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
@@ -129,6 +129,9 @@ dist
 # Stores VSCode versions used for testing VSCode extensions
 .vscode-test
 
+# Webstorm
+.idea
+
 # yarn v2
 .yarn/cache
 .yarn/unplugged

.npmrc

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

README.md

@@ -1,3 +1,14 @@
 # typocomath
 
 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.
+
+
+Convenience scripts:
+
+* `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',
@@ -18,6 +23,13 @@
       url: 'https://code.studioinfinity.org/glen/typocomath.git',
    },
    devDependencies: {
-      typescript: '^4.9.3',
+      '@types/node': '20.8.4',
+      'cpy-cli': '5.0.0',
+      '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

@@ -1,15 +1,920 @@
-lockfileVersion: 5.4
+lockfileVersion: '6.0'
 
-specifiers:
+settings:
-  typescript: ^4.9.3
+  autoInstallPeers: true
+  excludeLinksFromLockfile: false
 
 devDependencies:
-  typescript: 4.9.3
+  '@types/node':
+    specifier: 20.8.4
+    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
+    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: 5.1.6
+    version: 5.1.6
 
 packages:
 
-  /typescript/4.9.3:
+  /@babel/code-frame@7.22.13:
-    resolution: {integrity: sha512-CIfGzTelbKNEnLpLdGFgdyKhG23CKdKgQPOBc+OUNrkJ2vr+KSzsSV5kq5iWhEQbok+quxgGzrAtGWCyU7tHnA==}
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-    engines: {node: '>=4.2.0'}
+    engines: {node: '>=6.9.0'}
+    dependencies:
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+      chalk: 2.4.2
+    dev: true
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+    engines: {node: '>=6.9.0'}
+    dev: true
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+    engines: {node: '>=6.9.0'}
+    dependencies:
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+      chalk: 2.4.2
+      js-tokens: 4.0.0
+    dev: true
+
+  /@nodelib/fs.scandir@2.1.5:
+    resolution: {integrity: sha512-vq24Bq3ym5HEQm2NKCr3yXDwjc7vTsEThRDnkp2DK9p1uqLR+DHurm/NOTo0KG7HYHU7eppKZj3MyqYuMBf62g==}
+    engines: {node: '>= 8'}
+    dependencies:
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+      run-parallel: 1.2.0
+    dev: true
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+    engines: {node: '>= 8'}
+    dev: true
+
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+    resolution: {integrity: sha512-oGB+UxlgWcgQkgwo8GcEGwemoTFt3FIO9ababBmaGwXIoBKZ+GTy0pP185beGg7Llih/NSHSV2XAs1lnznocSg==}
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+    dependencies:
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+      fastq: 1.15.0
+    dev: true
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+    dev: true
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+    dev: true
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+    engines: {node: '>=12'}
+    dependencies:
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+    dev: true
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+  /arrify@1.0.1:
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+  /chalk@2.4.2:
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+    engines: {node: '>=16'}
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src/Complex/all.ts

@@ -1,8 +1,6 @@
-import {ForType} from '../core/Dispatcher.js'
 import * as Complex from './native.js'
+import * as complex from './arithmetic.js'
+
+export { complex }
 
 export {Complex}
-
-declare module "../core/Dispatcher" {
-   interface ImplementationTypes extends ForType<'Complex', typeof Complex> {}
-}

src/Complex/arithmetic.ts

@@ -1,88 +1,104 @@
-import {Complex, complex_binary} from './type.js'
+import {Complex} from './type.js'
-import {Dependency} from '../core/Dispatcher.js'
+import type {
+   Dependencies, Signature, Returns, RealType, AliasOf
+} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
 
-export const add = <T>(dep: Dependency<'add', [T,T]>) =>
+declare module "../interfaces/type" {
-   (w: Complex<T>, z: Complex<T>) =>
+   interface Signatures<T> {
-   complex_binary(dep.add(w.re, z.re), dep.add(w.im, z.im))
+      addReal: AliasOf<'add', (a: T, b: RealType<T>) => T>
+      divideReal: AliasOf<'divide', (a: T, b: RealType<T>) => T>
+   }
+}
 
