From 072b2a1f79e3fb4b4dea92647d368f6e0c5096be Mon Sep 17 00:00:00 2001
From: Glen Whitney <glen@studioinfinity.org>
Date: Sat, 24 Dec 2022 10:09:14 -0500
Subject: [PATCH] refactor: Streamline publishing operations

  Avoids clumsy naming properties by making the names the keys in
  an interface to which the signatures of all operations must be
  published. This also reduces the number of different symbols and
  avoids long lists of imports in the modules implementing multiple
  operations, which were redundant with the list of functions
  exported from such modules.
---
 src/Complex/arithmetic.ts    | 127 ++++++++++++++---------------------
 src/Complex/predicate.ts     |  11 ++-
 src/Complex/relational.ts    |   5 +-
 src/Complex/type.ts          |  29 ++++----
 src/generic/arithmetic.ts    |   5 +-
 src/generic/relational.ts    |   6 +-
 src/interfaces/arithmetic.ts |  42 ++++++------
 src/interfaces/predicate.ts  |  11 ++-
 src/interfaces/relational.ts |  11 ++-
 src/interfaces/type.ts       |  58 ++++++++++++----
 src/numbers/arithmetic.ts    |  30 ++++-----
 src/numbers/predicate.ts     |   6 +-
 src/numbers/relational.ts    |   9 ++-
 src/numbers/type.ts          |  13 ++--
 14 files changed, 189 insertions(+), 174 deletions(-)

diff --git a/src/Complex/arithmetic.ts b/src/Complex/arithmetic.ts
index de0e16d..f6089f4 100644
--- a/src/Complex/arithmetic.ts
+++ b/src/Complex/arithmetic.ts
@@ -1,47 +1,45 @@
-import {Complex, ComplexOp} from './type.js'
+import {Complex} from './type.js'
 import type {
-   AbsquareOp, AddOp, AddRealOp, ConjOp, ConservativeSqrtOp, DivideOp,
-   DivideByRealOp, MultiplyOp, ReciprocalOp, SqrtOp, SubtractOp,
-   UnaryMinusOp
-} from '../interfaces/arithmetic.js'
-import type {
-   NanOp, ReOp, ZeroOp, Depends, RealType, WithConstants, NaNType
+   Dependencies, OpType, OpReturns, RealType, ZeroType
 } from '../interfaces/type.js'
-import type {IsSquareOp, IsRealOp} from '../interfaces/predicate.js'
+
+declare module "../interfaces/type" {
+   interface Operations<T> {
+      // TODO: Make Dispatcher collapse operations that start with the same
+      // prefix up to a possible `_`
+      add_real:    {params: [T, RealType<T>], returns: T}
+      divide_real: {params: [T, RealType<T>], returns: T}
+   }
+}
 
 export const add =
-   <T>(dep: Depends<AddOp<T>> & Depends<ComplexOp<T>>): AddOp<Complex<T>> =>
+   <T>(dep: Dependencies<'add' | 'complex', T>): OpType<'add', Complex<T>> =>
    (w, z) => dep.complex(dep.add(w.re, z.re), dep.add(w.im, z.im))
 
-export const addReal =
-   <T>(dep: Depends<AddRealOp<T>> & Depends<ComplexOp<T>>):
-      AddRealOp<Complex<T>> =>
-   (z, r) => dep.complex(dep.addReal(z.re, r), z.im)
+export const add_real =
+   <T>(dep: Dependencies<'add_real' | 'complex', T>):
+      OpType<'add_real', Complex<T>> =>
+   (z, r) => dep.complex(dep.add_real(z.re, r), z.im)
 
 export const unaryMinus =
-   <T>(dep: Depends<UnaryMinusOp<T>> & Depends<ComplexOp<T>>):
-      UnaryMinusOp<Complex<T>> =>
+   <T>(dep: Dependencies<'unaryMinus' | 'complex', T>):
+      OpType<'unaryMinus', Complex<T>> =>
    z => dep.complex(dep.unaryMinus(z.re), dep.unaryMinus(z.im))
 
