Applicative functors are a generalisation of monads. Both allow the
expression of effectful computations into an otherwise pure language, like
Haskell. Applicative functors are to be preferred to monads when the structure
of a computation is fixed a priori. That makes it possible to perform certain
kinds of static analysis on applicative values. We define a notion of free
applicative functor, prove that it satisfies the appropriate laws, and that the
construction is left adjoint to a suitable forgetful functor. We show how free
applicative functors can be used to implement embedded DSLs which can be
statically analysed.