-export const unaryMinus = <T>(dep: Dependency<'unaryMinus', [T]>) =>
+export const add =
-   (z: Complex<T>) =>
+   <T>(dep: Dependencies<'add' | 'complex', T>): Signature<'add', Complex<T>> =>
-   complex_binary(dep.unaryMinus(z.re), dep.unaryMinus(z.im))
+   (w, z) => dep.complex(dep.add(w.re, z.re), dep.add(w.im, z.im))
 
-export const conj = <T>(dep: Dependency<'unaryMinus', [T]>) =>
+export const addReal =
-   (z: Complex<T>) =>
+   <T>(dep: Dependencies<'addReal' | 'complex', T>):
-   complex_binary(z.re, dep.unaryMinus(z.im))
+      Signature<'addReal', Complex<T>> =>
+   (z, r) => dep.complex(dep.addReal(z.re, r), z.im)
 
-export const subtract = <T>(dep: Dependency<'subtract', [T,T]>) =>
+export const unaryMinus =
-   (w: Complex<T>, z: Complex<T>) =>
+   <T>(dep: Dependencies<'unaryMinus' | 'complex', T>):
-   complex_binary(dep.subtract(w.re, z.re), dep.subtract(w.im, z.im))
+      Signature<'unaryMinus', Complex<T>> =>
+   z => dep.complex(dep.unaryMinus(z.re), dep.unaryMinus(z.im))
+
+export const conj =
+   <T>(dep: Dependencies<'unaryMinus' | 'conj' | 'complex', T>):
+      Signature<'conj', Complex<T>> =>
+   z => dep.complex(dep.conj(z.re), dep.unaryMinus(z.im))
+
+export const subtract =
+   <T>(dep: Dependencies<'subtract' | 'complex', T>):
+      Signature<'subtract', Complex<T>> =>
+   (w, z) => dep.complex(dep.subtract(w.re, z.re), dep.subtract(w.im, z.im))
 
 export const multiply =
-   <T>(dep: Dependency<'add', [T,T]>
+   <T>(dep: Dependencies<
-       & Dependency<'subtract', [T,T]>
+       'add' | 'subtract' | 'multiply' | 'conj' | 'complex', T>):
-       & Dependency<'multiply', [T,T]>
+      Signature<'multiply', Complex<T>> =>
-       & Dependency<'conj', [T]>) =>
+   (w, z) => {
-   (w: Complex<T>, z: Complex<T>) => {
       const mult = dep.multiply
       const realpart = dep.subtract(
          mult(         w.re,  z.re), mult(dep.conj(w.im), z.im))
       const imagpart = dep.add(
          mult(dep.conj(w.re), z.im), mult(         w.im,  z.re))
-      return complex_binary(realpart, imagpart)
+      return dep.complex(realpart, imagpart)
    }
 
-declare module "../core/Dispatcher" {
-   interface ImplementationTypes {
-      add_Complex: typeof add
-      multiply_Complex: typeof multiply
-   }
-}
-
-type AbsquareReturns<T> = T extends Complex<infer U> ? AbsquareReturns<U> : T
 export const absquare =
-   <T>(dep: Dependency<'absquare', [T]>
+   <T>(dep: Dependencies<'absquare', T>
-       & Dependency<'add', [AbsquareReturns<T>, AbsquareReturns<T>]>) =>
+       & Dependencies<'add', Returns<'absquare', T>>):
-   (z: Complex<T>) => dep.add(dep.absquare(z.re), dep.absquare(z.im))
+      Signature<'absquare', Complex<T>> =>
+   z => dep.add(dep.absquare(z.re), dep.absquare(z.im))
 
+export const divideReal =
+   <T>(dep: Dependencies<'divideReal' | 'complex', T>):
+      Signature<'divideReal', Complex<T>> =>
+   (z, r) => dep.complex(dep.divideReal(z.re, r), dep.divideReal(z.im, r))
 
 export const reciprocal =
-   <T>(dep: Dependency<'unaryMinus', [T]>
+   <T>(dep: Dependencies<'conj' | 'absquare' | 'divideReal', Complex<T>>):
-       & Dependency<'absquare', [Complex<T>]>
+      Signature<'reciprocal', Complex<T>> =>
-       & Dependency<'divide', [T, T]>) =>
+   z => dep.divideReal(dep.conj(z), dep.absquare(z))
-   (z: Complex<T>) => {
-      const denom = dep.absquare(z)
-      return complex_binary(
-         dep.divide(z.re, denom), dep.divide(dep.unaryMinus(z.im), denom))
-   }
 
 export const divide =
-   <T>(dep: Dependency<'multiply', [Complex<T>, Complex<T>]>
+   <T>(dep: Dependencies<'multiply' | 'reciprocal', Complex<T>>):
-       & Dependency<'reciprocal', [Complex<T>]>) =>
+      Signature<'divide', Complex<T>> =>
-   (w: Complex<T>, z: Complex<T>) => dep.multiply(w, dep.reciprocal(z))
+   (w, z) => dep.multiply(w, dep.reciprocal(z))
 
