feat: Allow self-reference in implementations

And use it to define negate and add for Complex numbers in a way that
  is independent of component types.

  Also add a bigint type and verify that pocomath will then handle Gaussian
  integers "for free".

PocomathInstance.mjs

@@ -41,7 +41,7 @@ export default class PocomathInstance {
       const opImps = this._imps[name]
       for (const signature in implementations) {
          if (signature in opImps) {
-            if (implemenatations[signature] === opImps[signature]) continue
+            if (implementations[signature] === opImps[signature]) continue
             throw new SyntaxError(
                `Conflicting definitions of ${signature} for ${name}`)
          } else {
@@ -80,18 +80,26 @@ export default class PocomathInstance {
             tf_imps[signature] = imp
          } else {
             const refs = {}
+            let self_referential = false
             for (const dep of deps) {
-               // TODO: handle self dependencies
-               if (dep.slice(0,4) === 'self') {
-                  throw new Error('self-reference unimplemented')
-               }
                // TODO: handle signature-specific dependencies
                if (dep.includes('(')) {
                   throw new Error('signature specific reference unimplemented')
                }
-               refs[dep] = this._ensureBundle(dep) // just assume acyclic for now
+               if (dep === 'self') {
+                  self_referential = true
+               } else {
+                  refs[dep] = this._ensureBundle(dep) // assume acyclic for now
+               }
+            }
+            if (self_referential) {
+               tf_imps[signature] = typed.referToSelf(self => {
+                  refs.self = self
+                  return imp(refs)
+               })
+            } else {
+               tf_imps[signature] = imp(refs)
             }
-            tf_imps[signature] = imp(refs)
          }
       }
       const tf = typed(name, tf_imps)

bigint/BigInt.mjs

@@ -0,0 +1,3 @@
+import typed from 'typed-function'
+
+typed.addType({name: 'bigint', test: b => typeof b === 'bigint'})

bigint/add.mjs

@@ -0,0 +1,4 @@
+import './BigInt.mjs'
+export const add = {
+   '...bigint': [[], addends => addends.reduce((x,y) => x+y, 0n)],
+}

bigint/all.mjs

@@ -0,0 +1,3 @@
+export {add} from './add.mjs'
+export {negate} from './negate.mjs'
+export {subtract} from '../generic/subtract.mjs'

bigint/negate.mjs

@@ -0,0 +1,2 @@
+import './BigInt.mjs'
+export const negate = {bigint: [[], b => -b ]}

complex/Complex.mjs

@@ -1,14 +1,29 @@
 import typed from 'typed-function'
 
-/* Use a plain object with keys re and im for a complex */
-typed.addType({
-   name: 'Complex',
-   test: z => z && typeof z === 'object' && 're' in z && 'im' in z
-})
+/* Use a plain object with keys re and im for a complex; note the components
+ * can be any type (for this proof-of-concept; in reality we'd want to
+ * insist on some numeric or scalar supertype).
+ */
+export function isComplex(z) { 
+   return z && typeof z === 'object' && 're' in z && 'im' in z
+}
 
+typed.addType({name: 'Complex', test: isComplex})
 typed.addConversion({
    from: 'number',
    to: 'Complex',
    convert: x => ({re: x, im: 0})
 })
+/* Pleasantly enough, it is OK to add this conversion even if there is no
+ * type 'bigint' defined, so everything should Just Work.
+ */
+typed.addConversion({
+   from: 'bigint',
+   to: 'Complex',
+   convert: x => ({re: x, im: 0n})
+})
 
