README.md

@@ -16,6 +16,10 @@ Furthermore, note that 'Complex' is implemented in a way that doesn't care about
 
 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 conditional loaders like `complex/extendToComplex.mjs` could be defined.
 
+Also see the comments for the public member functions of
+`core/PocomathInstance.mjs` for further details on the structure and API of this
+scheme for organizing a CAS.
+
 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.

src/bigint/add.mjs

@@ -1,5 +1,6 @@
+import {use} from '../core/PocomathInstance.mjs'
 export {Types} from './Types/bigint.mjs'
 
 export const add = {
-   '...bigint': [[], addends => addends.reduce((x,y) => x+y, 0n)],
+   '...bigint': use([], addends => addends.reduce((x,y) => x+y, 0n))
 }

src/bigint/negate.mjs

@@ -1,3 +1,4 @@
+import {use} from '../core/PocomathInstance.mjs'
 export {Types} from './Types/bigint.mjs'
 
-export const negate = {bigint: [[], b => -b ]}
+export const negate = {bigint: use([], b => -b)}

src/complex/add.mjs

@@ -1,10 +1,13 @@
 export {Types} from './Types/Complex.mjs'
 
 export const add = {
-   '...Complex': [['self'], ref => addends => {
+   '...Complex': {
+      uses: ['self'],
+      does: 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/complex.mjs

@@ -5,7 +5,7 @@ export const complex = {
     * have a numeric/scalar type, e.g. by implementing subtypes in
     * typed-function
     */
-   'any, any': [[], (x, y) => ({re: x, im: y})],
+   'any, any': {does: (x, y) => ({re: x, im: y})},
    /* Take advantage of conversions in typed-function */
-   Complex: [[], z => z]
+   Complex: {does: z => z}
 }

src/complex/negate.mjs

@@ -1,7 +1,10 @@
 export {Types} from './Types/Complex.mjs'
 
 export const negate = {
-   Complex: [['self'], ref => z => {
+   Complex: {
+      uses: ['self'],
+      does: ref => z => {
          return {re: ref.self(z.re), im: ref.self(z.im)}
-   }]
+      }
+   }
 }

src/core/PocomathInstance.mjs

@@ -1,6 +1,10 @@
 /* Core of pocomath: create an instance */
 import typed from 'typed-function'
 
+export function use(dependencies, implementation) {
+   return [dependencies, implementation]
+}
+
 export default class PocomathInstance {
    /* Disallowed names for ops; beware, this is slightly non-DRY
     * in that if a new top-level PocomathInstance method is added, its name
@@ -24,15 +28,16 @@ export default class PocomathInstance {
     * @param {Object<string, Object<Signature, [string[], function]>>} ops
     *    The only parameter ops gives the semantics of the operations to install.
     *    The keys are operation names. The value for a key is an object
-    *    mapping (typed-function) signature strings to pairs of dependency
+    *    mapping (typed-function) signature strings to specifications of
-    *    lists and implementation functions.
+    *    of dependency lists and implementation functions.
     *
     *    A dependency list is a list of strings. Each string can either be the
     *    name of a function that the corresponding implementation has to call,
     *    or a specification of a particular signature of a function that it has
-    *    to call, in the form 'FN(SIGNATURE)'. Note the function name can be
+    *    to call, in the form 'FN(SIGNATURE)' [not implemented yet].
-    *    the special value 'self' to indicate a recursive call to the given
+    *    Note the function name can be the special value 'self' to indicate a
-    *    operation (either with or without a particular signature.
+    *    recursive call to the given operation (either with or without a
+    *    particular signature.
     *
     *    There are two cases for the implementation function. If the dependency
     *    list is empty, it should be a function taking the arguments specified
@@ -41,6 +46,30 @@ export default class PocomathInstance {
     *    requested functions as values, to a function taking the arguments
     *    specified by the signature and returning the value.
     *
+    *    There are various specifications currently allowed for the
+    *    dependency list and implementation function:
+    *
+    *    1) Just a function. Then the dependency list is assumed to be empty.
+    *
+    *    2) A pair (= Array with two entries) of a dependency list and the
+    *        implementation function.
+    *
+    *    3) An object whose property named 'does' gives the implementation
+    *        function and whose property named 'uses', if present, gives the
+    *        dependency list (which is assumed to be empty if the property is
+    *        not present).
+    *
+    *    4) A call to the 'use' function exported from the this module, with
+    *        first argument the dependencies and second argument the
+    *        implementation.
+    *
+    *    For a visual comparison of the options, this proof-of-concept uses
+    *    option (1) when possible for the 'number' type, (3) for the 'Complex'
+    *    type, (4) for the 'bigint' type, and (2) under any other circumstances.
+    *    Likely a fleshed-out version of this scheme would settle on just one
+    *    or two of these options or variants thereof, rather than providing so
+    *    many different ones.
+    *
     *    Note that the "operation" named `Types` is special: it gives
     *    types that must be installed in the instance. In this case, the keys
     *    are type names, and the values are objects with a property 'test'
@@ -66,7 +95,12 @@ export default class PocomathInstance {
          for (const func in this._imps) {
             if (func === 'Types') continue
             for (const definition of Object.values(this._imps[func])) {
-               for (const dependency of definition[0]) {
+               let deps = []
+               if (Array.isArray(definition)) deps = definition[0]
+               else if (typeof definition === 'object') {
+                  deps = definition.uses || deps
+               }
+               for (const dependency of deps) {
                   const depName = dependency.split('(',1)[0]
                   if (doneSet.has(depName)) continue
                   requiredSet.add(depName)
@@ -154,7 +188,20 @@ export default class PocomathInstance {
       this._ensureTypes()
       const tf_imps = {}
       for (const signature in imps) {
-         const [deps, imp] = imps[signature]
+         const specifier = imps[signature]
+         let deps = []
+         let imp
+         if (typeof specifier === 'function') {
+            imp = specifier
+         } else if (Array.isArray(specifier)) {
+            [deps, imp] = specifier
+         } else if (typeof specifier === 'object') {
+            deps = specifier.uses || deps
+            imp = specifier.does
+         } else {
+            throw new SyntaxError(
+               `Cannot interpret signature definition ${specifier}`)
+         }
          if (deps.length === 0) {
             tf_imps[signature] = imp
          } else {

src/number/add.mjs

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

src/number/negate.mjs

@@ -1,3 +1,3 @@
 export { Types } from './Types/number.mjs'
 
-export const negate = {number: [[], n => -n]}
+export const negate = {number: n => -n}