I am trying to implement this pair data type as an applicative functor but I am told that 'a' is not in scope. I thought already stated what 'a' was in the instance declaration.

data Pair a b = Pair a b deriving (Show)

instance Functor (Pair a) where 
    fmap f (Pair a b) = Pair a (f b)

instance Applicative (Pair a) where
    
    pure x = Pair a x
    Pair a f <*> Pair a' x = Pair (a   a') (f x)

CodePudding user response：

a is a type variable, not something you can use in the definition of pure. pure needs some way of getting a value of type a to pair with x. There are a few ways you could do that:

1. A function of type b -> a that you could apply to x.
2. A function of type () -> a that you could apply to ().
3. Some predefined value of type a.

The Applicative instance of (,) a takes the third approach, by requiring that a have a Monoid instance so that you can define pure in terms of mempty.

instance Monoid a => Applicative (Pair a) where
    pure x = Pair mempty x
    Pair a f <*> Pair a' x = Pair (a <> a') (f x)

In your definition, you assumed that ( ) is defined for the a values, which means you are missing a Num constraint, but also that you could simply use 0 in your definition of pure.

instance Num a => Applicative (Pair a) where
    pure x = Pair 0 x
    Pair a f <*> Pair a' x = Pair (a   a') (f x)