refactor: tighter universal interface types

src/Complex/arithmetic.ts

@@ -1,103 +1,96 @@
-import {Complex, complex_binary, FnComplexUnary} from './type.js'
+import {Complex, ComplexOp} from './type.js'
 import type {
-    FnAbsSquare,
+   AbsquareOp, AddOp, AddRealOp, ConjOp, ConservativeSqrtOp, DivideOp,
-    FnAdd,
+   DivideByRealOp, MultiplyOp, ReciprocalOp, SqrtOp, SubtractOp,
-    FnAddReal,
+   UnaryMinusOp
-    FnConj, FnConservativeSqrt, FnDivide,
+} from '../interfaces/arithmetic.js'
-    FnDivideByReal, FnIsReal, FnIsSquare,
+import type {
-    FnMultiply, FnNaN, FnRe, FnReciprocal, FnSqrt,
+   NanOp, ReOp, ZeroOp, Depends, RealType, WithConstants, NaNType
-    FnSubtract,
+} from '../interfaces/type.js'
-    FnUnaryMinus, FnZero
+import type {IsSquareOp, IsRealOp} from '../interfaces/predicate.js'
-} from '../interfaces/arithmetic'
 
 export const add =
-   <T>(dep: {
+   <T>(dep: Depends<AddOp<T>> & Depends<ComplexOp<T>>): AddOp<Complex<T>> =>
-      add: FnAdd<T>
+   (w, z) => dep.complex(dep.add(w.re, z.re), dep.add(w.im, z.im))
-   }): FnAdd<Complex<T>> =>
-      (w, z) => complex_binary(dep.add(w.re, z.re), dep.add(w.im, z.im))
 
 export const addReal =
-   <T>(dep: {
+   <T>(dep: Depends<AddRealOp<T>> & Depends<ComplexOp<T>>):
-      addReal: FnAddReal<T, T>
+      AddRealOp<Complex<T>> =>
-   }): FnAddReal<Complex<T>, T> =>
+   (z, r) => dep.complex(dep.addReal(z.re, r), z.im)
-      (z, r) => complex_binary(dep.addReal(z.re, r), z.im)
 
 export const unaryMinus =
-   <T>(dep: {
+   <T>(dep: Depends<UnaryMinusOp<T>> & Depends<ComplexOp<T>>):
-      unaryMinus: FnUnaryMinus<T>
+      UnaryMinusOp<Complex<T>> =>
-   }): FnUnaryMinus<Complex<T>> =>
+   z => dep.complex(dep.unaryMinus(z.re), dep.unaryMinus(z.im))
-      (z) => complex_binary(dep.unaryMinus(z.re), dep.unaryMinus(z.im))
 
 export const conj =
-   <T>(dep: {
+   <T>(dep: Depends<UnaryMinusOp<T>>
-      unaryMinus: FnUnaryMinus<T>,
+       & Depends<ConjOp<T>>
-      conj: FnConj<T>
+       & Depends<ComplexOp<T>>):
-   }) : FnConj<Complex<T>> =>
+      ConjOp<Complex<T>> =>
-      (z) => complex_binary(dep.conj(z.re), dep.unaryMinus(z.im))
+   z => dep.complex(dep.conj(z.re), dep.unaryMinus(z.im))
 
 export const subtract =
-   <T>(dep: {
+   <T>(dep: Depends<SubtractOp<T>> & Depends<ComplexOp<T>>):
-      subtract: FnSubtract<T>
+      SubtractOp<Complex<T>> =>
-   }): FnSubtract<Complex<T>> =>
+   (w, z) => dep.complex(dep.subtract(w.re, z.re), dep.subtract(w.im, z.im))
-      (w, z) => complex_binary(dep.subtract(w.re, z.re), dep.subtract(w.im, z.im))
 
 export const multiply =
-   <T>(dep: {
+   <T>(dep: Depends<AddOp<T>>
-      add: FnAdd<T>,
+       & Depends<SubtractOp<T>>
-      subtract: FnSubtract<T>,
+       & Depends<MultiplyOp<T>>
-      multiply: FnMultiply<T>,
+       & Depends<ConjOp<T>>
-      conj: FnConj<T>
+       & Depends<ComplexOp<T>>):
-   }) =>
+      MultiplyOp<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 realpart = dep.subtract(
-         const imagpart = dep.add(mult(dep.conj(w.re), z.im), mult(w.im, z.re))
+         mult(         w.re,  z.re), mult(dep.conj(w.im), z.im))
-         return complex_binary(realpart, imagpart)
+      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, U>(dep: {
+   <T>(dep: Depends<AddOp<RealType<T>>> & Depends<AbsquareOp<T>>):
-      add: FnAdd<U>,
+      AbsquareOp<Complex<T>> =>
-      absquare: FnAbsSquare<T, U>
+   z => dep.add(dep.absquare(z.re), dep.absquare(z.im))
-   }): FnAbsSquare<Complex<T>, U> =>
-      (z) => dep.add(dep.absquare(z.re), dep.absquare(z.im))
 
