Effect Polymorphism in Higher-Order Logic (Proof Pearl)

  • Andreas LochbihlerEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10499)


The notion of a monad cannot be expressed within higher-order logic (HOL) due to type system restrictions. We show that if a monad is used with values of only one type, this notion can be formalised in HOL. Based on this idea, we develop a library of effect specifications and implementations of monads and monad transformers. Hence, we can abstract over the concrete monad in HOL definitions and thus use the same definition for different (combinations of) effects. We illustrate the usefulness of effect polymorphism with a monadic interpreter.



We thank Dmitriy Traytel and the anonymous reviewers for suggesting many improvements to the presentation. This work is supported by the Swiss National Science Foundation grant 153217 “Formalising Computational Soundness for Protocol Implementations”.


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© Springer International Publishing AG 2017

Authors and Affiliations

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

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