+// The dependencies are slightly tricky here, because there are three types
+// involved: Complex<T>, T, and RealType<T>, all of which might be different,
+// and we have to get it straight which operations we need on each type, and
+// in fact, we need `addReal` on both T and Complex<T>, hence the dependency
+// with a custom name, not generated via Dependencies<...>
 export const sqrt =
-   <T>(dep: Dependency<'equal', [T,T]>
+   <T>(dep: Dependencies<'equal' | 'conservativeSqrt' | 'unaryMinus', RealType<T>>
-       & Dependency<'add', [T,T]>
+       & Dependencies<'zero' | 'complex', T>
-       & Dependency<'isSquare', [T]>
+       & Dependencies<'absquare' | 're' | 'divideReal', Complex<T>>
-       & Dependency<'zero', [T]>
+       & {
-       & Dependency<'sqrt', [T]>
+         addTR: Signature<'addReal', T>,
-       & Dependency<'absquare', [Complex<T>]>
+         addRR: Signature<'add', RealType<T>>,
-       & Dependency<'one', [T]>
+         addCR: Signature<'addReal', Complex<T>>
-       & Dependency<'divide', [T,T]>
+       }): Signature<'sqrt', Complex<T>> =>
-       & Dependency<'subtract', [T,T]>
+   z => {
-       & Dependency<'unaryMinus', [T]>
+      const myabs = dep.conservativeSqrt(dep.absquare(z))
-      ) =>
+      const r = dep.re(z)
-   (z: Complex<T>) => {
+      const negr = dep.unaryMinus(r)
-      if (dep.equal(z.re, dep.add(z.re, z.im)) && dep.isSquare(z.re)) {
+      if (dep.equal(myabs, negr)) {
-         // imaginary part negligible, just take square root of real part
+         // pure imaginary square root; z.im already zero
-         return complex_binary(dep.sqrt(z.re), dep.zero(z.im))
+         return dep.complex(
+            dep.zero(z.re), dep.addTR(z.im, dep.conservativeSqrt(negr)))
       }
-      const myabs = dep.sqrt(dep.absquare(z))
+      const num = dep.addCR(z, myabs)
-      const real1 = dep.one(z.re)
+      const denomsq = dep.addRR(dep.addRR(myabs, myabs), dep.addRR(r, r))
-      const real2 = dep.add(real1, real1)
+      const denom = dep.conservativeSqrt(denomsq)
-      const realQuot = dep.divide(dep.add(myabs, z.re), real2)
+      return dep.divideReal(num, denom)
-      const imagQuot = dep.divide(dep.subtract(myabs, z.re), real2)
-      let realPart = dep.sqrt(realQuot)
-      if (!(dep.isSquare(z.im))) realPart = dep.unaryMinus(realPart)
-      return complex_binary(realPart, dep.sqrt(imagQuot))
    }
+
+$reflect!([
+   add, addReal, unaryMinus, conj, subtract, multiply, absquare, divideReal,
+   reciprocal, divide, sqrt
+])

src/Complex/predicate.ts

@@ -0,0 +1,13 @@
+import {Complex} from './type.js'
+import type {Dependencies, Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
+
+export const isReal =
+   <T>(dep: Dependencies<'add' | 'equal' | 'isReal', T>):
+      Signature<'isReal', Complex<T>> =>
+   z => dep.isReal(z.re) && dep.equal(z.re, dep.add(z.re, z.im))
+
+export const isSquare = (): Signature<'isSquare', Complex<unknown>> =>
+   z => true // FIXME: not correct for Complex<bigint> once we get there
+
+$reflect!([isReal, isSquare])

src/Complex/relational.ts

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

src/Complex/type.ts

@@ -1,28 +1,67 @@
-import {joinTypes, typeOfDependency, Dependency} from '../core/Dispatcher.js'
+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 type Complex<T> = { re: T; im: T; }
 
