diff --git a/code/compiler/13/main.cpp b/code/compiler/13/main.cpp
index ec21e2b..de2946f 100644
--- a/code/compiler/13/main.cpp
+++ b/code/compiler/13/main.cpp
@@ -25,7 +25,7 @@ void yy::parser::error(const yy::location& loc, const std::string& msg) {
 void typecheck_program(
         definition_group& defs,
         type_mgr& mgr, type_env_ptr& env) {
-    type_ptr int_type = type_ptr(new type_base("Int")); 
+    type_ptr int_type = type_ptr(new type_internal("Int")); 
     env->bind_type("Int", int_type);
     type_ptr int_type_app = type_ptr(new type_app(int_type));
 
diff --git a/code/compiler/13/type.cpp b/code/compiler/13/type.cpp
index 856c463..4dd18e1 100644
--- a/code/compiler/13/type.cpp
+++ b/code/compiler/13/type.cpp
@@ -5,8 +5,6 @@
 #include <vector>
 #include "error.hpp"
 
-bool type::is_arrow(const type_mgr& mgr) const { return false; }
-
 void type_scheme::print(const type_mgr& mgr, std::ostream& to) const {
     if(forall.size() != 0) {
         to << "forall ";
@@ -36,21 +34,17 @@ void type_var::print(const type_mgr& mgr, std::ostream& to) const {
     }
 }
 
-bool type_var::is_arrow(const type_mgr& mgr) const {
-    auto it = mgr.types.find(name);
-    if(it != mgr.types.end()) {
-        return it->second->is_arrow(mgr);
-    } else {
-        return false;
-    }
-}
-
 void type_base::print(const type_mgr& mgr, std::ostream& to) const {
     to << name;
 }
 
+void type_internal::print(const type_mgr& mgr, std::ostream& to) const {
+    to << "!" << name;
+}
+
 void type_arr::print(const type_mgr& mgr, std::ostream& to) const {
-    bool print_parenths = left->is_arrow(mgr);
+    type_var* var;
+    bool print_parenths = dynamic_cast<type_arr*>(mgr.resolve(left, var).get()) != nullptr;
     if(print_parenths) to << "(";
     left->print(mgr, to);
     if(print_parenths) to << ")";
@@ -58,10 +52,6 @@ void type_arr::print(const type_mgr& mgr, std::ostream& to) const {
     right->print(mgr, to);
 }
 
-bool type_arr::is_arrow(const type_mgr& mgr) const {
-    return true;
-}
-
 void type_app::print(const type_mgr& mgr, std::ostream& to) const {
     constructor->print(mgr, to);
     to << "*";
@@ -131,7 +121,10 @@ void type_mgr::unify(type_ptr l, type_ptr r, const std::optional<yy::location>&
         return;
     } else if((lid = dynamic_cast<type_base*>(l.get())) &&
             (rid = dynamic_cast<type_base*>(r.get()))) {
-        if(lid->name == rid->name && lid->arity == rid->arity) return;
+        if(lid->name == rid->name &&
+                lid->arity == rid->arity &&
+                lid->is_internal() == rid->is_internal())
+            return;
     } else if((lapp = dynamic_cast<type_app*>(l.get())) &&
             (rapp = dynamic_cast<type_app*>(r.get()))) {
         unify(lapp->constructor, rapp->constructor, loc);
diff --git a/code/compiler/13/type.hpp b/code/compiler/13/type.hpp
index 0edae1c..af417b6 100644
--- a/code/compiler/13/type.hpp
+++ b/code/compiler/13/type.hpp
@@ -13,7 +13,6 @@ struct type {
     virtual ~type() = default;
 
     virtual void print(const type_mgr& mgr, std::ostream& to) const = 0;
-    virtual bool is_arrow(const type_mgr& mgr) const;
 };
 
 using type_ptr = std::shared_ptr<type>;
@@ -37,7 +36,6 @@ struct type_var : public type {
         : name(std::move(n)) {}
 
     void print(const type_mgr& mgr, std::ostream& to) const;
-    bool is_arrow(const type_mgr& mgr) const;
 };
 
 struct type_base : public type {
@@ -48,6 +46,17 @@ struct type_base : public type {
         : name(std::move(n)), arity(a) {}
 
     void print(const type_mgr& mgr, std::ostream& to) const;
+
+    virtual bool is_internal() const { return false; }
+};
+
+struct type_internal : public type_base {
+    type_internal(std::string n, int32_t a = 0)
+        : type_base(std::move(n), a) {}
+
+    void print(const type_mgr& mgr, std::ostream& to) const;
+
+    bool is_internal() const { return true; }
 };
 
 struct type_data : public type_base {
@@ -69,7 +78,6 @@ struct type_arr : public type {
         : left(std::move(l)), right(std::move(r)) {}
 
     void print(const type_mgr& mgr, std::ostream& to) const;
-    bool is_arrow(const type_mgr& mgr) const;
 };
 
 struct type_app : public type {