Number/Pairing.bruijn

# MIT License, Copyright (c) 2024 Marvin Borner
# pairing functions for writing two integers as one, bijectionally

:import std/Logic .
:import std/Pair .
:import std/Number .
:import std/Math .

# strong Rosenberg pairing function
pair-ternary [[[0 ⋅ 0 + 0 + 2 - 1] (max 1 0)]] ⧗ Number → Number → Number

:test ((pair-ternary (+0) (+0)) =? (+0)) (true)
:test ((pair-ternary (+0) (+1)) =? (+1)) (true)
:test ((pair-ternary (+1) (+0)) =? (+3)) (true)
:test ((pair-ternary (+2) (+1)) =? (+7)) (true)

# strong Rosenberg unpairing function
unpair-ternary [[[go] (1 - (0 ⋅ 0))] (sqrt 0)] ⧗ Number → (Pair Number Number)
	go (0 <? 1) (0 : 1) (1 : (1 ⋅ 1 + 1 + 1 - 2))

:test (strip <$> (unpair-ternary (+0))) ((+0) : (+0))
:test (strip <$> (unpair-ternary (+1))) ((+0) : (+1))
:test (strip <$> (unpair-ternary (+3))) ((+1) : (+0))
:test (strip <$> (unpair-ternary (+7))) ((+2) : (+1))