feat: extract generic parameter from the reflectedType (see #18)

Now each behavior specification "knows" its type information.
  Also bumps version number and sets up so that the scripts will run on Windows as well as Unix (thanks to Jos).
  Resolves #5.
  Resolves #16.

Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
Reviewed-on: #17
Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Co-committed-by: Glen Whitney <glen@studioinfinity.org>

.gitignore

@@ -2,7 +2,7 @@
 *~
 # Typescript
 # emitted code
-obj
+build
 
 # ---> Node
 # Logs

.npmrc

@@ -0,0 +1 @@
+shell-emulator=true

README.md

@@ -2,9 +2,13 @@
 
 A final (?) prototype for a refactor of mathjs, culminating the picomath, pocomath, typomath series. Provides an extensible core with "fuzzy" types for its operations, that can at any time generate exact .d.ts file for its current state.
 
-To build and run the prototype, run:
 
-```
+Convenience scripts:
-npx tsc
+
-node obj
+* `pnpm build` -- compile the package
-```
+* `pnpm exec` -- run the compiled code produced by `pnpm build`
+* `pnpm go` -- both of the above in sequence.
+
+Important installation note:
+
+after `pnpm install`, you must execute `npx ts-patch install` to activate the ts-macros compiler plugin.

etc/package.json

@@ -0,0 +1 @@
+{"type": "module"}

package.json5

@@ -1,11 +1,16 @@
 {
    name: 'typocomath',
-   version: '0.0.1',
+   version: '0.0.2',
    description: 'A hopeful final typescipt-pragmatic mathjs proof-of-concept',
    main: 'index.ts',
    scripts: {
       test: 'echo "Error: no test specified" && exit 1',
+      build: 'mkdirp build && cpy etc/package.json build --flat && tsc',
+      start: 'node build',
+      go: 'pnpm clean && pnpm build && pnpm start',
+      clean: 'del-cli build',
    },
+   packageManager: 'pnpm',
    keywords: [
       'math',
       'algebra',
@@ -18,8 +23,13 @@
       url: 'https://code.studioinfinity.org/glen/typocomath.git',
    },
    devDependencies: {
-      '@types/node': '^20.5.0',
+      '@types/node': '20.8.4',
-      'source-map': '^0.7.4',
+      'cpy-cli': '5.0.0',
-      typescript: '^4.9.3',
+      'del-cli': '5.1.0',
+      mkdirp: '3.0.1',
+      'source-map': '0.7.4',
+      'ts-macros': '2.6.0',
+      'ts-patch': '3.0.2',
+      typescript: '5.1.6',
    },
 }

pnpm-lock.yaml

@@ -6,19 +6,771 @@ settings:
 
 devDependencies:
   '@types/node':
-    specifier: ^20.5.0
+    specifier: 20.8.4
-    version: 20.5.0
+    version: 20.8.4
+  cpy-cli:
+    specifier: 5.0.0
+    version: 5.0.0
+  del-cli:
+    specifier: 5.1.0
+    version: 5.1.0
+  mkdirp:
+    specifier: 3.0.1
+    version: 3.0.1
   source-map:
-    specifier: ^0.7.4
+    specifier: 0.7.4
     version: 0.7.4
+  ts-macros:
+    specifier: 2.6.0
+    version: 2.6.0(typescript@5.1.6)
+  ts-patch:
+    specifier: 3.0.2
+    version: 3.0.2
   typescript:
-    specifier: ^4.9.3
+    specifier: 5.1.6
-    version: 4.9.3
+    version: 5.1.6
 
 packages:
 
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+    resolution: {integrity: sha512-U9nH88a3fc/ekCF1l0/UP1IosiuIjyTh7hBvXVMHYgVcfGvt897Xguj2UOLDeI5BG2m7/uwyaLVT6fbtCwTyzw==}
+    engines: {iojs: '>=1.0.0', node: '>=0.10.0'}
+    dev: true
+
+  /rimraf@3.0.2:
+    resolution: {integrity: sha512-JZkJMZkAGFFPP2YqXZXPbMlMBgsxzE8ILs4lMIX/2o0L9UBw9O/Y3o6wFw/i9YLapcUJWwqbi3kdxIPdC62TIA==}
+    hasBin: true
+    dependencies:
+      glob: 7.2.3
+    dev: true
+
+  /run-parallel@1.2.0:
+    resolution: {integrity: sha512-5l4VyZR86LZ/lDxZTR6jqL8AFE2S0IFLMP26AbjsLVADxHdhB/c0GUsH+y39UfCi3dzz8OlQuPmnaJOMoDHQBA==}
+    dependencies:
+      queue-microtask: 1.2.3
+    dev: true
+
+  /semver@7.5.4:
+    resolution: {integrity: sha512-1bCSESV6Pv+i21Hvpxp3Dx+pSD8lIPt8uVjRrxAUt/nbswYc+tK6Y2btiULjd4+fnq15PX+nqQDC7Oft7WkwcA==}
+    engines: {node: '>=10'}
+    hasBin: true
+    dependencies:
+      lru-cache: 6.0.0
+    dev: true
+
+  /slash@4.0.0:
+    resolution: {integrity: sha512-3dOsAHXXUkQTpOYcoAxLIorMTp4gIQr5IW3iVb7A7lFIp0VHhnynm9izx6TssdrIcVIESAlVjtnO2K8bg+Coew==}
+    engines: {node: '>=12'}
     dev: true
 
