implementation module sem
import qualified Data.Map as Map
+
from Data.Func import $
-import Data.Maybe
-import Data.Void
-import Data.Either
-import Data.Functor
-import Control.Applicative
+from StdFunc import o, flip, const, id
+
import Control.Monad
-import Control.Monad.State
-import Control.Monad.Identity
-import Math.Random
import Control.Monad.Trans
-import StdMisc
-from StdFunc import id, const, o
+import Control.Monad.State
+import Data.Either
+import Data.Maybe
+import Data.Monoid
+import Data.List
+import Data.Functor
+import Data.Tuple
+
import StdString
import StdTuple
import StdList
-import StdBool
+import StdMisc
+import StdEnum
+import GenEq
from Text import class Text(concat), instance Text String
import AST
-from parse import :: ParserOutput, :: Error
-:: Gamma :== ('Map'.Map String Type, [String])
-:: Env a :== StateT Gamma (Either SemError) a
-//StateT (Gamma -> Either SemError (a, Gamma))
-//we need to redefine this even though it is in Control.Monad.State
-instance MonadTrans (StateT Gamma) where
- liftT m = StateT \s-> m >>= \a-> return (a, s)
-
-get = gets id
-
-sem :: AST -> SemOutput
-sem (AST vd fd) = case runStateT m ('Map'.newMap, getRandomStream 1) of
- Left e = Left [e]
- Right ((vds, fds), gamma) = Right ((AST vds fds), gamma)
-where
- m :: Env ([VarDecl], [FunDecl])
- m = mapM semVarDecl vd >>= \vds ->
- mapM semFunDecl fd >>= \fds ->
- pure (vds, fds)
-
-semFunDecl :: FunDecl -> Env FunDecl
-semFunDecl fd=:(FunDecl p f args mt vds stmts) =
- saveGamma >>= \gamma ->
- (case mt of
- Nothing = let t = IdType f in putIdent f t >>| pure t
- Just t = putIdent f t >>| pure t) >>= \ft ->
- matchFunctions args ft >>|
- mapM semVarDecl vds >>= \newvds->
- mapM_ (checkStmt $ resultType ft) stmts >>|
- restoreGamma gamma >>|
- pure (FunDecl p f args mt newvds stmts)
-
-matchFunctions :: [String] Type -> Env Void
-matchFunctions [] (_ ->> _) = liftT $ Left $ Error "Niet genoeg argumentenerror"
-matchFunctions [] t = pure Void
-matchFunctions [x:xs] (t1 ->> t2) =
- modify (\(st, r)->('Map'.put x t1 st, r)) >>| matchFunctions xs t2
-
-semVarDecl :: VarDecl -> Env VarDecl
-semVarDecl (VarDecl pos type ident ex) = unify type ex
- >>= \t-> putIdent ident t >>| (pure $ VarDecl pos t ident ex)
-
-checkStmt ::Type Stmt -> Env Stmt
-checkStmt t (IfStmt c st se) = unify BoolType c >>| mapM (checkStmt t) st
- >>= \st1-> mapM (checkStmt t) se >>= \se1-> pure (IfStmt c st1 se1)
-checkStmt t w=:(WhileStmt c et) = unify BoolType c >>| mapM (checkStmt t) et
- >>= \et1-> pure w
-checkStmt t a=:(AssStmt (VarDef ident fs) e) = gets (\(st, r)->'Map'.get ident st)
- >>= \mt->case mt of
- Nothing = liftT $ Left $ UndeclaredVariableError zero ident
- Just t = unify t fs >>= \t1 -> unify t1 e >>| pure a
-checkStmt t r=:(FunStmt (FunCall f es)) = typeFun f es >>| pure r
-checkStmt VoidType r=:(ReturnStmt Nothing) = pure r
-checkStmt t r=:(ReturnStmt (Just e)) = unify t e >>| pure r
-
-typeExpr :: Expr -> Env Type
-typeExpr (IntExpr _ _) = pure IntType
-typeExpr (CharExpr _ _) = pure CharType
-typeExpr (BoolExpr _ _) = pure BoolType
-typeExpr (Op1Expr p UnNegation expr) = unify BoolType expr
-typeExpr (Op1Expr p UnMinus expr) = unify IntType expr
-typeExpr (TupleExpr p (e1, e2)) = typeExpr e1
- >>= \t1-> typeExpr e2 >>= \t2-> pure $ TupleType (t1, t2)
-typeExpr (Op2Expr p e1 op e2)
-| isMember op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod] =
- typeOp2 e1 e2 op [IntType] IntType
-| isMember op [BiEquals, BiUnEqual] =
- typeOp2 e1 e2 op [IntType, BoolType, CharType] BoolType
-| isMember op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq] =
- typeOp2 e1 e2 op [IntType, CharType] BoolType
-| isMember op [BiAnd, BiOr] =
- typeOp2 e1 e2 op [BoolType] BoolType
-| op == BiCons = typeExpr e1 >>= \t1-> typeExpr e2
- >>= \t2-> unify (ListType t1) t2
-typeExpr (EmptyListExpr p) = freshIdent >>= \frsh-> let t = IdType frsh in
- putIdent frsh t >>| pure t
-typeExpr (FunExpr p (FunCall f es)) = typeFun f es
