liftA2

liftA2 is a function from the applicative programming paradigm that allows a binary function to be applied to two applicative values. In languages such as Haskell the function is defined in the Data.Functor.Apply module as liftA2 :: Applicative f => (a -> b -> c) -> f a -> f b -> f c, where f is any type that implements the Applicative type class.

The basic idea is that liftA2 takes a plain function of two arguments and lifts it into an applicative context by sequencing two effectful computations. The computation f a produces a value inside a context (e.g., a list, an option, or a monadic value). liftA2 then applies the binary function to the computed values, while preserving the applicative structure. For example, liftA2 (+) (Just 3) (Just 5) evaluates to Just 8, whereas liftA2 (,) [1,2] [3,4] yields [(1,3),(1,4),(2,3),(2,4)].

liftA2 is a generalization of liftA, the one-argument version. While liftA operates on unary functions and a single applicative argument, liftA2 supports binary functions and two arguments. There are variants for ternary functions called liftA3, and so forth. In practice liftA2 is frequently used to combine the results of multiple independent computations, such as parsing fields, validating inputs, or composing user interface widgets.

In functional programming communities, liftA2 is considered a fundamental combinator for working with applicatives because it abstracts away the boilerplate of applying a function inside a context. It is included in many standard libraries beyond Haskell, including the applicative library in Scala, the Arrow library in F#, and the functional extensions for JavaScript environments.