Module church 

Church numerals

Functions

add

Applied to two Church-encoded numbers it produces their sum.

div

Applied to two Church-encoded numbers it returns a Church-encoded pair with the result of their division - the quotient and the remainder.

eq

Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is equal to the second one.

fac

Applied to a Church-encoded number it yields its Church-encoded factorial.

geq

Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is greater than or equal to the second one.

gt

Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is greater than the second one.

is_even

Applied to a Church-encoded number it produces a lambda-encoded boolean, indicating whether its argument is even.

is_odd

Applied to a Church-encoded number it produces a lambda-encoded boolean, indicating whether its argument is odd.

is_zero

Applied to a Church-encoded number it produces a lambda-encoded boolean, indicating whether its argument is equal to zero.

leq

Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is less than or equal to the second one.

lt

Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is less than the second one.

max

Applied to two Church-encoded numbers it returns the greater one.

min

Applied to two Church-encoded numbers it returns the smaller one.

mul

Applied to two Church-encoded numbers it yields their product.

neq

Applied to two Church-encoded numbers it returns a lambda-encoded boolean indicating whether its first argument is not equal to the second one.

one

Produces a Church-encoded number one.

pow

Applied to two Church-encoded numbers it raises the first one to the power of the second one.

pred

Applied to a Church-encoded number it produces its predecessor.

quot

Applied to two Church-encoded numbers it returns a Church-encoded quotient of their division.

rem

Applied to two Church-encoded numbers it returns a Church-encoded remainder of their division.

shl

Applied to two Church-encoded numbers a and b it returns the left logical shift of a performed b times.

shr

Applied to two Church-encoded numbers a and b it returns the right logical shift of a performed b times.

sub

Applied to two Church-encoded numbers it subtracts the second one from the first one.

succ

Applied to a Church-encoded number it produces its successor.

to_parigot

Applied to a Church-encoded number it produces the equivalent Parigot-encoded number.

to_scott

Applied to a Church-encoded number it produces the equivalent Scott-encoded number.

to_stumpfu

Applied to a Church-encoded number it produces the equivalent Stump-Fu-encoded number.

zero

Produces a Church-encoded number zero; equivalent to boolean::fls.