-typeExpr (VarExpr p (VarDef ident fs)) = gets (\(st, r)->'Map'.get ident st)
- >>= \mt->case mt of
- Nothing = liftT $ Left $ UndeclaredVariableError p ident
- Just t = unify t fs
-typeOp2 :: Expr Expr Op2 [Type] Type -> Env Type
-typeOp2 e1 e2 op ts ret = typeExpr e1 >>= \t1-> typeExpr e2 >>= \t2->
- unify t1 t2 >>= \t3->if (isMember t3 ts) (pure ret)
- (liftT $ Left $ OperatorError (extrPos e1) op t3)
-
-buildFunctionType :: String [Expr] -> Env Type
-buildFunctionType frsh [] = let t = IdType frsh in putIdent frsh t >>| pure t
-buildFunctionType frsh [e:es] = (->>) <$> typeExpr e <*> buildFunctionType frsh es
-
-unifyApp :: Type [Expr] -> Env Type
-unifyApp t [] = pure t
-unifyApp (tf1 ->> tf2) [t1:ts] = unify tf1 t1 >>| unifyApp tf2 ts
-unifyApp t1 t2 = liftT $ Left $ UnifyError zero t1 (IdType "[expressions, FIXME]")
-
-typeFun :: String [Expr] -> Env Type
-typeFun f es = gets (\(st, r)->'Map'.get f st) >>= \mt-> case mt of
- Nothing = freshIdent >>= \frsh-> buildFunctionType frsh es
- >>= \ft-> putIdent f ft >>| (pure $ IdType frsh)
- Just t = unifyApp t es
-
-resultType :: Type -> Type
-resultType (_ ->> t) = resultType t
-resultType t = t
-
-class unify a :: Type a -> Env Type
-
-instance unify [FieldSelector] where
- unify t [] = pure t
- unify (ListType t) [FieldHd:fs] = unify t fs
- unify t=:(ListType _) [FieldTl:fs] = unify t fs
- unify (TupleType (t, _)) [FieldFst:fs] = unify t fs
- unify (TupleType (_, t)) [FieldSnd:fs] = unify t fs
- unify t [fs:_] = liftT $ Left $ FieldSelectorError zero t fs
-
-instance unify Expr where
- unify (_ ->> _) e = liftT $ Left $ ParseError (extrPos e)
- "Expression cannot be a higher order function. Yet..."
- unify VoidType e = liftT $ Left $ ParseError (extrPos e)
- "Expression cannot be a Void type."
- unify (IdType _) e = liftT $ Left $ ParseError (extrPos e)
- "Expression cannot be an polymorf type."
- unify VarType e = typeExpr e
- //we have to cheat to decorate the error, can be done nicer?
- unify t e = StateT $ \s0 -> let res = runStateT m s0 in case res of
- Left err = Left $ decErr e err
- Right t = Right t //note, t :: (Type, Gamma)
- where m = typeExpr e >>= \tex-> unify t tex
-
-instance unify Type where
- unify IntType IntType = pure IntType
- unify BoolType BoolType = pure BoolType
- unify CharType CharType = pure CharType
- unify (IdType i) t=:(IdType j) = replace i t >>| pure t
- unify t (IdType i) = unify (IdType i) t
- unify (IdType i) t = replace i t >>| pure t
- unify (ListType t1) (ListType t2) = unify t1 t2 >>| (pure $ ListType t1)
- unify (ta1 ->> ta2) (tb1 ->> tb2) = unify ta1 tb1 >>= \ta-> unify ta2 tb2
- >>= \tb-> pure (ta ->> tb)
- unify t1 t2 = liftT $ Left $ UnifyError zero t1 t2
-
-instance zero Pos where
- zero = {line=0,col=0}
-
-decErr :: Expr SemError -> SemError
-decErr e (UnifyError _ t1 t2) = UnifyError (extrPos e) t1 t2
-decErr e (FieldSelectorError _ t fs) = FieldSelectorError (extrPos e) t fs
-decErr e (ParseError _ s) = ParseError (extrPos e) s
-decErr e err = err
-
-dc2 :: Expr (Either SemError a) -> Either SemError a
-dc2 e (Right t) = Right t
-dc2 e (Left err) = Left err
-
-extrPos :: Expr -> Pos
-extrPos (VarExpr p _) = p
-extrPos (Op2Expr p _ _ _) = p
-extrPos (Op1Expr p _ _) = p
-extrPos (IntExpr p _) = p
-extrPos (CharExpr p _) = p
-extrPos (BoolExpr p _) = p
-extrPos (FunExpr p _) = p
-extrPos (EmptyListExpr p) = p
-extrPos (TupleExpr p _) = p
+:: Scheme = Forall [TVar] Type
+:: Gamma :== 'Map'.Map String Scheme //map from Variables! to types
+:: Substitution :== 'Map'.Map TVar Type
+:: Constraints :== [(Type, Type)]
+:: SemError
+ = ParseError Pos String
+ | UnifyError Pos Type Type
+ | InfiniteTypeError Pos Type
+ | FieldSelectorError Pos Type FieldSelector
+ | OperatorError Pos Op2 Type
+ | UndeclaredVariableError Pos String
+ | ArgumentMisMatchError Pos String
+ | SanityError Pos String
+ | Error String
+
+instance zero Gamma where
+ zero = 'Map'.newMap
+
+variableStream :: [TVar]
+variableStream = map toString [1..]
