diff --git a/generic/subtract.js b/generic/subtract.js
index 236885c..c64c15b 100644
--- a/generic/subtract.js
+++ b/generic/subtract.js
@@ -1,9 +1,9 @@
 export default function create(pmath) {
    const add = pmath('add')
    const negate = pmath('negate')
-   if (!pmath.subtract) { // avoid double definition at cost of extensibility
-      pmath('subtract', [args => args.length === 2,
-         (x, y) => add(x, negate(y))])
-   }
+   return pmath(
+      'subtract',
+      [args => args.length === 2, (x, y) => add(x, negate(y))],
+      create)
    return pmath.subtract
 }
diff --git a/picomathInstance.js b/picomathInstance.js
index 04afd13..0eed730 100644
--- a/picomathInstance.js
+++ b/picomathInstance.js
@@ -6,11 +6,11 @@ export default function picomathInstance (instName) {
      * as a function, it takes a name and 0 or more implementations add adds
      * them to its poortf property named name, returning that property value.
      */
-    function fn (name, imps) {
+    function fn (name, imps, author) {
         if (name in fn) {
-            fn[name].addImps(imps)
+            fn[name].addImps(imps, author)
         } else {
-            fn[name] = poortf(name, imps)
+            fn[name] = poortf(name, imps, author)
         }
         return fn[name]
     }
diff --git a/poortf.js b/poortf.js
index 0b212d7..afbb9dc 100644
--- a/poortf.js
+++ b/poortf.js
@@ -1,13 +1,29 @@
 /* Totally minimal "typed functions" */
 
-const addImps = (dest, imps) => {
+/* helper: dest is really a TF and imps is either nothing, an imp, or
+ * an array of implementations. author is the entity responsible for these
+ * implementations.
+ */
+const addImps = (dest, imps, author) => {
    if (imps) {
       if (!Array.isArray(imps[0])) imps = [imps]
-      for (const imp of imps) dest.push(imp)
+      if (author) {
+         if (dest.authors.has(author)) {
+            const [count, index] = dest.authors.get(author)
+            if (count) dest.imps.splice(index, count)
+         }
+         dest.authors.set(author, [imps.length, dest.imps.length])
+      }
+      for (const imp of imps) dest.imps.push(imp)
    }
 }
-
-export default function poortf (name, imps) {
+/* Create a TF, optionally adding some initial imps and further optionally
+ * registering them to an author. There are two advantages to author
+ * registration: (1) if the same author adds implementations, the prior imps
+ * will be deleted, and (2) the author can be invalidated, and the TF will
+ * lazily call the author back the next time it is called to re-add the imps.
+ */
+export default function poortf (name, imps, author) {
    /* This is the (function) object we will return */
    function fn () {
       for (const imp of fn.imps) {
@@ -20,8 +36,9 @@ export default function poortf (name, imps) {
    /* Now dress it up for use */
    Object.defineProperty(fn, 'name', {value: name})
    fn.imps = []
-   addImps(fn.imps, imps)
-   fn.addImps = newI => addImps(fn.imps, newI)
+   fn.authors = new Map() // tracks who made each implementation
+   addImps(fn, imps, author)
+   fn.addImps = (newI, author) => addImps(fn, newI, author)
 
    return fn
 }
diff --git a/test/_picomath.js b/test/_picomath.js
index 84ff19b..d0126e7 100644
--- a/test/_picomath.js
+++ b/test/_picomath.js
@@ -20,4 +20,8 @@ describe('The default full picomath instance "math"', () => {
          math.complex(11, -4))
       assert.deepStrictEqual(math.negate(math.complex(3, '8')).im, -8)
    })
+
+   it('does not double-define subtract', () => {
+      assert.deepStrictEqual(math.subtract.imps.length, 1)
+   })
 })