 export const divideByReal =
-   <T>(dep: {
+   <T>(dep: Depends<DivideByRealOp<T>> & Depends<ComplexOp<T>>):
-       divideByReal: FnDivideByReal<T, T>
+      DivideByRealOp<Complex<T>> =>
-   }): FnDivideByReal<Complex<T>, T> =>
+   (z, r) => dep.complex(dep.divideByReal(z.re, r), dep.divideByReal(z.im, r))
-      (z, r) => complex_binary(dep.divideByReal(z.re, r), dep.divideByReal(z.im, r))
 
 export const reciprocal =
-   <T>(dep: {
+   <T>(dep: Depends<ConjOp<Complex<T>>>
-      conj: FnConj<Complex<T>>,
+       & Depends<AbsquareOp<Complex<T>>>
-      absquare: FnAbsSquare<Complex<T>, T>,
+       & Depends<DivideByRealOp<Complex<T>>>):
-      divideByReal: FnDivideByReal<Complex<T>, T>
+      ReciprocalOp<Complex<T>> =>
-   }): FnReciprocal<Complex<T>> =>
+   z => dep.divideByReal(dep.conj(z), dep.absquare(z))
-      (z) => dep.divideByReal(dep.conj(z), dep.absquare(z))
 
 export const divide =
-   <T>(dep: {
+   <T>(dep: Depends<MultiplyOp<Complex<T>>>
-      multiply: FnMultiply<Complex<T>>,
+       & Depends<ReciprocalOp<Complex<T>>>):
-      reciprocal: FnReciprocal<Complex<T>>,
+      DivideOp<Complex<T>> =>
-   }): FnDivide<Complex<T>> =>
    (w, z) => dep.multiply(w, dep.reciprocal(z))
 
+export type ComplexSqrtOp<T> = {
+   op?: 'complexSqrt',
+   (a: T): Complex<WithConstants<T> | NaNType<WithConstants<T>>>
+}
+// Complex square root of a real type T
 export const complexSqrt =
-   <T>(dep: {
+   <T>(dep: Depends<ConservativeSqrtOp<T>>
-      conservativeSqrt: FnConservativeSqrt<T>,
+       & Depends<IsSquareOp<T>>
-      isSquare: FnIsSquare<T>,
+       & Depends<UnaryMinusOp<T>>
-      complex: FnComplexUnary<T>,
+       & Depends<ComplexOp<WithConstants<T>>>
-      unaryMinus: FnUnaryMinus<T>,
+       & Depends<ZeroOp<T>>
-      zero: FnZero<T>,
+       & Depends<NanOp<Complex<WithConstants<T>>>>): ComplexSqrtOp<T> =>
-      nan: FnNaN<Complex<T>>
+   r => {
-   }) =>
-      (r) => {
       if (dep.isSquare(r)) return dep.complex(dep.conservativeSqrt(r))
       const negative = dep.unaryMinus(r)
       if (dep.isSquare(negative)) {
-            return complex_binary(
+         return dep.complex(dep.zero(r), dep.conservativeSqrt(negative))
-               dep.zero(r), dep.conservativeSqrt(negative))
       }
       // neither the real number or its negative is a square; could happen
       // for example with bigint. So there is no square root. So we have to
@@ -106,17 +99,15 @@ export const complexSqrt =
    }
 
