QuickCheck - Non exhaustive patterns in function - Haskell

Question

I have two function. One is implemented using patterns and the other using intensive lists. I want to check if the result is the same always with QickCheck.

pares xs = [a | a <- xs , mod a 2 == 0]
cuadrados xs = [x^2 | x <- pares xs ]
cuadrados'' [] = []
cuadrados'' (x:xs) = [x^2] ++ cuadrados'' xs
cuadrados' (x:xs)  = cuadrados'' (pares (x:xs))

Im trying:

prop_cuadrados xs = cuadrados xs == cuadrados' xs

When I try quickCkeck prop_cuadrados the output is the following:

*Main> quickCheck prop_cuadrados *** Failed! (after 1 test): Exception: sesion4.hs:10:1-47: Non-exhaustive patterns in function cuadrados' []

How can I solve this problem? Thanks

Answer 1

We can find that problem immediately if we either apply -Wall in GHC (which automatically enables -Wincomplete-patterns ) or just try the found counter example by hand.

QuickCheck finds xs = [] as counterexample. So let us have a look at cuadrados' :

cuadrados' []

At that point, we cannot continue, as cuadrados' only binds on a single pattern: (x:xs) . Unfortunately, [] cannot match that pattern and you end up with an error. To fix it, simply add another pattern:

cuadrados' []     = []
cuadrados' (x:xs) = …

or just use

cuadrados' xs = cuadrados'' (pares xs)

as we don't use the first element explicitly.

That being said, pares is filter even , and cuadrados is map (^2) . filter even map (^2) . filter even . Try to use the standard library and higher order functions a little bit more.