   /source-map@0.7.4:
@@ -26,8 +778,143 @@ packages:
     engines: {node: '>= 8'}
     dev: true
 
-  /typescript@4.9.3:
+  /spdx-correct@3.2.0:
-    resolution: {integrity: sha512-CIfGzTelbKNEnLpLdGFgdyKhG23CKdKgQPOBc+OUNrkJ2vr+KSzsSV5kq5iWhEQbok+quxgGzrAtGWCyU7tHnA==}
+    resolution: {integrity: sha512-kN9dJbvnySHULIluDHy32WHRUu3Og7B9sbY7tsFLctQkIqnMh3hErYgdMjTYuqmcXX+lK5T1lnUt3G7zNswmZA==}
-    engines: {node: '>=4.2.0'}
+    dependencies:
+      spdx-expression-parse: 3.0.1
+      spdx-license-ids: 3.0.15
+    dev: true
+
+  /spdx-exceptions@2.3.0:
+    resolution: {integrity: sha512-/tTrYOC7PPI1nUAgx34hUpqXuyJG+DTHJTnIULG4rDygi4xu/tfgmq1e1cIRwRzwZgo4NLySi+ricLkZkw4i5A==}
+    dev: true
+
+  /spdx-expression-parse@3.0.1:
+    resolution: {integrity: sha512-cbqHunsQWnJNE6KhVSMsMeH5H/L9EpymbzqTQ3uLwNCLZ1Q481oWaofqH7nO6V07xlXwY6PhQdQ2IedWx/ZK4Q==}
+    dependencies:
+      spdx-exceptions: 2.3.0
+      spdx-license-ids: 3.0.15
+    dev: true
+
+  /spdx-license-ids@3.0.15:
+    resolution: {integrity: sha512-lpT8hSQp9jAKp9mhtBU4Xjon8LPGBvLIuBiSVhMEtmLecTh2mO0tlqrAMp47tBXzMr13NJMQ2lf7RpQGLJ3HsQ==}
+    dev: true
+
+  /strip-ansi@6.0.1:
+    resolution: {integrity: sha512-Y38VPSHcqkFrCpFnQ9vuSXmquuv5oXOKpGeT6aGrr3o3Gc9AlVa6JBfUSOCnbxGGZF+/0ooI7KrPuUSztUdU5A==}
+    engines: {node: '>=8'}
+    dependencies:
+      ansi-regex: 5.0.1
+    dev: true
+
+  /strip-indent@4.0.0:
+    resolution: {integrity: sha512-mnVSV2l+Zv6BLpSD/8V87CW/y9EmmbYzGCIavsnsI6/nwn26DwffM/yztm30Z/I2DY9wdS3vXVCMnHDgZaVNoA==}
+    engines: {node: '>=12'}
+    dependencies:
+      min-indent: 1.0.1
+    dev: true
+
+  /supports-color@5.5.0:
+    resolution: {integrity: sha512-QjVjwdXIt408MIiAqCX4oUKsgU2EqAGzs2Ppkm4aQYbjm+ZEWEcW4SfFNTr4uMNZma0ey4f5lgLrkB0aX0QMow==}
+    engines: {node: '>=4'}
+    dependencies:
+      has-flag: 3.0.0
+    dev: true
+
+  /supports-color@7.2.0:
+    resolution: {integrity: sha512-qpCAvRl9stuOHveKsn7HncJRvv501qIacKzQlO/+Lwxc9+0q2wLyv4Dfvt80/DPn2pqOBsJdDiogXGR9+OvwRw==}
+    engines: {node: '>=8'}
+    dependencies:
+      has-flag: 4.0.0
+    dev: true
+
+  /supports-preserve-symlinks-flag@1.0.0:
+    resolution: {integrity: sha512-ot0WnXS9fgdkgIcePe6RHNk1WA8+muPa6cSjeR3V8K27q9BB1rTE3R1p7Hv0z1ZyAc8s6Vvv8DIyWf681MAt0w==}
+    engines: {node: '>= 0.4'}
+    dev: true
+
+  /to-regex-range@5.0.1:
+    resolution: {integrity: sha512-65P7iz6X5yEr1cwcgvQxbbIw7Uk3gOy5dIdtZ4rDveLqhrdJP+Li/Hx6tyK0NEb+2GCyneCMJiGqrADCSNk8sQ==}
+    engines: {node: '>=8.0'}
+    dependencies:
+      is-number: 7.0.0
+    dev: true
+
+  /trim-newlines@4.1.1:
+    resolution: {integrity: sha512-jRKj0n0jXWo6kh62nA5TEh3+4igKDXLvzBJcPpiizP7oOolUrYIxmVBG9TOtHYFHoddUk6YvAkGeGoSVTXfQXQ==}