 export const sqrt =
-   <T>(dep: {
+   <T>(dep: Depends<IsRealOp<Complex<T>>>
-      isReal: FnIsReal<Complex<T>>,
+       & Depends<ComplexSqrtOp<T>>
-      complexSqrt: FnSqrt<T>,
+       & Depends<ConservativeSqrtOp<RealType<T>>>
-      conservativeSqrt: FnConservativeSqrt<T>,
+       & Depends<AbsquareOp<Complex<T>>>
-      absquare: FnAbsSquare<Complex<T>, T>,
+       & Depends<AddRealOp<Complex<T>>>
-      addReal: FnAddReal<Complex<T>, T>,
+       & Depends<DivideByRealOp<Complex<T>>>
-      divideByReal: FnDivideByReal<Complex<T>, T>,
+       & Depends<AddOp<RealType<T>>>
-      add: FnAdd<T>,
+       & Depends<ReOp<Complex<T>>>): SqrtOp<Complex<T>> =>
-      re: FnRe<Complex<T>, T>,
+   z => {
-   }) =>
-      (z: Complex<T>): Complex<T> | T => {
       if (dep.isReal(z)) return dep.complexSqrt(z.re)
       const myabs = dep.conservativeSqrt(dep.absquare(z))
       const num = dep.addReal(z, myabs)

src/Complex/predicate.ts

@@ -1,14 +1,12 @@
-import { Complex } from './type.js'
+import {Complex} from './type.js'
-import {FnEqual} from '../interfaces/relational'
+import {EqualOp} from '../interfaces/relational.js'
-import {FnAdd, FnIsReal, FnIsSquare} from '../interfaces/arithmetic'
+import {AddOp} from '../interfaces/arithmetic.js'
+import type {Depends} from '../interfaces/type.js'
+import type {IsRealOp, IsSquareOp} from '../interfaces/predicate.js'
 
 export const isReal =
-   <T>(dep: {
+   <T>(dep: Depends<AddOp<T>> & Depends<EqualOp<T>> & Depends<IsRealOp<T>>):
-      equal: FnEqual<T>,
+      IsRealOp<Complex<T>> =>
-      add: FnAdd<T>,
+   z => dep.isReal(z.re) && dep.equal(z.re, dep.add(z.re, z.im))
-      isReal: FnIsReal<T>
-   }): FnIsReal<Complex<T>> =>
-      (z) => dep.isReal(z.re) && dep.equal(z.re, dep.add(z.re, z.im))
 
-export const isSquare =
+export const isSquare: IsSquareOp<Complex<any>> = z => true // FIXME: not correct for Complex<bigint> once we get there
-   <T>(): FnIsSquare<Complex<T>> => (z) => true // FIXME: not correct for Complex<bigint> once we get there

src/Complex/relational.ts

@@ -1,8 +1,7 @@
-import { Complex } from './type.js'
+import {Complex} from './type.js'
-import {FnEqual} from '../interfaces/relational'
+import {Depends} from '../interfaces/type.js'
+import {EqualOp} from '../interfaces/relational.js'
 
 export const equal =
-   <T>(dep: {
+   <T>(dep: Depends<EqualOp<T>>): EqualOp<Complex<T>> =>
-      equal: FnEqual<T>
-   }): FnEqual<Complex<T>> =>
    (w, z) => dep.equal(w.re, z.re) && dep.equal(w.im, z.im)

src/Complex/type.ts

@@ -1,7 +1,9 @@
 import {
    joinTypes, typeOfDependency, Dependency,
 } from '../core/Dispatcher.js'
-import type {FnNaN, FnOne, FnRe, FnZero} from '../interfaces/arithmetic.js'
+import type {
+   OneOp, ZeroOp, NanOp, ReOp, ZeroType, OneType, NaNType, Depends
+} from '../interfaces/type.js'
 
 export type Complex<T> = { re: T; im: T; }
 
@@ -20,39 +22,41 @@ export const Complex_type = {
    }
 }
 
-export type FnComplexUnary<T> = (t: T) => Complex<T>
+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
+   }
+}
 
-export const complex_unary =
+export type ComplexOp<T> = {op?: 'complex', (a: T, b?: T): Complex<T>}
-   <T>(dep: {
-      zero: FnZero<T>
-   }): FnComplexUnary<T> =>
-      (t) => ({ re: t, im: dep.zero(t) })
 