 export const Complex_type = {
-   test: <T>(dep: {testT: (z: unknown) => z is T}) =>
+   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' && 're' in z && 'im' in z
+         typeof z === 'object' && z != null && 're' in z && 'im' in z
-      && dep.testT(z.re) && dep.testT(z.im),
+         && dep.testT(z['re']) && dep.testT(z['im']),
    infer: (dep: typeOfDependency) =>
       (z: Complex<unknown>) => joinTypes(dep.typeOf(z.re), dep.typeOf(z.im)),
    from: {
-      T: <T>(dep: Dependency<'zero', [T]>) => (t: T) =>
+      T: <T>(dep: Dependencies<'zero', T>) => (t: T) =>
-         ({re: t, im: dep.zero(t)}),
+         ({ re: t, im: dep.zero(t) }),
-      Complex: <U,T>(dep: {convert: (from: U) => T}) =>
+      Complex: <U, T>(dep: { convert: (from: U) => T }) =>
-         (z: Complex<U>) => ({re: dep.convert(z.re), im: dep.convert(z.im)})
+         (z: Complex<U>) => ({ re: dep.convert(z.re), im: dep.convert(z.im) })
    }
 }
 
-export const complex_unary = <T>(dep: Dependency<'zero', [T]>) =>
+declare module "../interfaces/type" {
-   (t: T) => ({re: t, im: dep.zero(t)})
+   interface AssociatedTypes<T> {
-export const complex_binary = <T>(t: T, u: T) => ({re: t, im: u})
+      Complex: T extends Complex<infer R> ? {
+         type: Complex<R>
+         zero: Complex<ZeroType<R>>
+         one:  Complex<OneType<R> | ZeroType<R>>
+         nan:  Complex<NaNType<R>>
+         real: RealType<R>
+      } : never
+   }
 
-export const zero = <T>(dep: Dependency<'zero', [T]>) => (z: Complex<T>) =>
+   interface Signatures<T> {
-   complex_binary(dep.zero(z.re), dep.zero(z.im))
+      complex: ((re: T) => Complex<T>) | ((re: T, im: T) => Complex<T>)
-export const one = <T>(dep: Dependency<'one', [T]> & Dependency<'zero', [T]>) =>
+   }
-   (z: Complex<T>) =>
+}
-   complex_binary(dep.one(z.re), dep.zero(z.im))
+
+export const complex =
+   <T>(dep: Dependencies<'zero', T>): Signature<'complex', T> =>
+   (a, b) => ({re: a, im: b || dep.zero(a)})
+
+export const zero =
+   <T>(dep: Dependencies<'zero', T>
+       & Dependencies<'complex', Returns<'zero', T>>):
+      Signature<'zero', Complex<T>> =>
+   z => dep.complex(dep.zero(z.re), dep.zero(z.im))
+
+export const one =
+   <T>(dep: Dependencies<'one' | 'zero', T>
+       & Dependencies<'complex', Returns<'one' | 'zero', T>>):
+      Signature<'one', Complex<T>> =>
+   z => dep.complex(dep.one(z.re), dep.zero(z.im))
+
+export const nan =
+   <T>(dep: Dependencies<'nan', T>
+       & Dependencies<'complex', Returns<'nan', T>>):
+      Signature<'nan', Complex<T>> =>
+   z => dep.complex(dep.nan(z.re), dep.nan(z.im))
+
+export const re =
+   <T>(dep: Dependencies<'re', T>): Signature<'re', Complex<T>> =>
+   z => dep.re(z.re)
+
+$reflect!([complex, zero, one, nan, re])

src/all.ts

@@ -1,2 +1,3 @@
 export * from './numbers/all.js'
 export * from './Complex/all.js'
+export * from './generic/all.js'

src/core/Dispatcher.ts

@@ -5,52 +5,29 @@
  * for specific types (including their own).
  */
 
+import {parseReflectedType, ImplementationDef} from './parseReflectedType.js'
+
 // First helper types and functions for the Dispatcher
 
 type TypeName = string
 type Parameter = TypeName
 type Signature = Parameter[]
+type DependenciesType = Record<string, Function>
 
-export interface ImplementationTypes {}
+// A "canned" dependency for a builtin function:
 export type typeOfDependency = {typeOf: (x: unknown) => TypeName}
 