+    engines: {node: '>=12'}
+    dev: true
+
+  /ts-macros@2.6.0(typescript@5.1.6):
+    resolution: {integrity: sha512-X7c4rHPTpBYY+MJUkIDIQMbTPAcv1y1sylrnDMsTvcbImleT4Wlheg3wNbORwnX8Zvq2ldZnttNXcZ1a0VE2Kg==}
+    hasBin: true
+    peerDependencies:
+      typescript: 4.7.x || 4.8.x || 4.9.x || 5.0.x || 5.1.x || 5.2.x
+    dependencies:
+      typescript: 5.1.6
+      yargs-parser: 21.1.1
+    dev: true
+
+  /ts-patch@3.0.2:
+    resolution: {integrity: sha512-iTg8euqiNsNM1VDfOsVIsP0bM4kAVXU38n7TGQSkky7YQX/syh6sDPIRkvSS0HjT8ZOr0pq1h+5Le6jdB3hiJQ==}
+    hasBin: true
+    dependencies:
+      chalk: 4.1.2
+      global-prefix: 3.0.0
+      minimist: 1.2.8
+      resolve: 1.22.4
+      semver: 7.5.4
+      strip-ansi: 6.0.1
+    dev: true
+
+  /type-fest@1.4.0:
+    resolution: {integrity: sha512-yGSza74xk0UG8k+pLh5oeoYirvIiWo5t0/o3zHHAO2tRDiZcxWP7fywNlXhqb6/r6sWvwi+RsyQMWhVLe4BVuA==}
+    engines: {node: '>=10'}
+    dev: true
+
+  /typescript@5.1.6:
+    resolution: {integrity: sha512-zaWCozRZ6DLEWAWFrVDz1H6FVXzUSfTy5FUMWsQlU8Ym5JP9eO4xkTIROFCQvhQf61z6O/G6ugw3SgAnvvm+HA==}
+    engines: {node: '>=14.17'}
     hasBin: true
     dev: true
+
+  /undici-types@5.25.3:
+    resolution: {integrity: sha512-Ga1jfYwRn7+cP9v8auvEXN1rX3sWqlayd4HP7OKk4mZWylEmu3KzXDUGrQUN6Ol7qo1gPvB2e5gX6udnyEPgdA==}
+    dev: true
+
+  /validate-npm-package-license@3.0.4:
+    resolution: {integrity: sha512-DpKm2Ui/xN7/HQKCtpZxoRWBhZ9Z0kqtygG8XCgNQ8ZlDnxuQmWhj566j8fN4Cu3/JmbhsDo7fcAJq4s9h27Ew==}
+    dependencies:
+      spdx-correct: 3.2.0
+      spdx-expression-parse: 3.0.1
+    dev: true
+
+  /which@1.3.1:
+    resolution: {integrity: sha512-HxJdYWq1MTIQbJ3nw0cqssHoTNU267KlrDuGZ1WYlxDStUtKUhOaJmh112/TZmHxxUfuJqPXSOm7tDyas0OSIQ==}
+    hasBin: true
+    dependencies:
+      isexe: 2.0.0
+    dev: true
+
+  /wrappy@1.0.2:
+    resolution: {integrity: sha512-l4Sp/DRseor9wL6EvV2+TuQn63dMkPjZ/sp9XkghTEbV9KlPS1xUsZ3u7/IQO4wxtcFB4bgpQPRcR3QCvezPcQ==}
+    dev: true
+
+  /yallist@4.0.0:
+    resolution: {integrity: sha512-3wdGidZyq5PB084XLES5TpOSRA3wjXAlIWMhum2kRcv/41Sn2emQ0dycQW4uZXLejwKvg6EsvbdlVL+FYEct7A==}
+    dev: true
+
+  /yargs-parser@20.2.9:
+    resolution: {integrity: sha512-y11nGElTIV+CT3Zv9t7VKl+Q3hTQoT9a1Qzezhhl6Rp21gJ/IVTW7Z3y9EWXhuUBC2Shnf+DX0antecpAwSP8w==}
+    engines: {node: '>=10'}
+    dev: true
+
+  /yargs-parser@21.1.1:
+    resolution: {integrity: sha512-tVpsJW7DdjecAiFpbIB1e3qxIQsE6NoPc5/eTdrbbIC4h0LVsWhnoa3g+m2HclBIujHzsxZ4VJVA+GUuc2/LBw==}
+    engines: {node: '>=12'}
+    dev: true
+
+  /yocto-queue@0.1.0:
+    resolution: {integrity: sha512-rVksvsnNCdJ/ohGc6xgPwyN8eheCxsiLM8mxuE/t/mOVqJewPuO1miLpTHQiRgTKCLexL4MeAFVagts7HmNZ2Q==}
+    engines: {node: '>=10'}
+    dev: true

