import Control.Monad
import Control.Monad.Trans
+import Control.Monad.State
import Data.Either
import Data.Maybe
import Data.Monoid
-import Data.List
+import Data.List
+import Data.Functor
+import Data.Tuple
import StdString
+import StdTuple
import StdList
import StdMisc
import StdEnum
-import RWST
import GenEq
from Text import class Text(concat), instance Text String
import AST
-:: Scheme = Forall [String] Type
-:: Gamma :== 'Map'.Map String Scheme
+
+:: Scheme = Forall [TVar] Type
+:: Gamma :== 'Map'.Map String Scheme //map from Variables! to types
+:: Substitution :== 'Map'.Map TVar Type
:: Constraints :== [(Type, Type)]
-:: Infer a :== RWST Gamma Constraints [String] (Either SemError) a
:: SemError
= ParseError Pos String
| UnifyError Pos Type Type
+ | InfiniteTypeError Pos Type
| FieldSelectorError Pos Type FieldSelector
| OperatorError Pos Op2 Type
| UndeclaredVariableError Pos String
instance zero Gamma where
zero = 'Map'.newMap
-variableStream :: [String]
+variableStream :: [TVar]
variableStream = map toString [1..]
sem :: AST -> Either [SemError] Constraints
>>| foldM (const isNiceMain) () fd
>>| hasMain fd of
Left e = Left [e]
- _ = case execRWST (constraints fd) zero variableStream of
- Left e = Left [e]
- Right (a, b) = Right b
+ _ = Right []
+ //_ = case execRWST (constraints fd) zero variableStream of
+ // Left e = Left [e]
+ // Right (a, b) = Right b
where
- constraints :: [FunDecl] -> Infer ()
- constraints fds = mapM_ funconstraint fds >>| pure ()
+ constraints :: [FunDecl] -> Typing ()
+ constraints _ = pure ()
+ //TODO: fix
+ //constraints fds = mapM_ funconstraint fds >>| pure ()
- funconstraint :: FunDecl -> Infer ()
+ funconstraint :: FunDecl -> Typing ()
funconstraint fd=:(FunDecl _ ident args mt vardecls stmts) = case mt of
Nothing = abort "Cannot infer functions yet"
- Just t = inEnv (ident, (Forall [] t)) (
- mapM_ vardeclconstraint vardecls >>| pure ())
+ _ = pure ()
+ //Just t = inEnv (ident, (Forall [] t)) (
+ // mapM_ vardeclconstraint vardecls >>| pure ())
- vardeclconstraint :: VarDecl -> Infer ()
- vardeclconstraint (VarDecl p mt ident expr) = infer expr
- >>= \it->inEnv (ident, (Forall [] it)) (pure ())
+ vardeclconstraint :: VarDecl -> Typing ()
+ vardeclconstraint _ = pure ()
+ //TODO: fix!
