Endrullis, J;
Hansen, HH;
Hendriks, D;
Polonsky, A;
Silva, A;
(2018)
Coinductive foundations of infinitary rewriting and infinitary equational logic.
Logical Methods in Computer Science
, 14
(1)
10.23638/LMCS-14(1:3)2018.
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Abstract
We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform way. We define Equation found, the infinitary extension of a given equational theory =R, and →∞, the standard notion of infinitary rewriting associated to a reduction relation →R, as follows: (Formula Presented) Equation found Here μ and ν are the least and greatest fixed-point operators, respectively, and (Formula Presented) Equation found The setup captures rewrite sequences of arbitrary ordinal length, but it has neither the need for ordinals nor for metric convergence. This makes the framework especially suitable for formalizations in theorem provers.
| Type: | Article |
|---|---|
| Title: | Coinductive foundations of infinitary rewriting and infinitary equational logic |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.23638/LMCS-14(1:3)2018 |
| Publisher version: | https://doi.org/10.23638/LMCS-14(1:3)2018 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit https://creativecommons.org/licenses/by-nd/4.0/ |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10061161 |
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