Produce #17640's anonymous type declarations from function types

[SamPruden]

This issue is branching out of discussion in #17636, and depends on #17636 and #17640.

Working together, these features aim to eliminate the need for #6606, by providing type switching and filtering within the type system, and making it possible to access the return types of functions.

Type declaration overloads provide all the power of function overloads.

declare function foo (num: number): {aNumber: number};
declare function foo <T> (other: T): {aDefault: T};

can be described by type declaration overloads as

type Foo <T extends number> = {aNumber: number};
type Foo <T> = {aDefault: T};

This proposal is for allowing the conversion of a function type into the equivalent anonymous overloaded type declaration.

interface Fizz {
    foo (num: number): {aNumber: number};
    foo <T> (other: T): {aDefault: T};
}

// Here we're getting the return type of foo by overload
type ANumber = (typeof Fizz["foo"])<number>;
type ADefault = (typeof Fizz["foo"])<string>;

where typeof Fizz["foo"] was expanded to

(
    type <U extends number> = {aNumber: number};
    type <U> = {aDefault: U};
)

[SamPruden]

The title of this issue is a mess, any suggestions?

[KiaraGrouwstra]

Might say 'type functions from function types' following Idris's nomenclature of 'type function' referring to types with generics (takes types, returns a type), but yeah haven't heard that here as much.

[SamPruden]

type functions from function types

That seems pretty confusing to me, given that I'm a filthy casual who's never even read a line of Idris. I've tried something else, not sure if I've actually improved things though.

[KiaraGrouwstra]

Yeah, mine sounded pretty rather than clear. Yours sounds clearer.

Idris

It's barely used afaik, but made some headlines in the Haskell community for doing some things better.

[mhegazy]

Looks like this should be in #17640 instead. i am not also convinced that even with #17640, this is possible for the general case. either ways, let's keep the discussion in #17640.

[mhegazy]

Automatically closing this issue for housekeeping purposes. The issue labels indicate that it is unactionable at the moment or has already been addressed.