diff --git a/programs/eq.lily b/programs/eq.lily
new file mode 100644
index 0000000..49a6471
--- /dev/null
+++ b/programs/eq.lily
@@ -0,0 +1,6 @@
+defn main = {
+    case eq 1 1 of {
+        True -> { 326 }
+        False -> { 404 }
+    }
+}
diff --git a/programs/not.lily b/programs/not.lily
index 7b2bf4b..cc0376e 100644
--- a/programs/not.lily
+++ b/programs/not.lily
@@ -1,4 +1,3 @@
-data Bool = { True, False }
 defn not b = {
     case b of {
         False -> { True }
diff --git a/src/gmachine.cpp b/src/gmachine.cpp
index 4becc62..ec454bb 100644
--- a/src/gmachine.cpp
+++ b/src/gmachine.cpp
@@ -62,6 +62,11 @@ namespace lily {
         return os;
     }
 
+    std::ostream& instruction_eq::to_stream(std::ostream& os) {
+        os << "eq";
+        return os;
+    }
+
     std::ostream& instruction_cond::to_stream(std::ostream& os) {
         os << "cond";
         return os;
@@ -166,6 +171,39 @@ namespace lily {
         builder.CreateCall(stack_push_func, { stack, new_node });
     }
 
+    void instruction_eq::gen_llvm(llvm_context& ctx) {
+        llvm::Value* stack = ctx.get_current_function()->arg_begin();
+        llvm::Value* param2 = builder.CreateCall(stack_pop_func, { stack }, "temp");
+        llvm::Value* param1 = builder.CreateCall(stack_pop_func, { stack }, "temp");
+        llvm::Value* param1_node_num = builder.CreatePointerCast(param1, llvm::PointerType::getUnqual(node_num_type), "temp");
+        llvm::Value* param2_node_num = builder.CreatePointerCast(param2, llvm::PointerType::getUnqual(node_num_type), "temp");
+        llvm::Value* param1_intptr = builder.CreateGEP(param1_node_num, { get_int32_constant(0), get_int32_constant(1) }, "temp");
+        llvm::Value* param2_intptr = builder.CreateGEP(param2_node_num, { get_int32_constant(0), get_int32_constant(1) }, "temp");
+        llvm::Value* param1_int = builder.CreateLoad(llvm::IntegerType::get(context, 32), param1_intptr, "temp");
+        llvm::Value* param2_int = builder.CreateLoad(llvm::IntegerType::get(context, 32), param2_intptr, "temp");
+        llvm::Value* compare_result = builder.CreateICmpEQ(param1_int, param2_int, "temp");
+
+        llvm::BasicBlock* false_block = llvm::BasicBlock::Create(context, "false", ctx.get_current_function());
+        llvm::BasicBlock* true_block = llvm::BasicBlock::Create(context, "true", ctx.get_current_function());
+        builder.CreateCondBr(compare_result, true_block, false_block);
+
+        llvm::BasicBlock* after = llvm::BasicBlock::Create(context, "after", ctx.get_current_function());
+
+        builder.SetInsertPoint(false_block);
+        llvm::Value* false_node = builder.CreateCall(malloc_node_global_func,
+                { get_int8_constant(0), ctx.get_supercombinator_function("False") }, "temp");
+        builder.CreateCall(stack_push_func, { stack, false_node });
+        builder.CreateBr(after);
+
+        builder.SetInsertPoint(true_block);
+        llvm::Value* true_node = builder.CreateCall(malloc_node_global_func,
+                { get_int8_constant(0), ctx.get_supercombinator_function("True") }, "temp");
+        builder.CreateCall(stack_push_func, { stack, true_node });
+        builder.CreateBr(after);
+
+        builder.SetInsertPoint(after);
+    }
+
     void instruction_cond::gen_llvm(llvm_context& ctx) {
         
     }
diff --git a/src/gmachine.hpp b/src/gmachine.hpp
index e37c4d7..d702ccc 100644
--- a/src/gmachine.hpp
+++ b/src/gmachine.hpp
@@ -94,6 +94,11 @@ namespace lily {
         void gen_llvm(llvm_context& ctx);
     };
 
+    struct instruction_eq : instruction {
+        std::ostream& to_stream(std::ostream& os);
+        void gen_llvm(llvm_context& ctx);
+    };
+
     struct instruction_cond : instruction {
         std::vector<instruction*> true_branch;
         std::vector<instruction*> false_branch;
diff --git a/src/parser.cpp b/src/parser.cpp
index 62f61ab..6af2e32 100644
--- a/src/parser.cpp
+++ b/src/parser.cpp
@@ -246,6 +246,13 @@ namespace lily {
         return prog;
     }
 
+    program::program() {
+        type_data* data = type_mgr.create_data_type("Bool");
+        std::vector<type*> params;
+        data->create_constructor("True", std::move(params));
+        data->create_constructor("False", std::move(params));
+    }
+
     void program::check() {
         // Each function has an environment, which will be used
         // as base for type checking.
@@ -281,6 +288,13 @@ namespace lily {
             base_env->set_type(pair.first, current_type);
         }
 
+        // Also add internal functions
+        type* eq_return_type = type_mgr.require_type("Bool");
+        type* eq_param_type = type_mgr.require_type("Int");
+        type* eq_app_1 = type_mgr.create_type<type_func>(eq_param_type, eq_return_type);
+        type* eq_app_2 = type_mgr.create_type<type_func>(eq_param_type, eq_app_1);
+        base_env->set_type("eq", eq_app_2);
+
         // We also want to gather all the constructor calls.
         type_mgr.register_constructors(base_env);
 
@@ -311,6 +325,16 @@ namespace lily {
         generate_binop<binop::subtract>(mgr, into);
         generate_binop<binop::times>(mgr, into);
         generate_binop<binop::divide>(mgr, into);
+
+        std::vector<instruction*> dest;
+        dest.push_back(mgr.add_instruction<instruction_push>(1));
+        dest.push_back(mgr.add_instruction<instruction_eval>());
+        dest.push_back(mgr.add_instruction<instruction_push>(1));
+        dest.push_back(mgr.add_instruction<instruction_eval>());
+        dest.push_back(mgr.add_instruction<instruction_eq>());
+        dest.push_back(mgr.add_instruction<instruction_update>(2));
+        dest.push_back(mgr.add_instruction<instruction_pop>(2));
+        into["eq"] = std::move(dest);
     }
 
     void program::compile(instruction_manager& mgr, std::map<std::string, std::vector<instruction*>>& into) {
diff --git a/src/parser.hpp b/src/parser.hpp
index 5f8d0d9..86b20ab 100644
--- a/src/parser.hpp
+++ b/src/parser.hpp
@@ -13,6 +13,8 @@ namespace lily {
         type_manager type_mgr;
         std::map<std::string, function> functions;
 
+        program();
+
         void check();
         void compile(instruction_manager& mgr, std::map<std::string, std::vector<instruction*>>& into);
         void gen_llvm();