refactor: Streamline types and signature specfications

The main mechanism for simplification was simply to assume that
  ZeroType<T> and OneType<T> will always be in T. That removed a lot
  of specialized typing, and presumably will be true in practice.

  Otherwise, removes extraneous type definitions and adds/clarifies
  a number of comments to hopefully make the scheme as clear as possible.

src/Complex/arithmetic.ts

@@ -5,8 +5,10 @@ import type {
 
 declare module "../interfaces/type" {
    interface Operations<T> {
-      // TODO: Make Dispatcher collapse operations that start with the same
+      // TODO: Make Dispatcher collapse operations that match
-      // prefix up to a possible `_`
+      // after removing any `_...` suffixes; the following should be
+      // additional dispatches for add and divide, not separate
+      // operations, in the final mathjs bundle.
       add_real:    {params: [T, RealType<T>], returns: T}
       divide_real: {params: [T, RealType<T>], returns: T}
    }
@@ -70,12 +72,15 @@ export const divide =
       OpType<'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 `add_real` on both T and Complex<T>, hence the dependency
+// with a custom name, not generated via Dependencies<...>
 export const sqrt =
-   <T>(dep:
+   <T>(dep: Dependencies<'add' | 'equal' | 'conservativeSqrt' | 'unaryMinus',
-       Dependencies<
+                         RealType<T>>
-          'conservativeSqrt' | 'add' | 'unaryMinus' | 'equal', RealType<T>>
+       & Dependencies<'zero' | 'add_real' | 'complex', 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>> =>
@@ -84,7 +89,7 @@ export const sqrt =
       const r = dep.re(z)
       const negr = dep.unaryMinus(r)
       if (dep.equal(myabs, negr)) {
-         // pure imaginary square root; z.im already sero
+         // pure imaginary square root; z.im already zero
          return dep.complex(
             dep.zero(z.re), dep.add_real(z.im, dep.conservativeSqrt(negr)))
       }

src/Complex/type.ts

@@ -1,6 +1,4 @@
-import {
+import {joinTypes, typeOfDependency} from '../core/Dispatcher.js'
-   joinTypes, typeOfDependency, Dependency,
-} from '../core/Dispatcher.js'
 import type {
    ZeroType, OneType, NaNType, Dependencies, OpType, OpReturns
 } from '../interfaces/type.js'
@@ -15,7 +13,7 @@ export const Complex_type = {
    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) }),
       Complex: <U, T>(dep: { convert: (from: U) => T }) =>
          (z: Complex<U>) => ({ re: dep.convert(z.re), im: dep.convert(z.im) })
@@ -39,7 +37,7 @@ declare module "../interfaces/type" {
 }
 
 export const complex =
-   <T>(dep: Dependencies<'zero', T>): OpType<'complex', T | ZeroType<T>> =>
+   <T>(dep: Dependencies<'zero', T>): OpType<'complex', T> =>
    (a, b) => ({re: a, im: b || dep.zero(a)})
 
 export const zero =

src/core/Dispatcher.ts

@@ -9,91 +9,19 @@
 
 type TypeName = string
 type Parameter = TypeName
-type InputSignature = Parameter[]
+type Signature = Parameter[]
 type DependenciesType = Record<string, Function>
 
+// A "canned" dependency for a builtin function:
 export type typeOfDependency = {typeOf: (x: unknown) => TypeName}
 