src/Complex/arithmetic.ts

@@ -2,6 +2,7 @@ import {Complex} from './type.js'
 import type {
    Dependencies, Signature, Returns, RealType, AliasOf
 } from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
 declare module "../interfaces/type" {
    interface Signatures<T> {
@@ -78,11 +79,10 @@ export const sqrt =
        & Dependencies<'zero' | 'complex', T>
        & Dependencies<'absquare' | 're' | 'divideReal', Complex<T>>
        & {
-         addTR: Signature<'addReal', T>, 
+         addTR: Signature<'addReal', T>,
          addRR: Signature<'add', RealType<T>>,
          addCR: Signature<'addReal', Complex<T>>
-      }):
+       }): Signature<'sqrt', Complex<T>> =>
-      Signature<'sqrt', Complex<T>> =>
    z => {
       const myabs = dep.conservativeSqrt(dep.absquare(z))
       const r = dep.re(z)
@@ -98,4 +98,7 @@ export const sqrt =
       return dep.divideReal(num, denom)
    }
 
-export const conservativeSqrt = sqrt
+$reflect!([
+   add, addReal, unaryMinus, conj, subtract, multiply, absquare, divideReal,
+   reciprocal, divide, sqrt
+])

src/Complex/predicate.ts

@@ -1,9 +1,13 @@
 import {Complex} from './type.js'
 import type {Dependencies, Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
 export const isReal =
    <T>(dep: Dependencies<'add' | 'equal' | 'isReal', T>):
       Signature<'isReal', Complex<T>> =>
    z => dep.isReal(z.re) && dep.equal(z.re, dep.add(z.re, z.im))
 
-export const isSquare: Signature<'isSquare', Complex<any>> = z => true // FIXME: not correct for Complex<bigint> once we get there
+export const isSquare = (): Signature<'isSquare', Complex<unknown>> =>
+   z => true // FIXME: not correct for Complex<bigint> once we get there
+
+$reflect!([isReal, isSquare])

src/Complex/relational.ts

@@ -1,6 +1,8 @@
 import {Complex} from './type.js'
 import {Dependencies, Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
 export const equal =
    <T>(dep: Dependencies<'equal', T>): Signature<'equal', Complex<T>> =>
    (w, z) => dep.equal(w.re, z.re) && dep.equal(w.im, z.im)
+$reflect!([equal])

src/Complex/type.ts

@@ -2,10 +2,12 @@ import {joinTypes, typeOfDependency} from '../core/Dispatcher.js'
 import type {
    ZeroType, OneType, NaNType, Dependencies, Signature, Returns
 } from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
 export type Complex<T> = { re: T; im: T; }
 
 export const Complex_type = {
+   name: 'Complex', // just until we have reflection to tell us
    test: <T>(dep: { testT: (z: unknown) => z is T }) =>
       (z: unknown): z is Complex<T> =>
          typeof z === 'object' && z != null && 're' in z && 'im' in z
@@ -61,3 +63,5 @@ export const nan =
 export const re =
    <T>(dep: Dependencies<'re', T>): Signature<'re', Complex<T>> =>
    z => dep.re(z.re)
+
+$reflect!([complex, zero, one, nan, re])

src/core/Dispatcher.ts

@@ -5,6 +5,8 @@
  * for specific types (including their own).
  */
 
+import {parseReflectedType, ImplementationDef} from './parseReflectedType.js'
+
 // First helper types and functions for the Dispatcher
 
 type TypeName = string
@@ -25,6 +27,7 @@ export function joinTypes(a: TypeName, b: TypeName) {
 // Now types used in the Dispatcher class itself
 
 type TypeSpecification = {
+   name: string, // just until we get reflection, then we can remove this property
    before?: TypeName[],
    test: ((x: unknown) => boolean)
       | ((d: DependenciesType) => (x: unknown) => boolean),
@@ -38,38 +41,44 @@ type SpecificationsGroup = Record<string, SpecObject>
 export class Dispatcher {
    installSpecification(
       name: string,
-      signature: Signature,
+      defn: ImplementationDef,
-      returns: TypeName,
-      dependencies: Record<string, Signature>,
       behavior: Function // possible todo: constrain this type based
       // on the signature, return type, and dependencies. Not sure if
       // that's really possible, though.
    ) {
-      console.log('Pretending to install', name, signature, '=>', returns)
+      console.log('Pretending to install', name, 'with signatures')
+      for (const signature of defn.fn.signatures) {
+         console.log('   ', signature.args, '=>', signature.returns)
+      }
+      if (defn.fn.aliasOf) {
+         console.log('   As an alias of', defn.fn.aliasOf)
+      }
       //TODO: implement me
    }
    installType(name: TypeName, typespec: TypeSpecification) {
       console.log('Pretending to install type', name, typespec)
       //TODO: implement me
    }
-   constructor(collection: SpecificationsGroup) { 
+   constructor(collection: SpecificationsGroup) {
+      const implementations = []
       for (const key in collection) {
          console.log('Working on', key)
          for (const identifier in collection[key]) {
-            console.log('Handling', key, ':', identifier)
+            const item = collection[key][identifier]
-            const parts = identifier.split('_')
+            if (typeof item === 'function') {
-            if (parts[parts.length - 1] === 'type') {
+               implementations.push([key, identifier, item])
-               parts.pop()
-               const name = parts.join('_')
-               this.installType(
-                  name, collection[key][identifier] as TypeSpecification)
             } else {
-               const name = parts[0]
+               console.log('Handling type', key, ':', identifier)
-               this.installSpecification(
+               this.installType(
-                  name, ['dunno'], 'unsure', {},
+                  item.name, collection[key][identifier] as TypeSpecification)
-                  collection[key][identifier] as Function)
             }
          }
       }
+      for (const trio of implementations) {
+         const [k, id, imp] = trio
+         console.log('Handling implementation', id, 'from', k)
+         this.installSpecification(
+            id, parseReflectedType(id, imp.reflectedType), imp)
+      }
    }
 }

