I'm following the CIS194 lectures and exercises. In particular, in one of the Applicative lectures [0] we're asked to implement mapA and sequenceA, from the name and given type signature alone. I renamed them mapA' and sequenceA' to avoid name clashes, and defined: import Control.Applicative mapA' :: Applicative f => (a -> f b) -> ([a] -> f [b]) mapA' f = sequenceA' . map f sequenceA' :: Applicative f => [f a] -> f [a] sequenceA' = foldr (\fa fla -> (:) <$> fa <*> fla) (pure []) These implementations seem to be correct, though undoubtedly not the nicest. Now, I ask for a type in ghci:

:t mapA' pure [1..5] mapA' pure [1..5] :: (Enum b, Num b, Applicative f) => f [b]

And so I try the following:

mapA' pure [1..5] :: [[Int]] [[1,2,3,4,5]] take 5 . getZipList $ (mapA' pure [1..5] :: ZipList [Int]) [[1,2,3,4,5],[1,2,3,4,5],[1,2,3,4,5],[1,2,3,4,5],[1,2,3,4,5]] mapA' pure [1..5] :: Maybe [Int] Just [1,2,3,4,5]

That makes sense. But I don't understand the following:

mapA' pure [1..5] [1,2,3,4,5]

:t pure

Which Applicative instance is being used here? The type test above says my expression should have type f [b], where f is an Applicative and b is a Num, but all I see is a result of type [b] when I compute mapA' pure [1..5]. What's going on? More simply pure :: Applicative f => a -> f a

pure [1..5] [1,2,3,4,5]

a must match a list of Nums, but then where did f go? Is ghci using some default instance? Actually, after I add the following lines to my source file: ggg = pure [1..5] hhh = mapA' pure [1..5] I get the errors: No instance for (Applicative f0) arising from a use of ‘pure’ No instance for (Applicative f1) arising from a use of ‘mapA'’ respectively. That makes sense to me. Graham [0] http://www.seas.upenn.edu/~cis194/fall14/spring13/lectures/11-applicative2.h...