Cyclic Proofs and Coinductive Principles

Gavin Mendel-Gleason; Geoff Hamilton

doi:10.29007/hxgm

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Cyclic Proofs and Coinductive Principles

7 pages•Published: May 15, 2012

Gavin Mendel-Gleason and Geoff Hamilton

Abstract

It is possible to provide a proof for a coinductive type using a corecursive function coupled with a guardedness condition. The guardedness condition, however, is quite restrictive and many programs which are in fact productive and do not compromise soundness will be rejected. We present a system of cyclic proof for an extension of System $F$ extended with sums, products and (co)inductive types. Using program transformation techniques we are able to take some programs whose productivity is suspected and transform them, using a suitable theory of equivalence, into programs for which guardedness is syntactically apparent. The equivalence of the proof prior and subsequent to transformation is given by a bisimulation relation.

Keyphrases: coinductive, constructive, inductive, transition systems, types

In: Ekaterina Komendantskaya, Ana Bove and Milad Niqui (editors). PAR-10. Partiality and Recursion in Interactive Theorem Provers, vol 5, pages 107--113

Links:	https://easychair.org/publications/paper/MDb
	https://doi.org/10.29007/hxgm

BibTeX entry

@inproceedings{PAR-10:Cyclic_Proofs_and_Coinductive,
  author    = {Gavin Mendel-Gleason and Geoff Hamilton},
  title     = {Cyclic Proofs and Coinductive Principles},
  booktitle = {PAR-10. Partiality and Recursion in Interactive Theorem Provers},
  editor    = {Ekaterina Komendantskaya and Ana Bove and Milad Niqui},
  series    = {EPiC Series in Computing},
  volume    = {5},
  pages     = {107--113},
  year      = {2012},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {https://easychair.org/publications/paper/MDb},
  doi       = {10.29007/hxgm}}

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