src/core/parseReflectedType.ts

@@ -0,0 +1,279 @@
+export type FunctionDef = {
+  name: string,
+  aliasOf?: string,
+  signatures: Array<{
+    args: Array<{ name: string, type: string }>
+    returns: string
+  }>
+}
+
+
+export type ImplementationDef = {
+  fn: FunctionDef,
+  dependencies: Record<string, FunctionDef>
+  genericParameter: string | null
+}
+
+/**
+ * Parse a reflected type coming out of TypeScript into a structured object, for example:
+ *
+ *   '<T>(dep: configDependency & { complex: ((re: number) => Complex<number>) | ((re: number, im: number) => Complex<number>); }) => (a: number) => number | Complex<number>'
+ */
+export function parseReflectedType(name: string, reflectedType: string): ImplementationDef {
+  console.log('For', name, 'parsing', reflectedType)
+  const [factoryArgs, fnsClause] = split(reflectedType, '=>', 2).map(trim)
+  const fn = parseAlias(name, fnsClause)
+
+  // extract the generic parameter like '<T>' at the start of the type
+  const genericParameter = factoryArgs.trim().startsWith('<')
+    ? findBlockContents(factoryArgs, '<', '>')?.innerText || null
+    : null
+
+  const factoryArgsInner = findBlockContents(factoryArgs, '(', ')')
+  const depArg = split(factoryArgsInner.innerText, ':').map(trim)[1]
+  const depArgBlocks: string[] = depArg ? split(depArg, '&').map(trim) : []
+
+  const deps = depArgBlocks
+    .filter(depArgBlock => {
+      if (depArgBlock.startsWith('{') || depArgBlock === 'configDependency') {
+        return true
+      } else {
+        throw new SyntaxError(`Cannot parse dependency "${depArgBlock}"`)
+      }
+    })
+    .flatMap(parseDependencies)
+
+  const dependencies: Record<string, FunctionDef> = groupBy(deps, 'name')
+
+  return {fn, dependencies, genericParameter }
+}
+
+function parseDependencies(deps: string): FunctionDef[] {
+  if (deps === 'configDependency') {
+    return [{name: 'config', signatures: [{args: [], returns: 'Config'}]}]
+  }
+  const inner = findBlockContents(deps, '{', '}').innerText
+  return split(inner, ';')
+    .map(trim)
+    .filter(notEmpty)
+    .map(parseDependency)
+}
+
+// parse a dependency like "complex: ((re: number) => Complex<number>) | ((re: number, im: number) => Complex<number>)"
+function parseDependency(dep: string): FunctionDef {
+  const [name, def] = split(dep, ':').map(trim)
+
+  return parseAlias(name, def)
+}
+
+// Parse a possibly aliased function
+function parseAlias(name: string, alias: string): FunctionDef {
+  const { aliasOf, innerSignature } = parseAliasOf(alias)
+
+  return { name, signatures: parseSignatures(innerSignature), aliasOf }
+}
+
+// parse function signatures like ((re: number) => Complex<number>) | ((re: number, im: number) => Complex<number>)
+// But also have to succeed on (a: number) => number | Complex<number>
+// That's why we only split on an alternation bar `|` that's followed by
+// a parenthesis; that way we avoid splitting a union return type. Note
+// this is not necessarily foolproof, as there could be a return type that
+// is a union with a complicated piece that has to be enclosed in parens;
+// but so far it seems to work in practice.
+function parseSignatures(sigs: string) {
+  return split(sigs, /[|]\s*(?=[(])/)
+    .map(trim)
+    .map(stripParenthesis)
+    .map(signature => {
+      const [argsBlock, returns] = split(signature, '=>').map(trim)
+
+      if (!returns) {
+        throw new SyntaxError(`Failed to find return type in '${signature}'`)
+      }
+
+      return {
+        args: parseArgs(argsBlock),
+        returns
+      }
+    })
+}
+
+// parse args like "(re: number, im: number)"
+function parseArgs(argsBlock: string) : Array<{name: string, type: string}> {
+  const args = findBlockContents(argsBlock, '(', ')').innerText
+
+  return split(args, ',')
+    .map(trim)
+    .map(arg => {
+      const [name, type] = split(arg, ':').map(trim)
+      return { name, type}
+    })
+}
+
+// parse "AliasOf<"divide", (a: Complex<T>, b: RealType<Complex<T>>) => Complex<T>>"
+function parseAliasOf(signature: string) : { innerSignature: string, aliasOf: string | undefined } {
+  if (!signature.startsWith('AliasOf')) {
+    return {
+      innerSignature: signature,
+      aliasOf: undefined
+    }
+  }
+
+  const inner = findBlockContents(signature, '<', '>').innerText.trim()
+  const [aliasOfWithQuotes, innerSignature] = split(inner, ',').map(trim)
+  return {
+    innerSignature,
+    aliasOf: aliasOfWithQuotes.substring(1, aliasOfWithQuotes.length - 1) // remove double quotes
+  }
+}
+
+// remove the outer parenthesis, for example "((re: number) => Complex<number>)" returns "(re: number) => Complex<number>"
+function stripParenthesis(text: string) : string {
+  return text.startsWith('(') && text.endsWith(')')
+    ? text.substring(1, text.length - 1)
+    : text
+}
+
+function findBlockContents(text: string, blockStart: string, blockEnd: string, startIndex = 0) : { start: number, end: number, innerText: string } | undefined {
+  let i = startIndex
+
+  while (!matchSubString(text, blockStart, i) && i < text.length) {
+    i++
+  }
+
+  if (i >= text.length) {
+    return undefined
+  }
+
+  i++
+  const start = i
+
+  while (!matchSubString(text, blockEnd, i) || matchSubString(text, '=>', i - 1)) {
+    i = skipBrackets(text, i)
+
+    i++
+  }
+
+  if (i >= text.length) {
+    return undefined
+  }
+  const end = i
+
+  return {
+    start,
+    end,
+    innerText: text.substring(start, end)
+  }
+}
+
+/**
+ * Given a string, generate a string source for a regexp that will match
+ * exactly the given string.
+ * Uses the fact that the only characters that need to be escaped in
+ * a character class are \, ], and ^
+ */
+function regexpQuote(s: string) {
+  const special = '\\]^'
+  let re = ''
+  for (const char of s) {
+    if (special.includes(char)) re += `\\${char}`
+    else re += `[${char}]`
+  }
+  return re
+}
+
+/**
+ * Split a string by a delimiter, but ignore all occurrences of the delimiter
+ * that are inside bracket pairs <> () [] {}
+ */
+export function split(
+     text: string, delimiter: string | RegExp, pieces = 0): string[] {
+  const delim: RegExp = typeof delimiter === 'string'
+     ? new RegExp(regexpQuote(delimiter), 'y')
+     : new RegExp(delimiter.source, 'y')
+  const parts: string[] = []
+
+  let i = 0
+  let n = 1
+  let start = 0
+  while (i < text.length && (pieces === 0 || n < pieces)) {
+    i = skipBrackets(text, i)
+
+    delim.lastIndex = i
+    const result = delim.exec(text)
+    if (result) {
+      parts.push(text.substring(start, i))
+      n += 1
+      i += result[0].length
+      start = i
+    }
+
+    i++
+  }
+
+  parts.push(text.substring(start))
+
+  return parts
+}
+
+function skipBrackets(text: string, startIndex: number) : number {
+  let level = 0
+  let i = startIndex
+
+  do {
+    if (isBracketOpen(text, i)) {
+      level++
+    }
+
+    if (isBracketClose(text, i) && level > 0) {
+      level--
+    }
+
+    if (level === 0) {
+      break
+    }
+
+    i++
+  } while(i < text.length)
+
+  return i
+}
+
+function isBracketOpen(text: string, index: number) {
+  const char = text[index]
+  return char === '(' || char === '<' || char === '[' || char === '{'
+}
+
+function isBracketClose(text: string, index: number) {
+  const char = text[index]
+  // we need to take care of not matching the ">" of the operator "=>"
+  return char === ')' || (char === '>' && text[index - 1] !== '=') || char === ']' || char === '}'
+}
+
+function matchSubString(text: string, search: string, index: number) : boolean {
+  for (let i = 0; i < search.length; i++) {
+    if (text[i + index] !== search[i]) {
+      return false
+    }
+  }
+
+  return true
+}
+
+function trim(text: string) : string {
+  return text.trim()
+}
+
+function notEmpty(text: string) : boolean {
+  return text.length > 0
+}
+
+function groupBy<T>(items: T[], key: string) : Record<string, T> {
+  const obj: Record<string, T> = {}
+
+  items.forEach((item) => {
+    obj[item[key]] = item
+  })
+
+  return obj
+}

