# Combinators

I = \x. x

K = \x y. x

S = \x y z. x z (y z)

Y = \f. (\x. f (x x)) (\x. f (x x))

Om = (\x y. y (x x y)) (\x y. y (x x y))

LOOP = (\x. x x) (\x. x x)

# Logic

T = \x y. x

F = \x y. y

NOT = \p. p F T

AND = \p q. p q F

OR = \p q. p T q

COND = \p x y. p x y

# Pairs

FST = \p. p T

SND = \p. p F

PAIR = \a b f. f a b

, = \a b f. f a b

# Arithmetic

ISZERO = \n. n (\x. F) T

SUCC = \n f x. f (n f x)

PLUS = \m n f x. n f (m f x)

+ = \m n f x. n f (m f x)

MULT = \m n f. m (n f)

* = \m n f. m (n f)

POW = \m n. n m

PRED = \n f x. n (\g h. h (g f)) (\u. x) I

TETR = \m n. n (\g. g m) I

FACT = Y (\f n. (ISZERO n) 1 (MULT (f (PRED n)) n))

# Lists

NIL = \z. z

CONS = \x y. , F (, x y)

: = \x y. , F (, x y)

NULL = \z. z T

HEAD = \z. FST (SND z)

TAIL = \z. SND (SND z)