+//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