src/Complex/all.ts

@@ -1,8 +1,10 @@
 import {ForType} from '../core/Dispatcher.js'
+import {ComplexReturn} from './type.js'
 import * as Complex from './native.js'
 
 export {Complex}
 
 declare module "../core/Dispatcher" {
-   interface ImplementationTypes extends ForType<'Complex', typeof Complex> {}
+   interface ReturnTypes<Params>
+      extends ForType<'Complex', ComplexReturn<Params>> {}
 }

src/Complex/type.ts

@@ -1,4 +1,6 @@
-import {joinTypes, typeOfDependency, Dependency} from '../core/Dispatcher.js'
+import {
+   joinTypes, typeOfDependency, Dependency, BBinary, ImpType, ImpReturns
+} from '../core/Dispatcher.js'
 
 export type Complex<T> = {re: T; im: T;}
 
@@ -17,6 +19,16 @@ export const Complex_type = {
    }
 }
 
-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})
+type Binary<B> = [B, B]
+
+export interface ComplexReturn<Params> {
+   complex: Params extends [infer U] ? Complex<U> // unary case
+      : Params extends BBinary<infer B> ? Complex<B> // binary case
+      : never 
+}
+
+export const complex_unary =
+   <T>(dep: Dependency<'zero', [T]>): ImpType<'complex', [T]> =>
+   t => ({re: t, im: dep.zero(t)})
+export const complex_binary = <T>(t: T, u: T): ImpReturns<'complex', [T,T]> =>
+   ({re: t, im: u})

src/core/Dispatcher.ts

@@ -10,14 +10,68 @@
 type TypeName = string
 type Parameter = TypeName
 type Signature = Parameter[]
+type DependenciesType = Record<string, Function>
 
-export interface ImplementationTypes {}
 export type typeOfDependency = {typeOf: (x: unknown) => TypeName}
 
-// Helper for collecting implementations
-// (Really just suffixes the type name onto the keys of exports)
-export type ForType<T extends string, Exports> = keyof Exports extends string
-   ? {[K in keyof Exports as `${K}_${T}`]: Exports[K]}
+// All of the implementations must publish descriptions of their
+// 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 homogenous binary operation (comes up a lot)
+// Typical usage: `foo_impl: Params extends BBinary<infer B> ? B : never`
+// says that this implementation takes two arguments, both of type B, and
+// returns the same type.
+export type BBinary<B> = [B, B]
+
+// Helper for collecting return types
+// (Really just adds the literal string Suffix onto the keys of interface IFace)
+export type ForType<Suffix extends string, IFace> = keyof IFace extends string
+   ? {[K in keyof IFace as `${K}_${Suffix}`]: IFace[K]}
    : never
 
 //dummy implementation for now
@@ -26,27 +80,27 @@ export function joinTypes(a: TypeName, b: TypeName) {
    return 'any'
 }
 
-/**
- * Build up to Dependency type lookup
- */
-type DependenciesType = Record<string, Function>
+// Used to filter keys that match a given operation name
+type BeginsWith<Name extends string> = Name | `${Name}_${string}`
 
-type FinalShape<FuncType> =
-   FuncType extends (arg: DependenciesType) => Function
-   ? ReturnType<FuncType> : FuncType
+// 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>]
 
-type BeginsWith<Name extends string> = `${Name}${string}`
-
-type DependencyTypes<Ob, Name extends string, Params extends unknown[]> =
-   {[K in keyof Ob]: K extends BeginsWith<Name>
-    ? FinalShape<Ob[K]> extends (...args: Params) => any
-      ? FinalShape<Ob[K]>
-      : never
-    : never}
+// 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]:
-    DependencyTypes<ImplementationTypes, N, Params>[keyof ImplementationTypes]}
+   {[N in Name]: ImpType<N, Params>}
 