src/generic/arithmetic.ts

@@ -1,32 +1,9 @@
 import type {Dependencies, Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
-// This stuff would really go in interfaces/type.js or someplace like that
+export const square =
-type Annotate<U> = U & {dependencies?: Record<string, string>, signature?: string}
+   <T>(dep: Dependencies<'multiply', T>): Signature<'square', T> =>
-
+   z => dep.multiply(z, z)
-function genericImplementation<Deps extends Record<string, string>, Sig extends string>(
+   // z => dep.fooBar(z, z) // fails as desired
-   deps: Deps, sig: Sig, impl: <T>(dep: Dependencies<keyof Deps, T>) => Signature<Sig, T>
+   // z => dep.multiply(z, 'foo') // still fails as desired
-) {
+$reflect!([square])
-   const rimpl: Annotate<typeof impl> = impl
-   rimpl.dependencies = deps
-   rimpl.signature = sig
-   return rimpl
-}
-// and of course it would need to be generalized somewhat from the above
-// --------------
-
-// Then here for the implementation we would have:
-export const square = genericImplementation(
-   {multiply: 'T'}, 'square', <T>(dep) => z => dep.multiply(z, z)
-)
-
-// Note this was previously
-
-// export const square =
-//    <T>(dep: Dependencies<'multiply', T>): Signature<'square', T> =>
-//    z => dep.multiply(z, z)
-
-// but then we couldn't get at the dependencies or the signature at runtime. So the point of
-// genericImplementation is that it takes literal values for the dependencies and signature,
-// from which it deduces the types of the actual dependencies of the implementation and the
-// the implementation itself, and then it copies those literal values onto properties of the
-// implementation, where they can be accessed at runtime as illustreated in ../index.ts

src/generic/relational.ts

@@ -1,5 +1,7 @@
 import {Dependencies, Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
 export const unequal =
    <T>(dep: Dependencies<'equal', T>): Signature<'unequal', T> =>
    (x, y) => !dep.equal(x, y)
+$reflect!([unequal])

src/index.ts

@@ -1,3 +1,4 @@
+import {inspect} from 'node:util'
 import {Dispatcher} from './core/Dispatcher.js'
 import * as Specifications from './all.js'
 
