head (a : b) == a
tail (a : b) == b
cns a b == a : b
add a b == a + b
sub a b == a - b
mul a b == a * b

length [] == 0
length (a : b) == 1 + length b

sum [] == 0
sum (a : b) == a + sum b

addtoend x [] == [ x ]
addtoend x (a : b) == a : addtoend x b

map f [] == []
map f (a : b) == f a : map f b

reduce1 f [a] == a
reduce1 f (a : b) == f a (reduce1 f b)

reduce2 f [a] == a
reduce2 f (a : b) == f (reduce2 f b) a

reduce3 f [] s == s
reduce3 f (a : b) s == f a (reduce3 f b s)

reduce4 f [] s == s
reduce4 f (a : b) s == f (reduce4 f b s) a

reduce5 f [] s == s
reduce5 f (a : b) s == reduce5 f b (f a s)

reduce6 f [] s == s
reduce6 f (a : b) s == reduce6 f b (f s a)

first 0 L == []
first n [] == []
first n (a : b) == a : first (n - 1) b

intsbetween a a == [ a ]
intsbetween a b == a : intsbetween (a + 1) b

insert x [] == [ x ]
insert x (a : b) == a : insert x b <| x > a |> x : a : b

sort [] == []
sort (a : b) == insert a (sort b)

head (a : b) == a
head x == "bad!"

min lst == head (sort lst)