diff --git a/schala-lang/language/src/builtin.rs b/schala-lang/language/src/builtin.rs
index e309c15..dddcb2c 100644
--- a/schala-lang/language/src/builtin.rs
+++ b/schala-lang/language/src/builtin.rs
@@ -3,30 +3,8 @@ use std::collections::HashMap;
 use std::fmt;
 
 use crate::tokenizing::TokenKind;
-use self::BuiltinTypeSpecifier::*;
-use self::BuiltinTConst::*;
-
-
-#[derive(Debug, PartialEq, Clone)]
-pub enum BuiltinTypeSpecifier {
-  Const(BuiltinTConst),
-  Func(Box<BuiltinTypeSpecifier>, Box<BuiltinTypeSpecifier>),
-}
-
-#[derive(Debug, PartialEq, Clone)]
-pub enum BuiltinTConst {
-  Nat,
-  Int,
-  Float,
-  StringT,
-  Bool,
-}
-
-impl fmt::Display for BuiltinTypeSpecifier {
-  fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-    write!(f, "{:?}", self)
-  }
-}
+use crate::typechecking::{TypeConst, Type};
+use crate::typechecking::TypeConst::*;
 
 #[derive(Debug, PartialEq, Clone)]
 pub struct BinOp {
@@ -110,36 +88,45 @@ impl PrefixOp {
   }
   */
 }
+
+//TODO make this macro exportable?
+macro_rules! mk_type {
+  ($type_name:ident) => { Type::Const(TypeConst::$type_name) };
+  ($t1:ident -> $t2:ident) => { Type::Arrow(Box::new(mk_type!($t1)), Box::new(mk_type!($t2))) };
+  ($t1:ident -> $t2:ident -> $t3:ident) => { Type::Arrow(Box::new(mk_type!($t1)), Box::new(mk_type!($t2 -> $t3))) };
+}
+
 lazy_static! {
-  static ref PREFIX_OPS: HashMap<&'static str, (BuiltinTypeSpecifier, ())> = 
+  static ref PREFIX_OPS: HashMap<&'static str, (Type, ())> = 
     hashmap! {
-      "+" => (Func(bx!(Const(Int)),  bx!(Const(Int))), ()),
-      "-" => (Func(bx!(Const(Int)),  bx!(Const(Int))), ()),
-      "!" => (Func(bx!(Const(Bool)),  bx!(Const(Bool))), ()),
+      "+" => (mk_type!(Int -> Int), ()),
+      "-" => (mk_type!(Int -> Int), ()),
+      "!" => (mk_type!(Bool -> Bool), ()),
     };
 }
 
 /* the second tuple member is a placeholder for when I want to make evaluation rules tied to the
  * binop definition */
+//TODO some of these types are going to have to be adjusted
 lazy_static! {
-  static ref BINOPS: HashMap<&'static str, (BuiltinTypeSpecifier, (), i32)> =
+  static ref BINOPS: HashMap<&'static str, (Type, (), i32)> =
     hashmap! {
-      "+" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 10),
-      "-" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 10),
-      "*" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      "/" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Float))))), (), 20),
-      "quot" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      "%" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      "++" => (Func(bx!(Const(StringT)), bx!(Func(bx!(Const(StringT)), bx!(Const(StringT))))), (), 30),
-      "^" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      "&" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      "|" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      ">" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      ">=" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      "<" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      "<=" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      "==" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      "=" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
-      "<=>" => (Func(bx!(Const(Nat)), bx!(Func(bx!(Const(Nat)), bx!(Const(Nat))))), (), 20),
+      "+" => (mk_type!(Nat -> Nat -> Nat), (), 10),
+      "-" => (mk_type!(Nat -> Nat -> Nat), (), 10),
+      "*" => (mk_type!(Nat -> Nat -> Nat), (), 20),
+      "/" => (mk_type!(Nat -> Nat -> Float), (), 20),
+      "quot" => (mk_type!(Nat -> Nat -> Nat), (), 20),
+      "%" => (mk_type!(Nat -> Nat -> Nat), (), 20),
+      "++" => (mk_type!(StringT -> StringT -> StringT), (), 30),
+      "^" => (mk_type!(Nat -> Nat -> Nat), (), 20),
+      "&" => (mk_type!(Nat -> Nat -> Nat), (), 20),
+      "|" => (mk_type!(Nat -> Nat -> Nat), (), 20),
+      ">" => (mk_type!(Nat -> Nat -> Bool), (), 20),
+      ">=" => (mk_type!(Nat -> Nat -> Bool), (), 20),
+      "<" => (mk_type!(Nat -> Nat -> Bool), (), 20),
+      "<=" => (mk_type!(Nat -> Nat -> Bool), (), 20),
+      "==" => (mk_type!(Nat -> Nat -> Bool), (), 20),
+      "=" => (mk_type!(Unit), (), 20), //TODO not sure what the type of this should be b/c special fmr
+      "<=>" => (mk_type!(Nat -> Nat -> Order), (), 20), //TODO figure out how to treat Order
     };
 }
diff --git a/schala-lang/language/src/typechecking.rs b/schala-lang/language/src/typechecking.rs
index 4c10b73..fd5787a 100644
--- a/schala-lang/language/src/typechecking.rs
+++ b/schala-lang/language/src/typechecking.rs
@@ -22,6 +22,32 @@ impl TypeError {
   }
 }
 
+#[derive(Debug)]
+pub enum Type {
+  Const(TypeConst),
+  Arrow(Box<Type>, Box<Type>)
+}
+
+#[derive(Debug)]
+pub enum TypeConst {
+  Unit,
+  Nat,
+  Int,
+  Float,
+  StringT,
+  Bool,
+  Order,
+  UserDefined
+}
+
+impl Type {
+  fn arrow(a: Type, b: Type) -> Type {
+    Type::Arrow(Box::new(a), Box::new(b))
+  }
+}
+
+
+
 /*
 /// `Type` is parameterized by whether the type variables can be just universal, or universal or
 /// existential.