+/* test if an entity is Complex<number>, so to speak: */
+export function numComplex(z) {
+   return isComplex(z) && typeof z.re === 'number' && typeof z.im === 'number'
+}

complex/add.mjs

@@ -1,12 +1,15 @@
-import './Complex.mjs'
+import {numComplex} from './Complex.mjs'
 
 export const add = {
-   '...Complex': [[], addends => {
-      const sum = {re: 0, im: 0}
-      addends.forEach(addend => {
-         sum.re += addend.re
-         sum.im += addend.im
-      })
-      return sum
+   '...Complex': [['self'], ref => addends => {
+      if (addends.length === 0) return {re:0, im:0}
+      const seed = addends.shift()
+      return addends.reduce((w,z) => {
+         /* Need a "base case" to avoid infinite self-reference loops */
+         if (numComplex(z) && numComplex(w)) {
+            return {re: w.re + z.re, im: w.im + z.im}
+         }
+         return {re: ref.self(w.re, z.re), im: ref.self(w.im, z.im)}
+      }, seed)
    }]
 }

complex/all.mjs

@@ -1,2 +1,4 @@
 export {complex} from './complex.mjs'
 export {add} from './add.mjs'
+export {negate} from './negate.mjs'
+export {subtract} from '../generic/subtract.mjs'

complex/complex.mjs

@@ -1,6 +1,11 @@
 import './Complex.mjs'
 
 export const complex = {
-   'number, number': [[], (x, y) => ({re: x, im: y})],
+   /* Very permissive for sake of proof-of-concept; would be better to
+    * have a numeric/scalar type, e.g. by implementing subtypes in
+    * typed-function
+    */
+   'any, any': [[], (x, y) => ({re: x, im: y})],
+   /* Take advantage of conversions in typed-function */
    Complex: [[], z => z]
 }

complex/negate.mjs

@@ -0,0 +1,4 @@
+import './Complex.mjs'
+export const negate = {
+   Complex: [['self'], ref => z => ({re: ref.self(z.re), im: ref.self(z.im)})]
+}

pocomath.mjs

@@ -1,10 +1,12 @@
 /* Core of pocomath: generates the default instance */
 import PocomathInstance from './PocomathInstance.mjs'
 import * as numbers from './number/all.mjs'
+import * as bigints from './bigint/all.mjs'
 import * as complex from './complex/all.mjs'
 
 const math = new PocomathInstance('math')
 math.install(numbers)
+math.install(bigints)
 math.install(complex)
 
 export default math

test/_pocomath.mjs

@@ -29,5 +29,27 @@ describe('The default full pocomath instance "math"', () => {
       assert.deepStrictEqual(math.complex(2,3), norm13)
       assert.deepStrictEqual(math.complex(2), math.complex(2,0))
       assert.deepStrictEqual(math.add(2, math.complex(0,3)), norm13)
+      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', () => {
+      assert.strictEqual(math.negate(5n), -5n)
+      assert.strictEqual(math.subtract(12n, 5n), 7n)
+      assert.strictEqual(math.add(15n, 25n, 35n), 75n)
+      assert.strictEqual(math.add(10n, math.negate(3n)), 7n)
+   })
+
+   it('handles Gaussian integers', () => {
+      const norm13n = {re: 2n, im: 3n}
+      assert.deepStrictEqual(math.complex(2n,3n), norm13n)
+      assert.deepStrictEqual(math.complex(2n), math.complex(2n, 0n))
+      assert.deepStrictEqual(math.add(2n, math.complex(0n, 3n)), norm13n)
+      assert.deepStrictEqual(
+         math.subtract(16n, math.add(3n, math.complex(0n,4n), 2n)),
+         math.complex(11n, -4n))
+      assert.strictEqual(math.negate(math.complex(3n, 8n)).im, -8n)
    })
 })

test/custom.mjs

@@ -1,4 +1,5 @@
 import assert from 'assert'
+import math from '../pocomath.mjs'
 import typed from 'typed-function'
 import PocomathInstance from '../PocomathInstance.mjs'
 import * as numbers from '../number/all.mjs'
@@ -17,5 +18,9 @@ describe('A custom instance', () => {
       assert.strictEqual(bw.subtract(16, bw.add(3,4,2)), 7)
       assert.strictEqual(bw.negate('8'), -8)
       assert.deepStrictEqual(bw.add(bw.complex(1,3), 1), {re: 2, im: 3})
+      assert.deepStrictEqual(
+         bw.subtract(16, bw.add(3, bw.complex(0,4), 2)),
+         math.complex(11, -4)) // note both instances coexist
+      assert.deepStrictEqual(bw.negate(math.complex(3, '8')).im, -8)
    })
 })