X-Git-Url: https://git.martlubbers.net/?a=blobdiff_plain;f=sem.icl;h=272ef5a38d0f0a5d3cef5652ad84f16d990f5a40;hb=1f01e39fb2383aa2c63234d0750c0459fe3de752;hp=ab7aa9c005ef0722e7ab5449df484f477a4a144c;hpb=fa73f7e0d251020e47185a94699c41d9575f4052;p=cc1516.git

diff --git a/sem.icl b/sem.icl
index ab7aa9c..272ef5a 100644
--- a/sem.icl
+++ b/sem.icl
@@ -1,169 +1,423 @@
 implementation module sem
 
 import qualified Data.Map as Map
+
 from Data.Func import $
-import Data.Maybe
-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 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)
+:: 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
 
-get = gets id
+instance zero Gamma where
+	zero = 'Map'.newMap
 
-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]
+variableStream :: [TVar]
+variableStream = map toString [1..]
 
-freshIdent :: Env String
-freshIdent = get >>= \(st, [ident:rest])-> put (st, rest) 
-    >>| case 'Map'.get ident st of
-        Nothing = pure ident
-        _       = freshIdent
+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 ()
 
-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))
+		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 ())
 
-instance toString SemError where
-	toString (ParseError p e) = concat [
-		toString p,"SemError: ParseError: ", e]
-	toString (Error e) = "SemError: " +++ e
-	toString (UnifyErrorStub t1 t2) = toString (UnifyError {line=0,col=0} t1 t2)
-	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) = 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 f = pure f
-
-semVarDecl :: VarDecl -> Env VarDecl
-semVarDecl (VarDecl pos type ident ex) = unify type ex
-    >>= \t-> putIdent ident t >>| (pure $ VarDecl pos t ident ex)
-
-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)
-//Int
-typeExpr (Op2Expr p e1 BiPlus e2) = unify IntType e1 >>| unify IntType e2
-typeExpr (Op2Expr p e1 BiMinus e2) = unify IntType e1 >>| unify IntType e2
-typeExpr (Op2Expr p e1 BiTimes e2) = unify IntType e1 >>| unify IntType e2
-typeExpr (Op2Expr p e1 BiDivide e2) = unify IntType e1 >>| unify IntType e2
-typeExpr (Op2Expr p e1 BiMod e2) = unify IntType e1 >>| unify IntType e2
-//bool, char of int
-typeExpr (Op2Expr p e1 BiEquals e2) = typeExpr e1 >>= \t1 -> unify t1 e2 
-    >>| pure BoolType //todo, actually check t1 in Char,Bool,Int
-typeExpr (Op2Expr p e1 BiUnEqual e2) = typeExpr (Op2Expr p e1 BiEquals e2)
-//char of int
-typeExpr (Op2Expr p e1 BiLesser e2) = typeExpr e1 >>= \t1 -> unify t1 e2 
-    >>| pure BoolType //todo, actually check t1 in Char, Int
-typeExpr (Op2Expr p e1 BiGreater e2) = typeExpr (Op2Expr p e1 BiLesser e2)
-typeExpr (Op2Expr p e1 BiLesserEq e2) = typeExpr (Op2Expr p e1 BiLesser e2)
-typeExpr (Op2Expr p e1 BiGreaterEq e2) = typeExpr (Op2Expr p e1 BiLesser e2)
-//bool
-typeExpr (Op2Expr p e1 BiAnd e2) = unify BoolType e1 >>| unify BoolType e2
-typeExpr (Op2Expr p e1 BiOr e2) = unify BoolType e1 >>| unify BoolType e2
-//a
-typeExpr (Op2Expr p e1 BiCons e2) = 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) = undef
-//typeExpr (VarExpr Pos VarDef) = undef //when checking var-expr, be sure to
-    //put the infered type in the context
-
-class unify a :: Type a -> Env Type
-
-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
-    unify (IdType i) e = undef
-    //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 
-
-replace :: String Type -> Env Void
-replace _ _ = undef
-
-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
-	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 (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
+		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]
+    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