Equational Reasoning with Applicative Functors

  • Andreas Lochbihler
  • Joshua Schneider
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9807)


In reasoning about effectful computations, it often suffices to focus on the effect-free parts. We present a package for automatically lifting equations to effects modelled by applicative functors. It exploits properties of the concrete functor thanks to a modular classification based on combinators. We formalise the meta theory and demonstrate the usability of our Isabelle/HOL package with two case studies. This is a first step towards practical reasoning with effectful computations.


Normal Form Combinatory Logic Proof Method Applicative Functor Idiomatic Expression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Peter Gammie triggered our interest in reasoning about applicative functors and helped with the Stern-Brocot tree. We thank Dmitriy Traytel, Joachim Breitner, and the anonymous reviewers for suggesting many textual improvements. The first author was supported by SNSF grant 153217 “Formalising Computational Soundness for Protocol Implementations”.

Supplementary material


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Information Security, Department of Computer ScienceETH ZurichZürichSwitzerland

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