If I write:
> let xs = [1,5,19,2,-3,5]
> foldr max 0 xs
19
> foldr1 max xs
19
And if I write (I know, the initial value is incorrect here for a generic maximum function...):
> let maximum' = foldr max 0
> maximum' xs
19
But if I write:
> let maximum2' = foldr1 max
> maximum2' xs
the response is:
<interactive>:61:11:
Couldn't match expected type `()' with actual type `Integer'
Expected type: [()]
Actual type: [Integer]
In the first argument of maximum2', namely `xs'
In the expression: maximum2' xs
I am new to Haskell. What am I doing wrong? (Can't decipher the error message...) How to use foldr1
with max
? Thanks.
EDIT (AFTER ACCEPTING ANSWER):
Just to show some more examples of the defaulting rules' effect (the answer explains these, too):
Example 1:
> let max' = max
> :t max
max :: Ord a => a -> a -> a
> :t max'
max' :: () -> () -> ()
Example 2:
> let plus = (+)
> :t (+)
(+) :: Num a => a -> a -> a
> :t plus
plus :: Integer -> Integer -> Integer
The problem is to do with the polymorphism of the types and GHCi's defaulting. The type of max
is polymorphic:
> :t max
max :: Ord a => a -> a -> a
In the case of maximum'
, the compiler can see that a
is some sort of number, and GHCi defaults the number to Integer:
> :t maximum'
maximum' :: [Integer] -> Integer
In the case of maximum2'
it has less clues, and defaults a
to the unit type:
> :t maximum2'
maximum2' :: [()] -> ()
If you provide a type signature, all is well:
> let maximum3' :: Ord a => [a] -> a ; maximum3' = foldr1 max
> :t maximum3'
maximum3' :: Ord a => [a] -> a
I think GHCi's defaulting rules are there to make certain other cases where the types are omitted easier -- see http://www.haskell.org/ghc/docs/7.6.2/html/users_guide/interactive-evaluation.html#id484837
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