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Conference Papers Year : 2021

Canonical proof-objects for coinductive programming: infinets with infinitely many cuts

Abstract

Non-wellfounded and circular proofs have been recognised over the past decade as a valuable tool to study logics expressing (co)inductive properties, e.g.-calculi. Such proofs are non-wellfounded sequent derivations together with a global validity condition expressed in terms of progressing threads. While the cut-free fragment of circular proofs is satisfactory, cuts are poorly treated and the non-canonicity of sequent proofs becomes a major issue in the non-wellfounded setting. The present paper develops for MLL (multiplicative linear logic with fixed points) the theory of infinets-proof-nets for nonwellfounded proofs. Our structures handles infinitely many cuts therefore solving a crucial shortcoming of the previous work. We characterise correctness, define a more complete cut-reduction system and proving a cut-elimination theorem. To that end, we also provide an alternate cut reduction for non-wellfounded sequent calculus.
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Dates and versions

hal-03371935 , version 1 (09-10-2021)

Identifiers

Cite

Abhishek De, Luc Pellissier, Alexis Saurin. Canonical proof-objects for coinductive programming: infinets with infinitely many cuts. PPDP 2021: 23rd International Symposium on Principles and Practice of Declarative Programming, Sep 2021, Tallinn, Estonia. pp.1-15, ⟨10.1145/3479394.3479402⟩. ⟨hal-03371935⟩
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