-export type FnComplexBinary<T> = (re: T, im: T) => Complex<T>
+export const complex =
-
+   <T>(dep: Depends<ZeroOp<T>>): ComplexOp<T | ZeroType<T>> =>
-export const complex_binary = <T>(t: T, u: T): Complex<T> => ({ re: t, im: u })
+   (a, b) => ({re: a, im: b || dep.zero(a)})
 
 export const zero =
-   <T>(dep: {
+   <T>(dep: Depends<ZeroOp<T>> & Depends<ComplexOp<ZeroType<T>>>):
-      zero: FnZero<T>
+      ZeroOp<Complex<T>> =>
-   }): FnZero<Complex<T>> =>
+   z => dep.complex(dep.zero(z.re), dep.zero(z.im))
-      (z) => complex_binary(dep.zero(z.re), dep.zero(z.im))
 
 export const one =
-   <T>(dep: {
+   <T>(dep: Depends<OneOp<T>>
-      zero: FnZero<T>,
+       & Depends<ZeroOp<T>>
-      one: FnOne<T>
+       & Depends<ComplexOp<ZeroType<T>|OneType<T>>>):
-   }): FnOne<Complex<T>> =>
+      OneOp<Complex<T>> =>
-      (z) => complex_binary(dep.one(z.re), dep.zero(z.im))
+   z => dep.complex(dep.one(z.re), dep.zero(z.im))
 
 export const nan =
-   <T>(dep: {
+   <T>(dep: Depends<NanOp<T>> & Depends<ComplexOp<NaNType<T>>>):
-      nan: FnNaN<T>
+      NanOp<Complex<T>> =>
-   }): FnNaN<Complex<T>> =>
+   z => dep.complex(dep.nan(z.re), dep.nan(z.im))
-      (z) => complex_binary(dep.nan(z.re), dep.nan(z.im))
 
 export const re =
-   <T>(dep: {
+   <T>(dep: Depends<ReOp<T>>): ReOp<Complex<T>> =>
-      re: FnRe<T,T>
+   z => dep.re(z.re)
-   }): FnRe<Complex<T>, T> =>
-      (z) => dep.re(z.re)

src/generic/all.ts

@@ -1,3 +1 @@
-import * as generic from './arithmetic.js'
+export * as generic from './native.js'
-
-export { generic }

src/generic/arithmetic.ts

@@ -1,7 +1,6 @@
-import type { FnMultiply, FnSquare } from "../interfaces/arithmetic"
+import type {Depends} from '../interfaces/type.js'
+import type {MultiplyOp, SquareOp} from '../interfaces/arithmetic.js'
 
 export const square =
-  <T>(dep: {
+   <T>(dep: Depends<MultiplyOp<T>>): SquareOp<T> =>
-    multiply: FnMultiply<T>
+   z => dep.multiply(z, z)
-  }): FnSquare<T> =>
-    (z) => dep.multiply(z, z)

src/generic/native.ts

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

src/generic/relational.ts

@@ -0,0 +1,5 @@
+import {Depends} from '../interfaces/type.js'
+import type {EqualOp, UnequalOp} from '../interfaces/relational.js'
+
+export const unequal = <T>(dep: Depends<EqualOp<T>>): UnequalOp<T> =>
+   (x, y) => !dep.equal(x, y)

src/interfaces/arithmetic.ts

@@ -1,28 +1,25 @@
-// shared interfaces
+import type {Complex} from '../Complex/type.js'
+import type {RealType, WithConstants, NaNType} from './type.js'
 
-import { Complex } from "../Complex/type"
+// Note: right now I've added an 'Op' suddix,
-
+// so it is clear that the type holds the function type of an operation
-// Note: right now I've added an 'Fn*' prefix,
-// so it is clear that the type hold a function type definition
 // This is not necessary though, it is just a naming convention.
-export type FnAdd<T> = (a: T, b: T) => T
+export type AddOp<T> = {op?: 'add', (a: T, b: T): T}
-export type FnAddReal<T, U> = (a: T, b: U) => T
+export type AddRealOp<T> = {op?: 'addReal', (a: T, b: RealType<T>): T}
-export type FnUnaryMinus<T> = (a: T) => T
+export type UnaryMinusOp<T> = {op?: 'unaryMinus', (a: T): T}
-export type FnConj<T> = (a: T) => T
+export type ConjOp<T> = {op?: 'conj', (a: T): T}
-export type FnSubtract<T> = (a: T, b: T) => T
+export type SubtractOp<T> = {op?: 'subtract', (a: T, b: T): T}
-export type FnMultiply<T> = (a: T, b: T) => T
+export type MultiplyOp<T> = {op?: 'multiply', (a: T, b: T): T}
-export type FnAbsSquare<T, U> = (a: T) => U
+export type AbsquareOp<T> = {op?: 'absquare', (a: T): RealType<T>}
-export type FnReciprocal<T> = (a: T) => T
+export type ReciprocalOp<T> = {op?: 'reciprocal', (a: T): T}
-export type FnDivide<T> = (a: T, b: T) => T
+export type DivideOp<T> = {op?: 'divide', (a: T, b: T): T}
-export type FnDivideByReal<T, U> = (a: T, b: U) => T
+export type DivideByRealOp<T> = {op?: 'divideByReal', (a: T, b: RealType<T>): T}
-export type FnConservativeSqrt<T> = (a: T) => T
+export type ConservativeSqrtOp<T> = {op?: 'conservativeSqrt', (a: T): T}
-export type FnSqrt<T> = (a: T) => T | Complex<T>
+export type SqrtOp<T> = {
-export type FnSquare<T> = (z: T) => T
+   op?: 'sqrt',
+   (a: T): T extends Complex<infer R>
+      ? Complex<WithConstants<R> | NaNType<WithConstants<R>>>
+      : T | Complex<T>
+}
+export type SquareOp<T> = {op?: 'square', (z: T): T}
 
