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En Garde! Unguarded Iteration for Reversible Computation in the Delay Monad

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Mathematics of Program Construction (MPC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11825))

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Abstract

Reversible computation studies computations which exhibit both forward and backward determinism. Among others, it has been studied for half a century for its applications in low-power computing, and forms the basis for quantum computing.

Though certified program equivalence is useful for a number of applications (e.g., certified compilation and optimization), little work on this topic has been carried out for reversible programming languages. As a notable exception, Carette and Sabry have studied the equivalences of the finitary fragment of \(\mathsf {\Pi }^{\mathsf {o}}\), a reversible combinator calculus, yielding a two-level calculus of type isomorphisms and equivalences between them. In this paper, we extend the two-level calculus of finitary \(\mathsf {\Pi }^{\mathsf {o}}\) to one for full \(\mathsf {\Pi }^{\mathsf {o}}\) (i.e., with both recursive types and iteration by means of a trace combinator) using the delay monad, which can be regarded as a “computability-aware” analogue of the usual maybe monad for partiality. This yields a calculus of iterative (and possibly non-terminating) reversible programs acting on user-defined dynamic data structures together with a calculus of certified program equivalences between these programs.

Niccolò Veltri was supported by a research grant (13156) from VILLUM FONDEN.

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Notes

  1. 1.

    Here we give the definition of complete Elgot monad on \(\mathsf {Set}\), but the definition of complete Elgot monad makes sense in any category with finite coproducts.

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Authors and Affiliations

  1. DIKU, Department of Computer Science, University of Copenhagen, Copenhagen, Denmark

    Robin Kaarsgaard

  2. Department of Computer Science, IT University of Copenhagen, Copenhagen, Denmark

    Niccolò Veltri

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  1. Robin Kaarsgaard
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Correspondence to Niccolò Veltri .

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  1. University of Nottingham, Nottingham, UK

    Graham Hutton

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Kaarsgaard, R., Veltri, N. (2019). En Garde! Unguarded Iteration for Reversible Computation in the Delay Monad. In: Hutton, G. (eds) Mathematics of Program Construction. MPC 2019. Lecture Notes in Computer Science(), vol 11825. Springer, Cham. https://doi.org/10.1007/978-3-030-33636-3_13

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  • DOI: https://doi.org/10.1007/978-3-030-33636-3_13

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