 export const conj =
-   <T>(dep: Depends<UnaryMinusOp<T>>
-       & Depends<ConjOp<T>>
-       & Depends<ComplexOp<T>>):
-      ConjOp<Complex<T>> =>
+   <T>(dep: Dependencies<'unaryMinus' | 'conj' | 'complex', T>):
+      OpType<'conj', Complex<T>> =>
    z => dep.complex(dep.conj(z.re), dep.unaryMinus(z.im))
 
 export const subtract =
-   <T>(dep: Depends<SubtractOp<T>> & Depends<ComplexOp<T>>):
-      SubtractOp<Complex<T>> =>
+   <T>(dep: Dependencies<'subtract' | 'complex', T>):
+      OpType<'subtract', Complex<T>> =>
    (w, z) => dep.complex(dep.subtract(w.re, z.re), dep.subtract(w.im, z.im))
 
 export const multiply =
-   <T>(dep: Depends<AddOp<T>>
-       & Depends<SubtractOp<T>>
-       & Depends<MultiplyOp<T>>
-       & Depends<ConjOp<T>>
-       & Depends<ComplexOp<T>>):
-      MultiplyOp<Complex<T>> =>
+   <T>(dep: Dependencies<
+       'add' | 'subtract' | 'multiply' | 'conj' | 'complex', T>):
+      OpType<'multiply', Complex<T>> =>
    (w, z) => {
       const mult = dep.multiply
       const realpart = dep.subtract(
@@ -52,69 +50,48 @@ export const multiply =
    }
 
 export const absquare =
-   <T>(dep: Depends<AddOp<RealType<T>>> & Depends<AbsquareOp<T>>):
-      AbsquareOp<Complex<T>> =>
+   <T>(dep: Dependencies<'absquare', T>
+       & Dependencies<'add', OpReturns<'absquare', T>>):
+      OpType<'absquare', Complex<T>> =>
    z => dep.add(dep.absquare(z.re), dep.absquare(z.im))
 
 export const divideByReal =
-   <T>(dep: Depends<DivideByRealOp<T>> & Depends<ComplexOp<T>>):
-      DivideByRealOp<Complex<T>> =>
-   (z, r) => dep.complex(dep.divideByReal(z.re, r), dep.divideByReal(z.im, r))
+   <T>(dep: Dependencies<'divide_real' | 'complex', T>):
+      OpType<'divide_real', Complex<T>> =>
+   (z, r) => dep.complex(dep.divide_real(z.re, r), dep.divide_real(z.im, r))
 
 export const reciprocal =
-   <T>(dep: Depends<ConjOp<Complex<T>>>
-       & Depends<AbsquareOp<Complex<T>>>
-       & Depends<DivideByRealOp<Complex<T>>>):
-      ReciprocalOp<Complex<T>> =>
-   z => dep.divideByReal(dep.conj(z), dep.absquare(z))
+   <T>(dep: Dependencies<'conj' | 'absquare' | 'divide_real', Complex<T>>):
+      OpType<'reciprocal', Complex<T>> =>
+   z => dep.divide_real(dep.conj(z), dep.absquare(z))
 
