds
-
-splitEithers :: [Either a b] -> Either [a] [b]
-splitEithers [] = Right []
-splitEithers [Right x:xs] = splitEithers xs >>= \rest->Right [x:rest]
-splitEithers xs = Left $ [x\\(Left x)<-xs]
-
-semFunDecl :: FunDecl -> Env FunDecl
-semFunDecl f = pure $ Right f
-
-semVarDecl :: VarDecl -> Env VarDecl
-semVarDecl v = pure $ Right v
-//Right v
-//semVarDecl vd=:(VarDecl pos type ident expr) = case unify type expr of // Left e = Left e
-// //TODO ident in de environment
-// Right e = Right $ pure vd
-
-typeOp1 :: Pos Expr Type -> Env Type
-typeOp1 p expr rtype = typeExpr expr >>= \exprtype->case exprtype of
- Left e = pure $ Left e
- Right rtype = pure $ Right rtype
- Right (IdType ident) = putIdent ident rtype >>| pure (Right rtype)
- Right t = pure $ Left $ UnifyError p rtype t
-
-typeExpr :: Expr -> Env Type
-typeExpr (IntExpr _ _) = pure $ Right IntType
-typeExpr (CharExpr _ _) = pure $ Right CharType
-typeExpr (BoolExpr _ _) = pure $ Right BoolType
-typeExpr (Op1Expr p UnNegation expr) = typeOp1 p expr BoolType
-typeExpr (Op1Expr p UnMinus expr) = typeOp1 p expr IntType
-typeExpr (TupleExpr p (e1, e2)) = typeExpr e1
- >>= \ete1->typeExpr e2 >>= \ete2->pure (
- ete1 >>= \te1->ete2 >>= \te2->Right $ TupleType (te1, te2))
-//typeExpr (Op1Expr p UnMinus expr) = typeExpr expr
-// >>= \exprtype->case exprtype of
-// IntType = pure $ Right IntType
-// t = Left $ UnifyError p IntType exprtype
-//typeExpr (Op2Expr Pos Expr Op2 Expr) = undef
-//typeExpr (FunExpr Pos FunCall) = undef
-//typeExpr (EmptyListExpr Pos) = undef
-//typeExpr (VarExpr Pos VarDef) = undef
-
-class unify a :: Type a -> Env Type
-
-instance unify Type where
- unify IntType IntType = pure $ Right IntType
- unify BoolType BoolType = pure $ Right BoolType
- unify CharType CharType = pure $ Right CharType
- unify _ _ = undef
-//
-//instance unify Expr where
-// unify type expr = case type of
-// _ ->> _ = Left $ ParseError (extrPos expr)
-// "Expression cannot be a higher order function. Yet..."
-// VoidType = Left $ ParseError (extrPos expr)
-// "Expression cannot be a Void type."
-// IdType _ = Left $ ParseError (extrPos expr)
-// "Expression cannot be an polymorf type."
-// TupleType (_, _) = undef
-// ListType _ = undef
-// IntType = undef
-// BoolType = undef
-// CharType = undef
-// VarType = undef
+ toString (SanityError p e) = concat [toString p,
+ "SemError: SanityError: ", e]
+ toString se = "SemError: "
+
+inEnv :: (String, Scheme) (Infer a) -> Infer a
+inEnv (x, sc) m = local ('Map'.put x sc) m
+
+class Typeable a where
+ ftv :: a -> [TVar]
+ subst :: Substitution a -> a
+
+instance Typeable Scheme where
+ ftv (Forall bound t) = difference (ftv t) bound
+ subst s (Forall bound t) = Forall bound $ subst s_ t
+ where s_ = 'Map'.filterWithKey (\k _ -> not (elem k bound)) s
+
+instance Typeable [a] | Typeable a where
+ ftv types = foldr (\t ts-> ftv t ++ ts) [] types
+ subst s ts = map (\t->subst s t) ts
+
+instance Typeable Type where
+ ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2
+ ftv (ListType t) = ftv t
+ ftv (IdType tvar) = [tvar]
+ ftv (t1 ->> t2) = ftv t1 ++ ftv t2
+ ftv _ = []
+ subst s (TupleType (t1, t2))= TupleType (subst s t1, subst s t2)
+ subst s (ListType t1) = ListType (subst s t1)
+ subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2)
+ subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s
+ subst s t = t
+
+instance Typeable Gamma where
+ ftv gamma = concatMap id $ map ftv ('Map'.elems gamma)
+ subst s gamma = Mapmap (subst s) gamma
+
+//// ------------------------
+//// algorithm U, Unification
+//// ------------------------
+instance zero Substitution where zero = 'Map'.newMap
+
+compose :: Substitution Substitution -> Substitution
+compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
+//Note: unlike function composition, compose prefers left!
