from Data.Func import $
from StdFunc import o, flip, const, id
+import Control.Applicative
import Control.Monad
import Control.Monad.Trans
import Control.Monad.State
import AST
-
:: Scheme = Forall [TVar] Type
:: Gamma :== 'Map'.Map String Scheme //map from Variables! to types
+:: Typing a :== StateT (Gamma, [TVar]) (Either SemError) a
:: Substitution :== 'Map'.Map TVar Type
:: Constraints :== [(Type, Type)]
:: SemError
variableStream :: [TVar]
variableStream = map toString [1..]
-sem :: AST -> Either [SemError] Constraints
+defaultGamma :: Gamma //includes all default functions
+defaultGamma = extend "print" (Forall ["a"] ((IdType "a") ->> VoidType))
+ $ extend "isEmpty" (Forall ["a"] ((ListType (IdType "a")) ->> BoolType))
+ $ extend "read" (Forall [] (FuncType CharType))
+ $ extend "1printchar" (Forall [] (CharType ->> VoidType))
+ $ extend "1printint" (Forall [] (IntType ->> VoidType))
+ $ extend "1printbool" (Forall [] (BoolType ->> VoidType))
+ zero
+
+sem :: AST -> Either [SemError] (AST, Gamma)
sem (AST fd) = case foldM (const $ hasNoDups fd) () fd
- >>| foldM (const isNiceMain) () fd
- >>| hasMain fd of
+ >>| foldM (const isNiceMain) () fd
+ >>| hasMain fd
+ >>| runStateT (unfoldLambda fd >>= type) (defaultGamma, variableStream) of
Left e = Left [e]
- _ = Right []
- //_ = case execRWST (constraints fd) zero variableStream of
- // Left e = Left [e]
- // Right (a, b) = Right b
+ Right ((_,fds),(gam,_)) = Right (AST fds, gam)
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
_ = Left $ SanityError p "main has to return Void")
isNiceMain _ = pure ()
+
+//------------------
+// LAMBDA UNFOLDING
+//------------------
+unfoldLambda :: [FunDecl] -> Typing [FunDecl]
+unfoldLambda [] = pure []
+unfoldLambda [fd:fds] = unfoldL_ fd >>= \(gen1, fs_)->
+ unfoldLambda fds >>= \gen2->
+ pure $ gen1 ++ [fs_] ++ gen2
+
+flattenT :: [([a],b)] -> ([a],[b])
+flattenT ts = (flatten $ map fst ts, map snd ts)
+
+class unfoldL_ a :: a -> Typing ([FunDecl], a)
+
+instance unfoldL_ FunDecl where
+ unfoldL_ (FunDecl p f args mt vds stmts) =
+ flattenT <$> mapM unfoldL_ vds >>= \(fds1,vds_) ->
+ flattenT <$> mapM unfoldL_ stmts >>= \(fds2,stmts_)->
+ pure (fds1 ++ fds2, FunDecl p f args mt vds_ stmts_)
+
+instance unfoldL_ VarDecl where
+ unfoldL_ (VarDecl p mt v e) = unfoldL_ e >>= \(fds, e_)->pure (fds, VarDecl p mt v e_)
+
+instance unfoldL_ Stmt where
+ unfoldL_ (IfStmt e th el) = unfoldL_ e >>= \(fds, e_)->pure (fds, IfStmt e_ th el)
+ unfoldL_ (WhileStmt e c) = unfoldL_ e >>= \(fds, e_)->pure (fds, WhileStmt e_ c)
+ unfoldL_ (AssStmt vd e) = unfoldL_ e >>= \(fds, e_)->pure (fds, AssStmt vd e_)
+ unfoldL_ (FunStmt f es fs) = flattenT <$> mapM unfoldL_ es >>= \(fds, es_)->
+ pure (fds, FunStmt f es_ fs)
+ unfoldL_ (ReturnStmt (Just e)) = unfoldL_ e >>= \(fds, e_) ->
+ pure (fds, ReturnStmt (Just e_))
+ unfoldL_ (ReturnStmt Nothing) = pure ([], ReturnStmt Nothing)
+
+instance unfoldL_ Expr where
+ unfoldL_ (LambdaExpr p args e) =
+ fresh >>= \(IdType n) ->
+ let f = ("2lambda_"+++n) in
+ let fd = FunDecl p f args Nothing [] [ReturnStmt $ Just e] in
+ let fe = VarExpr p (VarDef f []) in
+ pure ([fd], fe)
+ unfoldL_ (FunExpr p f es fs) = flattenT <$> mapM unfoldL_ es >>= \(fds, es_)->
+ pure (fds, FunExpr p f es_ fs)
+ unfoldL_ (Op2Expr p e1 op e2) = unfoldL_ e1 >>= \(fds1, e1_)->
+ unfoldL_ e2 >>= \(fds2, e2_)->
+ pure (fds1++fds2, Op2Expr p e1_ op e2_)
+ unfoldL_ (Op1Expr p op e1) = unfoldL_ e1 >>= \(fds, e1_)->pure (fds, Op1Expr p op e1_)
+ unfoldL_ (TupleExpr p (e1, e2)) = unfoldL_ e1 >>= \(fds1, e1_)->