 export const divide =
-   <T>(dep: Depends<MultiplyOp<Complex<T>>>
-       & Depends<ReciprocalOp<Complex<T>>>):
-      DivideOp<Complex<T>> =>
+   <T>(dep: Dependencies<'multiply' | 'reciprocal', Complex<T>>):
+      OpType<'divide', 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: Depends<ConservativeSqrtOp<T>>
-       & Depends<IsSquareOp<T>>
-       & Depends<UnaryMinusOp<T>>
-       & Depends<ComplexOp<WithConstants<T>>>
-       & Depends<ZeroOp<T>>
-       & Depends<NanOp<Complex<WithConstants<T>>>>): ComplexSqrtOp<T> =>
-   r => {
-      if (dep.isSquare(r)) return dep.complex(dep.conservativeSqrt(r))
-      const negative = dep.unaryMinus(r)
-      if (dep.isSquare(negative)) {
-         return dep.complex(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
-      // return the NaN of the type.
-      return dep.nan(dep.complex(r))
-   }
-
 export const sqrt =
-   <T>(dep: Depends<IsRealOp<Complex<T>>>
-       & Depends<ComplexSqrtOp<T>>
-       & Depends<ConservativeSqrtOp<RealType<T>>>
-       & Depends<AbsquareOp<Complex<T>>>
-       & Depends<AddRealOp<Complex<T>>>
-       & Depends<DivideByRealOp<Complex<T>>>
-       & Depends<AddOp<RealType<T>>>
-       & Depends<ReOp<Complex<T>>>): SqrtOp<Complex<T>> =>
+   <T>(dep:
+       Dependencies<
+          'conservativeSqrt' | 'add' | 'unaryMinus' | 'equal', RealType<T>>
+       & Dependencies<'zero' | 'add_real', T>
+       & Dependencies<'complex', T | ZeroType<T>>
+       & Dependencies<'absquare' | 're' | 'divide_real', Complex<T>>
+       & {add_complex_real: OpType<'add_real', Complex<T>>}):
+      OpType<'sqrt', Complex<T>> =>
    z => {
-      if (dep.isReal(z)) return dep.complexSqrt(z.re)
       const myabs = dep.conservativeSqrt(dep.absquare(z))
-      const num = dep.addReal(z, myabs)
       const r = dep.re(z)
+      const negr = dep.unaryMinus(r)
+      if (dep.equal(myabs, negr)) {
+         // pure imaginary square root; z.im already sero
+         return dep.complex(
+            dep.zero(z.re), dep.add_real(z.im, dep.conservativeSqrt(negr)))
+      }
+      const num = dep.add_complex_real(z, myabs)
       const denomsq = dep.add(dep.add(myabs, myabs), dep.add(r, r))
       const denom = dep.conservativeSqrt(denomsq)
-      return dep.divideByReal(num, denom)
+      return dep.divide_real(num, denom)
    }
 
 export const conservativeSqrt = sqrt
diff --git a/src/Complex/predicate.ts b/src/Complex/predicate.ts
index cddd383..e6c4c7f 100644
--- a/src/Complex/predicate.ts
+++ b/src/Complex/predicate.ts
@@ -1,12 +1,9 @@
 import {Complex} from './type.js'
-import {EqualOp} from '../interfaces/relational.js'
-import {AddOp} from '../interfaces/arithmetic.js'
-import type {Depends} from '../interfaces/type.js'
-import type {IsRealOp, IsSquareOp} from '../interfaces/predicate.js'
+import type {Dependencies, OpType} from '../interfaces/type.js'
 
 export const isReal =
-   <T>(dep: Depends<AddOp<T>> & Depends<EqualOp<T>> & Depends<IsRealOp<T>>):
-      IsRealOp<Complex<T>> =>
+   <T>(dep: Dependencies<'add' | 'equal' | 'isReal', T>):
+      OpType<'isReal', Complex<T>> =>
    z => dep.isReal(z.re) && dep.equal(z.re, dep.add(z.re, z.im))
 
-export const isSquare: IsSquareOp<Complex<any>> = z => true // FIXME: not correct for Complex<bigint> once we get there
+export const isSquare: OpType<'isSquare', Complex<any>> = z => true // FIXME: not correct for Complex<bigint> once we get there
diff --git a/src/Complex/relational.ts b/src/Complex/relational.ts
index 89db758..d0b9e52 100644
--- a/src/Complex/relational.ts
+++ b/src/Complex/relational.ts
@@ -1,7 +1,6 @@
 import {Complex} from './type.js'
-import {Depends} from '../interfaces/type.js'
-import {EqualOp} from '../interfaces/relational.js'
+import {Dependencies, OpType} from '../interfaces/type.js'
 
