diff --git a/index.d.ts b/index.d.ts
index 577d835..4767b58 100644
--- a/index.d.ts
+++ b/index.d.ts
@@ -342,6 +342,8 @@ export function prodType(typeParam: any): any;
 
 export function recomputeTypeVars(types: any, skip: number): any;
 
+export function recomputeTypeVarsWithInverse(types: any, skip: number): [any, Map<string, string>];
+
 export function setType(typeParam: any): any;
 
 export function structType(fields: any, rootSelf: any): any;
diff --git a/lib/generics/generics.js b/lib/generics/generics.js
index 0f984e3..71ef01a 100644
--- a/lib/generics/generics.js
+++ b/lib/generics/generics.js
@@ -93,16 +93,22 @@ export const assignFn = (funType, paramType, skip=0) => {
 
 // Ensures that no type variables overlap
 export const recomputeTypeVars = (types, skip=0) => {
+  return recomputeTypeVarsWithInverse(types, skip)[0];
+};
+
+export const recomputeTypeVarsWithInverse = (types, skip=0) => {
   let nextIdx = skip;
-  return types.map(type => {
+  const inverse = new Map();
+  return [types.map(type => {
       const substitutions = new Map();
       const typeVars = occurring(type);
       for (const typeVar of typeVars) {
         const idx = nextIdx++;
         if (typeVar !== UNBOUND_SYMBOLS[idx]) {
           substitutions.set(typeVar, TYPE_VARS[idx]);
+          inverse.set(UNBOUND_SYMBOLS[idx], typeVar);
         }
       }
       return substitute(type, substitutions);
-    });
-};
+    }), inverse];
+}
\ No newline at end of file