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@sebinsua
Last active July 21, 2023 22:47
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type _Tuple<
T,
N extends number,
R extends readonly T[] = []
> = R["length"] extends N ? R : _Tuple<T, N, readonly [T, ...R]>;
type Tuple<T, N extends number> = _Tuple<T, N> & {
readonly length: N;
[I: number]: T;
[Symbol.iterator]: () => IterableIterator<T>;
};
function zip<
A extends readonly any[],
Length extends A["length"],
B extends Tuple<any, Length>
>(a: A, b: B): Tuple<readonly [A[number], B[number]], Length> {
if (a.length !== b.length) {
throw new Error(`zip cannot operate on different length arrays; ${a.length} !== ${b.length}`);
}
return a.map((v, index) => [v, b[index]]) as Tuple<
readonly [A[number], B[number]],
Length
>;
}
const a = [1, 2, 3] as const;
const b1 = [1, 2, 6, 2, 4] as const;
const b2 = [1, 2, 6] as const;
// @ts-expect-error Source has 5 element(s) but target allows only 3.
const c1 = zip(a, b1);
const c2 = zip(a, b2);
console.log(c2);
// ^?
@sebinsua
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I've been wondering whether it was possible to create a type-safe zip operation and did so today.

Although, maybe this isn't how people normally use zip, recently I've been thinking about how in Python you join series/frames and end up with NaN or nulls in columns which are empty, and how this can cause bugs downstream. I was wondering whether it'd be possible to make a type-safe data programming language... Basically, by having invariants on things like lengths, and only letting people ignore these if they provide a function to "impute" missing values, etc.

@sebinsua
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sebinsua commented Oct 20, 2022

I was able to take this helper and create an assertsHasLength:

type _Tuple<
  T,
  N extends number,
  R extends readonly T[] = []
> = R["length"] extends N ? R : _Tuple<T, N, readonly [T, ...R]>;

type Tuple<T, N extends number> = _Tuple<T, N> & {
  readonly length: N;
  [I: number]: T;
  [Symbol.iterator]: () => IterableIterator<T>;
};

function zip<
  A extends readonly any[],
  Length extends A["length"],
  B extends Tuple<any, Length>
>(a: A, b: B): Tuple<readonly [A[number], B[number]], Length> {
  if (a.length !== b.length) {
    throw new Error(
      `zip cannot operate on different length arrays; ${a.length} !== ${b.length}`
    );
  }

  return a.map((v, index) => [v, b[index]]) as Tuple<
    readonly [A[number], B[number]],
    Length
  >;
}

// ...

type TupleSeq_<T, L, A extends [...any]> = A["length"] extends L
  ? A
  : TupleSeq_<T, L, [...A, T]>;
type TupleSeq<T, L> = TupleSeq_<T, L, []>;

function assertsHasLength<T, L extends number>(
  arr: T[],
  length: L
): asserts arr is TupleSeq<T, L> {
  if (arr.length !== length) {
    throw new Error(
      `Array has a length of ${arr.length} instead of ${length}.`
    );
  }
}

declare const a: string[];
declare const b: number[];

assertsHasLength(a, 3);
assertsHasLength(b, 3);

const [first, second, third] = a;

const arr = zip(a, b);

See playground: https://www.typescriptlang.org/play?#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-eHkFec-BYk4GEkQbqiqCft+wJZKB257geHjAr+QFROcVw3HcXa0BwwC0AAEl206mBBD5pMOmT6tgvrsD0gIEMKzhPhSPq0Jh7DYT6OpQGM3a5OB8GaPKnH8gSOoRuC4oqMKcopkqqrqlqOqzORhrGq8foyCYXY+jUMq2vyoaUaJpjRpWtAUGIulxomgTJoaaYEBm86tpcyC+tAlySKZPrOKZ7CVoYCiRE5LnCOaHk2qSDCkewAVRBhWG4fhMoEl4ADMdlxaxCW0ARJjzCwqV2Rg7mUJ5sinGM7CmV4mHFdQXimBV1CKCoIgnMVnmUVoprJY2dlAA

@sebinsua
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sebinsua commented Oct 20, 2022

It's not as helpful as we'd like, since (1) our Tuple type resolves number into an empty tuple instead of an array of a non-fixed length, and (2) rather than prescribing that an array has a length of a particular numeric literal, we want to be able to specify that an array has a Length which is the same as the length of another array.

I wonder if the latter is possible already or whether it could be a feature request that the TypeScript team might be able to implement...

Rather than using length in this case, could we make use of opaque/branded types?

