feat: Allow self-reference in implementations (#4)

This PR also uses such self-reference to define negate and add
  for Complex numbers in a way that is independent of component types.

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

  Ensures that if one function is invalidated, then any that depend on it will be.

Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Reviewed-on: #4

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 +1,8 @@
+import {numComplex} from './Complex.mjs'
+export const negate = {
+   /* need a "base case" to avoid infinite self-reference */
+   Complex: [['self'], ref => z => {
+      if (numComplex(z)) return {re: -z.re, im: -z.im}
+      return {re: ref.self(z.re), im: ref.self(z.im)}
+   }]
+}