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Communication Dans Un Congrès Année : 2023

Proofs as Terms, Terms as Graphs

Résumé

Starting from an encoding of untyped λ-terms with sharing, defined using synthetic inference rules based on a focused proof system for Gentzen's LJ, we introduce the positive λ-calculus, a call-by-value calculus with explicit substitutions. This calculus is closely related to Accattoli and Paolini's value substitution calculus but has a different style of reduction rules that provides a good notion of sharing along the reduction. We also propose a graphical representation in order to capture the structural equivalence on terms that can be described using rule permutations. On one hand, this graphical representation provides a way to remove redundancy in the syntax, and on the other hand, it allows implementing basic operations such as substitution and reduction in a straightforward way.
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hal-04222527 , version 1 (29-09-2023)

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  • HAL Id : hal-04222527 , version 1

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Jui-Hsuan Wu. Proofs as Terms, Terms as Graphs. APLAS 2023 - 21st Asian Symposium on Programming Languages and Systems, Nov 2023, Taipei, Taiwan. ⟨hal-04222527⟩
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