Haskell type signatures with varying parameters

Question

Project Euler #4: A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Find the largest palindrome made from the product of two 3-digit numbers.

This solution works:

p004largestPalindrome :: Integer
p004largestPalindrome = largest [ a * b | a <- [100..999], b <- [100..999], isPalindrome $ show(a*b) ]
    where
        isPalindrome [] = True
        isPalindrome [_] = True
        isPalindrome (x:xs) = if x == last xs then isPalindrome (init xs) else False
        largest [] = 0
        largest [x] = x
        largest (x:xs) = if x > head xs then largest (x:(tail xs)) else largest xs

My question is: can you assign type signatures to the functions in the where clause, given that the both have different arrangements of parameters ([], [x], (x:xs))? Sticking in isPalindrome :: (Eq a) -> [a] -> Bool throws an error.

Edit: I am trying to insert a type signature like so:

p004largestPalindrome :: Integer
p004largestPalindrome = largest [ a * b | a <- [100..999], b <- [100..999], isPalindrome $ show(a*b) ]
    where
        isPalindrome :: (Eq a) -> [a] -> Bool
        isPalindrome [] = True
        isPalindrome [_] = True
        isPalindrome (x:xs) = if x == last xs then isPalindrome (init xs) else False
        largest [] = 0
        largest [x] = x
        largest (x:xs) = if x > head xs then largest (x:(tail xs)) else largest xs

right before isPalindrome [] = True, directly beneath where — Mark Karavan
You have a typo. Shod be (Eq a) =>... (arrow should be made with equal sign) — Michal Seweryn
By the way, isPalindrome has quadratic complexity when the simpler \x -> x == reverse x has linear complexity. It does not really matters, since we have only short inputs, of course. — chi

Unknown Unknown · Accepted Answer · 2015-01-20T19:01:43

You have a typo. [Should] be (Eq a) =>... (arrow should be made with equal sign) – Michal Seweryn

Class constraints are separated from the types they constrain with =>.

Haskell type signatures with varying parameters

1 Answers