fix: Separate typed instance for each PocomathInstance (#15)

Also starts each PocomathInstance with no types at all, and uses the new
  situation to eliminate the need for a Complex "base case".

  Resolves #14.
  Resolves #13.

Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Reviewed-on: #15

src/complex/Types/Complex.mjs

@@ -0,0 +1,20 @@
+/* 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
+}
+
+export const Types = {
+   Complex: {
+      test: isComplex,
+      number: x => ({re: x, im: 0}),
+      bigint: 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'
+}

src/complex/add.mjs

@@ -0,0 +1,10 @@
+export {Types} from './Types/Complex.mjs'
+
+export const add = {
+   '...Complex': [['self'], ref => addends => {
+      if (addends.length === 0) return {re:0, im:0}
+      const seed = addends.shift()
+      return addends.reduce((w,z) =>
+         ({re: ref.self(w.re, z.re), im: ref.self(w.im, z.im)}), seed)
+   }]
+}

src/complex/all.mjs

@@ -0,0 +1,5 @@
+export {Types} from './Types/Complex.mjs'
+export {complex} from './complex.mjs'
+export {add} from './add.mjs'
+export {negate} from './negate.mjs'
+export {subtract} from '../generic/subtract.mjs'

src/complex/complex.mjs

@@ -0,0 +1,11 @@
+export {Types} from './Types/Complex.mjs'
+
+export const complex = {
+   /* 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]
+}

src/complex/extendToComplex.mjs

@@ -0,0 +1,18 @@
+import * as complex from './complex.mjs'
+
+/* Add all the complex implementations for functions already
+   in the instance:
+*/
+
+export default async function extendToComplex(pmath) {
+   pmath.install(complex)
+   for (const name in pmath._imps) {
+      const modulePath = `./${name}.mjs`
+      try {
+         const mod = await import(modulePath)
+         pmath.install(mod)
+      } catch (err) {
+         // Guess it wasn't a method available in complex; no worries
+      }
+   }
+}

src/complex/negate.mjs

@@ -0,0 +1,7 @@
+export {Types} from './Types/Complex.mjs'
+
+export const negate = {
+   Complex: [['self'], ref => z => {
+      return {re: ref.self(z.re), im: ref.self(z.im)}
+   }]
+}