In functional programming, an applicative functor, or an applicative for short, is an intermediate structure between functors and monads. In Category Theory they are called Closed Monoidal Functors. Applicative functors allow for functorial computations to be sequenced (unlike plain functors), but don't allow using results from prior computations in the definition of subsequent ones (unlike monads). Applicative functors are the programming equivalent of lax monoidal functors with tensorial strength in category theory.
Applicative functors were introduced in 2008 by Conor McBride and Ross Paterson in their paper Applicative programming with effects.[1]
Applicative functors first appeared as a library feature in Haskell, but have since spread to other languages as well, including Idris, Agda, OCaml, Scala and F#. Glasgow Haskell, Idris, and F# offer language features designed to ease programming with applicative functors.
In Haskell, applicative functors are implemented in the Applicative type class.
While in languages like Haskell monads are applicative functors, it is not always so in general settings of Category Theory - examples of monads that are not strong can be found on Math Overflow.