Free Applicative Functors
arXiv:1403.0749 · doi:10.4204/EPTCS.153.2
Abstract
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.
In Proceedings MSFP 2014, arXiv:1406.1534