+
+occurs :: TVar a -> Bool | Typeable a
+occurs tvar a = elem tvar (ftv a)
+
+unify :: Type Type -> Either SemError Substitution
+unify t1=:(IdType tv) t2 = unify t2 t1
+unify t1 t2=:(IdType tv) | t1 == (IdType tv) = Right zero
+ | occurs tv t1 = Left $ InfiniteTypeError zero t1
+ | otherwise = Right $ 'Map'.singleton tv t1
+unify (ta1->>ta2) (tb1->>tb2) = unify ta1 tb1 >>= \s1->
+ unify tb1 tb2 >>= \s2->
+ Right $ compose s1 s2
+unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
+ unify ta2 tb2 >>= \s2->
+ Right $ compose s1 s2
+unify (ListType t1) (ListType t2) = unify t1 t2
+unify t1 t2 | t1 == t2 = Right zero
+ | otherwise = Left $ UnifyError zero t1 t2
+
+//// ------------------------
+//// Algorithm M, Inference and Solving
+//// ------------------------
+//:: Typing a :== StateT (Gamma, [TVar]) Either a
+
+//map a schemes type variables to variables with fresh names
+//i.e. a->[b] becomes c->[d]
+
+
+
+
+
+Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
+Mapmap _ 'Map'.Tip = 'Map'.Tip
+Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)
+ (Mapmap f ml)
+ (Mapmap f mr)
+
+//// ------------------------
+//// First step: Inference
+//// ------------------------//
+
+//unify :: Type Type -> Infer ()
+//unify t1 t2 = tell [(t1, t2)]//
+
+//fresh :: Infer Type
+//fresh = (gets id) >>= \vars-> (put $ tail vars) >>| (pure $ IdType $ head vars)//
+
+//op2Type :: Op2 -> Infer Type
+//op2Type op
+//| elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
+// = pure (IntType ->> IntType ->> IntType)
+//| elem op [BiEquals, BiUnEqual]
+// = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
+//| elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
+// = pure (IntType ->> IntType ->> BoolType)
+//| elem op [BiAnd, BiOr]
+// = pure (BoolType ->> BoolType ->> BoolType)
+//| op == BiCons
+// = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)//
+
+//op1Type :: Op1 -> Infer Type
+//op1Type UnNegation = pure $ (BoolType ->> BoolType)
+//op1Type UnMinus = pure $ (IntType ->> IntType)//
+
+////instantiate :: Scheme -> Infer Type
+////instantiate (Forall as t) = mapM (const fresh) as//
+
+//lookupEnv :: String -> Infer Type
+//lookupEnv ident = asks ('Map'.get ident)
+// >>= \m->case m of
+// Nothing = liftT $ Left $ UndeclaredVariableError zero ident
+// Just (Forall as t) = pure t //instantiate ???//
+
+//class infer a :: a -> Infer Type
+//instance infer Expr where
+// infer (VarExpr _ (VarDef ident fs)) = lookupEnv ident
+// infer (Op2Expr _ e1 op e2) =
+// infer e1 >>= \t1 ->
+// infer e2 >>= \t2 ->
+// fresh >>= \frsh ->
+// let given = t1 ->> (t2 ->> frsh) in
+// op2Type op >>= \expected ->
+// unify expected given >>|
+// return frsh
+// infer (Op1Expr _ op e) =
+// infer e >>= \t1 ->
+// fresh >>= \frsh ->
+// let given = t1 ->> frsh in
+// op1Type op >>= \expected ->
+// unify expected given >>|
+// pure frsh
+// infer (IntExpr _ _) = pure IntType
+// infer (CharExpr _ _) = pure CharType
+// infer (BoolExpr _ _) = pure BoolType
+// infer (FunExpr _ f args sels) = //todo, iets met field selectors
+// lookupEnv f >>= \expected ->
+// fresh >>= \frsh ->
+// mapM infer args >>= \argTypes ->
+// let given = foldr (->>) frsh argTypes in
+// unify expected given >>|
+// pure frsh
+// infer (EmptyListExpr _) = ListType <$> fresh
+// infer (TupleExpr _ (e1, e2)) =
+// infer e1 >>= \et1->infer e2 >>= \et2->pure $ TupleType (et1, et2)//
+
+////:: VarDef = VarDef String [FieldSelector]
+////:: FieldSelector = FieldHd | FieldTl | FieldFst | FieldSnd
+////:: Op1 = UnNegation | UnMinus
+////:: Op2 = BiPlus | BiMinus | BiTimes | BiDivide | BiMod | BiEquals | BiLesser |
+//// BiGreater | BiLesserEq | BiGreaterEq | BiUnEqual | BiAnd | BiOr | BiCons
+////:: FunDecl = FunDecl Pos String [String] (Maybe Type) [VarDecl] [Stmt]
+////:: FunCall = FunCall String [Expr]
+////:: Stmt
+//// = IfStmt Expr [Stmt] [Stmt]
+//// | WhileStmt Expr [Stmt]
+//// | AssStmt VarDef Expr
+//// | FunStmt FunCall
+//// | ReturnStmt (Maybe Expr)
+////:: Pos = {line :: Int, col :: Int}
+////:: AST = AST [VarDecl] [FunDecl]
+////:: VarDecl = VarDecl Pos Type String Expr
+////:: Type
+//// = TupleType (Type, Type)
+//// | ListType Type
+//// | IdType String
+//// | IntType
+//// | BoolType
+//// | CharType
+//// | VarType
+//// | VoidType
+//// | (->>) infixl 7 Type Type