liftA3

liftA3 is a function in functional programming, notably in Haskell, that lifts a pure function of three arguments to operate over three applicative values. It enables applying a three-argument function to values wrapped in a context, such as Maybe, List, IO, or other Applicative instances.

The type signature is liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d. It can be defined in terms of other applicative operators as liftA3 f x y z = f <$> x <*> y <*> z, or equivalently as liftA3 f x y z = liftA2 f x y <*> z. This makes it a natural generalization of mapping and applying within an applicative context.

Example usage with Maybe: liftA3 (,,) (Just 1) (Just 2) (Just 3) yields Just (1, 2, 3). If any argument is Nothing, the result is Nothing. With lists, liftA3 (,,) [1,2] [3,4] [5,6] produces all combinations, such as [(1,3,5),(1,3,6),(1,4,5),(1,4,6),(2,3,5),...], reflecting the cross-product behavior of lists as an applicative.

In summary, liftA3 provides a convenient means to apply a three-argument function within an applicative context, aligning with the Functor (<$>) and Applicative (<*>) framework and relating to liftA2 and liftA for functions with fewer arguments.