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509898 (4) [Avatar] Offline
2-tuple (,) is instance of Applicative when the first parameter is instance of Monoid.

instance Monoid a => Applicative ((,) a) where
  pure = (,) empty
  (x, f) <*> (x', y) = (x `mappend` x', f y)

Later, it also says:

Quick check 29.3 Suppose you want to make it so that (pure +) <*> (1,2) <*> (3,4) =
(1+2,1+4,2+3,2+4) = (3,5,5,6). Why doesn’t this work?

QC 29.3 answer This doesn’t work because (3,5,5,6) is an entirely different type than (1,2) or
(3,4). The first is type (a,b,c,d), and the other two are (a,b).

I think the reasoning is not right. The reasons why it does not work are other:

a) kind of (,) is * -> * -> *, and Applicative is * -> *. The first parameter must be set.
b) The first parameter is a number and it is instance of Moniod. But it has two ways of being Moniod: with the sum and with the product and you have to choose which one you want to use.
c) Minor typo: The + operator must appear in brackets.

With these considerations, it does work:

GHCi> pure (+) <*> (Sum 1,2) <*> (Sum 3,4)
(Sum {getSum = 4},6)

GHCi> pure (+) <*> (Product 1,2) <*> (Product 3,4)
(Product {getProduct = 3},6)