+ //vardeclconstraint (VarDecl p mt ident expr) = infer expr
+ //>>= \it->inEnv (ident, (Forall [] it)) (pure ())
hasNoDups :: [FunDecl] FunDecl -> Either SemError ()
hasNoDups fds (FunDecl p n _ _ _ _)
_ = Left $ SanityError p "main has to return Void")
isNiceMain _ = pure ()
-instance toString Scheme where
- toString (Forall x t) =
- concat ["Forall ": map ((+++) "\n") x] +++ toString t
+class Typeable a where
+ ftv :: a -> [TVar]
+ subst :: Substitution a -> a
-instance toString Gamma where
- toString mp =
- concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
+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 toString SemError where
- toString (SanityError p e) = concat [toString p,
- "SemError: SanityError: ", e]
- toString se = "SemError: "
+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
+
+extend :: String Scheme Gamma -> Gamma
+extend k t g = 'Map'.put k t g
+
+//// ------------------------
+//// 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: just like function compositon compose does snd first
+
+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
+//// ------------------------
+//The typing monad
+:: Typing a :== StateT (Gamma, [TVar]) (Either SemError) a
+gamma :: Typing Gamma
+gamma = gets fst
+putGamma :: Gamma -> Typing ()
+putGamma g = modify (appFst $ const g) >>| pure ()
+changeGamma :: (Gamma -> Gamma) -> Typing Gamma
+changeGamma f = modify (appFst f) >>| gamma
+withGamma :: (Gamma -> a) -> Typing a
+withGamma f = f <$> gamma
+fresh :: Typing Type
+fresh = gets snd >>= \vars->
+ modify (appSnd $ const $ tail vars) >>|
+ pure (IdType (head vars))
-uni :: Type Type -> Infer ()
-uni t1 t2 = tell [(t1, t2)]
+lift :: (Either SemError a) -> Typing a
+lift (Left e) = liftT $ Left e
+lift (Right v) = pure v
-inEnv :: (String, Scheme) (Infer a) -> Infer a
-inEnv (x, sc) m = local ('Map'.put x sc) m
+//instantiate maps a schemes type variables to variables with fresh names
+//and drops the quantification: i.e. forall a,b.a->[b] becomes c->[d]
+instantiate :: Scheme -> Typing Type
+instantiate (Forall bound t) =
+ mapM (const fresh) bound >>= \newVars->
+ let s = 'Map'.fromList (zip (bound,newVars)) in
+ pure (subst s t)
-fresh :: Infer Type
-fresh = (gets id) >>= \vars-> (put $ tail vars) >>| (pure $ IdType $ head vars)
+//generalize quentifies all free type variables in a type which are not
+//in the gamma
+generalize :: Type -> Typing Scheme
+generalize t = gamma >>= \g-> pure $ Forall (difference (ftv t) (ftv g)) t
-op2Type :: Op2 -> Infer Type
+lookup :: String -> Typing Type
+lookup k = gamma >>= \g-> case 'Map'.member k g of
+ False = liftT (Left $ UndeclaredVariableError zero k)
+ True = instantiate $ 'Map'.find k g
+
+//The inference class
+//When tying it all together we will treat the program is a big
+//let x=e1 in let y=e2 in ....
+class infer a :: a -> Typing (Substitution, Type)
+
+////---- Inference for Expressions ----
+
+instance infer Expr where
+ infer e = case e of
+ VarExpr _ (VarDef k fs) = (\t->(zero,t)) <$> lookup k
+ //instantiate is key for the let polymorphism!
+ //TODO: field selectors
+
+ Op2Expr _ e1 op e2 =
+ infer e1 >>= \(s1, t1) ->
+ infer e2 >>= \(s2, t2) ->
+ fresh >>= \tv ->
+ let given = t1 ->> t2 ->> tv in
+ op2Type op >>= \expected ->
+ lift (unify expected given) >>= \s3 ->
+ pure ((compose s3 $ compose s2 s1), subst s3 tv)
+
+ Op1Expr _ op e1 =
+ infer e1 >>= \(s1, t1) ->
+ fresh >>= \tv ->
+ let given = t1 ->> tv in
+ op1Type op >>= \expected ->
+ lift (unify expected given) >>= \s2 ->
+ pure (compose s2 s1, subst s2 tv)
+
+ EmptyListExpr _ = (\tv->(zero,tv)) <$> fresh
+
+ TupleExpr _ (e1, e2) =
+ infer e1 >>= \(s1, t1) ->
+ infer e2 >>= \(s2, t2) ->
+ pure (compose s2 s1, TupleType (t1,t2))
+
