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arXiv · 1403.0749

Free Applicative Functors

Paolo Capriotti·Ambrus Kaposi
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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.

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Paolo Capriotti, Ambrus Kaposi. 2014-06-09. Free Applicative Functors. https://doi.org/10.4204/eptcs.153.2

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