-// Helper for collecting implementations
+// Utility needed in type definitions
-// (Really just suffixes the type name onto the keys of exports)
-export type ForType<T extends string, Exports> = keyof Exports extends string
-   ? {[K in keyof Exports as `${K}_${T}`]: Exports[K]}
-   : never
-
 //dummy implementation for now
 export function joinTypes(a: TypeName, b: TypeName) {
    if (a === b) return a
    return 'any'
 }
 
-/**
- * Build up to Dependency type lookup
- */
-type DependenciesType = Record<string, Function>
-
-type FinalShape<FuncType> =
-   FuncType extends (arg: DependenciesType) => Function
-   ? ReturnType<FuncType> : FuncType
-
-type BeginsWith<Name extends string> = `${Name}${string}`
-
-type DependencyTypes<Ob, Name extends string, Params extends unknown[]> =
-   {[K in keyof Ob]: K extends BeginsWith<Name>
-    ? FinalShape<Ob[K]> extends (...args: Params) => any
-      ? FinalShape<Ob[K]>
-      : never
-    : never}
-
-export type Dependency<Name extends string, Params extends unknown[]> =
-   {[N in Name]:
-    DependencyTypes<ImplementationTypes, N, Params>[keyof ImplementationTypes]}
-
 // 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),
@@ -64,14 +41,18 @@ 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) {
@@ -79,23 +60,25 @@ export class Dispatcher {
       //TODO: implement me
    }
    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.installType(
+                  item.name, collection[key][identifier] as TypeSpecification)
+            }
+         }
+      }
+      for (const trio of implementations) {
+         const [k, id, imp] = trio
+         console.log('Handling implementation', id, 'from', k)
          this.installSpecification(
-                  name, ['dunno'], 'unsure', {},
+            id, parseReflectedType(id, imp.reflectedType), imp)
-                  collection[key][identifier] as Function)
-            }
-         }
       }
    }
 }

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/all.ts

@@ -0,0 +1 @@
+export * as generic from './native.js'

src/generic/arithmetic.ts

@@ -0,0 +1,9 @@
+import type {Dependencies, Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
+
+export const square =
+   <T>(dep: Dependencies<'multiply', T>): Signature<'square', T> =>
+   z => dep.multiply(z, z)
+   // z => dep.fooBar(z, z) // fails as desired
+   // z => dep.multiply(z, 'foo') // still fails as desired
+$reflect!([square])

src/generic/native.ts

@@ -0,0 +1,2 @@
+export * from './arithmetic.js'
+export * from './relational.js'

src/generic/relational.ts

@@ -0,0 +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

@@ -1,4 +1,53 @@
+import {inspect} from 'node:util'
 import {Dispatcher} from './core/Dispatcher.js'
 import * as Specifications from './all.js'
 
 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,
+  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)
+
+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()
+console.log('1) NUMBER SQRT')
+console.log(`1.1) REFLECTED TYPE: "${Specifications.numbers.sqrt.reflectedType}"`)
+console.log(
+  '1.2) PARSED TYPE:',
+  inspect(
+    parseReflectedType('sqrt', Specifications.numbers.sqrt.reflectedType),
+    { depth: null, colors: true }))
+
+console.log()
+console.log('2) GENERIC SQUARE')
+console.log(`1.1) REFLECTED TYPE: "${Specifications.generic.square.reflectedType}"`)
+console.log('2.2) PARSED TYPE:', inspect(parseReflectedType('square', Specifications.generic.square.reflectedType), { depth: null, colors: true }))
+
+console.log()
+console.log('3) COMPLEX SQRT')
+console.log(`1.1) REFLECTED TYPE: "${Specifications.complex.sqrt.reflectedType}"`)
+console.log('3.2) PARSED TYPE:', inspect(parseReflectedType('sqrt', Specifications.complex.sqrt.reflectedType), { depth: null, colors: true }))

src/interfaces/arithmetic.ts

@@ -0,0 +1,18 @@
+import type {Complex} from '../Complex/type.js'
+import type {RealType} from './type.js'
+
+declare module "./type" {
+   interface Signatures<T> {
+      add:              (a: T, b: T) => T
+      unaryMinus:       (a: T) => T
+      conj:             (a: T) => T
+      subtract:         (a: T, b: T) => T
+      multiply:         (a: T, b: T) => T
+      square:           (a: T) => T
+      absquare:         (a: T) => RealType<T>
+      reciprocal:       (a: T) => T
+      divide:           (a: T, b: T) => T
+      conservativeSqrt: (a: T) => T
+      sqrt: (a: T)=> T extends Complex<unknown> ? T : T | Complex<T>
+   }
+}

