import { Type, Kind, Digit, DigitList } from '..';
/**
 * `_$increment` is a type-level function that takes in a digit list `A` and
 * returns a new digit list representing the result of incrementing the input
 * digit list by 1. If the input digit list is empty or represents zero, the
 * result will be a digit list representing zero.
 *
 * @template A - A digit list type.
 *
 * @example
 * For example, we can use `_$increment` to increment a digit list representing
 * the number 42 by 1. In this example, the digit list `["4", "2"]` is passed as
 * a type argument to the type-level function:
 *
 * ```ts
 * import { DigitList } from "hkt-toolbelt";
 *
 * type Result = DigitList._$increment<["4", "2"]>; // ["4", "3"]
 * ```
 *
 * @example
 * We can also use `_$increment` with an empty digit list or a digit list
 * representing zero. In both cases, the result will be a digit list
 * representing one:
 *
 * ```ts
 * import { DigitList } from "hkt-toolbelt";
 *
 * type Result1 = DigitList._$increment<[]>; // ["1"]
 * type Result2 = DigitList._$increment<["0"]>; // ["1"]
 * ```
 */
export type _$increment<
/**
 * The digit-list to increment.
 */
A extends DigitList.DigitList, 
/**
 * The carry bit, which encodes whether the increment operation should carry
 * over to the next digit.
 */
CARRY extends Digit.Digit = '1', 
/**
 * The current output digit-list, i.e. the list of processed digits, generated
 * from right to left.
 */
OUTPUT extends DigitList.DigitList = [], 
/**
 * The last digit of A.
 */
A_LAST extends Digit.Digit = DigitList._$last<A>, 
/**
 * The next digit list of A, which is the current digit list without its last
 * element.
 */
NEXT_A extends DigitList.DigitList = DigitList._$pop<A>, 
/**
 * The sum of the last digit of A and the carry digit.
 */
INCREMENT extends Digit.Digit = CARRY extends '1' ? Digit._$increment<A_LAST> : A_LAST, 
/**
 * The carry digit from the sum of the last digit of A and the carry digit.
 * This encodes the 'tens' place of the result.
 */
NEXT_CARRY extends Digit.Digit = CARRY extends '1' ? Digit._$incrementTens<A_LAST> : '0', 
/**
 * The next output result, which is the result of this iteration prepended to
 * the previous iteration's result.
 */
NEXT_OUTPUT extends DigitList.DigitList = [INCREMENT, ...OUTPUT], 
/**
 * When A is empty, we prepend the carry digit to the output if it is "1".
 */
FINAL_RESULT extends DigitList.DigitList = CARRY extends '1' ? [CARRY, ...OUTPUT] : OUTPUT, 
/**
 * Is the carry bit is "0", we can skip the rest of the computation and return
 * the rest of 'A' prepended to the output.
 */
SHORT_CIRCUIT extends DigitList.DigitList = [...A, ...OUTPUT]> = A extends [] ? FINAL_RESULT : CARRY extends '0' ? SHORT_CIRCUIT : _$increment<NEXT_A, NEXT_CARRY, NEXT_OUTPUT>;
/**
 * `Increment` is a type-level function that increments a digit list.
 * It returns the incremented digit list.
 *
 * @template A - The digit list to increment.
 *
 * @example
 * For example, we can use `Increment` to increment a digit list:
 *
 * ```ts
 * import { $, DigitList, Type } from "hkt-toolbelt";
 *
 * type Result = $<DigitList.Increment, ["1", "0"]>; // ["1", "1"]
 * ```
 *
 * In this example, `Result` is a type that represents the digit list ["1", "1"], which is the result of incrementing the digit list ["1", "0"].
 */
export interface Increment extends Kind.Kind {
    f(x: Type._$cast<this[Kind._], DigitList.DigitList>): _$increment<typeof x>;
}