-// All of the implementations must publish descriptions of their
+// Utility needed in type definitions
-// return types into the following interface, using the format
-// described just below:
-export interface ReturnTypes<Params> {}
-
-/*****
-   To describe one implementation for a hypothetical operation `foo`, there
-   should be a property of the interface whose name starts with `foo` and whose
-   next character, if any, is an underscore. The type of this property
-   must be the return type of that implementation when Params matches the
-   parameter types of the implementation, and `never` otherwise.
-   Thus to describe an implementation that takes a number and a string and
-   returns a boolean, for example, you could write
-   ```
-   declare module "Dispatcher" {
-      interface ReturnTypes<Params> {
-         foo_example: Params extends [number, string] ? boolean : never
-      }
-   }
-   ```
-   If there is another, generic implementation that takes one argument
-   of any type and returns a Vector of that type, you can say
-   ```
-   ...
-      foo_generic: Params extends [infer T] ? Vector<T> : never
-   ...
-   ```
-   In practice, each subdirectory corresponding to a type, like Complex,
-   defines an interface, like `ComplexReturn<Params>` for the implementations
-   in that subdirectory, which can mostly be defined without suffixes because
-   there's typically just a single implementation within that domain.
-   Then the module responsible for collating all of the implementations for
-   that type inserts all of the properties of that interface into `ReturnTypes`
-   suitably suffixed to avoid collisions.
-
-   One might think that simply defining an implementation for `foo`
-   of type `(n: number, s: string) => boolean` would provide all of the same
-   information as the type of the key `foo_example` in the ReturnTypes
-   interface above, but in practice TypeScript has challenges in extracting
-   types relating to functions. (In particular, there is no
-   way to get the specialized return type of a generic function when it is
-   called on aguments whose specific types match the generic parameters.)
-   Hence the need for this additional mechanism to specify return types, in
-   a way readily suited for TypeScript type computations.
-*****/
-
-// Helpers for specifying signatures
-
-// A basic signature with concrete types
-export type Signature<CandidateParams, ActualParams, Returns> =
-   CandidateParams extends ActualParams ? Returns : never
-
 //dummy implementation for now
 export function joinTypes(a: TypeName, b: TypeName) {
    if (a === b) return a
    return 'any'
 }
 
-// Used to filter keys that match a given operation name
-type BeginsWith<Name extends string> = Name | `${Name}_${string}`
-
-// Look up the return type of an implementation based on its name
-// and the parameters it takes
-export type ImpReturns<Name extends string, Params> =
-   {[K in keyof ReturnTypes<Params>]: K extends BeginsWith<Name>
-    ? ReturnTypes<Params>[K] : never}[keyof ReturnTypes<Params>]
-
-// The type of an implementation (with dependencies satisfied,
-// based on its name and the parameters it takes
-export type ImpType<Name extends string, Params extends unknown[]> =
-   (...args: Params) => ImpReturns<Name, Params>
-
-// The type of a dependency on an implementation based on its name
-// and the parameters it takes (just a simple object with one property
-// named the same as the operation, of value type equal to the type of
-// that implementation. These can be `&`ed together in case of multiple
-// dependencies:
-export type Dependency<Name extends string, Params extends unknown[]> =
-   {[N in Name]: ImpType<N, Params>}
-
 // Now types used in the Dispatcher class itself
 
 type TypeSpecification = {
@@ -110,9 +38,9 @@ type SpecificationsGroup = Record<string, SpecObject>
 export class Dispatcher {
    installSpecification(
       name: string,
-      signature: InputSignature,
+      signature: Signature,
       returns: TypeName,
-      dependencies: Record<string, InputSignature>,
+      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.

src/interfaces/arithmetic.ts

@@ -1,5 +1,5 @@
 import type {Complex} from '../Complex/type.js'
-import type {RealType, WithConstants, NaNType} from './type.js'
+import type {RealType} from './type.js'
 
 type UnaryOperator<T>  = {params: [T], returns: T}
 type BinaryOperator<T> = {params: [T, T], returns: T}
@@ -17,9 +17,7 @@ declare module "./type" {
       conservativeSqrt: UnaryOperator<T>
       sqrt: {
          params: [T],
-         returns: T extends Complex<infer R>
+         returns: T extends Complex<any> ? T : T | Complex<T>
-            ? Complex<R | ZeroType<R>>
-            : T | Complex<T>
       }
    }
 }

