diff --git a/interfaces/serializable.js b/interfaces/serializable.js
index 1c1d2f7..abac7f6 100644
--- a/interfaces/serializable.js
+++ b/interfaces/serializable.js
@@ -1,10 +1,10 @@
-import { fnType, getListType } from "../type_registry.js";
+import { fnType, lsType } from "../type_registry.js";
 import {Type, Function} from "../metacircular.js";
 import { Byte } from "../primitives/symbols.js";
 
 export const Serializable = Symbol('Serializable');
 
-const ListOfByte = getListType(Byte);
+const ListOfByte = lsType(Byte);
 
 const   serializeFnType = fnType({in: Serializable, out: ListOfByte});
 const deserializeFnType = fnType({in: ListOfByte, out: Serializable});
diff --git a/lib/values.js b/lib/values.js
index ec46389..ea9df41 100644
--- a/lib/values.js
+++ b/lib/values.js
@@ -2,15 +2,15 @@ import {Int, Bool, Double, Byte} from "../primitives/symbols.js";
 import { makeListModule } from "../structures/list_common.js";
 import { makeProductType } from "../structures/product.js";
 import { makeSumType } from "../structures/sum.js";
-import { getListType, prodType, sumType } from "../type_registry.js";
+import { lsType, prodType, sumType } from "../type_registry.js";
 
-const ListOfDouble = getListType(Double);
+const ListOfDouble = lsType(Double);
 const ListOfDoubleModule = makeListModule(Double);
 
-const ListOfListOfDouble = getListType(ListOfDouble);
+const ListOfListOfDouble = lsType(ListOfDouble);
 const ListOfListOfDoubleModule = makeListModule(ListOfDouble);
 
-const ListOfByte = getListType(Byte);
+const ListOfByte = lsType(Byte);
 const ListOfByteModule = makeListModule(Byte);
 
 export const ModuleValues = [
diff --git a/structures/list.js b/structures/list.js
index b2f528a..f1d5e9c 100644
--- a/structures/list.js
+++ b/structures/list.js
@@ -1,4 +1,4 @@
-import { fnType, getListType } from "../type_registry.js";
+import { fnType, lsType } from "../type_registry.js";
 import {Type, Function} from "../metacircular.js";
 import { makeListModule } from "./list_common.js";
 import { Module } from "./module.js";
@@ -7,7 +7,7 @@ const Type_to_Type = fnType({in: Type, out: Type});
 const Type_to_Module = fnType({in: Type, out: Module});
 
 export const ModuleList = [
-  {i: getListType   , t: Type_to_Type},
+  {i: lsType        , t: Type_to_Type},
   {i: Type_to_Type  , t: Function},
 
   {i: makeListModule, t: Type_to_Module},
diff --git a/structures/list_common.js b/structures/list_common.js
index fe8762a..f1dbc45 100644
--- a/structures/list_common.js
+++ b/structures/list_common.js
@@ -1,4 +1,4 @@
-import { fnType, getListType } from "../type_registry.js";
+import { fnType, lsType } from "../type_registry.js";
 import {Type, Function} from "../metacircular.js";
 import {Int, Byte} from "../primitives/symbols.js";
 
@@ -22,7 +22,7 @@ const byteListImpl = {
 export const makeListModule = elementType => {
   // List<elementType> type depends on elementType
   // generating it another time, will give the same type (structurally equivalent):
-  const ListOfElement = getListType(elementType);
+  const ListOfElement = lsType(elementType);
 
   const getFnType1 = fnType({in: Int          , out: elementType});
   const getFnType  = fnType({in: ListOfElement, out: getFnType1});
diff --git a/structures/module.js b/structures/module.js
index 5f1e6ac..528206f 100644
--- a/structures/module.js
+++ b/structures/module.js
@@ -1,7 +1,7 @@
 import { makeListModule } from "./list_common.js";
 import { Typed } from "../typed.js";
-import { getListType } from "../type_registry.js";
+import { lsType } from "../type_registry.js";
 
-export const Module = getListType(Typed); // a Module is a list of Typeds
+export const Module = lsType(Typed); // a Module is a list of Typeds
 
 export const ModuleModule = makeListModule(Typed); // the module containing operations on Module
diff --git a/structures/product.js b/structures/product.js
index 9814a06..9dfec02 100644
--- a/structures/product.js
+++ b/structures/product.js
@@ -1,5 +1,5 @@
 import { fnType, prodType } from "../type_registry.js";
-import { Function } from "../metacircular.js";
+import { Function, Type } from "../metacircular.js";
 
 // In JS, all products are encoded in the same way:
 const constructor = left => right => ({left, right});
@@ -8,15 +8,17 @@ const getRight    = product => product.right;
 
 // Given two types A and B, create the type (A × B).
 export const makeProductType = (leftType, rightType) => {
-  const productType = prodType(leftType, rightType);
+  const pType = prodType(leftType, rightType);
 
-  const leftFnType  = fnType({in: productType, out: leftType});
-  const rightFnType = fnType({in: productType, out: rightType});
+  const leftFnType  = fnType({in: pType, out: leftType});
+  const rightFnType = fnType({in: pType, out: rightType});
 
-  const constructorBoundType = fnType({in: rightType, out: productType});
+  const constructorBoundType = fnType({in: rightType, out: pType});
   const constructorType      = fnType({in: leftType , out: constructorBoundType});
 
   return [
+    {i: pType, t: Type},
+
     {i: getLeft    , t: leftFnType},
     {i: getRight   , t: rightFnType},
     {i: leftFnType , t: Function},
diff --git a/structures/sum.js b/structures/sum.js
index 85bbf27..8d38982 100644
--- a/structures/sum.js
+++ b/structures/sum.js
@@ -5,6 +5,8 @@ import { Module } from "./module.js";
 const constructorLeft  = left  => ({variant: "L", value: left });
 const constructorRight = right => ({variant: "R", value: right});
 
+// signature:
+//   sum-type -> (leftType -> resultType, rightType -> resultType) -> resultType
 const match = sum => handlers => sum.variant === "L"
   ? handlers.left(sum.value)
   : handlers.right(sum.value);
@@ -31,6 +33,7 @@ export const makeSumType = (leftType, rightType) => {
   };
 
   return [
+    {i: sType               , t: Type},
     {i: constructorLeft     , t: constructorLeftType},
     {i: constructorRight    , t: constructorRightType},
     {i: constructorLeftType , t: Function},
diff --git a/type_registry.js b/type_registry.js
index dbc0ec8..2d6b880 100644
--- a/type_registry.js
+++ b/type_registry.js
@@ -20,14 +20,16 @@ export const fnType = ({in: inType, out: outType}) => {
 
 // Global store of list types:
 const listTypes = new Map();
-export function getListType(elementType) {
+export const lsType = (elementType) => {
   if (listTypes.has(elementType)) {
     // only generate each list type once
     // this would not be necessary if we could define our own equality and hash functions on objects in JavaScript.
     return listTypes.get(elementType);
   }
   else {
-    const type = Symbol('ListOf:' + elementType.toString());
+    const type = {
+      listOf: elementType,
+    };
     listTypes.set(elementType, type);
     return type;
   }