atom0 [[[[[4]]]]]
atom1 [[[[[3]]]]]
atom2 [[[[[2]]]]]
atom3 [[[[[1]]]]]
atom4 [[[[[0]]]]]

# =========
# Reduction
# =========

:test [0] atom0 = atom0
:test [[0 1 0]] atom0 atom1 = atom1 atom0 atom1
:test [[[[3 2 1 0]]]] atom0 atom1 atom2 atom3 = atom0 atom1 atom2 atom3

# ===============
# Church numerals
# ===============

chrch_n0 [[0]]
chrch_n1 [[1 0]]
chrch_n2 [[1 (1 0)]]
chrch_n3 [[1 (1 (1 0))]]
chrch_n4 [[1 (1 (1 (1 0)))]]
chrch_n5 [[1 (1 (1 (1 (1 0))))]]
chrch_n6 [[1 (1 (1 (1 (1 (1 0)))))]]
chrch_n7 [[1 (1 (1 (1 (1 (1 (1 0))))))]]
chrch_n8 [[1 (1 (1 (1 (1 (1 (1 (1 0)))))))]]
chrch_n9 [[1 (1 (1 (1 (1 (1 (1 (1 (1 0))))))))]]
chrch_add [[[[3 1 (2 1 0)]]]]
chrch_mul [[[2 (1 0)]]]
chrch_pow [[0 1]]

:test chrch_add chrch_n2 chrch_n3 = chrch_n5
:test chrch_mul chrch_n2 chrch_n3 = chrch_n6
:test chrch_pow chrch_n2 chrch_n3 = chrch_n8

# ==================
# Lennart
# From Lambda-n-ways
# ==================

lnnrt_true [[0]]
lnnrt_false [[1]]
lnnrt_if [[[2 0 1]]]
lnnrt_zero [[1]]
lnnrt_succ [[[0 2]]]
lnnrt_one lnnrt_succ lnnrt_zero
lnnrt_two lnnrt_succ lnnrt_one
lnnrt_three lnnrt_succ lnnrt_two
lnnrt_const [[1]]
lnnrt_pair [[[0 2 1]]]
lnnrt_fst [[1 0 [[1]]]]
lnnrt_snd [[1 0 [[0]]]]
lnnrt_fix [[1 (0 0)] [1 (0 0)]]
lnnrt_add lnnrt_fix [[[1 0 [lnnrt_succ (3 0 1)]]]]
lnnrt_mul lnnrt_fix [[[1 lnnrt_zero [lnnrt_add 1 (3 0 1)]]]]
lnnrt_fac lnnrt_fix [[0 lnnrt_one [lnnrt_mul 1 (2 0)]]]
lnnrt_eqnat lnnrt_fix [[[1 (0 lnnrt_true (lnnrt_const lnnrt_false)) [1 lnnrt_false [4 1 0]]]]]
lnnrt_sumto lnnrt_fix [[0 lnnrt_zero [lnnrt_add 1 (2 0)]]]
lnnrt_n5 lnnrt_add lnnrt_two lnnrt_three
lnnrt_n6 lnnrt_add lnnrt_three lnnrt_three
lnnrt_n17 lnnrt_add lnnrt_n6 (lnnrt_add lnnrt_n6 lnnrt_n5)
lnnrt_n37 lnnrt_succ (lnnrt_mul lnnrt_n6 lnnrt_n6)
lnnrt_n703 lnnrt_sumto lnnrt_n37
lnnrt_n720 lnnrt_fac lnnrt_n6

# this test can take a minute, comment it if you're in a hurry
:test lnnrt_eqnat lnnrt_n720 (lnnrt_add lnnrt_n703 lnnrt_n17) = lnnrt_true

main [[1]]