@@ -5,27 +6,48 @@ export default new Dispatcher(Specifications)
 
 import {Complex} from './Complex/type.js'
 import {absquare as absquare_complex} from './Complex/arithmetic.js'
+import {parseReflectedType} from './core/parseReflectedType.js'
 
 const mockRealAdd = (a: number, b: number) => a+b
 const mockComplexAbsquare = (z: Complex<number>) => z.re*z.re + z.im*z.im
+const mockComplex = (re: number, im: number) => ({ re, im })
+
+const config = {
+  predictable: false,
+  epsilon: 1e-14
+}
 
 const quatAbsquare = absquare_complex({
-    add: mockRealAdd,
+  add: mockRealAdd,
-    absquare: mockComplexAbsquare
+  absquare: mockComplexAbsquare
 })
 
 const myabs = quatAbsquare({re: {re: 0, im: 1}, im: {re:2, im: 3}})
 const typeTest: typeof myabs = 7 // check myabs is just a number
+console.log('Result is myabs=', myabs)
 
-console.log('Result is', myabs)
+const sqrt = Specifications.numbers.sqrt({
+  config,
+  complex: mockComplex
+})
+console.log('Result of sqrt(16)=', sqrt(16))
+console.log('Result of sqrt(-4)=', sqrt(-4))
 
-console.log('Dependencies of square are', Specifications.generic.square.dependencies)
+console.log()
-console.log('Signature of square is', Specifications.generic.square.signature)
+console.log('1) NUMBER SQRT')
+console.log(`1.1) REFLECTED TYPE: "${Specifications.numbers.sqrt.reflectedType}"`)
+console.log(
+  '1.2) PARSED TYPE:',
+  inspect(
+    parseReflectedType('sqrt', Specifications.numbers.sqrt.reflectedType),
+    { depth: null, colors: true }))
 
-const realSquare = Specifications.generic.square<number>({multiply: (a,b) => a*b})
+console.log()
-console.log('Square of 2.5 is', realSquare(2.5))
+console.log('2) GENERIC SQUARE')
+console.log(`1.1) REFLECTED TYPE: "${Specifications.generic.square.reflectedType}"`)
+console.log('2.2) PARSED TYPE:', inspect(parseReflectedType('square', Specifications.generic.square.reflectedType), { depth: null, colors: true }))
 
-// and note the following fail with a type error as desired:
+console.log()
-// const fakeSquare = Specifications.generic.square<number>({multiply: (a,b,c) => a*b*c})
+console.log('3) COMPLEX SQRT')
-// const stringSquare = Specifications.generic.square<string>({multiply: (a,b) => a*b})
+console.log(`1.1) REFLECTED TYPE: "${Specifications.complex.sqrt.reflectedType}"`)
-// console.log('Square of three is', stringSquare('three'))
+console.log('3.2) PARSED TYPE:', inspect(parseReflectedType('sqrt', Specifications.complex.sqrt.reflectedType), { depth: null, colors: true }))

src/interfaces/type.ts

@@ -1,3 +1,5 @@
+import {$$typeToString} from 'ts-macros'
+
 /*****
  * Every typocomath type has some associated types; they need
  * to be published in the following interface. The key is the
@@ -13,6 +15,10 @@
  * but that's OK, the generic parameter doesn't hurt in those cases.
  ****/
 
+type ValueIntersectionByKeyUnion<T,  TKey extends keyof T> = {
+  [P in TKey]: (k: T[P])=>void
+} [TKey] extends ((k: infer I)=>void) ? I : never
+
 export interface AssociatedTypes<T> {
    undefined: {
       type: undefined
@@ -24,10 +30,10 @@ export interface AssociatedTypes<T> {
 }
 
 type AssociatedTypeNames = keyof AssociatedTypes<unknown>['undefined']
-type ALookup<T, Name extends AssociatedTypeNames> = {
+type ALookup<T, Name extends AssociatedTypeNames> = ValueIntersectionByKeyUnion<{
    [K in keyof AssociatedTypes<T>]:
-   T extends AssociatedTypes<T>[K]['type'] ? AssociatedTypes<T>[K][Name] : never
+   T extends AssociatedTypes<T>[K]['type'] ? AssociatedTypes<T>[K][Name] : unknown},
-}[keyof AssociatedTypes<T>]
+   keyof AssociatedTypes<T>>
 
 // For everything to compile, zero and one must be subtypes of T:
 export type ZeroType<T> = ALookup<T, 'zero'> & T
@@ -68,8 +74,17 @@ export interface Signatures<T> {
 
 type SignatureKey<T> = keyof Signatures<T>
 
-export type Signature<Name, T> = Signatures<T>[Name & SignatureKey<T>]
+export type Signature<Name extends SignatureKey<T>, T> = Signatures<T>[Name]
-export type Returns<Name extends SignatureKey<T>, T> = ReturnType<Signatures<T>[Name]>
+export type Returns<Name extends SignatureKey<T>, T> =
-export type Dependencies<Name, T> = {[K in Name & SignatureKey<T>]: Signature<K, T>}
+   ReturnType<Signatures<T>[Name]>
+type Deps<T> =  T extends unknown ? { [K in keyof T]: T[K] } : never;
+export type Dependencies<Name extends SignatureKey<T>, T> =
+   Deps<{[K in Name]: Signature<K, T>}>
 
 export type AliasOf<Name extends string, T> = T & {aliasOf?: Name}
+
+// For defining implementations with type reflection
+export function $reflect<ImplTuple>(tup: ImplTuple) {
+   +[[tup], <T>(elt: T) =>
+     elt.reflectedType = $$typeToString!<T>(true, false, true)]
+}

