+//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 s2 s1, 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 s2 s1, 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
+
+//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) ->
+ applySubst s1 >>|
+ infer ss >>= \(s2, t2) ->
+ applySubst s2 >>|
+ case t1 of
+ VoidType = pure (compose s2 s1, t2)
+ _ = case t2 of
+ VoidType = pure (compose s2 s1, t1)
+ _ = lift (unify t1 t2) >>= \s3 ->
+ pure (compose s3 $ compose s2 s1, t1)
+
+//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 a
+
+instance type VarDecl where
+ type (VarDecl p expected k e) =
+ infer e >>= \(s1, given) ->
+ 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 (VarDecl p (Just vtype) k e)
+
+instance type FunDecl where
+ type (FunDecl p f args expected vds stmts) =
+ introduce f >>|
+ mapM introduce args >>= \argTs->
+ type vds >>= \tVds->
+ infer stmts >>= \(s1, result)->
+ let given = foldr (->>) result argTs in
+ applySubst s1 >>|
+ (case expected of
+ Nothing = pure zero
+ Just expected_ = lift (unify expected_ given))
+ >>= \s2 ->
+ let ftype = subst (compose s2 s1) given in
+ generalize ftype >>= \t->
+ changeGamma (extend f t) >>|
+ pure (FunDecl p f args (Just ftype) tVds stmts)
+
+instance toString (Maybe a) | toString a where
+ toString Nothing = "Nothing"
+ toString (Just e) = concat ["Just ", toString e]
+
+instance type [a] | type a where
+ type dcls = mapM type dcls
+
+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 ": 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]