import { $, Combinator, Conditional, Function, NaturalNumberTheory } from '..';
/**
 * `CollatzSequence` is a type-level function that represents the Collatz sequence.
 * This is a sequence of numbers generated by repeatedly applying the Collatz function,
 * starting from a given number, until reaching 1. This sequence is generated using the FixSequence type-level function,
 * which creates a fixed-point sequence for the Collatz function until it reaches a fixed point, which in this case is 1.
 *
 * Note: We're "artificially" making `Collatz(1)` return `1` so that we can use the fixed sequence operation.
 *
 * @template T - The starting number of the sequence.
 *
 * @example
 * type T0 = $<CollatzSequence, 6> // [6, 3, 10, 5, 16, 8, 4, 2, 1]
 * type T1 = $<CollatzSequence, 5> // [5, 16, 8, 4, 2, 1]
 */
export type CollatzSequence = $<Combinator.FixSequence, $<$<$<Conditional.If, $<Conditional.Equals, 1>>, $<Function.Constant, 1>>, NaturalNumberTheory.Collatz>>;