 export const equal =
-   <T>(dep: Depends<EqualOp<T>>): EqualOp<Complex<T>> =>
+   <T>(dep: Dependencies<'equal', T>): OpType<'equal', Complex<T>> =>
    (w, z) => dep.equal(w.re, z.re) && dep.equal(w.im, z.im)
diff --git a/src/Complex/type.ts b/src/Complex/type.ts
index f995f92..8c669ea 100644
--- a/src/Complex/type.ts
+++ b/src/Complex/type.ts
@@ -2,7 +2,7 @@ import {
    joinTypes, typeOfDependency, Dependency,
 } from '../core/Dispatcher.js'
 import type {
-   OneOp, ZeroOp, NanOp, ReOp, ZeroType, OneType, NaNType, Depends
+   ZeroType, OneType, NaNType, Dependencies, OpType, OpReturns
 } from '../interfaces/type.js'
 
 export type Complex<T> = { re: T; im: T; }
@@ -32,31 +32,34 @@ declare module "../interfaces/type" {
          real: RealType<R>
       } : never
    }
+
+   interface Operations<T> {
+      complex: {params: [T] | [T,T], returns: Complex<T>}
+   }
 }
 
-export type ComplexOp<T> = {op?: 'complex', (a: T, b?: T): Complex<T>}
-
 export const complex =
-   <T>(dep: Depends<ZeroOp<T>>): ComplexOp<T | ZeroType<T>> =>
+   <T>(dep: Dependencies<'zero', T>): OpType<'complex', T | ZeroType<T>> =>
    (a, b) => ({re: a, im: b || dep.zero(a)})
 
 export const zero =
-   <T>(dep: Depends<ZeroOp<T>> & Depends<ComplexOp<ZeroType<T>>>):
-      ZeroOp<Complex<T>> =>
+   <T>(dep: Dependencies<'zero', T>
+       & Dependencies<'complex', OpReturns<'zero', T>>):
+      OpType<'zero', Complex<T>> =>
    z => dep.complex(dep.zero(z.re), dep.zero(z.im))
 
 export const one =
-   <T>(dep: Depends<OneOp<T>>
-       & Depends<ZeroOp<T>>
-       & Depends<ComplexOp<ZeroType<T>|OneType<T>>>):
-      OneOp<Complex<T>> =>
+   <T>(dep: Dependencies<'one' | 'zero', T>
+       & Dependencies<'complex', OpReturns<'one' | 'zero', T>>):
+      OpType<'one', Complex<T>> =>
    z => dep.complex(dep.one(z.re), dep.zero(z.im))
 
 export const nan =
-   <T>(dep: Depends<NanOp<T>> & Depends<ComplexOp<NaNType<T>>>):
-      NanOp<Complex<T>> =>
+   <T>(dep: Dependencies<'nan', T>
+       & Dependencies<'complex', OpReturns<'nan', T>>):
+      OpType<'nan', Complex<T>> =>
    z => dep.complex(dep.nan(z.re), dep.nan(z.im))
 
 export const re =
-   <T>(dep: Depends<ReOp<T>>): ReOp<Complex<T>> =>
+   <T>(dep: Dependencies<'re', T>): OpType<'re', Complex<T>> =>
    z => dep.re(z.re)
diff --git a/src/generic/arithmetic.ts b/src/generic/arithmetic.ts
index a7cf2b7..e0f55e8 100644
--- a/src/generic/arithmetic.ts
+++ b/src/generic/arithmetic.ts
@@ -1,6 +1,5 @@
-import type {Depends} from '../interfaces/type.js'
-import type {MultiplyOp, SquareOp} from '../interfaces/arithmetic.js'
+import type {Dependencies, OpType} from '../interfaces/type.js'
 
 export const square =
-   <T>(dep: Depends<MultiplyOp<T>>): SquareOp<T> =>
+   <T>(dep: Dependencies<'multiply', T>): OpType<'square', T> =>
    z => dep.multiply(z, z)
diff --git a/src/generic/relational.ts b/src/generic/relational.ts
index f47c392..2932e13 100644
--- a/src/generic/relational.ts
+++ b/src/generic/relational.ts
@@ -1,5 +1,5 @@
-import {Depends} from '../interfaces/type.js'
-import type {EqualOp, UnequalOp} from '../interfaces/relational.js'
+import {Dependencies, OpType} from '../interfaces/type.js'
 