+
+sem :: AST -> Either [SemError] Constraints
+sem (AST fd) = case foldM (const $ hasNoDups fd) () fd
+ >>| foldM (const isNiceMain) () fd
+ >>| hasMain fd of
+ Left e = Left [e]
+ _ = Right []
+ //_ = case execRWST (constraints fd) zero variableStream of
+ // Left e = Left [e]
+ // Right (a, b) = Right b
+where
+ constraints :: [FunDecl] -> Typing ()
+ constraints _ = pure ()
+ //TODO: fix
+ //constraints fds = mapM_ funconstraint fds >>| pure ()
+
+ funconstraint :: FunDecl -> Typing ()
+ funconstraint fd=:(FunDecl _ ident args mt vardecls stmts) = case mt of
+ Nothing = abort "Cannot infer functions yet"
+ _ = pure ()
+ //Just t = inEnv (ident, (Forall [] t)) (
+ // mapM_ vardeclconstraint vardecls >>| 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 _ _ _ _)
+ # mbs = map (\(FunDecl p` n` _ _ _ _)->if (n == n`) (Just p`) Nothing) fds
+ = case catMaybes mbs of
+ [] = Left $ SanityError p "HUH THIS SHOULDN'T HAPPEN"
+ [x] = pure ()
+ [_:x] = Left $ SanityError p (concat
+ [n, " multiply defined at ", toString p])
+
+ hasMain :: [FunDecl] -> Either SemError ()
+ hasMain [(FunDecl _ "main" _ _ _ _):fd] = pure ()
+ hasMain [_:fd] = hasMain fd
+ hasMain [] = Left $ SanityError zero "no main function defined"
+
+ isNiceMain :: FunDecl -> Either SemError ()
+ isNiceMain (FunDecl p "main" as mt _ _) = case (as, mt) of
+ ([_:_], _) = Left $ SanityError p "main must have arity 0"
+ ([], t) = (case t of
+ Nothing = pure ()
+ Just VoidType = pure ()
+ _ = Left $ SanityError p "main has to return Void")
+ isNiceMain _ = pure ()
+
+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
+
+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))
+
+lift :: (Either SemError a) -> Typing a
+lift (Left e) = liftT $ Left e
+lift (Right v) = pure v
+
+//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)
+
+//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
+
+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)
+| 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 -> Typing Type
+op1Type UnNegation = pure $ (BoolType ->> BoolType)
+op1Type UnMinus = pure $ (IntType ->> IntType)
+
+////----- 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]
-
-getRandomStream :: Int -> [String]
-getRandomStream i = genIdents $ filter (isAlpha o toChar) (genRandInt i)
- where
- genIdents r = let (ic, r2) = splitAt 5 r in [toString ic: genIdents r2]
-
-freshIdent :: Env String
-freshIdent = get >>= \(st, [ident:rest])-> put (st, rest)
- >>| case 'Map'.get ident st of
- Nothing = pure ident
- _ = freshIdent
-
-putIdent :: String Type -> Env Void
-putIdent i t = gets (\(st, r)->'Map'.get i st) >>= \mt -> case mt of
- Nothing = modify (\(st, r)->('Map'.put i t st, r))
- Just t2 = unify t t2 >>= \t3-> modify (\(st, r)->('Map'.put i t3 st, r))
-
-replace :: String Type -> Env Void
-replace ident type = get >>= \(st, fr)->put ('Map'.fromList $
- map (itupdate ident type) ('Map'.toList st), fr)
- where
- itupdate :: String Type (String, Type) -> (String, Type)
- itupdate ident newtype ov=:(key, IdType type) = if (ident == type)
- (key, newtype) ov
- itupdate ident newtype (key, TupleType (t1, t2))
- # (_, t1) = itupdate ident newtype (key, t1)
- # (_, t2) = itupdate ident newtype (key, t2)
- = (key, TupleType (t1, t2))
- itupdate ident newtype (key, ListType t1)
- # (_, t1) = itupdate ident newtype (key, t1)
- = (key, ListType t1)
- itupdate _ _ k = k
+ toString mp =
+ concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
instance toString SemError where
- 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]
- toString (FieldSelectorError p t fs) = concat [
- toString p,
- "SemError: Cannot select ", toString fs, " from type: ",
- toString t]
- toString (OperatorError p o t) = concat [
- toString p,
- "SemError: No ", toString o, " for type ",
- toString t]
- toString (UndeclaredVariableError p ident) = concat [
- toString p, "SemError: identifier: ", ident, " undefined."]
-
-saveGamma :: Env Gamma
-saveGamma = get
-
-restoreGamma :: Gamma -> Env Void
-restoreGamma g = put g
+ 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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