module HomeworkOne
import Data.Vect

%default total

zipW : (a -> b -> c) -> Vect n a -> Vect n b -> Vect n c
zipW _ [] [] = []
zipW f (x::xs) (y::ys) = f x y :: zipWith f xs ys 

lst : Vect (S n) a -> a
lst (x::[]) = x 
lst (_::x::xs) = lst (x::xs)

initial : Vect (S n) a -> Vect n a
initial (x::[]) = []
initial (x1::x2::xs) = x1 :: initial (x2::xs)

palin : Eq a => Vect n a -> Bool
palin [] = True
palin [x] = True
palin (x1::l@(x2::xs)) = x1 == lst l && (palin $ initial l)