Typescript: Allow Inifinity and -Infinity as number literal types

[smikitky]

Please accept Infinity and -Infinity as valid number literal types.

/** A range of BigInt that may be unbounded, e.g., (-∞, 5] */
class BigIntRange {
  public min: bigint | -Infinity = 0n; // <= Error!
  public max: bigint | Infinity = 1n; // <= Error!
  public isValid(): boolean {
    return this.min <= this.max;
  }
}

Currently, This causes a compile error, 'Infinity' refers to a value, but is being used as a type here. (2749).

I understand this was once rejected as part of #15135 and #15356, and the given reasons were: 1) difficult to implement, and 2) lacks a compelling use case.

However, while I understand why NaN as a literal type is tricky to implement, NaN and Infinity are not the same. And I have a clear use case for Infinity as a meaningful literal type, as shown above.

Infinity is not tricky to compare

Unlike notorious NaN or -0, Infinity works just like an ordinary numeric constant as far as equality is concerned. We don't need a special function like isNaN() or Object.is(). Ever since the ES5/IE6 era, there has been nothing counter-intuitive:

Infinity === Infinity // => true
-Infinity === -Infinity // => true
Number.POSITIVE_INFINITY === Infinity // => true
Object.is(-Infinity, Number.NEGATIVE_INFINITY) // => true
10 ** 500 === Infinity // => true (because 10**500 is above Number.MAX_VALUE)

typeof Infinity === 'number' // => true
typeof Number.NEGATIVE_INFINITY === 'number' // => true

// FWIW, comparison works just as expected, too
50 < Infinity // => true
-Infinity < 50; // => true
10n ** 500n < Infinity // => true
Number.MAX_VALUE < Infinity // => true
Infinity < Infinity // => false

Most importantly, Infinity === Infinity is true (while NaN === NaN is false). Unless I'm missing something, predictable equality is all that's required to safely use Infinity as a literal type, right? Even though the design note (#15356) says "there is more than one NaN, Infinity, etc", you can think of Infinity in JavaScript as "just a fixed number" which happens to be larger than Number.MAX_VALUE.

My use case

My library deals with unbounded (aka infinite) integer ranges, and I have been using Infinity and -Infinity without any issue to denote what they literally mean, _infinity in the mathematical sense_. I have instructed my users to use these interesting constants, too. Recently I started to extend my library to support bigint in addition to number, and ran into this problem.

You may ask "Why don't you just use string 'Infinity' or Symbol('unbounded')", but Infinity is a predefined and predictable constant, and it can be directly compared with any bigint (e.g., 10n ** 1000n < Infinity is true). See how simple the implementation of isValid can be in the first example.

PS: Looks like there is a hacky workaround (#31752), but I'd like to see the official support.

[poseidonCore]

Also, to state the obvious in favour of this, typeof Infinity = "number", not some odd object.

Quizzically, Infinity has some odd type conversions internally that may be at the heart of this:

TS Playground ts3.5.1

type numberNames = {0: "zero", 1: "one", Infinity: "inf"};
type numberTypes = keyof numberNames;

// These are fine:
var zero:numberTypes = 0;
var one:numberTypes = 1;

// This is an expected error:
var two:numberTypes = 2;
/* ERROR
var two: 0 | 1 | "Infinity"
Type '2' is not assignable to type '0 | 1 | "Infinity"'.
*/

// This is an unexpected error:
var inf:numberTypes = Infinity;
/* ERROR
var inf: 0 | 1 | "Infinity"
Type 'number' is not assignable to type '0 | 1 | "Infinity"'.
*/

Here, Infinity is treated as a string ... not a number, unlike the other number keys.

So, Infinity might be treated just like any other simple string key here, at least.

[AnyhowStep]

const Inf = 999e308;
type Infinity = 999e999999; //Just for fun, it's still the same as `Inf`

//We use `Inf` instead of `Infinity`
type numberNames = {0: "zero", 1: "one", [Inf]: "inf"};
type numberTypes = keyof numberNames;

// These are fine:
var zero:numberTypes = 0;
var one:numberTypes = 1;

// This is an expected error:
var two:numberTypes = 2;
/* ERROR
var two: 0 | 1 | "Infinity"
Type '2' is not assignable to type '0 | 1 | "Infinity"'.
*/

// OK!
var inf:numberTypes = Infinity as Infinity;

Playground

[shreyasminocha]

I have a very similar use case and was surprised that this doesn't work.