-export const unequal = <T>(dep: Depends<EqualOp<T>>): UnequalOp<T> =>
+export const unequal =
+   <T>(dep: Dependencies<'equal', T>): OpType<'unequal', T> =>
    (x, y) => !dep.equal(x, y)
diff --git a/src/interfaces/arithmetic.ts b/src/interfaces/arithmetic.ts
index 80e1155..1e4904e 100644
--- a/src/interfaces/arithmetic.ts
+++ b/src/interfaces/arithmetic.ts
@@ -1,25 +1,25 @@
 import type {Complex} from '../Complex/type.js'
 import type {RealType, WithConstants, NaNType} from './type.js'
 
-// Note: right now I've added an 'Op' suddix,
-// so it is clear that the type holds the function type of an operation
-// This is not necessary though, it is just a naming convention.
-export type AddOp<T> = {op?: 'add', (a: T, b: T): T}
-export type AddRealOp<T> = {op?: 'addReal', (a: T, b: RealType<T>): T}
-export type UnaryMinusOp<T> = {op?: 'unaryMinus', (a: T): T}
-export type ConjOp<T> = {op?: 'conj', (a: T): T}
-export type SubtractOp<T> = {op?: 'subtract', (a: T, b: T): T}
-export type MultiplyOp<T> = {op?: 'multiply', (a: T, b: T): T}
-export type AbsquareOp<T> = {op?: 'absquare', (a: T): RealType<T>}
-export type ReciprocalOp<T> = {op?: 'reciprocal', (a: T): T}
-export type DivideOp<T> = {op?: 'divide', (a: T, b: T): T}
-export type DivideByRealOp<T> = {op?: 'divideByReal', (a: T, b: RealType<T>): T}
-export type ConservativeSqrtOp<T> = {op?: 'conservativeSqrt', (a: T): T}
-export type SqrtOp<T> = {
-   op?: 'sqrt',
-   (a: T): T extends Complex<infer R>
-      ? Complex<WithConstants<R> | NaNType<WithConstants<R>>>
-      : T | Complex<T>
+type UnaryOperator<T>  = {params: [T], returns: T}
+type BinaryOperator<T> = {params: [T, T], returns: T}
+declare module "./type" {
+   interface Operations<T> {
+      add:              BinaryOperator<T>
+      unaryMinus:       UnaryOperator<T>
+      conj:             UnaryOperator<T>
+      subtract:         BinaryOperator<T>
+      multiply:         BinaryOperator<T>
+      square:           UnaryOperator<T>
+      absquare:         {params: [T], returns: RealType<T>}
+      reciprocal:       UnaryOperator<T>
+      divide:           BinaryOperator<T>
+      conservativeSqrt: UnaryOperator<T>
+      sqrt: {
+         params: [T],
+         returns: T extends Complex<infer R>
+            ? Complex<R | ZeroType<R>>
+            : T | Complex<T>
+      }
+   }
 }
-export type SquareOp<T> = {op?: 'square', (z: T): T}
-
diff --git a/src/interfaces/predicate.ts b/src/interfaces/predicate.ts
index 37a69ea..16efd16 100644
--- a/src/interfaces/predicate.ts
+++ b/src/interfaces/predicate.ts
@@ -1,2 +1,9 @@
-export type IsRealOp<T> = {op?: 'isReal', (a: T): boolean}
-export type IsSquareOp<T> = {op?: 'isSquare', (a: T): boolean}
+// Warning: a module must have something besides just a "declare module"
+// section; otherwise it is ignored.
+export type UnaryPredicate<T> = {params: [T], returns: boolean}
+declare module "./type" {
+   interface Operations<T> {
+      isReal:   UnaryPredicate<T>
+      isSquare: UnaryPredicate<T>
+   }
+}
diff --git a/src/interfaces/relational.ts b/src/interfaces/relational.ts
index 29529ff..3149beb 100644
--- a/src/interfaces/relational.ts
+++ b/src/interfaces/relational.ts
@@ -1,2 +1,9 @@
-export type EqualOp<T> = {op?: 'equal', (a: T, b: T): boolean}
-export type UnequalOp<T> = {op?: 'unequal', (a: T, b: T): boolean}
+// Warning: a module must have something besides just a "declare module"
+// section; otherwise it is ignored.
+export type BinaryPredicate<T> = {params: [T, T], returns: boolean}
+declare module "./type" {
+   interface Operations<T> {
+      equal:   BinaryPredicate<T>
+      unequal: BinaryPredicate<T>
+   }
+}
diff --git a/src/interfaces/type.ts b/src/interfaces/type.ts
index 1d7e103..8460235 100644
--- a/src/interfaces/type.ts
+++ b/src/interfaces/type.ts
@@ -1,3 +1,15 @@
+// Every typocomath type has some associated types; they need
+// to be published as 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 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 either) or any concrete type, but that's OK, the
+// generic parameter doesn't hurt in those cases.
 export interface AssociatedTypes<T> {
    undefined: {
       type: undefined
@@ -9,24 +21,46 @@ export interface AssociatedTypes<T> {
 }
 
