Coinductive foundations of infinitary rewriting and infinitary equational logic

Endrullis, Jörg; Hansen, H.H.; Hendriks, Dimitri; Polonsky, Andrew; Silva, Alexandra

doi:10.23638/LMCS-14(1:3)2018

Coinductive foundations of infinitary rewriting and infinitary equational logic

Title

Coinductive foundations of infinitary rewriting and infinitary equational logic

Author

Endrullis, Jörg (Vrije Universiteit Amsterdam)
Hansen, H.H. (TU Delft Energy and Industry)
Hendriks, Dimitri (Vrije Universiteit Amsterdam)
Polonsky, Andrew (Universite Paris Diderot)
Silva, Alexandra (University College London)

Date

2018

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.

Subject

Coinduction
Infinitary equational reasoning
Infinitary rewriting

To reference this document use:

http://resolver.tudelft.nl/uuid:e2b88d01-096a-4de1-81f9-5e135256e528

DOI

https://doi.org/10.23638/LMCS-14(1:3)2018

ISSN

1860-5974

Source

Logical Methods in Computer Science, 14 (1)

Part of collection

Institutional Repository