diff --git a/code/compiler/11/ast.cpp b/code/compiler/11/ast.cpp
index b55c347..5bdd00c 100644
--- a/code/compiler/11/ast.cpp
+++ b/code/compiler/11/ast.cpp
@@ -18,7 +18,7 @@ void ast_int::find_free(type_mgr& mgr, type_env_ptr& env, std::set<std::string>&
 }
 
 type_ptr ast_int::typecheck(type_mgr& mgr) {
-    return type_ptr(new type_base("Int"));
+    return type_ptr(new type_app(env->lookup_type("Int")));
 }
 
 void ast_int::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
@@ -161,7 +161,9 @@ type_ptr ast_case::typecheck(type_mgr& mgr) {
     }
 
     input_type = mgr.resolve(case_type, var);
-    if(!dynamic_cast<type_data*>(input_type.get())) {
+    type_app* app_type;
+    if(!(app_type = dynamic_cast<type_app*>(input_type.get())) ||
+            !dynamic_cast<type_data*>(app_type->constructor.get())) {
         throw type_error("attempting case analysis of non-data type");
     }
 
@@ -169,7 +171,8 @@ type_ptr ast_case::typecheck(type_mgr& mgr) {
 }
 
 void ast_case::compile(const env_ptr& env, std::vector<instruction_ptr>& into) const {
-    type_data* type = dynamic_cast<type_data*>(input_type.get());
+    type_app* app_type = dynamic_cast<type_app*>(input_type.get());
+    type_data* type = dynamic_cast<type_data*>(app_type->constructor.get());
 
     of->compile(env, into);
     into.push_back(instruction_ptr(new instruction_eval()));
diff --git a/code/compiler/11/definition.cpp b/code/compiler/11/definition.cpp
index 91b0178..79d53af 100644
--- a/code/compiler/11/definition.cpp
+++ b/code/compiler/11/definition.cpp
@@ -56,28 +56,38 @@ void definition_defn::generate_llvm(llvm_context& ctx) {
     ctx.builder.CreateRetVoid();
 }
 
-void definition_data::insert_types(type_mgr& mgr, type_env_ptr& env) {
+void definition_data::insert_types(type_env_ptr& env) {
     this->env = env;
     env->bind_type(name, type_ptr(new type_data(name)));
 }
 
 void definition_data::insert_constructors() const {
-    type_ptr return_type = env->lookup_type(name);
-    type_data* this_type = static_cast<type_data*>(return_type.get());
+    type_ptr this_type_ptr = env->lookup_type(name);
+    type_data* this_type = static_cast<type_data*>(this_type_ptr.get());
     int next_tag = 0;
 
+    std::set<std::string> var_set;
+    type_app* return_app = new type_app(std::move(this_type_ptr));
+    type_ptr return_type(return_app);
+    for(auto& var : vars) {
+        if(var_set.find(var) != var_set.end()) throw 0;
+        var_set.insert(var);
+        return_app->arguments.push_back(type_ptr(new type_var(var)));
+    }
+
     for(auto& constructor : constructors) {
         constructor->tag = next_tag;
         this_type->constructors[constructor->name] = { next_tag++ };
 
         type_ptr full_type = return_type;
         for(auto it = constructor->types.rbegin(); it != constructor->types.rend(); it++) {
-            type_ptr type = env->lookup_type(*it);
-            if(!type) throw 0;
+            type_ptr type = (*it)->to_type(var_set, env);
             full_type = type_ptr(new type_arr(type, full_type));
         }
 
-        env->bind(constructor->name, full_type);
+        type_scheme_ptr full_scheme(new type_scheme(std::move(full_type)));
+        full_scheme->forall.insert(full_scheme->forall.begin(), vars.begin(), vars.end());
+        env->bind(constructor->name, full_scheme);
     }
 }
 
diff --git a/code/compiler/11/definition.hpp b/code/compiler/11/definition.hpp
index b72bed6..c14ec0f 100644
--- a/code/compiler/11/definition.hpp
+++ b/code/compiler/11/definition.hpp
@@ -4,6 +4,7 @@
 #include <set>
 #include "instruction.hpp"
 #include "llvm_context.hpp"
+#include "parsed_type.hpp"
 #include "type_env.hpp"
 
 struct ast;
@@ -11,10 +12,10 @@ using ast_ptr = std::unique_ptr<ast>;
 
 struct constructor {
     std::string name;
-    std::vector<std::string> types;
+    std::vector<parsed_type_ptr> types;
     int8_t tag;
 
-    constructor(std::string n, std::vector<std::string> ts)
+    constructor(std::string n, std::vector<parsed_type_ptr> ts)
         : name(std::move(n)), types(std::move(ts)) {}
 };
 
@@ -52,14 +53,18 @@ using definition_defn_ptr = std::unique_ptr<definition_defn>;
 
 struct definition_data {
     std::string name;
+    std::vector<std::string> vars;
     std::vector<constructor_ptr> constructors;
 
     type_env_ptr env;
 
