2023-10-17 22:02:18 +00:00
19 changed files with 1317 additions and 56 deletions
--- a/README.md
+++ b/README.md
@ -8,3 +8,7 @@ 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.
--- a/package.json5
+++ b/package.json5
@ -1,13 +1,14 @@
 {
   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: 'tsc && cp etc/package.json build',
-      exec: 'node build',
-      go: 'pnpm --sequential "/build|exec/"',
+      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: [
@ -22,8 +23,13 @@
      url: 'https://code.studioinfinity.org/glen/typocomath.git',
   },
   devDependencies: {
-      '@types/node': '^20.5.0',
-      'source-map': '^0.7.4',
-      typescript: '^5.1.6',
+      '@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',
   },
 }
--- a/pnpm-lock.yaml
+++ b/pnpm-lock.yaml
@ -6,19 +6,771 @@ settings:

 devDependencies:
  '@types/node':
-    specifier: ^20.5.0
-    version: 20.5.0
+    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
+    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
+    specifier: 5.1.6
    version: 5.1.6

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+    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

+  /spdx-correct@3.2.0:
+    resolution: {integrity: sha512-kN9dJbvnySHULIluDHy32WHRUu3Og7B9sbY7tsFLctQkIqnMh3hErYgdMjTYuqmcXX+lK5T1lnUt3G7zNswmZA==}
+    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
--- a/src/Complex/arithmetic.ts
+++ b/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
+$reflect!([
+   add, addReal, unaryMinus, conj, subtract, multiply, absquare, divideReal,
+   reciprocal, divide, sqrt
+])
--- a/src/Complex/predicate.ts
+++ b/src/Complex/predicate.ts
@ -1,9 +1,13 @@
 import {Complex} from './type.js'
 import type {Dependencies, Signature} from '../interfaces/type.js'
+import {$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
+
+$reflect!([isReal, isSquare])
--- a/src/Complex/relational.ts
+++ b/src/Complex/relational.ts
@ -1,6 +1,8 @@
 import {Complex} from './type.js'
 import {Dependencies, Signature} from '../interfaces/type.js'
+import {$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)
+$reflect!([equal])
--- a/src/Complex/type.ts
+++ b/src/Complex/type.ts
@ -2,6 +2,7 @@ import {joinTypes, typeOfDependency} from '../core/Dispatcher.js'
 import type {
   ZeroType, OneType, NaNType, Dependencies, Signature, Returns
 } from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'

 export type Complex<T> = { re: T; im: T; }

@ -62,3 +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])
--- a/src/core/Dispatcher.ts
+++ b/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
@ -39,21 +41,25 @@ type SpecificationsGroup = Record<string, SpecObject>
 export class Dispatcher {
   installSpecification(
      name: string,
-      signature: Signature,
-      returns: TypeName,
-      dependencies: Record<string, Signature>,
+      defn: ImplementationDef,
      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)
@ -71,7 +77,8 @@ export class Dispatcher {
      for (const trio of implementations) {
         const [k, id, imp] = trio
         console.log('Handling implementation', id, 'from', k)
-         this.installSpecification(id, ['dunno'], 'unsure', {}, imp)
+         this.installSpecification(
+            id, parseReflectedType(id, imp.reflectedType), imp)
      }
   }
 }
--- a/src/core/parseReflectedType.ts
+++ b/src/core/parseReflectedType.ts
@ -0,0 +1,273 @@
+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>
+}
+
+/**
+ * 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)
+
+  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 "${depArgBlock}"`)
+      }
+    })
+    .flatMap(parseDependencies)
+
+  const dependencies: Record<string, FunctionDef> = groupBy(deps, 'name')
+
+  return {fn, dependencies}
+}
+
+function parseDependencies(deps: string): FunctionDef[] {
+  if (deps === 'configDependency') {
+    return [{name: 'config', signatures: [{args: [], returns: 'Config'}]}]
+  }
+  const inner = findBlockContents(deps, '{', '}').innerText
+  return split(inner, ';')
+    .map(trim)
+    .filter(notEmpty)
+    .map(parseDependency)
+}
+
+// parse a dependency like "complex: ((re: number) => Complex<number>) | ((re: number, im: number) => Complex<number>)"
+function parseDependency(dep: string): FunctionDef {
+  const [name, def] = split(dep, ':').map(trim)
+
+  return parseAlias(name, def)
+}
+
+// Parse a possibly aliased function
+function parseAlias(name: string, alias: string): FunctionDef {
+  const { aliasOf, innerSignature } = parseAliasOf(alias)
+
+  return { name, signatures: parseSignatures(innerSignature), aliasOf }
+}
+
+// parse function signatures like ((re: number) => Complex<number>) | ((re: number, im: number) => Complex<number>)
+// But also have to succeed on (a: number) => number | Complex<number>
+// That's why we only split on an alternation bar `|` that's followed by
+// a parenthesis; that way we avoid splitting a union return type. Note
+// this is not necessarily foolproof, as there could be a return type that
+// is a union with a complicated piece that has to be enclosed in parens;
+// but so far it seems to work in practice.
+function parseSignatures(sigs: string) {
+  return split(sigs, /[|]\s*(?=[(])/)
+    .map(trim)
+    .map(stripParenthesis)
+    .map(signature => {
+      const [argsBlock, returns] = split(signature, '=>').map(trim)
+
+      if (!returns) {
+        throw new SyntaxError(`Failed to find return type in '${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
+}
--- a/src/generic/arithmetic.ts
+++ b/src/generic/arithmetic.ts
@ -1,7 +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') // fails as desired
+   // z => dep.multiply(z, 'foo') // still fails as desired
+$reflect!([square])
--- a/src/generic/relational.ts
+++ b/src/generic/relational.ts
@ -1,5 +1,7 @@
 import {Dependencies, Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'

