Rule110 Entirely in TypeScript Type System

rule110.ts

// tsc -noErrorTruncation rule110.ts | sed 's/\[/\n[/g'
type Tail<Xs extends Array<any>> = Xs extends [infer _, ...infer Rest] ? Rest : never;
type Head<Xs extends Array<any>> = Xs extends [infer X, ...infer _] ? X : never;
type Pair<X, Xs extends Array<X>> = [X, ...Xs]

type Reverse<
    Items extends Array<any>,
    Acc extends Array<any> = []
> = Items extends [] ? Acc : Reverse<Tail<Items>, Pair<Items[0], Acc>>;

type Cell = 0 | 1;
type Rule110<A extends Cell, B extends Cell, C extends Cell> = {
    "000": 0,
    "001": 1,
    "010": 1,
    "011": 1,
    "100": 0,
    "101": 1,
    "110": 1,
    "111": 0,
}[`${A}${B}${C}`]

// 0 0 [1 0]
// 0 

type Start<Xs extends Array<Cell>> =
    Xs extends [infer X extends Cell, ...infer Rest extends Array<Cell>]
    ? [X, ...Next<X, Rest>]
    : [];

type Next<
    X extends Cell,
    Items extends Array<Cell>,
> = Items extends [infer Y extends Cell,
                   infer Z extends Cell,
                   ...infer Rest extends Array<Cell>]
    ? [Rule110<X, Y, Z>, ...Next<Y, [Z, ...Rest]>]
    : Items extends [infer Y extends Cell]
      ? [Y]
      : [];

type Gen<N extends Array<any>, State extends Array<Cell>> =
    N extends []
    ? []
    : [State, ...Gen<Tail<N>, Start<State>>]

type N = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];

let x: Gen<N, [...N, 1, 0]> = 69;