 // Now types used in the Dispatcher class itself
 

src/numbers/all.ts

@@ -1,8 +1,10 @@
 import {ForType} from '../core/Dispatcher.js'
+import {NumbersReturn} from './type.js'
 import * as numbers from './native.js'
 
 export {numbers}
 
 declare module "../core/Dispatcher" {
-   interface ImplementationTypes extends ForType<'numbers', typeof numbers> {}
+   interface ReturnTypes<Params>
+      extends ForType<'numbers', NumbersReturn<Params>> {}
 }

src/numbers/arithmetic.ts

@@ -1,18 +1,45 @@
 import {configDependency} from '../core/Config.js'
-import {Dependency} from '../core/Dispatcher.js'
+import {BBinary, Dependency, ImpType} from '../core/Dispatcher.js'
+import type {Complex} from '../Complex/type.js'
 
-export const add = (a: number, b: number) => a + b
-export const unaryMinus = (a: number) => -a
-export const subtract = (a: number, b: number) => a - b
-export const multiply = (a: number, b: number) => a * b
-export const divide = (a: number, b: number) => a / b
+declare module "./type" {
+   interface NumbersReturn<Params> {
+      // This description loses information: some subtypes like NumInt or
+      // Positive are closed under addition, but this says that the result
+      // of add is just a number, not still of the reduced type
+      add: Params extends BBinary<number> ? number : never
+      // Whereas this one would preserve information, but would lie
+      // because it claims all subtypes of number are closed under addition,
+      // which is not true for `1 | 2 | 3`, for example.
+      // add: Params extends BBinary<infer B>
+      //    ? B extends number ? B : never
+      //    : never
+      //
+      // Not sure how this will need to go when we introduce NumInt.
+      unaryMinus: Params extends [number] ? number : never
+      subtract: Params extends BBinary<number> ? number : never
+      multiply: Params extends BBinary<number> ? number : never
+      divide: Params extends BBinary<number> ? number : never
+      // Best we can do for sqrt at compile time, since actual return
+      // type depends on config. Not sure how this will play out
+      // when we make a number-only bundle, but at least the import type
+      // above for Complex<> does not lead to any emitted JavaScript.
+      sqrt: Params extends [number] ? (number | Complex<number>) : never
+   }
+}
+
+export const add: ImpType<'add', [number, number]> = (a, b) => a + b
+export const unaryMinus: ImpType<'unaryMinus', [number]> = a => -a
+export const subtract: ImpType<'subtract', [number, number]> = (a, b) => a - b
+export const multiply: ImpType<'multiply', [number, number]> = (a, b) => a * b
+export const divide: ImpType<'divide', [number, number]> = (a, b) => a / b
 export const sqrt =
    (dep: configDependency
-    & Dependency<'complex', [number, number]>) => {
+    & Dependency<'complex', [number, number]>): ImpType<'sqrt', [number]> => {
        if (dep.config.predictable || !dep.complex) {
-          return (a: number) => isNaN(a) ? NaN : Math.sqrt(a)
+          return a => isNaN(a) ? NaN : Math.sqrt(a)
        }
-       return (a: number) => {
+       return a => {
           if (isNaN(a)) return NaN
           if (a >= 0) return Math.sqrt(a)
           return dep.complex(0, Math.sqrt(unaryMinus(a)))

src/numbers/type.ts

@@ -1,7 +1,26 @@
+import {ImpType} from '../core/Dispatcher.js'
+
 export const number_type = {
    before: ['Complex'],
    test: (n: unknown): n is number => typeof n === 'number',
    from: {string: s => +s}
 }
 
-export const zero = (a: number) => 0
+
+export interface NumbersReturn<Params> {
+   // The following description of the return type of `zero` on a single
+   // number argument has ended up unfortunately rather complicated. However,
+   // it illustrates the typing is really working: Suppose we have a
+   // `type Small = 1 | 2 | 3`. Then Small indeed extends number, but we
+   // can't use the operation `zero(s: Small)` because zero is supposed to
+   // return something of the same type as its argument, but there is no
+   // zero in Small. Anyhow, in plain language the below says that given
+   // one parameter of a subtype of number, as long as that subtype includes 0,
+   // the zero operation returns a member of the type `0` (so we know even
+   // at compile time that its value will be 0).
+   zero: Params extends [infer T]
+      ? T extends number ? 0 extends T ? 0 : never : never
+      : never
+}
+
+export const zero: ImpType<'zero', [number]> = a => 0