+ unfoldL_ e2 >>= \(fds2, e2_)->
+ pure (fds1++fds2, TupleExpr p (e1_, e2_))
+ unfoldL_ e = pure ([], e)
+
+//------------
+//------------
+// TYPING
+//------------
+//------------
+
class Typeable a where
ftv :: a -> [TVar]
subst :: Substitution a -> a
ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2
ftv (ListType t) = ftv t
ftv (IdType tvar) = [tvar]
+ ftv (FuncType t) = ftv t
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 (FuncType t) = FuncType (subst s t)
subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2)
subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s
subst s t = t
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 t1=:(IdType tv) t2 = unify t2 t1
unify (ta1->>ta2) (tb1->>tb2) = unify ta1 tb1 >>= \s1->
- unify tb1 tb2 >>= \s2->
- Right $ compose s1 s2
+ unify (subst s1 ta2) (subst s1 tb2) >>= \s2->
+ Right $ compose s2 s1
unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
- unify ta2 tb2 >>= \s2->
- Right $ compose s1 s2
+ unify (subst s1 ta2) (subst s1 tb2) >>= \s2->
+ Right $ compose s2 s1
unify (ListType t1) (ListType t2) = unify t1 t2
+unify (FuncType t1) (FuncType 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 ()
//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)
+class infer a :: a -> Typing (Substitution, Type, a)
////---- 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
+ VarExpr _ (VarDef k fs) = lookup k >>= \t ->
+ foldM foldFieldSelectors t fs >>= \finalT ->
+ pure (zero, finalT, e)
- Op2Expr _ e1 op e2 =
- infer e1 >>= \(s1, t1) ->
- infer e2 >>= \(s2, t2) ->
+ Op2Expr p e1 op e2 =
+ infer e1 >>= \(s1, t1, e1_) ->
+ applySubst s1 >>|
+ infer e2 >>= \(s2, t2, e2_) ->
+ applySubst s2 >>|
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)
+ applySubst s3 >>|
+ pure ((compose s3 $ compose s2 s1), subst s3 tv, Op2Expr p e1_ op e2_)
- Op1Expr _ op e1 =
- infer e1 >>= \(s1, t1) ->
+ Op1Expr p op e1 =
+ infer e1 >>= \(s1, t1, e1_) ->
+ applySubst s1 >>|
fresh >>= \tv ->
let given = t1 ->> tv in
op1Type op >>= \expected ->
lift (unify expected given) >>= \s2 ->
- pure (compose s2 s1, subst s2 tv)
+ applySubst s2 >>|
+ pure (compose s2 s1, subst s2 tv, Op1Expr p op e1)
- EmptyListExpr _ = (\tv->(zero,tv)) <$> fresh
+ EmptyListExpr _ = (\tv->(zero,ListType tv,e)) <$> 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)
+ TupleExpr p (e1, e2) =
+ infer e1 >>= \(s1, t1, e1_) ->
+ applySubst s1 >>|
+ infer e2 >>= \(s2, t2, e2_) ->
+ applySubst s2 >>|
+ pure (compose s2 s1, TupleType (t1,t2), TupleExpr p (e1_,e2_))
- IntExpr _ _ = pure $ (zero, IntType)
- BoolExpr _ _ = pure $ (zero, BoolType)
- CharExpr _ _ = pure $ (zero, CharType)
+ LambdaExpr _ _ _ = liftT $ Left $ Error "PANIC: lambdas should be Unfolded"
+ FunExpr p f args fs =
+ lookup f >>= \expected ->
+ let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
+ foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
+ applySubst s1 >>|
+ (case f of
+ "print" = case head argTs of
+ IntType = pure "1printint"
+ CharType = pure "1printchar"
+ BoolType = pure "1printbool"
+ ListType (CharType) = pure "1printstr"
+ t = liftT $ Left $ SanityError p ("can not print " +++ toString t)
+ _ = pure f
+ ) >>= \newF->
+ fresh >>= \tv->case expected of
+ FuncType t = foldM foldFieldSelectors t fs >>= \returnType ->
+ pure (s1, returnType, (FunExpr p newF args fs))
+ _ = (let given = foldr (->>) tv argTs in
+ lift (unify expected given) >>= \s2->
+ applySubst s2 >>|
+ let fReturnType = subst s2 tv in
+ foldM foldFieldSelectors fReturnType fs >>= \returnType ->
