TypeScriptの型で自然数を作る
TypeScriptの型
code:ts
type N_ZERO = []
type NUM = N_ZERO | NUM
type INC<N> = N
type DEC<N> = (
N extends infer M
? M
: never
)
{
let x: DEC<INC<N_ZERO>> = [];
}
type ADD<N, M> = (
M extends N_ZERO
? N
:
// ADD<INC<N>, DEC<N>>
// Type alias 'ADD' circularly references itself.
{
0: ADD<INC<N>, DEC<M>>,
1: never
}N extends any ? 0 : 1
)
{
let x: ADD<]], [[> = []; // 1 + 1 == 2
}
type N_ONE = INC<N_ZERO>;
type MUL<N, M, S = N_ZERO> = (
M extends N_ZERO
? S
:
{
0: MUL<N, DEC<M>, ADD<S, N>>,
1: never
}N extends any ? 0 : 1
)
type N_TWO = INC<N_ONE>
type N_THREE = INC<N_TWO>
{
let x: MUL<N_ONE, N_ONE> = [[]]; // 1 * 1 == 1
} {
let x: MUL<N_TWO, N_ONE> = []; // 2 * 1 == 2
} {
let x: MUL<N_ONE, N_TWO> = []; // 1 * 2 == 1
} {
let x: MUL<N_TWO, N_TWO> = [[[]]]; // 2 * 2 == 4
}
code:ts
type N_0 = N_ZERO;
type N_1 = N_ONE;
type N_2 = N_TWO;
type N_3 = N_2;
type N_4 = N_3;
type N_5 = N_4;
type N_6 = N_5;
type N_7 = N_6;
type N_8 = N_7;
type N_9 = N_8;
type N_TEN = N_9;
type DIGITS2<N, M> = MUL<N, N_TEN, M>
// try "N - M", return answer or null
type MINUS<N, M> = (
M extends N_0
? N
: (
{
0: null,
1: MINUS<DEC<N>, DEC<M>>
}N extends N_0 ? 0 : 1
)
)
{
let x: MINUS<N_5, N_2> = {} as N_3
} {
let x: MINUS<N_2, N_5> = null;
}
type DIVIDE<
N, M,
Q = N_0,
N1 = MINUS<N, M>
= (
{
0: Q, N,
1: DIVIDE<N1, M, INC<Q>>
}N1 extends null ? 0 : 1
)
{
let x: DIVIDE<MUL<N_3, N_4>, N_TEN> = {} as N_1, N_2
}
{
let x: DIVIDE<MUL<N_7, N_8>, N_TEN> = {} as N_5, N_6
// Type instantiation is excessively deep and possibly infinite.
}
5 * 6 == 30 はできるけど 6 * 7 == 42 はできない