src/interfaces/type.ts

@@ -1,15 +1,18 @@
-// Every typocomath type has some associated types; they need
+/*****
-// to be published as in the following interface. The key is the
+ * Every typocomath type has some associated types; they need
-// name of the type, and within the subinterface for that key,
+ * to be published in the following interface. The key is the
-// the type of the 'type' property is the actual TypeScript type
+ * name of the type, and within the subinterface for that key,
-// we are associating the other properties to. Note the interface
+ * the type of the 'type' property is the actual TypeScript type
-// is generic with one parameter, corresponding to the fact that
+ * we are associating the other properties to. Note the interface
-// typocomath currently only allows types with a single generic parameter.
+ * is generic with one parameter, corresponding to the fact that
-// This way, AssociatedTypes<SubType> can give the associated types
+ * typocomath currently only allows generic types with a single
-// for a generic type instantiated with SubType. That's not necessary for
+ * generic parameter. This way, AssociatedTypes<SubType> can give the
-// the 'undefined' type (or if you look in the `numbers` subdirectory,
+ * associated types for a generic type instantiated with SubType.
-// the 'number' type either) or any concrete type, but that's OK, the
+ * That's not necessary for the 'undefined' type (or if you look in the
-// generic parameter doesn't hurt in those cases.
+ * `numbers` subdirectory, the 'number' type) or any concrete type,
+ * but that's OK, the generic parameter doesn't hurt in those cases.
+ ****/
+
 export interface AssociatedTypes<T> {
    undefined: {
       type: undefined
@@ -26,32 +29,39 @@ type ALookup<T, Name extends AssociatedTypeNames> = {
    T extends AssociatedTypes<T>[K]['type'] ? AssociatedTypes<T>[K][Name] : never
 }[keyof AssociatedTypes<T>]
 
-export type ZeroType<T> = ALookup<T, 'zero'>
+// For everything to compile, zero and one must be subtypes of T:
-export type OneType<T> = ALookup<T, 'one'>
+export type ZeroType<T> = ALookup<T, 'zero'> & T
-export type WithConstants<T> = T | ZeroType<T> | OneType<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 global signature patterns for all operations need to be published in the
-// the Dispatcher will automatically merge operations that have the same
+ * following interface. Each key is the name of an operation (but note that
-// name when the first underscore `_` and everything thereafter is stripped).
+ * the Dispatcher will automatically merge operations that have the same
-// The type of each key should be an interface with two properties: 'params'
+ * name when the first underscore `_` and everything thereafter is stripped).
-// whose type is the type of the parameter list for the operation, and
+ * The type of each key should be an interface with two properties: 'params'
-// 'returns' whose type is the return type of the operation on those
+ * whose type is the type of the parameter list for the operation, and
-// parameters. These types are generic in a parameter type T which should
+ * 'returns' whose type is the return type of the operation on those
-// be interpreted as the type that the operation is supposed to "primarily"
+ * parameters. These types are generic in a parameter type T which should
-// operate on, although note that some of the parameters and/or return types
+ * be interpreted as the type that the operation is supposed to "primarily"
-// may depend on T rather than be exactly T.
+ * operate on, although note that some of the parameters and/or return types
-// So note that the example 're' below provides essentially the same
+ * may depend on T rather than be exactly T.
-// information that e.g.
+ * So note that the example 're' below provides essentially the same
-// `type ReOp<T> = (t: T) => RealType<T>`
+ * information that e.g.
-// would, but in a way that is much easier to manipulate in TypeScript,
+ * `type ReOp<T> = (t: T) => RealType<T>`
-// and it records the name of the operation as 're' also by virtue of the
+ * would, but in a way that is much easier to manipulate in TypeScript,
-// key 're' in the interface.
+ * 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>}
+   zero: {params: [T], returns: ZeroType<T>}
-   one:  {params: [WithConstants<T>], returns: OneType<T>}
+   one:  {params: [T], returns: 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:  {params: [T | NaNType<T>], returns: NaNType<T>}
    re:   {params: [T], returns: RealType<T>}
 }
@@ -62,5 +72,3 @@ 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>}
-
-