Parsing integers in TypeScript's type system

num.ts

type NumCat<X, Y> = X extends any[] ? Y extends any[] ? [...X, ...X, ...X, ...X, ...X, ...X, ...X, ...X, ...X, ...X, ...Y] : never : never;
type OneDigit = {
    '0': [], '1': [any], '2': [any, any], '3': [any, any, any],
    '4': [any, any, any, any], '5': [any, any, any, any, any],
    '6': [any, any, any, any, any, any], '7': [any, any, any, any, any, any, any],
    '8': [any, any, any, any, any, any, any, any],
    '9': [any, any, any, any, any, any, any, any, any],
};
type Digit<S> = S extends keyof OneDigit ? OneDigit[S] : never;
type Len<X> = X extends any[] ? X['length'] : never;

type Chars<X extends string> = X extends `${infer A}${infer B}` ? [A, ...Chars<B>] : [];
type ListStr<X extends any[]> =
    X extends [any, ...any] ? X extends [...infer tens, infer ones] ? NumCat<ListStr<tens>, Digit<ones>> : never : [];
type Num<X extends string> = Len<ListStr<Chars<X>>>;

type Anys<X> = X extends [any, ...infer U] ? [any, ...Anys<[...U]>] : [];
type _Cmp<X, Y> = X extends [...Anys<Y>, ...any[]] ? Y extends [...Anys<X>, ...any[]] ? _Cmp1<X, Y> : 'gt' : 'lt';
type _Cmp1<X, Y> = X extends [] ? 'eq' : X extends [infer X1, ...infer X2] ? Y extends [infer Y1, ...infer Y2] ? _Cmp2<Digit<X1>, Digit<Y1>, X2, Y2> : never : never;
type _Cmp2<X1 extends any[], Y1 extends any[], X2, Y2> = X1 extends [...Y1, ...any[]] ? Y1 extends [...X1, ...any[]] ? _Cmp1<X2, Y2> : 'gt' : 'lt';
type Cmp<X extends number, Y extends number> = _Cmp<Chars<`${X}`>, Chars<`${Y}`>>;

type Tail<L> = L extends [any, ...infer U] ? U : {tail: L};
type List<N extends number> = N extends 0 ? [] : _List<N, [[any]]>;
type _List<N extends number, L extends any[][]> = _List1<N, L, Cmp<N, L[0]['length']>>;
type _List1<N extends number, L extends any[][], C> = C extends 'eq' ? L[0] : C extends 'lt' ? _List2<N, Tail<L>, []> : _List<N, [[...L[0], ...L[0]], ...L]>;
type _List2<N extends number, L, O extends any[]> = L extends any[][] ? _List3<N, L, O> : {N: N, L: L, O: O};
type _List3<N extends number, L extends any[][], O extends any[]> = _List4<N, L, O, [...L[0], ...O]>;
type _List4<N extends number, L extends any[][], O1 extends any[], O2 extends any[]> =
    _List5<N, L, O1, O2, Cmp<N, O2['length']>>;
type _List5<N extends number, L extends any[][], O1 extends any[], O2 extends any[], C> =
    C extends 'eq' ? O2 : C extends 'gt' ? _List2<N, Tail<L>, O2> : _List2<N, Tail<L>, O1>

type Add<X extends number, Y extends number> = Len<[...List<X>, ...List<Y>]>;
type Mul<X extends number, Y extends number> = Len<_Mul<List<X>, List<Y>>>;
type _Mul<X extends any[], Y extends any[]> = X extends [any, ...infer U] ? [...Y, ..._Mul<U, Y>] : [];

// Usage:
type five = Num<'5'>;
type twelveHundred = Num<'1200'>;
type sum = Add<123, 434>;
type product = Mul<23, 53>;

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