Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Least and Greatest Fixed Points in Ludics

David Baelde 1, * Amina Doumane 2, 3 Alexis Saurin 2, 3
* Corresponding author
2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, Inria Paris-Rocquencourt, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique : UMR7126
Abstract : Various logics have been introduced in order to reason over (co)inductive specifications and, through the Curry-Howard correspondence, to study computation over inductive and coinductive data. The logic µMALL is one of those logics, extending multiplicative and additive linear logic with least and greatest fixed point operators. In this paper, we investigate the semantics of µMALL proofs in (computational) ludics. This framework is built around the notion of design, which can be seen as an analogue of the strategies of game semantics. The infinitary nature of designs makes them particularly well suited for representing computations over infinite data. We provide µMALL with a denotational semantics, interpreting proofs by designs and formulas by particular sets of designs called behaviours. Then we prove a completeness result for the class of "essentially finite designs" , which are those designs performing a finite computation followed by a copycat. On the way to completeness, we establish decidability and completeness of semantic inclusion.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [2 references]  Display  Hide  Download

https://hal.inria.fr/hal-01178396
Contributor : David Baelde <>
Submitted on : Monday, July 20, 2015 - 4:32:53 PM
Last modification on : Friday, April 30, 2021 - 9:53:44 AM
Long-term archiving on: : Wednesday, October 21, 2015 - 5:11:17 PM

File

main.pdf
Publisher files allowed on an open archive

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

  • HAL Id : hal-01178396, version 1

Citation

David Baelde, Amina Doumane, Alexis Saurin. Least and Greatest Fixed Points in Ludics. 2015. ⟨hal-01178396⟩

Share

Metrics

Record views

725

Files downloads

334