+ FunExpr _ f args fs = //todo: fieldselectors
+ lookup f >>= \expected ->
+ let accST = (\(s,ts) e->infer e >>= \(s_,et)->pure (compose s_ s,ts++[et])) in
+ foldM accST (zero,[]) args >>= \(s1, argTs)->
+ fresh >>= \tv->
+ let given = foldr (->>) tv argTs in
+ lift (unify expected given) >>= \s2->
+ pure (compose s2 s1, subst s2 tv)
+
+ IntExpr _ _ = pure $ (zero, IntType)
+ BoolExpr _ _ = pure $ (zero, BoolType)
+ CharExpr _ _ = pure $ (zero, CharType)
+
+
+op2Type :: Op2 -> Typing Type
op2Type op
| elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
- = pure (IntType ->> IntType ->> IntType)
+ = pure (IntType ->> IntType ->> IntType)
| elem op [BiEquals, BiUnEqual]
- = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
+ = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
| elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
- = pure (IntType ->> IntType ->> BoolType)
+ = pure (IntType ->> IntType ->> BoolType)
| elem op [BiAnd, BiOr]
- = pure (BoolType ->> BoolType ->> BoolType)
+ = pure (BoolType ->> BoolType ->> BoolType)
| op == BiCons
- = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)
+ = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)
-op1Type :: Op1 -> Infer Type
+op1Type :: Op1 -> Typing 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) = case op of
- BiPlus = pure IntType
- BiMinus = pure IntType
- BiTimes = pure IntType
- BiDivide = pure IntType
- BiMod = pure IntType
- BiLesser = pure IntType
- BiGreater = pure IntType
- BiLesserEq = pure IntType
- BiGreaterEq = pure IntType
- BiAnd = pure BoolType
- BiOr = pure BoolType
- BiEquals = infer e1
- BiUnEqual = infer e1 // maybe check e2?
- BiCons = infer e1 >>= \it1->pure $ ListType it1
- infer (Op1Expr _ op e) = case op of
- UnMinus = pure IntType
- UnNegation = pure BoolType
- infer (IntExpr _ _) = pure IntType
- infer (CharExpr _ _) = pure CharType
- infer (BoolExpr _ _) = pure BoolType
- infer (FunExpr _ _ _ _) = undef
- infer (EmptyListExpr _) = undef
- 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
+////----- Inference for Statements -----
+applySubst :: Substitution -> Typing Gamma
+applySubst s = changeGamma (subst s)
+
+instance infer Stmt where
+ infer s = case s of
+ IfStmt e th el =
+ infer e >>= \(s1, et)->
+ lift (unify et BoolType) >>= \s2 ->
+ applySubst (compose s2 s1) >>|
+ infer th >>= \(s3, tht)->
+ applySubst s3 >>|
+ infer el >>= \(s4, elt)->
+ applySubst s4 >>|
+ lift (unify tht elt) >>= \s5->
+ pure (compose s5 $ compose s4 $ compose s3 $ compose s1 s2, subst s5 tht)
+
+ WhileStmt e wh =
+ infer e >>= \(s1, et)->
+ lift (unify et BoolType) >>= \s2 ->
+ applySubst (compose s2 s1) >>|
+ infer wh >>= \(s3, wht)->
+ pure (compose s3 $ compose s1 s2, subst s3 wht)
+
+ AssStmt (VarDef k fs) e =
+ infer e >>= \(s1, et)->
+ applySubst s1 >>|
+ changeGamma (extend k (Forall [] et)) >>| //todo: fieldselectors
+ pure (s1, VoidType)
+
+ FunStmt f es = undef //what is this?
+
+ ReturnStmt Nothing = pure (zero, VoidType)
+ ReturnStmt (Just e) = infer e
+
+
+instance infer [a] | infer a where
+ infer _ = undef
+
+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)
+
+instance toString Scheme where
+ toString (Forall x t) =
+ concat ["Forall ": map ((+++) "\n") x] +++ toString t
+
+instance toString Gamma where
+ toString mp =
+ concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
+
+instance toString SemError where
+ toString (SanityError p e) = concat [toString p,
+ "SemError: SanityError: ", e]
+ toString se = "SemError: "
+
+instance MonadTrans (StateT (Gamma, [TVar])) where
+ liftT m = StateT \s-> m >>= \a-> return (a, s)
+
+//// ------------------------
+//// 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
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