See: https://twitter.com/sebinsua/status/1583064897432477696?s=61&t=Fb9i9QQ8Pp-4n0iSmZ05CA

@sebinsua
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sebinsua commented Oct 21, 2022

Unfortunately, regarding not matching on number, it doesn't seem possible to use extends in this way as by definition all numeric literals inherit from number. I guess we'd need TypeScript to add a NumberLiteral type that is the superset of all numeric literals in between individual numeric literals and number. (Maybe this type could just be an infinite number interval.)

And, regarding the possibility of using a runtime assertion of equal lengths (or some other property) to assign an opaque/branded/flavoured type to two or more values, this isn't currently possible as TypeScript doesn't support multiple/aggregate function assertions or propagation of type assertions outside of their scope.

@sebinsua
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I think that everything I attempted is possible, as I've found that somebody has implemented type-safe tensors here: https://github.com/newhouseb/potatogpt/tree/main#-fully-typed-tensors

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sebinsua commented May 1, 2023

See Playground.

// Utilities
type UnionToIntersection<U> = (U extends any ? (k: U) => void : never) extends (
  k: infer I
) => void
  ? I
  : never;
type IsUnion<T> = [T] extends [UnionToIntersection<T>] ? false : true;

type And<A, B> = A extends true ? (B extends true ? true : false) : false;
type Or<A, B> = A extends true ? true : B extends true ? true : false;
type Not<A> = A extends true ? false : true;

// Defines a branded dimension with a runtime-determined size and an associated label.
export type Var<Label extends string> = number & { label: Label };
export const Var = <Label extends string>(d: number, label: Label) => {
  return d as Var<Label>;
};
export const isVar = <Label extends string>(
  value: any
): value is Var<Label> => {
  return typeof value === "object" && "label" in value;
};

// We check whether `T` is a numeric literal by checking that `number` does not
// extend from it but that it does extend from `number`.
type IsNumericLiteral<T> = number extends T
  ? false
  : T extends number
  ? true
  : false;
type IsVar<T> = T extends Var<string> ? true : false;

// For type-checking of tensors to work they can only be created using
// numeric literals (e.g. `5`)  or `Var<string>` and not types like
// `number` or `1 | 2 | 3`.
type IsNumericLiteralOrVar<T extends number | (string & number)> = And<
  // We disallow `T` to be a union of types.
  Not<IsUnion<T>>,
  Or<
    // We allow `T` to be a numeric literal but not a number.
    IsNumericLiteral<T>,
    // We allow `T` to be a `Var`.
    IsVar<T>
  >
>;
type IsShapeContainingOnlyNumericLiteralsOrVarDimensions<
  T extends ReadonlyArray<number | Var<string>>
> = T extends ReadonlyArray<unknown>
  ? { [K in keyof T]: IsNumericLiteralOrVar<T[K]> } extends {
      [K in keyof T]: true;
    }
    ? T
    : never
  : never;

export type Dimension = number | Var<string>;
export type Tensor<Shape extends readonly Dimension[]> = {
  data: Float32Array;
  shape: Shape;
};
export type InvalidTensor<Shape extends readonly Dimension[]> = [
  never,
  "Invalid shape: please provide an array of only numeric literals or `Var`s.",
  Shape
];
export function tensor<const Shape extends readonly Dimension[]>(
  shape: Shape,
  init?: number[]
): Shape extends IsShapeContainingOnlyNumericLiteralsOrVarDimensions<Shape>
  ? Tensor<Shape>
  : InvalidTensor<Shape> {
  return {
    data: new Float32Array(init || (shape.reduce((a, b) => a * b, 1) as any)),
    shape,
  } as any;
}

export type Vector<T extends number> = Tensor<[1, T]>;
export function vector<Size extends number>(
  size: Size,
  init?: number[]
): Vector<Size>;
export function vector<Label extends string>(
  size: Var<Label>,
  init?: number[]
): Vector<Var<Label>>;
export function vector<N extends readonly [number, ...number[]]>(
  init: N
): Vector<N["length"]>;
export function vector(
  size: number | Var<string> | readonly number[],
  init?: number[]
): Vector<any> {
  let shape: Dimension[];
  if (typeof size === "number") {
    shape = [1, size];
  } else if (isVar(size)) {
    shape = [1, size];
  } else if (Array.isArray(size)) {
    shape = [1, size.length];
    init = size;
  } else {
    throw new Error("Invalid input type for vector.");
  }

  return tensor(shape, init) as any;
}

function zip<V extends Vector<number>>(a: V, b: V): Tensor<[V["shape"][1], 2]> {
  if (a.shape[1] !== b.shape[1]) {
    throw new Error(
      `zip cannot operate on different length vectors; ${a.shape[1]} !== ${b.shape[1]}`
    );
  }

  const length = a.shape[1];
  const resultData: number[] = [];
  for (let i = 0; i < length; i++) {
    resultData.push(a.data[i], b.data[i]);
  }

