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Algeo: An Algebraic Approach to Reversibility

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 13354)

Abstract

We present Algeo, a functional logic programming language based on the theory of infinite dimensional modules. Algeo is reversible in the sense that every function has a generalised inverse, an adjoint, which can be thought of as an inverse execution of the forward function. In particular, when the given function is invertible, the adjoint is guaranteed to coincide with the inverse.

Algeo generalises “ordinary” forward-backward deterministic reversible programming by permitting relational and probabilistic features. This allows functions to be defined in a multitude of ways, which we summarise by the motto that “all definitions are extensional characterisations; all extensional characterisations are definitions.”

We describe the syntax, type system, and the axiomatic semantics of Algeo, and showcase novel features of the language through examples.

R. Kaarsgaard—Supported by DFF–International Postdoctoral Grant 0131-00025B.

M. K. Mathiesen—Supported by DFF Research Grant 8022-00415B.

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Correspondence to Mikkel Kragh Mathiesen .

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Henglein, F., Kaarsgaard, R., Mathiesen, M.K. (2022). Algeo: An Algebraic Approach to Reversibility. In: Mezzina, C.A., Podlaski, K. (eds) Reversible Computation. RC 2022. Lecture Notes in Computer Science, vol 13354. Springer, Cham. https://doi.org/10.1007/978-3-031-09005-9_9

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  • DOI: https://doi.org/10.1007/978-3-031-09005-9_9

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