 type AssociatedTypeNames = keyof AssociatedTypes<unknown>['undefined']
-export type Lookup<T, Name extends AssociatedTypeNames> = {
+type ALookup<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 ZeroType<T> = ALookup<T, 'zero'>
+export type OneType<T> = ALookup<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 NaNType<T> = ALookup<T, 'nan'>
+export type RealType<T> = ALookup<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>}
+// 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 Operations<T> {
+   zero: {params: [WithConstants<T>], returns: ZeroType<T>}
+   one:  {params: [WithConstants<T>], returns: OneType<T>}
+   nan:  {params: [T | NaNType<T>],   returns: NaNType<T>}
+   re:   {params: [T],                returns: RealType<T>}
+}
 
-type NamedFunction = {op?: string, (...params: any[]): any}
-export type Depends<FuncType extends NamedFunction> =
-   {[K in FuncType['op']]: FuncType}
+type OpKey = keyof Operations<unknown>
+
+export type OpReturns<Name extends OpKey, T> = Operations<T>[Name]['returns']
+export type OpType<Name extends OpKey, T> =
+   (...args: Operations<T>[Name]['params']) => OpReturns<Name, T>
+export type Dependencies<Name extends OpKey, T> = {[K in Name]: OpType<K, T>}
 
                         
diff --git a/src/numbers/arithmetic.ts b/src/numbers/arithmetic.ts
index 6a05fe8..a902f0c 100644
--- a/src/numbers/arithmetic.ts
+++ b/src/numbers/arithmetic.ts
@@ -1,27 +1,21 @@
 import type {configDependency} from '../core/Config.js'
-import type {ComplexOp} from '../Complex/type.js'
-import type {
-   AddOp, ConjOp, SubtractOp, UnaryMinusOp, MultiplyOp,
-   AbsquareOp, ReciprocalOp, DivideOp, ConservativeSqrtOp, SqrtOp
-} from '../interfaces/arithmetic.js'
-import type {Depends} from '../interfaces/type.js'
+import type {Dependencies, OpType} from '../interfaces/type.js'
 