  return tensor([length, 2], resultData) as any;
}

const t1 = tensor([5, Var(3, "word")]);

const v1 = vector(5);
const v2 = vector(Var(3, "hello"));
const v3 = vector([1, 2, 3]);
const v4 = vector([1, 2, 3]);
const v5 = vector([4, 5, 6]);
const v6 = vector([7, 8, 9, 10]);
const v7 = vector(Var(3, "three"), [1, 2, 3]);
const v8 = vector(Var(3, "three"), [5, 10, 15]);
const v9 = vector(Var(4, "four"), [10, 11, 12, 13]);

const zipped = zip(v4, v5); // Works fine
const zippedError = zip(v4, v6); // Now it's a compile-time error
const zipped2 = zip(v7, v8); // Works fine
const zippedError2 = zip(v7, v9); // Now it's a compile-time error

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sebinsua commented May 2, 2023

// Utilities
type UnionToIntersection<U> = (U extends any ? (k: U) => void : never) extends (
  k: infer I
) => void
  ? I
  : never;
type IsUnion<T> = [T] extends [UnionToIntersection<T>] ? false : true;

type And<A, B> = A extends true ? (B extends true ? true : false) : false;
type Or<A, B> = A extends true ? true : B extends true ? true : false;
type Not<A> = A extends true ? false : true;

// Defines a branded dimension with a runtime-determined size and an associated label.
export type Var<Label extends string> = number & { label: Label };
export const Var = <Label extends string>(d: number, label: Label) => {
  return d as Var<Label>;
};

// We check whether `T` is a numeric literal by checking that `number` does not
// extend from it but that it does extend from `number`.
type IsNumericLiteral<T> = number extends T
  ? false
  : T extends number
  ? true
  : false;
type IsVar<T> = T extends Var<string> ? true : false;

// For type-checking of tensors to work they can only be created using
// numeric literals (e.g. `5`)  or `Var<string>` and not types like
// `number` or `1 | 2 | 3`.
type IsNumericLiteralOrVar<T extends number | (string & number) | readonly number[]> = And<
  // We disallow `T` to be a union of types.
  Not<IsUnion<T>>,
  Or<
    // We allow `T` to be a numeric literal but not a number.
    IsNumericLiteral<T>,
    // We allow `T` to be a `Var`.
    IsVar<T>
  >
>;
type IsShapeContainingOnlyNumericLiteralsOrVarDimensions<
  T extends ReadonlyArray<number | Var<string>>
> = T extends ReadonlyArray<unknown>
  ? { [K in keyof T]: IsNumericLiteralOrVar<T[K]> } extends {
      [K in keyof T]: true;
    }
    ? T
    : never
  : never;

export type Dimension = number | Var<string>;
export type Tensor<Shape extends readonly Dimension[]> = {
  data: Float32Array;
  shape: Shape;
};
export type InvalidTensor<Shape extends readonly Dimension[]> = [
  never,
  "Invalid tensor: please provide an array of only numeric literals or `Var`s.",
  Shape
];
export function tensor<const Shape extends readonly Dimension[]>(
  shape: Shape,
  init?: number[]
): Shape extends IsShapeContainingOnlyNumericLiteralsOrVarDimensions<Shape>
  ? Tensor<Shape>
  : InvalidTensor<Shape> {
  return {
    data: new Float32Array(init || (shape.reduce((a, b) => a * b, 1) as any)),
    shape,
  } as any;
}

export type Matrix<Rows extends Dimension, Columns extends Dimension> = Tensor<[Rows, Columns]>;
export type InvalidMatrix<Shape extends readonly [Dimension, Dimension]> = [
  never,
  "Invalid matrix: please provide an array of only numeric literals or `Var`s.",
  Shape
];
export function matrix<const Shape extends readonly [Dimension, Dimension]>(
  shape: Shape,
  init?: number[]
): Shape extends IsShapeContainingOnlyNumericLiteralsOrVarDimensions<Shape>
  ? Matrix<Shape[0], Shape[1]>
  : InvalidMatrix<Shape> {
  return tensor(shape, init) as any;
}