-export type FnIsReal<T> = (a: T) => boolean
-export type FnIsSquare<T> = (a: T) => boolean
-
-export type FnZero<T> = (a: T) => T
-export type FnOne<T> = (a: T) => T
-export type FnNaN<T> = (a: T) => T
-export type FnRe<T, U> = (a: T) => U

src/interfaces/predicate.ts

@@ -0,0 +1,2 @@
+export type IsRealOp<T> = {op?: 'isReal', (a: T): boolean}
+export type IsSquareOp<T> = {op?: 'isSquare', (a: T): boolean}

src/interfaces/relational.ts

@@ -1,3 +1,2 @@
-
+export type EqualOp<T> = {op?: 'equal', (a: T, b: T): boolean}
-export type FnEqual<T> = (a: T, b: T) => boolean
+export type UnequalOp<T> = {op?: 'unequal', (a: T, b: T): boolean}
-export type FnUnequal<T> = (a: T, b: T) => boolean

src/interfaces/type.ts

@@ -0,0 +1,32 @@
+export interface AssociatedTypes<T> {
+   undefined: {
+      type: undefined
+      zero: undefined
+      one: undefined
+      nan: undefined
+      real: undefined
+   }
+}
+
+type AssociatedTypeNames = keyof AssociatedTypes<unknown>['undefined']
+export type Lookup<T, Name extends AssociatedTypeNames> = {
+   [K in keyof AssociatedTypes<T>]:
+   T extends AssociatedTypes<T>[K]['type'] ? AssociatedTypes<T>[K][Name] : never
+}[keyof AssociatedTypes<T>]
+
+export type ZeroType<T> = Lookup<T, 'zero'>
+export type OneType<T> = Lookup<T, 'one'>
+export type WithConstants<T> = T | ZeroType<T> | OneType<T>
+export type NaNType<T> = Lookup<T, 'nan'>
+export type RealType<T> = Lookup<T, 'real'>
+
+export type ZeroOp<T> = {op?: 'zero', (a: WithConstants<T>): ZeroType<T>}
+export type OneOp<T>  = {op?: 'one',  (a: WithConstants<T>): OneType<T>}
+export type NanOp<T>  = {op?: 'nan',  (a: T|NaNType<T>): NaNType<T>}
+export type ReOp<T>   = {op?: 're',   (a: T): RealType<T>}
+
+type NamedFunction = {op?: string, (...params: any[]): any}
+export type Depends<FuncType extends NamedFunction> =
+   {[K in FuncType['op']]: FuncType}
+
+                        

src/numbers/arithmetic.ts

@@ -1,26 +1,28 @@
-import { Config } from '../core/Config.js'
+import type {configDependency} from '../core/Config.js'
-import type { FnComplexBinary } from '../Complex/type.js'
+import type {ComplexOp} from '../Complex/type.js'
-import { FnAdd, FnConj, FnSubtract, FnUnaryMinus, FnMultiply, FnAbsSquare, FnReciprocal, FnDivide, FnConservativeSqrt, FnSqrt } from '../interfaces/arithmetic.js'
+import type {
+   AddOp, ConjOp, SubtractOp, UnaryMinusOp, MultiplyOp,
+   AbsquareOp, ReciprocalOp, DivideOp, ConservativeSqrtOp, SqrtOp
+} from '../interfaces/arithmetic.js'
+import type {Depends} from '../interfaces/type.js'
 
