feat: Add all remaining features of original Picomath PoC (#5)

Namely, a README describing the proof-of-concept,
  a custom selective loader, and some additional tests.

Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Reviewed-on: #5

README.md

@@ -1,3 +1,21 @@
 # pocomath
 
 A little proof-of-concept for organizing mathjs by module inclusion, avoiding factory functions.
+
+Note this project is package-managed by [pnpm](https://pnpm.io/). I do not expect that a clone can easily be manipulated with `npm`.
+
+Defines a class PocomathInstance to embody independent instances of a mathjs-style CAS. Basically, it keeps track of a collection of implementations (in the sense of typed-function) for each of the functions to be used in the CAS, rather than just the finalized typed-functions. It also tracks the dependencies of each implementation (which must form a directed acyclic network). When a method is requested from the instance, it assembles the proper typed-function (and caches it, of course). Whenever an implementation is added to that function name or any of its dependencies, the previously assembled typed-function is discarded, so that a new one will be constructed on its next use.
+
+Multiple different instances can coexist and have different collections of operations. Moreover, only the source files for the operations actually desired are ever visited in the import tree, so minimizing a bundle for a specific subset of operations should be quite straightforward.
+
+Hopefully the test cases, especially `test/_pocomath.mjs` and `test/custom.js`, will show off these aspects in action.
+
+Note that 'subtract' is implemented as a 'generic' operation, that depends only on the 'add' and 'negate' operations (and so doesn't care what types it is operating on).
+
+Furthermore, note that 'Complex' is implemented in a way that doesn't care about the types of the real and imaginary components, so with the 'bigint' type defined here as well, we obtain Gaussian integers for free.
+
+This core could be extended with many more operations, and more types could be defined, and additional sub-bundles like `number/all.mjs` or clever conditonal loaders like `complex/extendByComplex.mjs` could be defined.
+
+Hopefully this shows promise. It is an evolution of the concept first prototyped in [picomath](https://code.studioinfinity.org/glen/picomath). However, picomath depended on typed-function allowing mutable function entities, which turned out not to be performant. Pocomath, on the other hand, uses typed-function v3 as it stands, although it does suggest that it would be helpful to extend typed-function with subtypes, and it could even be reasonable to move the dependency tracking into typed-function itself (given that typed-function already supports self-dependencies, it would not be difficult to extend that to inter-dependencies between different typed-functions).
+
+Note the conception of Pocomath includes allowing one implementation to depend just on a specific signature of another function, for efficiency's sake (if for example 'bar(Matrix)' knows it will only call 'foo(Matrix)', it avoids another type-dispatch). That capability did not actually come up in this toy example, so it remains unimplemented, but it should and could easily be added.

complex/extendToComplex.mjs

@@ -0,0 +1,19 @@
+import './Complex.mjs'
+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
+      }
+   }
+}

test/_PocomathInstance.mjs

@@ -0,0 +1,13 @@
+import assert from 'assert'
+import PocomathInstance from '../PocomathInstance.mjs'
+
+describe('PocomathInstance', () => {
+   it('creates an instance that can define typed-functions', () => {
+      const pi = new PocomathInstance('dummy')
+      pi.install({'add': {'any,any': [[], (a,b) => a+b]}})
+      assert.strictEqual(pi.add(2,2), 4)
+      assert.strictEqual(pi.add('Kilroy', 17), 'Kilroy17')
+      assert.strictEqual(pi.add(1, undefined), NaN)
+      assert.throws(() => pi.add(1), TypeError)
+   })
+})

test/custom.mjs

@@ -3,9 +3,11 @@ import math from '../pocomath.mjs'
 import typed from 'typed-function'
 import PocomathInstance from '../PocomathInstance.mjs'
 import * as numbers from '../number/all.mjs'
+import * as numberAdd from '../number/add.mjs'
 import * as complex from '../complex/all.mjs'
 import * as complexAdd from '../complex/add.mjs'
 import * as complexNegate from '../complex/negate.mjs'
+import extendToComplex from '../complex/extendToComplex.mjs'
 
 const bw = new PocomathInstance('backwards')
 describe('A custom instance', () => {
@@ -38,4 +40,18 @@ describe('A custom instance', () => {
       assert.deepStrictEqual(
          pm.subtract({re:5, im:0}, {re:10, im:1}), {re:-5, im: -1})
    })
+
+   it("can selectively import in cute ways", async function () {
+      const cherry = new PocomathInstance('cherry')
+      cherry.install(numberAdd)
+      await extendToComplex(cherry)
+      // Now we have an instance that supports addition for number and complex
+      // and little else:
+      assert.strictEqual(cherry.add(3, 4, 2), 9)
+      assert.deepStrictEqual(
+         cherry.add(cherry.complex(3, 3), 4, cherry.complex(2, 2)),
+         math.complex(9,5))
+      assert.strictEqual('subtract' in cherry, false)
+      assert.strictEqual('negate' in cherry, false)
+   })
 })