src/numbers/arithmetic.ts

@@ -1,25 +1,35 @@
 import type {configDependency} from '../core/Config.js'
 import type {Dependencies, Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
-export const add:        Signature<'add',        number> = (a, b) => a + b
+export const add =        (): Signature<'add',        number> => (a, b) => a + b
-export const unaryMinus: Signature<'unaryMinus', number> = a => -a
+const unaMinus = (a: number) => -a
-export const conj:       Signature<'conj',       number> = a => a
+export const unaryMinus = (): Signature<'unaryMinus', number> => unaMinus
-export const subtract:   Signature<'subtract',   number> = (a, b) => a - b
+export const conj =       (): Signature<'conj',       number> => a => a
-export const multiply:   Signature<'multiply',   number> = (a, b) => a * b
+export const subtract =   (): Signature<'subtract',   number> => (a, b) => a - b
-export const absquare:   Signature<'absquare',   number> = a => a * a
+export const multiply =   (): Signature<'multiply',   number> => (a, b) => a * b
-export const reciprocal: Signature<'reciprocal', number> = a => 1 / a
+export const absquare =   (): Signature<'absquare',   number> => a => a * a
-export const divide:     Signature<'divide',     number> = (a, b) => a / b
+export const reciprocal = (): Signature<'reciprocal', number> => a => 1 / a
+export const divide =     (): Signature<'divide',     number> => (a, b) => a / b
 
-const basicSqrt = a => isNaN(a) ? NaN : Math.sqrt(a)
+const basicSqrt = (a: number) => isNaN(a) ? NaN : Math.sqrt(a)
-export const conservativeSqrt: Signature<'conservativeSqrt', number> = basicSqrt
+export const conservativeSqrt = (): Signature<'conservativeSqrt', number> =>
+  basicSqrt
 
 export const sqrt =
-   (dep: configDependency & Dependencies<'complex', number>):
+  (dep: configDependency
-   Signature<'sqrt', number> => {
+   & Dependencies<'complex', number>): Signature<'sqrt', number> => {
-      if (dep.config.predictable || !dep.complex) return basicSqrt
+    if (dep.config.predictable || !dep.complex) {
-      return a => {
+      return basicSqrt
-         if (isNaN(a)) return NaN
+    }
-         if (a >= 0) return Math.sqrt(a)
+    return a => {
-         return dep.complex(0, Math.sqrt(unaryMinus(a)))
+      if (isNaN(a)) return NaN
-      }
+      if (a >= 0) return Math.sqrt(a)
+      return dep.complex(0, Math.sqrt(unaMinus(a)))
+    }
    }
+
+$reflect!([
+  add, unaryMinus, conj, subtract, multiply, absquare, reciprocal, divide,
+  conservativeSqrt, sqrt
+])

src/numbers/native.ts

@@ -1,2 +1,4 @@
 export * from './type.js'
 export * from './arithmetic.js'
+export * from './predicate.js'
+export * from './relational.js'

src/numbers/predicate.ts

@@ -1,4 +1,7 @@
 import type {Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
-export const isReal:   Signature<'isReal',   number> = (a) => true
+export const isReal =   (): Signature<'isReal',   number> => (a) => true
-export const isSquare: Signature<'isSquare', number> = (a) => a >= 0
+export const isSquare = (): Signature<'isSquare', number> => (a) => a >= 0
+
+$reflect!([isReal, isSquare])

src/numbers/relational.ts

@@ -1,5 +1,6 @@
 import {configDependency} from '../core/Config.js'
 import {Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
 const DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16
 
@@ -19,3 +20,4 @@ export const equal =
 
       return false
    }
+$reflect!([equal])

src/numbers/type.ts

@@ -1,6 +1,8 @@
 import type { Signature } from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
 export const number_type = {
+   name: 'number', // just until we have reflection to tell us
    before: ['Complex'],
    test: (n: unknown): n is number => typeof n === 'number',
    from: { string: (s: string) => +s }
@@ -8,7 +10,7 @@ export const number_type = {
 
 declare module "../interfaces/type" {
    interface AssociatedTypes<T> {
-      numbers: {
+      number: {
          type: number
          zero: 0
          one: 1
@@ -19,7 +21,9 @@ declare module "../interfaces/type" {
 }
 
 // I don't like the redundancy of repeating 'zero'; any way to eliminate that?
-export const zero: Signature<'zero', number> = (a) => 0
+export const zero = (): Signature<'zero', number> => (a) => 0
-export const one:  Signature<'one',  number> = (a) => 1
+export const one =  (): Signature<'one',  number> => (a) => 1
-export const nan:  Signature<'nan',  number> = (a) => NaN
+export const nan =  (): Signature<'nan',  number> => (a) => NaN
-export const re:   Signature<'re',   number> = (a) => a
+export const re =   (): Signature<'re',   number> => (a) => a
+
+$reflect!([zero, one, nan, re])

tsconfig.json

@@ -1,8 +1,12 @@
 {
     "compilerOptions": {
-        "target": "ES2022",
+        "target": "esnext",
         "rootDir": "./src",
-        "outDir": "./obj",
+        "outDir": "./build",
-        "moduleResolution": "nodenext"
+        "moduleResolution": "nodenext",
+        "plugins": [ {
+            "transform": "ts-macros/dist/type-resolve",
+            "transformProgram": true
+        } ]
     }
 }