-export const add: AddOp<number> = (a, b) => a + b
-export const addReal = add
-export const unaryMinus: UnaryMinusOp<number> = a => -a
-export const conj: ConjOp<number> = a => a
-export const subtract: SubtractOp<number> = (a, b) => a - b
-export const multiply: MultiplyOp<number> = (a, b) => a * b
-export const absquare: AbsquareOp<number> = a => a * a
-export const reciprocal: ReciprocalOp<number> = a => 1 / a
-export const divide: DivideOp<number> = (a, b) => a / b
-export const divideByReal = divide
+export const add:        OpType<'add',        number> = (a, b) => a + b
+export const unaryMinus: OpType<'unaryMinus', number> = a => -a
+export const conj:       OpType<'conj',       number> = a => a
+export const subtract:   OpType<'subtract',   number> = (a, b) => a - b
+export const multiply:   OpType<'multiply',   number> = (a, b) => a * b
+export const absquare:   OpType<'absquare',   number> = a => a * a
+export const reciprocal: OpType<'reciprocal', number> = a => 1 / a
+export const divide:     OpType<'divide',     number> = (a, b) => a / b
 
 const basicSqrt = a => isNaN(a) ? NaN : Math.sqrt(a)
-export const conservativeSqrt: ConservativeSqrtOp<number> = basicSqrt
+export const conservativeSqrt: OpType<'conservativeSqrt', number> = basicSqrt
 
 export const sqrt =
-   (dep: configDependency & Depends<ComplexOp<number>>): SqrtOp<number> => {
+   (dep: configDependency & Dependencies<'complex', number>):
+   OpType<'sqrt', number> => {
       if (dep.config.predictable || !dep.complex) return basicSqrt
       return a => {
          if (isNaN(a)) return NaN
diff --git a/src/numbers/predicate.ts b/src/numbers/predicate.ts
index 2018e56..ae065f8 100644
--- a/src/numbers/predicate.ts
+++ b/src/numbers/predicate.ts
@@ -1,4 +1,4 @@
-import type { IsRealOp, IsSquareOp } from '../interfaces/predicate.js'
+import type {OpType} from '../interfaces/type.js'
 
-export const isReal: IsRealOp<number> = (a) => true
-export const isSquare: IsSquareOp<number> = (a)  => a >= 0
+export const isReal:   OpType<'isReal',   number> = (a) => true
+export const isSquare: OpType<'isSquare', number> = (a) => a >= 0
diff --git a/src/numbers/relational.ts b/src/numbers/relational.ts
index 5dbb3c5..6bb0597 100644
--- a/src/numbers/relational.ts
+++ b/src/numbers/relational.ts
@@ -1,12 +1,11 @@
-import {Config} from '../core/Config.js'
-import type {EqualOp} from '../interfaces/relational.js'
+import {configDependency} from '../core/Config.js'
+import {OpType} from '../interfaces/type.js'
 
 const DBL_EPSILON = Number.EPSILON || 2.2204460492503130808472633361816E-16
 
 export const equal =
-   (dep: {
-      config: Config
-   }): EqualOp<number> => (x, y) => {
+   (dep: configDependency): OpType<'equal', number> =>
+   (x, y) => {
       const eps = dep.config.epsilon
       if (eps === null || eps === undefined) return x === y
       if (x === y) return true
diff --git a/src/numbers/type.ts b/src/numbers/type.ts
index ff1ff61..a8e6dfa 100644
--- a/src/numbers/type.ts
+++ b/src/numbers/type.ts
@@ -1,4 +1,4 @@
-import type { OneOp, ZeroOp, NanOp, ReOp } from '../interfaces/type.js'
+import type { OpType } from '../interfaces/type.js'
 
 export const number_type = {
    before: ['Complex'],
@@ -18,9 +18,8 @@ declare module "../interfaces/type" {
    }
 }
 
-// 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
+// I don't like the redundancy of repeating 'zero'; any way to eliminate that?
+export const zero: OpType<'zero', number> = (a) => 0
+export const one:  OpType<'one',  number> = (a) => 1
+export const nan:  OpType<'nan',  number> = (a) => NaN
+export const re:   OpType<'re',   number> = (a) => a