src/interfaces/predicate.ts

@@ -0,0 +1,10 @@
+// Warning: a module must have something besides just a "declare module"
+// section; otherwise it is ignored.
+export type UnaryPredicate<T> = (a: T) => boolean
+
+declare module "./type" {
+   interface Signatures<T> {
+      isReal:   (a: T) => boolean
+      isSquare: (a: T) => boolean
+   }
+}

src/interfaces/relational.ts

@@ -0,0 +1,9 @@
+// Warning: a module must have something besides just a "declare module"
+// section; otherwise it is ignored.
+export type BinaryPredicate<T> = (a: T, b: T) => T
+declare module "./type" {
+   interface Signatures<T> {
+      equal:   (a: T, b: T) => boolean
+      unequal: (a: T, b: T) => boolean
+   }
+}

src/interfaces/type.ts

@@ -0,0 +1,90 @@
+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
+ * name of the type, and within the subinterface for that key,
+ * the type of the 'type' property is the actual TypeScript type
+ * we are associating the other properties to. Note the interface
+ * is generic with one parameter, corresponding to the fact that
+ * typocomath currently only allows generic types with a single
+ * generic parameter. This way, AssociatedTypes<SubType> can give the
+ * associated types for a generic type instantiated with SubType.
+ * That's not necessary for the 'undefined' type (or if you look in the
+ * `numbers` subdirectory, the 'number' type) or any concrete type,
+ * 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
+      zero: undefined
+      one: undefined
+      nan: undefined
+      real: undefined
+   }
+}
+
+type AssociatedTypeNames = keyof AssociatedTypes<unknown>['undefined']
+type ALookup<T, Name extends AssociatedTypeNames> = ValueIntersectionByKeyUnion<{
+   [K in keyof AssociatedTypes<T>]:
+   T extends AssociatedTypes<T>[K]['type'] ? AssociatedTypes<T>[K][Name] : unknown},
+   keyof AssociatedTypes<T>>
+
+// For everything to compile, zero and one must be subtypes of T:
+export type ZeroType<T> = ALookup<T, 'zero'> & T
+export type OneType<T> = ALookup<T, 'one'> & T
+// But I believe 'nan' really might not be, like I think we will have to use
+// 'undefined' for the nan of 'bigint', as it has nothing at all like NaN,
+// so don't force it:
+export type NaNType<T> = ALookup<T, 'nan'>
+export type RealType<T> = ALookup<T, 'real'>
+
+/*****
+ * The global signature patterns for all operations need to be published in the
+ * following interface. Each key is the name of an operation (but note that
+ * the Dispatcher will automatically merge operations that have the same
+ * name when the first underscore `_` and everything thereafter is stripped).
+ * The type of each key should be an interface with two properties: 'params'
+ * whose type is the type of the parameter list for the operation, and
+ * 'returns' whose type is the return type of the operation on those
+ * parameters. These types are generic in a parameter type T which should
+ * be interpreted as the type that the operation is supposed to "primarily"
+ * operate on, although note that some of the parameters and/or return types
+ * may depend on T rather than be exactly T.
+ * So note that the example 're' below provides essentially the same
+ * information that e.g.
+ * `type ReOp<T> = (t: T) => RealType<T>`
+ * would, but in a way that is much easier to manipulate in TypeScript,
+ * and it records the name of the operation as 're' also by virtue of the
+ * key 're' in the interface.
+ ****/
+export interface Signatures<T> {
+   zero: (a: T) => ZeroType<T>
+   one:  (a: T) => OneType<T>
+   // nan needs to be able to operate on its own output for everything
+   // else to compile. That's why its parameter type is widened:
+   nan:  (a: T | NaNType<T>) => NaNType<T>
+   re:   (a: T) => RealType<T>
+}
+
+type SignatureKey<T> = keyof Signatures<T>
+
+export type Signature<Name extends SignatureKey<T>, T> = Signatures<T>[Name]
+export type Returns<Name extends SignatureKey<T>, 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/all.ts

