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# ==================
# Common combinators
# ==================
S [[[2 0 (1 0)]]]
K [[1]]
I [0]
B [[[2 (1 0)]]]
C [[[2 0 1]]]
T [[1]]
F [[0]]
ω [0 0]
Ω ω ω
Y [[1 (0 0)] [1 (0 0)]]
Θ [[0 (1 1 0)]] [[0 (1 1 0)]]
i [0 S K]
# =================
# Alternative names
# =================
true T
false F
id I
# =====
# Pairs
# =====
pair [[[0 2 1]]]
fst [0 T]
snd [0 F]
# ===================================
# Binary
# According to works of T.Æ. Mogensen
# ===================================
# TODO: contract-like type-checking
# like: `+ ... : [[[[# 3]]]]`
# TODO: Fix for negative 4x abstraction
upZero [[[[1 (3 2 1 0)]]]]
upOne [[[[0 (3 2 1 0)]]]]
up [[[[[4 1 0 (3 2 1 0)]]]]]
zero? [0 T I [F]]
binZero [[[2]]]
binOne [[[0 2]]]
_succZ (pair binZero binOne)
_succA [0 [[pair (upZero 1) (upOne 1)]]]
_succB [0 [[pair (upOne 1) (upZero 0)]]]
succ [snd (0 _succZ _succA _succB)]
_predZ (pair binZero binZero)
_predA [0 [[pair (upZero 1) (upOne 0)]]]
_predB [0 [[pair (upOne 1) (upZero 1)]]]
pred [snd (0 _predZ _predA _predB)]
# ===================================
# Ternary
# According to works of T.Æ. Mogensen
# ===================================
# zero? [0 T [F] I [F]]
# upNeg [[[[[2 (4 3 2 1 0)]]]]]
# upZero [[[[[1 (4 3 2 1 0)]]]]]
# upPos [[[[[0 (4 3 2 1 0)]]]]]
# up [[[[[[5 2 1 0 (4 3 2 1 0)]]]]]]
#
# negate [[[[[4 3 0 1 2]]]]]
#
# tritNeg [[[2]]]
# tritZero [[[1]]]
# tritPos [[[0]]]
# lst [0 tritZero [tritNeg] [tritZero] [tritPos]]
#
# _stripZ pair +0 T
# _stripANeg [0 [[pair (0 +0 (upNeg 1)) 0]]]
# _stripAZero [0 [[pair (upZero 1) F]]]
# _stripAPos [0 [[pair (upPos 1) F]]]
# strip [fst (0 _stripZ _stripANeg _stripAZero _stripAPos)]
#
# _succZ pair +0 +1
# _succANeg [0 [[[pair (upNeg 2) (upZero 2)]]]]
# _succAZero [0 [[[pair (upZero 2) (upPos 2)]]]]
# _succAPos [0 [[[pair (upPos 2) (upNeg 1)]]]]
# succ [snd (0 _succZ _succANeg _succAZero _succAPos)]
#
# _predZ pair +0 -1
# _predANeg [0 [[[pair (upNeg 2) (upPos 1)]]]]
# _predAZero [0 [[[pair (upZero 2) (upNeg 2)]]]]
# _predAPos [0 [[[pair (upPos 2) (upZero 2)]]]]
# pred [snd (0 _predZ _predANeg _predAZero _predAPos)]
#
# _absNeg [[[[[2 4]]]]]
# _absZero [[[[[1 4]]]]]
# _absPos [[[[[0 4]]]]]
# abstractify [0 [[[[3]]]] _absNeg _absZero _absPos]
#
# _normalize [[0 [ +0 ] [[upNeg (1 1 0)]] [[upZero (1 1 0)]] [[upPos (1 1 0)]] 1]]
# normalize ω _normalize
#
# _eqZero? [zero? (normalize 0)]
# _eqNeg [[0 F [2 0] [F] [F]]]
# _eqZero [[0 (1 0) [F] [2 0] [F]]]
# _eqPos [[0 F [F] [F] [2 0]]]
# _eqAbs [0 _eqZero? _eqNeg _eqZero _eqPos]
# eq [[_eqAbs 1 (abstractify 0)]]
#
# _addZ [[0 (pred (normalize 1)) (normalize 1) (succ (normalize 1))]]
# _addC [[1 0 tritZero]]
# _addBNeg2 [1 (upZero (3 0 tritNeg)) (upPos (3 0 tritNeg)) (upNeg (3 0 tritZero))]
# _addBNeg [1 (upPos (3 0 tritNeg)) (upNeg (3 0 tritZero)) (upZero (3 0 tritZero))]
# _addBZero [up 1 (3 0 tritZero)]
# _addBPos [1 (upZero (3 0 tritZero)) (upPos (3 0 tritZero)) (upNeg (3 0 tritPos))]
# _addBPos2 [1 (upPos (3 0 tritZero)) (upNeg (3 0 tritPos)) (upZero (3 0 tritPos))]
# _addANeg [[[1 (_addBNeg 1) _addBNeg2 _addBNeg _addBZero]]]
# _addAZero [[[1 (_addBZero 1) _addBNeg _addBZero _addBPos]]]
# _addAPos [[[1 (_addBPos 1) _addBZero _addBPos _addBPos2]]]
# _addAbs [_addC (0 _addZ _addANeg _addAZero _addAPos)]
# add [[_addAbs 1 (abstractify 0)]]
#
# sub [[add 1 (negate 0)]]
# ===============
# Boolean algebra
# ===============
not [0 F T]
and [[1 0 F]]
or [[1 T 0]]
xor [[1 (not 0) 0]]
if [[[2 1 0]]]
# ===============
# Church numerals
# ===============
churchZero [[0]]
churchSucc [[[1 (2 1 0)]]]
churchAdd [[[[3 1 (2 1 0)]]]]
churchMul [[[2 (1 0)]]]
churchExp [[0 1]]
main [[[0 2 1]]]
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