diff --git a/compare/primitives.js b/compare/primitives.js
index e4b7088..d5e2638 100644
--- a/compare/primitives.js
+++ b/compare/primitives.js
@@ -1,7 +1,5 @@
 // Total ordering of primitive types
 
-import { getSymbol } from "../type_constructor.js";
-
 export const compareNumbers = x => y => {
   if (typeof(x) !== 'number' || typeof(y) !== 'number') {
     throw new Error(`was only meant to compare numbers! got ${x} and ${y}`);
@@ -26,12 +24,6 @@ export const compareBools = x => y => {
 // The Unit-type has only one instance, which is equal to itself:
 export const compareUnits = x => y => 0;
 
-export const compareTypes = x => y => {
-  return compareSymbols(getSymbol(x))(getSymbol(y))
-    || compareNumbers(x.params.length)(y.params.length)
-    || x.params.reduce((acc, _, i) => acc || compareTypes(x.params[i])(y.params[i]), 0)
-}
-
 // Note: dirty assumption that every symbol has unique description.
 // This will be fixed once we move from symbols to real UUIDs.
 export const compareSymbols = a => b => (a !== b) && compareStrings(a.description)(b.description);
diff --git a/compare/registry.js b/compare/registry.js
index c7156ff..9852e01 100644
--- a/compare/registry.js
+++ b/compare/registry.js
@@ -1,7 +1,8 @@
-import { SymbolBool, SymbolChar, SymbolDouble, SymbolInt, SymbolUnit } from "../primitives/types.js";
+import { SymbolBool, SymbolChar, SymbolDouble, SymbolInt, SymbolType, SymbolUnit } from "../primitives/types.js";
 import { symbolList, symbolProduct, symbolSet, symbolSum } from "../structures/types.js";
 import { compareBools, compareNumbers, compareStrings, compareUnits } from "./primitives.js";
 import { compareLists, compareProducts, compareSets, compareSums } from "./structures.js";
+import { compareTypes } from "./type.js";
 
 const typeSymbolToCmp = new Map([
   [SymbolInt   , compareNumbers],
@@ -9,6 +10,7 @@ const typeSymbolToCmp = new Map([
   [SymbolDouble, compareNumbers],
   [SymbolBool  , compareBools],
   [SymbolUnit  , compareUnits],
+  [SymbolType  , compareTypes],
 
   // these functions take extra comparison callbacks:
   [symbolList   , compareLists],
diff --git a/compare/type.js b/compare/type.js
new file mode 100644
index 0000000..a91f841
--- /dev/null
+++ b/compare/type.js
@@ -0,0 +1,7 @@
+import { getParams, getSymbol } from "../type_constructor.js";
+import { compareSymbols } from "./primitives.js";
+import { compareLists } from "./structures.js";
+
+export const compareTypes = x => y =>
+  compareSymbols(getSymbol(x))(getSymbol(y))
+    || compareLists(compareTypes)(getParams(x))(getParams(y));