+ pure (compose s2 s1, returnType, FunExpr p newF args_ fs))
+
+ IntExpr _ _ = pure $ (zero, IntType, e)
+ BoolExpr _ _ = pure $ (zero, BoolType, e)
+ CharExpr _ _ = pure $ (zero, CharType, e)
+
+foldFieldSelectors :: Type FieldSelector -> Typing Type
+foldFieldSelectors (ListType t) (FieldHd) = pure t
+foldFieldSelectors t=:(ListType _) (FieldTl) = pure t
+foldFieldSelectors (TupleType (t1, _)) (FieldFst) = pure t1
+foldFieldSelectors (TupleType (_, t2)) (FieldSnd) = pure t2
+foldFieldSelectors t fs = liftT $ Left $ FieldSelectorError zero t fs
op2Type :: Op2 -> Typing Type
op2Type op
instance infer Stmt where
infer s = case s of
IfStmt e th el =
- infer e >>= \(s1, et)->
+ infer e >>= \(s1, et, e_)->
lift (unify et BoolType) >>= \s2 ->
applySubst (compose s2 s1) >>|
- infer th >>= \(s3, tht)->
+ infer th >>= \(s3, tht, th_)->
applySubst s3 >>|
- infer el >>= \(s4, elt)->
+ infer el >>= \(s4, elt, el_)->
applySubst s4 >>|
lift (unify tht elt) >>= \s5->
- pure (compose s5 $ compose s4 $ compose s3 $ compose s1 s2, subst s5 tht)
+ let sub = compose s5 $ compose s4 $ compose s3 $ compose s2 s1 in
+ pure (sub, subst s5 tht, IfStmt e_ th_ el_)
WhileStmt e wh =
- infer e >>= \(s1, et)->
+ infer e >>= \(s1, et, e_)->
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)
-
-
+ infer wh >>= \(s3, wht, wh_)->
+ pure (compose s3 $ compose s2 s1, subst s3 wht, WhileStmt e_ wh_)
+
+ AssStmt vd=:(VarDef k fs) e =
+ lookup k >>= \expected ->
+ infer e >>= \(s1, given, e_)->
+ foldM reverseFs given (reverse fs) >>= \varType->
+ lift (unify expected varType) >>= \s2->
+ let s = compose s2 s1 in
+ applySubst s >>|
+ changeGamma (extend k (Forall [] (subst s varType))) >>|
+ pure (s, VoidType, AssStmt vd e_)
+
+ FunStmt f args fs =
+ lookup f >>= \expected ->
+ let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
+ foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
+ fresh >>= \tv->
+ let given = foldr (->>) tv argTs in
+ lift (unify expected given) >>= \s2->
+ let fReturnType = subst s2 tv in
+ foldM foldFieldSelectors fReturnType fs >>= \returnType ->
+ (case f of
+ "print" = case head argTs of
+ IntType = pure "1printint"
+ CharType = pure "1printchar"
+ BoolType = pure "1printbool"
+ ListType (CharType) = pure "1printstr"
+ t = liftT $ Left $ SanityError zero ("can not print " +++ toString t)
+ _ = pure f) >>= \newF->
+ pure (compose s2 s1, VoidType, FunStmt newF args_ fs)
+
+ ReturnStmt Nothing = pure (zero, VoidType, s)
+ //hier ook sub applyen
+ ReturnStmt (Just e) = infer e >>= \(sub, t, e_)-> pure (sub, t, ReturnStmt (Just e_))
+
+reverseFs :: Type FieldSelector -> Typing Type
+reverseFs t FieldHd = pure $ ListType t
+reverseFs t FieldTl = pure t
+reverseFs t FieldFst = fresh >>= \tv -> pure $ TupleType (t, tv)
+reverseFs t FieldSnd = fresh >>= \tv -> pure $ TupleType (tv, t)
+
+//The type of a list of statements is either an encountered
+//return, or VoidType
instance infer [a] | infer a where
- infer _ = undef
+ infer [] = pure (zero, VoidType, [])
+ infer [stmt:ss] =
+ infer stmt >>= \(s1, t1, s_) ->
+ applySubst s1 >>|
+ infer ss >>= \(s2, t2, ss_) ->
+ applySubst s2 >>|
+ case t1 of
+ VoidType = pure (compose s2 s1, t2, [s_:ss_])
+ _ = case t2 of
+ VoidType = pure (compose s2 s1, t1, [s_:ss_])
+ _ = lift (unify t1 t2) >>= \s3 ->
+ pure (compose s3 $ compose s2 s1, t1, [s_:ss_])
+
+//the type class inferes the type of an AST element (VarDecl or FunDecl)
+//and adds it to the AST element
+class type a :: a -> Typing (Substitution, a)
+
+instance type VarDecl where
+ type (VarDecl p expected k e) =