export type Vector<Size extends number> = Tensor<[1, Size]>;
export type InvalidVector<Size extends Dimension | readonly number[]> = [
  never,
  "Invalid vector: please provide either a numeric literal or a `Var`.",
  Size
];
export function vector<const Size extends number>(
  size: Size,
  init?: number[]
): true extends IsNumericLiteralOrVar<Size>
  ? Vector<Size>
  : InvalidVector<Size>;
export function vector<const Size extends Dimension>(
  size: Size,
  init?: number[]
): true extends IsNumericLiteralOrVar<Size>
  ? Vector<Size>
  : InvalidVector<Size>;
export function vector<const Array extends readonly [number, ...number[]]>(
  init: Array
): Vector<Array["length"]>;
export function vector<const Size extends number | Var<string> | readonly number[]>(
  size: Size,
  init?: number[]
): Vector<any> {
  let shape: Dimension[];
  if (typeof size === "number") {
    shape = [1, size];
  } else if (Array.isArray(size)) {
    shape = [1, size.length];
    init = size;
  } else {
    throw new Error("Invalid input type for vector.");
  }

  return tensor(shape, init) as any;
}

function zip<SameVector extends Vector<number>>(a: SameVector, b: SameVector): Matrix<SameVector["shape"][1], 2> {
  if (a.shape[1] !== b.shape[1]) {
    throw new Error(
      `zip cannot operate on different length vectors; ${a.shape[1]} !== ${b.shape[1]}`
    );
  }

  const length = a.shape[1];
  const resultData: number[] = [];
  for (let i = 0; i < length; i++) {
    resultData.push(a.data[i], b.data[i]);
  }

  return matrix([length, 2], resultData) as any;
}

const t1 = tensor([5, Var(3, "three"), 10]);

const m1 = matrix([5, Var(3, "three")]);

const v1 = vector(2);
const v2 = vector(Var(3, "three"));
const v3 = vector([1, 2, 3]);
const v4 = vector([1, 2, 3]);
const v5 = vector([4, 5, 6]);
const v6 = vector([7, 8, 9, 10]);
const v7 = vector(Var(3, "three"), [1, 2, 3]);
const v8 = vector(Var(3, "three"), [5, 10, 15]);
const v9 = vector(Var(4, "four"), [10, 11, 12, 13]);

const zipped = zip(v4, v5); // Works fine
const zippedError = zip(v4, v6); // Now it's a compile-time error
const zipped2 = zip(v7, v8); // Works fine
const zippedError2 = zip(v7, v9); // Now it's a compile-time error

@sebinsua
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I improved upon this and wrote it up as a blog post here: https://twitter.com/sebinsua/status/1656297294008819712

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sebinsua commented Jul 21, 2023

type Zipped<A extends readonly (readonly any[])[]> = {
  [RowIndex in keyof A[0]]: RowIndex extends "length" ? number : {
    [ArrayIndex in keyof A]: A[ArrayIndex] extends readonly any[] ? A[ArrayIndex][RowIndex] : never;
  };
};

type NumericRange<TotalLength extends number, TempRange extends any[] = []> =
  TempRange['length'] extends TotalLength ? TempRange : NumericRange<TotalLength, [...TempRange, TempRange['length']]>;

type TupleFromKeys<T, K extends readonly (keyof T)[]> = {
  [I in keyof K]: K[I] extends keyof T ? T[K[I]] : never;
};

type Tuple<T extends readonly (readonly any[])[]> = TupleFromKeys<Zipped<T>, NumericRange<T[0]['length']>>;

function zip<const T extends readonly (readonly any[])[]>(...arrays: T): Tuple<T> {
  const minLength = Math.min(...arrays.map(arr => arr.length));
  const result: any[][] = [];

  for (let i = 0; i < minLength; i++) {
    const zippedItem = arrays.map(arr => arr[i]);
    result.push(zippedItem);
  }

  return result as Tuple<T>;
}

const grid = [
  ['a', 1, true],
  ['b', 2, false],
  ['c', 3, true]
] as const;

const [col1, col2, col3] = zip(...grid);
console.log(col1);
console.log(col2);
console.log(col3);

^ This approach would be useful if you needed to convert a grid of rows into a list of columns.

See here: https://www.typescriptlang.org/play?#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-UmMqu40+FHGLTqeQSiBCDYtRPY36RHqm3gW1BwlpyZy-gBZch+anLvCD2kj9qEHfkMCMQ9iESH6kcvz8fjjWTzxdkQihWjAGx9roVcR8XmyIYVCxIwnitnAfxmKMmhQCgS4rmi0FwAA1Mh-CSBMT7Nq29YpkgKi4OEfyHukx7hKe56pJeHCpNwcACI+iSvu+wDUmAoSEL4jC4cgBHPA+EyTHMshkMAoQkNozEfhwxA+p4+wlh6czPq2XgkHASB-NwEyQuQEIPAAjA8wAkKEEC8HcOkQpE+lQAATA8hjHIQ5mWUkELrLZADMxmmeZUgVOQxAqbyKlyE2tBGVAEUOdFVC0F5v51gg+7UmpGkCc+8UQDeVBeIwEUGZlzbZbl+UxcVC6lbQeUFfFXkPkAA

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