変な計算

calc.hs

eqz :: Integer -> Bool
eqz a = a == 0

add :: Integer -> Integer -> Integer
add a b
	| eqz b = a
	| otherwise = succ $ add a $ pred b

mul :: Integer -> Integer -> Integer
mul a b
	| eqz b = 0
	| otherwise = add a $ mul a $ pred b

pow :: Integer -> Integer -> Integer
pow a b
	| eqz b = 1
	| otherwise = mul a $ pow a $ pred b

sub :: Integer -> Integer -> Integer
sub a b
	| eqz b = a
	| otherwise = pred $ sub a $ pred b

mod' :: Integer -> Integer -> Integer
mod' a b
	| eqz a = 0
	| eqz (sub a b) = 0
	| a < b = a
	| otherwise = mod' (sub a b) b

gcd' :: Integer -> Integer -> Integer
gcd' a b
	| eqz b = a
	| otherwise = gcd' b (mod' a b)

per :: Integer -> Integer -> Integer
per a b
	| eqz b = a
	| otherwise = mul a $ per (pred a) (pred b)