 export const unequal =
   <T>(dep: Dependencies<'equal', T>): Signature<'unequal', T> =>
   (x, y) => !dep.equal(x, y)
+$reflect!([unequal])
--- a/src/index.ts
+++ b/src/index.ts
@ -1,3 +1,4 @@
+import {inspect} from 'node:util'
 import {Dispatcher} from './core/Dispatcher.js'
 import * as Specifications from './all.js'

@ -5,16 +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,
-    absquare: mockComplexAbsquare
+  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)

-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()
+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 }))
--- a/src/interfaces/type.ts
+++ b/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
@ -73,7 +75,16 @@ export interface Signatures<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]>
-export type Dependencies<Name extends SignatureKey<T>, T> = {[K in Name]: Signature<K, T>}
+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)]
+}
--- a/src/numbers/arithmetic.ts
+++ b/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 unaryMinus: Signature<'unaryMinus', number> = a => -a
-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
+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 => isNaN(a) ? NaN : Math.sqrt(a)
-export const conservativeSqrt: Signature<'conservativeSqrt', number> = basicSqrt
+const basicSqrt = (a: number) => isNaN(a) ? NaN : Math.sqrt(a)
+export const conservativeSqrt = (): Signature<'conservativeSqrt', number> =>
+  basicSqrt

 export const sqrt =
-   (dep: configDependency & Dependencies<'complex', number>):
-   Signature<'sqrt', number> => {
-      if (dep.config.predictable || !dep.complex) return basicSqrt
-      return a => {
-         if (isNaN(a)) return NaN
-         if (a >= 0) return Math.sqrt(a)
-         return dep.complex(0, Math.sqrt(unaryMinus(a)))
-      }
+  (dep: configDependency
+   & Dependencies<'complex', number>): Signature<'sqrt', number> => {
+    if (dep.config.predictable || !dep.complex) {
+      return basicSqrt
+    }
+    return a => {
+      if (isNaN(a)) return NaN
+      if (a >= 0) return Math.sqrt(a)
+      return dep.complex(0, Math.sqrt(unaMinus(a)))
+    }
   }
+
+$reflect!([
+  add, unaryMinus, conj, subtract, multiply, absquare, reciprocal, divide,
+  conservativeSqrt, sqrt
+])
--- a/src/numbers/native.ts
+++ b/src/numbers/native.ts
@ -1,2 +1,4 @@
 export * from './type.js'
 export * from './arithmetic.js'
+export * from './predicate.js'
+export * from './relational.js'
--- a/src/numbers/predicate.ts
+++ b/src/numbers/predicate.ts
@ -1,4 +1,7 @@
 import type {Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'

-export const isReal:   Signature<'isReal',   number> = (a) => true
-export const isSquare: Signature<'isSquare', number> = (a) => a >= 0
+export const isReal =   (): Signature<'isReal',   number> => (a) => true
+export const isSquare = (): Signature<'isSquare', number> => (a) => a >= 0
+
+$reflect!([isReal, isSquare])
--- a/src/numbers/relational.ts
+++ b/src/numbers/relational.ts
@ -1,5 +1,6 @@
 import {configDependency} from '../core/Config.js'
 import {Signature} from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'

 const DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16

@ -19,3 +20,4 @@ export const equal =

      return false
   }
+$reflect!([equal])
--- a/src/numbers/type.ts
+++ b/src/numbers/type.ts
@ -1,4 +1,5 @@
 import type { Signature } from '../interfaces/type.js'
+import {$reflect} from '../interfaces/type.js'

 export const number_type = {
   name: 'number', // just until we have reflection to tell us
@ -20,7 +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 one:  Signature<'one',  number> = (a) => 1
-export const nan:  Signature<'nan',  number> = (a) => NaN
-export const re:   Signature<'re',   number> = (a) => a
+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])
--- a/tsconfig.json
+++ b/tsconfig.json
@ -1,8 +1,12 @@
 {
    "compilerOptions": {
-        "target": "ES2022",
+        "target": "esnext",
        "rootDir": "./src",
        "outDir": "./build",
-        "moduleResolution": "nodenext"
+        "moduleResolution": "nodenext",
+        "plugins": [ {
+            "transform": "ts-macros/dist/type-resolve",
+            "transformProgram": true
+        } ]
    }
 }