-export const add: FnAdd<number> = (a, b) => a + b
+export const add: AddOp<number> = (a, b) => a + b
 export const addReal = add
-export const unaryMinus: FnUnaryMinus<number> = (a) => -a
+export const unaryMinus: UnaryMinusOp<number> = a => -a
-export const conj: FnConj<number> = (a) => a
+export const conj: ConjOp<number> = a => a
-export const subtract: FnSubtract<number> = (a, b) => a - b
+export const subtract: SubtractOp<number> = (a, b) => a - b
-export const multiply: FnMultiply<number> = (a, b) => a * b
+export const multiply: MultiplyOp<number> = (a, b) => a * b
-export const absquare: FnAbsSquare<number, number> = (a) => a * a
+export const absquare: AbsquareOp<number> = a => a * a
-export const reciprocal: FnReciprocal<number> = (a) => 1 / a
+export const reciprocal: ReciprocalOp<number> = a => 1 / a
-export const divide: FnDivide<number> = (a, b) => a / b
+export const divide: DivideOp<number> = (a, b) => a / b
 export const divideByReal = divide
 
-export const conservativeSqrt: FnConservativeSqrt<number> = (a) => isNaN(a) ? NaN : Math.sqrt(a)
+const basicSqrt = a => isNaN(a) ? NaN : Math.sqrt(a)
+export const conservativeSqrt: ConservativeSqrtOp<number> = basicSqrt
 
 export const sqrt =
-   (dep: {
+   (dep: configDependency & Depends<ComplexOp<number>>): SqrtOp<number> => {
-      config: Config,
+      if (dep.config.predictable || !dep.complex) return basicSqrt
-      complex: FnComplexBinary<number>
-   }): FnSqrt<number> => {
-      if (dep.config.predictable || !dep.complex) return conservativeSqrt
       return a => {
          if (isNaN(a)) return NaN
          if (a >= 0) return Math.sqrt(a)

src/numbers/predicate.ts

@@ -1,4 +1,4 @@
-import type { FnIsReal, FnIsSquare } from "../interfaces/arithmetic"
+import type { IsRealOp, IsSquareOp } from '../interfaces/predicate.js'
 
-export const isReal: FnIsReal<number> = (a) => true
+export const isReal: IsRealOp<number> = (a) => true
-export const isSquare: FnIsSquare<number> = (a)  => a >= 0
+export const isSquare: IsSquareOp<number> = (a)  => a >= 0

src/numbers/relational.ts

@@ -1,12 +1,12 @@
-import { Config } from '../core/Config.js'
+import {Config} from '../core/Config.js'
-import type { FnEqual, FnUnequal } from '../interfaces/relational.js'
+import type {EqualOp} from '../interfaces/relational.js'
 
 const DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16
 
 export const equal =
    (dep: {
       config: Config
-   }): FnEqual<number> => (x, y) => {
+   }): EqualOp<number> => (x, y) => {
       const eps = dep.config.epsilon
       if (eps === null || eps === undefined) return x === y
       if (x === y) return true
@@ -20,8 +20,3 @@ export const equal =
 
       return false
    }
-
-export const unequal = (dep: {
-   equal: FnEqual<number>
-}): FnUnequal<number> =>
-   (x, y) => !dep.equal(x, y)

src/numbers/type.ts

@@ -1,4 +1,4 @@
-import type { FnNaN, FnOne, FnZero, FnRe } from "../interfaces/arithmetic"
+import type { OneOp, ZeroOp, NanOp, ReOp } from '../interfaces/type.js'
 
 export const number_type = {
    before: ['Complex'],
@@ -6,7 +6,21 @@ export const number_type = {
    from: { string: (s: string) => +s }
 }
 
-export const zero: FnZero<number> = (a) => 0
+declare module "../interfaces/type" {
-export const one: FnOne<number> = (a) => 1
+   interface AssociatedTypes<T> {
-export const nan: FnNaN<number> = (a) => NaN
+      numbers: {
-export const re: FnRe<number, number> = (a) => a
+         type: number
+         zero: 0
+         one: 1
+         nan: typeof NaN
+         real: number
+      }
+   }
+}
+
+// I don't like the redundancy of repeating 'zero' and 'ZeroOp', any
+// way to eliminate that?
+export const zero: ZeroOp<number> = (a) => 0
+export const one:  OneOp<number>  = (a) => 1
+export const nan:  NanOp<number>  = (a) => NaN
+export const re:   ReOp<number>   = (a) => a