src/bigint/add.mjs

@@ -1,5 +1,3 @@
 export * from './Types/bigint.mjs'
 
-export const add = {
-   '...bigint': () => addends => addends.reduce((x,y) => x+y, 0n)
-}
+export const add = {'bigint,bigint': () => (a,b) => a+b}

src/complex/add.mjs

@@ -1,10 +1,12 @@
 export * from './Types/Complex.mjs'
 
 export const add = {
-   '...Complex': ({self}) => addends => {
-      if (addends.length === 0) return {re:0, im:0}
-      const seed = addends.shift()
-      return addends.reduce(
-         (w,z) => ({re: self(w.re, z.re), im: self(w.im, z.im)}), seed)
-   }
+   'Complex,number': ({
+      'self(number,number)': addNum,
+      'complex(any,any)': cplx
+   }) => (z,x) => cplx(addNum(z.re, x), z.im),
+   'Complex,Complex': ({
+      self,
+      'complex(any,any)': cplx
+   }) => (w,z) => cplx(self(w.re, z.re), self(w.im, z.im))
 }

src/core/PocomathInstance.mjs

@@ -443,7 +443,26 @@ export default class PocomathInstance {
          for (const instType of behavior.instantiations) {
             const signature =
                   substituteInSig(rawSignature, theTemplateParam, instType)
-            this._addTFimplementation(tf_imps, signature, behavior, instType)
+            const uses = new Set()
+            for (const dep of behavior.uses) {
+               if (this._templateParam(dep)) continue
+               uses.add(substituteInSig(dep, theTemplateParam, instType))
+            }
+            const patch = (refs) => {
+               const innerRefs = {}
+               for (const dep of behavior.uses) {
+                  if (this._templateParam(dep)) {
+                     innerRefs[dep] = instType
+                  } else {
+                     const outerName = substituteInSig(
+                        dep, theTemplateParam, instType)
+                     innerRefs[dep] = refs[outerName]
+                  }
+               }
+               const original = behavior.does(innerRefs)
+               return behavior.does(innerRefs)
+            }
+            this._addTFimplementation(tf_imps, signature, {uses, does: patch})
          }
          /* Now add the catchall signature */
          const signature = substituteInSig(rawSignature, theTemplateParam, 'any')
@@ -464,13 +483,21 @@ export default class PocomathInstance {
                `Cannot find template parameter in ${rawSignature}`)
          }
          const self = this
-         const patch = (refs) => {
-            const original = behavior.does(refs)
-            return (...args) => {
+         const patch = (refs) => (...args) => {
             const example = args[exemplar]
-               console.log('Have to match template to', example)
-               return original(...args)
+            const instantiateFor = self.typeOf(example)
+            refs[theTemplateParam] = instantiateFor
+            const instCount = behavior.instantiations.size
+            for (const earlier of self._priorTypes[instantiateFor]) {
+               behavior.instantiations.add(earlier)
             }
+            behavior.instantiations.add(instantiateFor)
+            if (behavior.instantiations.size > instCount) {
+               self._invalidate(name)
+            }
+            // And for now, we have to rely on the "any" implementation. Hope
+            // it matches the instantiated one!
+            return behavior.does(refs)(...args)
          }
          this._addTFimplementation(
             tf_imps, signature, {uses: behavior.uses, does: patch})
@@ -484,7 +511,7 @@ export default class PocomathInstance {
     * to typed-function implementations and inserts the result into plain object
     * imps
     */
-   _addTFimplementation(imps, signature, behavior, instType) {
+   _addTFimplementation(imps, signature, behavior) {
       const {uses, does} = behavior
       if (uses.length === 0) {
          imps[signature] = does()

src/generic/arithmetic.mjs

@@ -1,8 +1,11 @@
+import {reducingOperation} from './reducingOperation.mjs'
+
 export * from './Types/generic.mjs'
 
+export const add = reducingOperation
 export {lcm} from './lcm.mjs'
 export {mod} from './mod.mjs'
-export {multiply} from './multiply.mjs'
+export const multiply = reducingOperation
 export {divide} from './divide.mjs'
 export {sign} from './sign.mjs'
 export {sqrt} from './sqrt.mjs'

src/generic/reducingOperation.mjs

@@ -0,0 +1,12 @@
+export * from './Types/generic.mjs'
+
+export const reducingOperation = {
+   'undefined': () => u => u,
+   'undefined,...any': () => (u, rest) => u,
+   'any,undefined': () => (x, u) => u,
+   any: () => x => x,
+   'any,any,...any': ({
+      self
+   }) => (a,b,rest) => [b, ...rest].reduce((x,y) => self(x,y), a)
+}
+

src/generic/subtract.mjs

@@ -1,3 +1,3 @@
 export const subtract = {
-   'T,T': ({'add(T)': addT, 'negate(T)': negT}) => (x,y) => addT(x, negT(y))
+   'T,T': ({'add(T,T)': addT, 'negate(T)': negT}) => (x,y) => addT(x, negT(y))
 }

src/number/add.mjs

@@ -1,5 +1,3 @@
 export * from './Types/number.mjs'
 
-export const add = {
-   '...number': () => addends => addends.reduce((x,y) => x+y, 0),
-}
+export const add = {'number,number': () => (m,n) => m+n}

test/_pocomath.mjs

@@ -21,12 +21,14 @@ describe('The default full pocomath instance "math"', () => {
 
    it('can subtract numbers', () => {
       assert.strictEqual(math.subtract(12, 5), 7)
+      //assert.strictEqual(math.subtract(3n, 1.5), 1.5)
    })
 
    it('can add numbers', () => {
       assert.strictEqual(math.add(3, 4), 7)
       assert.strictEqual(math.add(1.5, 2.5, 3.5), 7.5)
       assert.strictEqual(math.add(Infinity), Infinity)
+      assert.throws(() => math.add(3n, -1.5), TypeError)
    })
 
    it('can negate numbers', () => {
@@ -55,10 +57,10 @@ describe('The default full pocomath instance "math"', () => {
       assert.deepStrictEqual(
          math.subtract(math.complex(1,1), math.complex(2,-2)),
          math.complex(-1,3))
+      assert.strictEqual(math.negate(math.complex(3, 8)).im, -8)
       assert.deepStrictEqual(
          math.subtract(16, math.add(3, math.complex(0,4), 2)),
          math.complex(11, -4))
-      assert.strictEqual(math.negate(math.complex(3, 8)).im, -8)
    })
 
    it('handles bigints', () => {

test/custom.mjs

@@ -3,6 +3,7 @@ import math from '../src/pocomath.mjs'
 import PocomathInstance from '../src/core/PocomathInstance.mjs'
 import * as numbers from '../src/number/all.mjs'
 import * as numberAdd from '../src/number/add.mjs'
+import {add as genericAdd} from '../src/generic/arithmetic.mjs'
 import * as complex from '../src/complex/all.mjs'
 import * as complexAdd from '../src/complex/add.mjs'
 import * as complexNegate from '../src/complex/negate.mjs'
@@ -66,6 +67,7 @@ describe('A custom instance', () => {
       const cherry = new PocomathInstance('cherry')
       cherry.install(numberAdd)
       await extendToComplex(cherry)
+      cherry.install({add: genericAdd})
       /* Now we have an instance that supports addition for number and complex
          and little else:
       */