Suggestion: Distributive code inference "as dist"

### 🔍 Search Terms

- distributive inference
- distributed function
- as dist
- as distributed

### ✅ Viability Checklist

- [x] This wouldn't be a breaking change in existing TypeScript/JavaScript code
- [x] This wouldn't change the runtime behavior of existing JavaScript code
- [x] This could be implemented without emitting different JS based on the types of the expressions
- [x] This isn't a runtime feature (e.g. library functionality, non-ECMAScript syntax with JavaScript output, new syntax sugar for JS, etc.)
- [x] This isn't a request to add a new utility type: https://github.com/microsoft/TypeScript/wiki/No-New-Utility-Types
- [x] This feature would agree with the rest of our Design Goals: https://github.com/Microsoft/TypeScript/wiki/TypeScript-Design-Goals

### ⭐ Suggestion

Add `dist` / `distributed` keyword to enable inference in a distributive manner.

### Concept 1: Inline `as dist`

Handle the inference by distributing over all types used by the expression:

```ts
const transform = (val: [1, 1] | [2, 2]) => [val[0], val[1]] as dist;
typeof transform; // (val: [1, 1] | [2, 2]) => [1, 1] | [2, 2]

//

const add = (...[a, b]: [number, number] | [bigint, bigint]) => a + b as dist;
typeof add; // (...[a, b]: [number, number] | [bigint, bigint]) => number | bigint
```

### Concept 2: Function-level `dist` return type

Allow distribution across an entire function body:

```ts
const f = (...[a, b]: T): dist => {
const sum = a + b; // number | bigint
const arr = [a, b]; // [number, number] | [bigint, bigint];
return {
sum,
arr
} // {sum: number, arr: [number, number]} | {sum: bigint, arr: [bigint, bigint]}
}

const res = f(3,7); // {sum: number, arr: [number, number]}
const rez = f(3n,7n); // {sum: bigint, arr: [bigint, bigint]}

typeof f; // ((...[a, b]: T) => { sum: number; arr: [number, number]; }) & ((...[a, b]: T) => { sum: bigint; arr: [bigint, bigint]; })
```

Concept 1 could also be supported on function expressions with equivalent behavior to Concept 2:

```ts
const f2 = ((...[a, b]: T) => {/*code*/}) as dist; // Equivalent to "f"
```

### Notes

These are early-stage concepts meant to illustrate the core idea. The specific syntax and behaviors should be refined during implementation.

**Open questions:** Interaction with `as const`, generics, nested functions, opt-out mechanisms, etc. will need consideration.
**Potential breaking change:** Codebases with a type called `dist` would conflict, though this would go against TypeScript's PascalCase naming convention for types.

### 📃 Motivating Example

Currently, code is inferred in a non-distributive manner:

> Example inspired by [geon](https://www.reddit.com/user/geon/)
```ts
const transform = (val: [1, 1] | [2, 2]) => [val[0], val[1]] as const;
// Inferred return type: readonly [1 | 2, 1 | 2]
// Expected return type: readonly [1, 1] | readonly [2, 2]
```

This can be addressed by duplicating your code logic within a distributive context in the typesystem:

```ts
const transform = (val: T) => [val[0], val[1]] as T extends unknown
? [T[0], T[1]]
: never
;

const res = transform(undefined! as [1, 1] | [2, 2]); // [1, 1] | [2, 2]
const rez = transform([1, 1]); // [1, 1]
```

But this is very repetitive and awkward. Besides that, this only works if the automatic inference doesn't cause a conflict to begin with and can be simply translated into the type system:

> Example inspired by [Emilio Platzer](https://github.com/emilioplatzer) and Mudloop
```ts
// @ts-expect-error: Operator '+' cannot be applied to types 'number | bigint' and 'number | bigint'.(2365)
const add = (...[a, b]: [number, number] | [bigint, bigint]) => a + b;
```

### 💻 Use Cases

1. What do you want to use this for?
Preserving precise type relationships when transforming union types, and enabling operations across union branches that are currently rejected by the type checker.
2. What shortcomings exist with current approaches?
Current workarounds require manually duplicating code logic in the type system using conditional types. This is verbose, error-prone, and fails when TypeScript rejects the runtime-aligned code itself
3. What workarounds are you using in the meantime?
Manually encoding distributive logic using conditional types

No implementation files, tests, or compiler entry points are identified. Start by reviewing the two proposed syntaxes, the motivating examples, and the open questions around generics, nested functions, and opt-outs. Done would require a settled design before implementation can be scoped.

Written by the indexing model from the issue text.