-    definition_data(std::string n, std::vector<constructor_ptr> cs)
-        : name(std::move(n)), constructors(std::move(cs)) {}
+    definition_data(
+            std::string n,
+            std::vector<std::string> vs,
+            std::vector<constructor_ptr> cs)
+        : name(std::move(n)), vars(std::move(vs)), constructors(std::move(cs)) {}
 
-    void insert_types(type_mgr& mgr, type_env_ptr& env);
+    void insert_types(type_env_ptr& env);
     void insert_constructors() const;
     void generate_llvm(llvm_context& ctx);
 };
diff --git a/code/compiler/11/main.cpp b/code/compiler/11/main.cpp
index bc181d6..5cd3aa1 100644
--- a/code/compiler/11/main.cpp
+++ b/code/compiler/11/main.cpp
@@ -30,17 +30,18 @@ void typecheck_program(
         type_mgr& mgr, type_env_ptr& env) {
     type_ptr int_type = type_ptr(new type_base("Int")); 
     env->bind_type("Int", int_type);
+    type_ptr int_type_app = type_ptr(new type_app(int_type));
 
     type_ptr binop_type = type_ptr(new type_arr(
-                int_type,
-                type_ptr(new type_arr(int_type, int_type))));
+                int_type_app,
+                type_ptr(new type_arr(int_type_app, int_type_app))));
     env->bind("+", binop_type);
     env->bind("-", binop_type);
     env->bind("*", binop_type);
     env->bind("/", binop_type);
 
     for(auto& def_data : defs_data) {
-        def_data.second->insert_types(mgr, env);
+        def_data.second->insert_types(env);
     }
     for(auto& def_data : defs_data) {
         def_data.second->insert_constructors();
diff --git a/code/compiler/11/parser.y b/code/compiler/11/parser.y
index 57f4be9..81ef4ac 100644
--- a/code/compiler/11/parser.y
+++ b/code/compiler/11/parser.y
@@ -5,6 +5,7 @@
 #include "ast.hpp"
 #include "definition.hpp"
 #include "parser.hpp"
+#include "parsed_type.hpp"
 
 std::map<std::string, definition_data_ptr> defs_data;
 std::map<std::string, definition_defn_ptr> defs_defn;
@@ -36,9 +37,11 @@ extern yy::parser::symbol_type yylex();
 %define api.value.type variant
 %define api.token.constructor
 
-%type <std::vector<std::string>> lowercaseParams uppercaseParams
+%type <std::vector<std::string>> lowercaseParams
 %type <std::vector<branch_ptr>> branches
 %type <std::vector<constructor_ptr>> constructors
+%type <std::vector<parsed_type_ptr>> typeList
+%type <parsed_type_ptr> type nullaryType
 %type <ast_ptr> aAdd aMul case app appBase
 %type <definition_data_ptr> data 
 %type <definition_defn_ptr> defn
@@ -75,11 +78,6 @@ lowercaseParams
     | lowercaseParams LID { $$ = std::move($1); $$.push_back(std::move($2)); }
     ;
 
-uppercaseParams
-    : %empty { $$ = std::vector<std::string>(); }
-    | uppercaseParams UID { $$ = std::move($1); $$.push_back(std::move($2)); }
-    ;
-
 aAdd
     : aAdd PLUS aMul { $$ = ast_ptr(new ast_binop(PLUS, std::move($1), std::move($3))); }
     | aAdd MINUS aMul { $$ = ast_ptr(new ast_binop(MINUS, std::move($1), std::move($3))); }
@@ -127,8 +125,8 @@ pattern
     ;
 
 data
-    : DATA UID EQUAL OCURLY constructors CCURLY
-        { $$ = definition_data_ptr(new definition_data(std::move($2), std::move($5))); }
+    : DATA UID lowercaseParams EQUAL OCURLY constructors CCURLY
+        { $$ = definition_data_ptr(new definition_data(std::move($2), std::move($3), std::move($6))); }
     ;
 
 constructors
@@ -138,7 +136,22 @@ constructors
     ;
 
 constructor
-    : UID uppercaseParams
+    : UID typeList
         { $$ = constructor_ptr(new constructor(std::move($1), std::move($2))); }
     ;
 
+type
+    : nullaryType ARROW type { $$ = parsed_type_ptr(new parsed_type_arr(std::move($1), std::move($3))); }
+    | nullaryType { $$ = std::move($1); }
+    ;
+
+nullaryType
+    : OPAREN UID typeList CPAREN { $$ = parsed_type_ptr(new parsed_type_app(std::move($2), std::move($3))); }
+    | UID { $$ = parsed_type_ptr(new parsed_type_app(std::move($1), { })); }
+    | LID { $$ = parsed_type_ptr(new parsed_type_var(std::move($1))); }
+    ;
+
+typeList
+    : %empty { $$ = std::vector<parsed_type_ptr>(); }
+    | typeList type { $$ = std::move($1); $$.push_back(std::move($2)); }
+    ;