macros.lamb

# How to use exported files in lamb:
#
# [Syntax Highlighting]
#	Most languages' syntax highlighters will
#	highlight this code well. Set it manually
#	in your editor.
#
#	Don't use a language for which you have a
#	linter installed, you'll get lots of errors.
#
#	Choose a language you don't have extenstions for,
#	and a language that uses # comments.
#
# The following worked well in vscode:
# - Julia
# - Perl
# - Coffeescript
# - R

# [Writing macros]
#	If you don't have a custom keyboard layout that can
#	create λs, you may use backslashes instead.
#	(As in `T = \ab.b`)
#
#	This file must only contain macro definitons. Commands will be ignored.
#	Statements CANNOT be split among multiple lines.
#	Comments CANNOT be on the same line as macro defintions.
#	All leading whitespace is ignored.


# Misc Combinators
M = λx.(x x)
W = (M M)
Y = λf.( (λx.(f (x x))) (λx.(f (x x))) )


# Booleans
T = λab.a
F = λab.b
NOT = λa.(a F T)
AND = λab.(a b F)
OR = λab.(a T b)
XOR = λab.((a (NOT b)) b)


# Numbers
# PAIR: prerequisite for H.
#	Makes a two-value tuple, indexed with T and F.
#
# H: shift-and-add, prerequisite for D
#
# S: successor (adds 1)
#
# D: predecessor (subtracts 1)
#
# Z: tests if a number is zero
# NZ: equivalent to `NOT Z`
#
# ADD: adds two numbers
#
# MULT: multiply two numbers
#
# FAC:
#	Recursive factorial. Call with `Y FAC <number>`
#	Don't call this with numbers bigger than 5 unless you're very patient.
#
#	`Y FAC 6` required 867,920 reductions and took 10 minutes to run.

PAIR = λabi.(i a b)
S = λnfa.(f (n f a))
H = λp.((PAIR (p F)) (S (p F)))
D = λn.(n H (PAIR 0 0) T)
Z = λn.(n (λa.F) T)
NZ = λn.(n (λa.T) F)
ADD = λmn.(m S n)
MULT = λnmf.(n (m f))
FAC = λyn.(Z n) (1) (MULT n (y (D n)))