+////----- 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, e_)->
+ lift (unify et BoolType) >>= \s2 ->
+ applySubst (compose s2 s1) >>|
+ infer th >>= \(s3, tht, th_)->
+ applySubst s3 >>|
+ infer el >>= \(s4, elt, el_)->
+ applySubst s4 >>|
+ lift (unify tht elt) >>= \s5->
+ 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, e_)->
+ lift (unify et BoolType) >>= \s2 ->
+ applySubst (compose s2 s1) >>|
+ 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)
+ ReturnStmt (Just e) = infer e >>= \(sub, t, _)-> pure (sub, t, s)
+
+reverseFs :: Type FieldSelector -> Typing Type
+reverseFs t FieldHd = pure $ ListType t
+reverseFs t FieldTl = pure $ ListType 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 [] = 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 (FunDecl p f args expected vds stmts) =
+ gamma >>= \outerScope-> //functions are infered in their own scopde
+ introduce f >>|
+ mapM introduce args >>= \argTs->
+ type vds >>= \(s1, tVds)->
+ applySubst s1 >>|
+ infer stmts >>= \(s2, result, stmts_)->
+ applySubst s1 >>|
+ let argTs_ = map (subst $ compose s2 s1) argTs in
+ let given = foldr (->>) result argTs_ in
+ (case expected of
+ Nothing = pure zero
+ Just expected_ = lift (unify expected_ given))
+ >>= \s3 ->
+ let ftype = subst (compose s3 $ compose s2 s1) given in
+ generalize ftype >>= \t->
+ putGamma outerScope >>|
+ changeGamma (extend f t) >>|
+ pure (compose s3 $ compose s2 s1, 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_])
+
+introduce :: String -> Typing Type
+introduce k =
+ fresh >>= \tv ->
+ changeGamma (extend k (Forall [] tv)) >>|
+ pure tv