+////----- 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