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arXiv:1403.0749cs.PL

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.

arXiv comments
In Proceedings MSFP 2014, arXiv:1406.1534
Journal reference
EPTCS 153, 2014, pp. 2-30
DOI
doi:10.4204/EPTCS.153.2
Subjects
cs.PLProgramming Languages math.CTCategory Theory

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  1. Modern Functional Programming: The Onion Architecture 1 comment

    • Yeah, the free monad structures involve lots of lambdas. It's not so much that information is "lost", more that you cannot see beyond the next lambda abstraction. From a DSL perspective, it's like you can only inspect the program so far as to know the next statement in the "do"…

      mbrockView on HNParent context

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