CODEWITHSUNDEEP
haskelltypes
Aleksei Sery
Aleksei Sery

Reputation: 5

Type of the Haskell expression takeWhile even

If anyone can help me out with clearing this question?

The Standard Prelude function takeWhile has type (a -> Bool) -> [a] -> [a]

Write down the type of the Haskell expression takeWhile even The function even is defined as:

even x = x `mod` 2 == 0

Would this be considered right?

takeWhile:: Num a => (a->Bool) -> [a] -> [a]

Upvotes: 0

Views: 474

Answers (1)

Chris
Chris

Reputation: 1957

To derive the type signature of takeWhile even you need to first take a look at the type signature for takeWhile and even. According to GHCi, the type signatures for those functions are the following.

takeWhile :: (a -> Bool) -> [a] -> [a]

even :: Integral a => a -> Bool

In the case of takeWhile even, takeWhile takes in a function of type (a -> Bool), thus a function that takes in some value of type a and returns a Bool.

The even function takes in an Integral value and returns a Bool value, so it can be passed in as the first argument to takeWhile. Since the Integral typeclass is implemented by several different types such as Int and Integer, you can pass in a value of any such type that implements the Integer typeclass.

You will want to notice that in takeWhile, the a in (a -> Bool) is not bound to any typeclass, however in even the corresponding a is bound to the Integral typeclass. In this case, this causes the resulting expression to bind the a in the takeWhile type signature to Integral. For example, you could imagine takeWhile to have the following type signature in this case:

takeWhile :: Integral a => (a -> Bool) -> [a] -> [a]

Also, since the first argument of takeWhile is filled by even, the type signature of the resulting expression does not have the (a -> Bool) term.

Thus, you are left with the following type signature for takeWhile even. Therefore takeWhile even takes in a list of Integral values and returns a list of Integral values of the same type.

takeWhile even :: Integral a => [a] -> [a]

If you want to confirm this using GHCi, you can run the following command to get the type signature of the expression:

:t takeWhile even

Upvotes: 2

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