Number/Wadsworth.bruijn

# MIT License, Copyright (c) 2023 Marvin Borner
# from Wadsworth's "some unusual numeral systems" (p224, see refs in README)

:import std/Combinator .

zero [0 [k]] ⧗ Wadsworth

# increment Wadsworth number
inc [[[2 [2 (1 0) 1]]]] ⧗ Wadsworth → Wadsworth

:test (inc (inc zero)) ([[[2 (1 (0 (k [[1]]))) 1 0]]])

# decrement Wadsworth number
dec [[1 [k (1 0)] i]] ⧗ Wadsworth → Wadsworth

:test (dec (dec (inc (inc zero)))) (zero)

# returns true if Wadsworth number is zero
zero? [0 i (k (k [[0]]))] ⧗ Wadsworth → Bool

:test (zero? zero) ([[1]])
:test (zero? (inc zero)) ([[0]])
:test (zero? (inc (inc zero))) ([[0]])