[Haskell-beginners] Why does this list comprehension return an empty list?

[Frerich Raabe]

On 2013-07-23 10:53, Costello, Roger L. wrote:
> I have a list of singletons:
>
> 	xs = [("a")]
>
> f is a function that, given an argument x, it returns the argument:
>
> 	f x = x
>
> g is a function that, given an argument x, it returns the empty list:
>
> 	g x = []
>
> I have a list comprehension that extracts the singletons from xs
> using f and g, and creates a pair from their output:
>
> 	[(a,b) | a <- f xs, b <- g xs]
>
> I executed this and the result is the empty list:
>
> 	[]
>
> That is odd. Why is the empty list the result?

Consider how the list comprehension looks like when written as monadic 
code:

   f xs >>= \a ->
   g xs >>= \b ->
   return (a,b)

I.e. "for each element 'a' drawn from the result of "f sx", draw an 
element 'b' from the result of "g xs" and yield a new element "(a,b)". 
So the resulting list will always be 'length (f xs) * length (g xs)' 
items in length. Consequently, if either of the two lists is empty, the 
result will be empty.

-- 
Frerich Raabe - raabe at froglogic.com
www.froglogic.com - Multi-Platform GUI Testing