@@ -1,8 +1,3 @@
-import {ForType} from '../core/Dispatcher.js'
 import * as numbers from './native.js'
 
 export {numbers}
-
-declare module "../core/Dispatcher" {
-   interface ImplementationTypes extends ForType<'numbers', typeof numbers> {}
-}

src/numbers/arithmetic.ts

@@ -1,23 +1,35 @@
-import {configDependency} from '../core/Config.js'
+import type {configDependency} from '../core/Config.js'
-import {Dependency} from '../core/Dispatcher.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
+const unaMinus = (a: number) => -a
+export const unaryMinus = (): Signature<'unaryMinus', number> => unaMinus
+export const conj =       (): Signature<'conj',       number> => a => a
+export const subtract =   (): Signature<'subtract',   number> => (a, b) => a - b
+export const multiply =   (): Signature<'multiply',   number> => (a, b) => a * b
+export const absquare =   (): Signature<'absquare',   number> => a => a * a
+export const reciprocal = (): Signature<'reciprocal', number> => a => 1 / a
+export const divide =     (): Signature<'divide',     number> => (a, b) => a / b
+
+const basicSqrt = (a: number) => isNaN(a) ? NaN : Math.sqrt(a)
+export const conservativeSqrt = (): Signature<'conservativeSqrt', number> =>
+  basicSqrt
 
-export const add = (a: number, b: number) => a + b
-export const unaryMinus = (a: number) => -a
-export const conj = (a: number) => a
-export const subtract = (a: number, b: number) => a - b
-export const multiply = (a: number, b: number) => a * b
-export const absquare = (a: number) => a * a
-export const reciprocal = (a: number) => 1 / a
-export const divide = (a: number, b: number) => a / b
 export const sqrt =
   (dep: configDependency
-    & Dependency<'complex', [number, number]>) => {
+   & Dependencies<'complex', number>): Signature<'sqrt', number> => {
     if (dep.config.predictable || !dep.complex) {
-          return (a: number) => isNaN(a) ? NaN : Math.sqrt(a)
+      return basicSqrt
     }
-       return (a: number) => {
+    return a => {
       if (isNaN(a)) return NaN
       if (a >= 0) return Math.sqrt(a)
-          return dep.complex(0, Math.sqrt(unaryMinus(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 +1,7 @@
-export const isSquare = (a:number) => a >=0
+import type {Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'
+
+export const isReal =   (): Signature<'isReal',   number> => (a) => true
+export const isSquare = (): Signature<'isSquare', number> => (a) => a >= 0
+
+$reflect!([isReal, isSquare])

src/numbers/relational.ts

@@ -1,8 +1,12 @@
 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
 
-export const equal = (dep: configDependency) => (x: number, y: number) => {
+export const equal =
+   (dep: configDependency): Signature<'equal', number> =>
+   (x, y) => {
       const eps = dep.config.epsilon
       if (eps === null || eps === undefined) return x === y
       if (x === y) return true
@@ -15,4 +19,5 @@ export const equal = (dep: configDependency) => (x: number, y: number) => {
       }
 
       return false
-}
+   }
+$reflect!([equal])

src/numbers/type.ts

@@ -1,8 +1,29 @@
+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 => +s}
+   from: { string: (s: string) => +s }
 }
 
-export const zero = (a: number) => 0
+declare module "../interfaces/type" {
-export const one = (a: number) => 0
+   interface AssociatedTypes<T> {
+      number: {
+         type: number
+         zero: 0
+         one: 1
+         nan: typeof NaN
+         real: number
+      }
+   }
+}
+
+// I don't like the redundancy of repeating 'zero'; any way to eliminate that?
+export const zero = (): Signature<'zero', number> => (a) => 0
+export const one =  (): Signature<'one',  number> => (a) => 1
+export const nan =  (): Signature<'nan',  number> => (a) => NaN
+export const re =   (): Signature<'re',   number> => (a) => a
+
+$reflect!([zero, one, nan, re])

tsconfig.json

@@ -1,7 +1,12 @@
 {
     "compilerOptions": {
-        "target": "ES2022",
+        "target": "esnext",
         "rootDir": "./src",
-        "outDir": "./obj"
+        "outDir": "./build",
+        "moduleResolution": "nodenext",
+        "plugins": [ {
+            "transform": "ts-macros/dist/type-resolve",
+            "transformProgram": true
+        } ]
     }
 }