Declare implementations and dependencies via standard interfaces for operations (#8)

Adds a new subdirectory `interfaces` where standard interfaces
  are defined. Additional interfaces for a given operation can
  be added with an `AliasOf` type operator. Provides type
  operators that give the return type, full function type, and
  the type of a dependency on, a given operator.

  Resolves #6.

Co-authored-by: Glen Whitney <glen@studioinfinity.org>
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
Reviewed-on: #8

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

@@ -0,0 +1,101 @@
+import {Complex} from './type.js'
+import type {
+   Dependencies, Signature, Returns, RealType, AliasOf
+} from '../interfaces/type.js'
+
+declare module "../interfaces/type" {
+   interface Signatures<T> {
+      addReal: AliasOf<'add', (a: T, b: RealType<T>) => T>
+      divideReal: AliasOf<'divide', (a: T, b: RealType<T>) => T>
+   }
+}
+
+export const add =
+   <T>(dep: Dependencies<'add' | 'complex', T>): Signature<'add', Complex<T>> =>
+   (w, z) => dep.complex(dep.add(w.re, z.re), dep.add(w.im, z.im))
+
+export const addReal =
+   <T>(dep: Dependencies<'addReal' | 'complex', T>):
+      Signature<'addReal', Complex<T>> =>
+   (z, r) => dep.complex(dep.addReal(z.re, r), z.im)
+
+export const unaryMinus =
+   <T>(dep: Dependencies<'unaryMinus' | 'complex', T>):
+      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: Dependencies<
+       'add' | 'subtract' | 'multiply' | 'conj' | 'complex', T>):
+      Signature<'multiply', Complex<T>> =>
+   (w, z) => {
+      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 dep.complex(realpart, imagpart)
+   }
+
+export const absquare =
+   <T>(dep: Dependencies<'absquare', T>
+       & Dependencies<'add', Returns<'absquare', T>>):
+      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: Dependencies<'conj' | 'absquare' | 'divideReal', Complex<T>>):
+      Signature<'reciprocal', Complex<T>> =>
+   z => dep.divideReal(dep.conj(z), dep.absquare(z))
+
+export const divide =
+   <T>(dep: Dependencies<'multiply' | 'reciprocal', Complex<T>>):
+      Signature<'divide', Complex<T>> =>
+   (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: Dependencies<'equal' | 'conservativeSqrt' | 'unaryMinus', RealType<T>>
+       & Dependencies<'zero' | 'complex', T>
+       & Dependencies<'absquare' | 're' | 'divideReal', Complex<T>>
+       & {
+         addTR: Signature<'addReal', T>, 
+         addRR: Signature<'add', RealType<T>>,
+         addCR: Signature<'addReal', Complex<T>>
+      }):
+      Signature<'sqrt', Complex<T>> =>
+   z => {
+      const myabs = dep.conservativeSqrt(dep.absquare(z))
+      const r = dep.re(z)
+      const negr = dep.unaryMinus(r)
+      if (dep.equal(myabs, negr)) {
+         // pure imaginary square root; z.im already zero
+         return dep.complex(
+            dep.zero(z.re), dep.addTR(z.im, dep.conservativeSqrt(negr)))
+      }
+      const num = dep.addCR(z, myabs)
+      const denomsq = dep.addRR(dep.addRR(myabs, myabs), dep.addRR(r, r))
+      const denom = dep.conservativeSqrt(denomsq)
+      return dep.divideReal(num, denom)
+   }
+
+export const conservativeSqrt = sqrt

src/Complex/predicate.ts

@@ -0,0 +1,9 @@
+import {Complex} from './type.js'
+import type {Dependencies, Signature} 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

src/Complex/relational.ts

@@ -0,0 +1,6 @@
+import {Complex} from './type.js'
+import {Dependencies, Signature} 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)

src/Complex/type.ts

@@ -1,22 +1,63 @@
-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'
 
-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}) =>
+   test: <T>(dep: { testT: (z: unknown) => z is T }) =>
       (z: unknown): z is Complex<T> =>
-      typeof z === 'object' && 're' in z && 'im' in z
-      && dep.testT(z.re) && dep.testT(z.im),
+         typeof z === 'object' && z != null && 're' in z && 'im' in z
+         && 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) =>
-         ({re: t, im: dep.zero(t)}),
-      Complex: <U,T>(dep: {convert: (from: U) => T}) =>
-         (z: Complex<U>) => ({re: dep.convert(z.re), im: dep.convert(z.im)})
+      T: <T>(dep: Dependencies<'zero', T>) => (t: T) =>
+         ({ re: t, im: dep.zero(t) }),
+      Complex: <U, T>(dep: { convert: (from: U) => T }) =>
+         (z: Complex<U>) => ({ re: dep.convert(z.re), im: dep.convert(z.im) })
    }
 }
 
-export const complex_unary = <T>(dep: Dependency<'zero', [T]>) =>
-   (t: T) => ({re: t, im: dep.zero(t)})
-export const complex_binary = <T>(t: T, u: T) => ({re: t, im: u})
+declare module "../interfaces/type" {
+   interface AssociatedTypes<T> {
+      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
+   }
+
+   interface Signatures<T> {
+      complex: ((re: T) => Complex<T>) | ((re: T, im: T) => Complex<T>)
+   }
+}
+
+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)