+ infer e >>= \(s1, given, e_) ->
+ applySubst s1 >>|
+ case expected of
+ Nothing = pure zero
+ Just expected_ = lift (unify expected_ given)
+ >>= \s2->
+ applySubst s2 >>|
+ let vtype = subst (compose s2 s1) given in
+ generalize vtype >>= \t ->
+ changeGamma (extend k t) >>|
+ pure (compose s2 s1, VarDecl p (Just vtype) k e_)
+
+instance type FunDecl where
+ type fd=:(FunDecl p f args expected vds stmts) =
+ gamma >>= \outerScope-> //functions are infered in their own scopde
+ introduce f >>|
+ mapM introduce args >>= \argTs->
+ fresh >>= \tempTv ->
+ let temp = foldr (->>) tempTv argTs in
+ (case expected of
+ Just expected_ = lift (unify expected_ temp)
+ _ = pure zero
+ ) >>= \s0->
+ applySubst s0 >>|
+ type vds >>= \(s1, tVds)->
+ applySubst s1 >>|
+ infer stmts >>= \(s2, result, stmts_)->
+ applySubst s1 >>|
+ let argTs_ = map (subst $ compose s2 $ compose s1 s0) argTs in
+ let given = foldr (->>) result argTs_ in
+ (case expected of
+ Nothing = pure zero
+ Just (FuncType expected_) = lift (unify expected_ given)
+ Just expected_ = lift (unify expected_ given)
+ ) >>= \s3 ->
+ let ftype = subst (compose s3 $ compose s2 $ compose s1 s0) given in
+ (case ftype of
+ _ ->> _ = pure ftype
+ _ = pure $ FuncType ftype
+ ) >>= \ftype_->
+ generalize ftype_ >>= \t->
+ putGamma outerScope >>|
+ changeGamma (extend f t) >>|
+ pure (compose s3 $ compose s2 $ compose s1 s0,
+ FunDecl p f args (Just ftype_) tVds stmts_)
+
+instance type [a] | type a where
+ type [] = pure (zero, [])
+ type [v:vs] =
+ type v >>= \(s1, v_)->
+ applySubst s1 >>|
+ type vs >>= \(s2, vs_)->
+ applySubst (compose s2 s1) >>|
+ pure (compose s2 s1, [v_:vs_])
-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)
+introduce :: String -> Typing Type
+introduce k =
+ fresh >>= \tv ->
+ changeGamma (extend k (Forall [] tv)) >>|
+ pure tv
instance toString Scheme where
toString (Forall x t) =
- concat ["Forall ": map ((+++) "\n") x] +++ toString t
+ concat ["Forall ": intersperse "," x] +++ concat [". ", toString t];
instance toString Gamma where
toString mp =
concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
+instance toString Substitution where
+ toString subs =
+ concat [concat [k, ": ", toString t, "\n"]\\(k, t)<-'Map'.toList subs]
+
instance toString SemError where
toString (SanityError p e) = concat [toString p,
"SemError: SanityError: ", e]
- toString se = "SemError: "
+ toString (ParseError p s) = concat [toString p,
+ "ParseError: ", s]
+ toString (UnifyError p t1 t2) = concat [toString p,
+ "Can not unify types, expected|given:\n", toString t1,
+ "\n", toString t2]
+ toString (InfiniteTypeError p t) = concat [toString p,
+ "Infinite type: ", toString t]
+ toString (FieldSelectorError p t fs) = concat [toString p,
+ "Can not run fieldselector '", toString fs, "' on type: ",
+ toString t]
+ toString (OperatorError p op t) = concat [toString p,
+ "Operator error, operator '", toString op, "' can not be",
+ "used on type: ", toString t]
+ toString (UndeclaredVariableError p k) = concat [toString p,
+ "Undeclared identifier: ", k]
+ toString (ArgumentMisMatchError p str) = concat [toString p,
+ "Argument mismatch: ", str]
+ toString (Error e) = concat ["Unknown error during semantical",
+ "analysis: ", e]
+
+instance toString (Maybe a) | toString a where
+ toString Nothing = "Nothing"
+ toString (Just e) = concat ["Just ", toString e]
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
+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)
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