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The graph rewriting calculus: properties and expressive capabilities

Clara Bertolissi 1
1 PROTHEO - Constraints, automatic deduction and software properties proofs
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : The last few years have seen the development of the rewriting calculus (also called rho-calculus) that uniformly integrates first-order term rewriting and lambda-calculus.
This thesis is devoted to the study of the expressiveness of the rewriting
calculus, with special interest for higher-order rewriting
and the possibility of dealing with graph-like structures.

The first part of the thesis is dedicated to the relationship between the rewriting calculus
and higher-order term rewriting, namely the Combinatory Reduction Systems (CRSs).
First, an original matching algorithm for CRSs terms that uses a simple term translation and the classical higher-order pattern matching of lambda terms is proposed and then
an encoding of CRSs in the rho-calculus based on a translation of each possible CRS-reduction into a corresponding rho-reduction is presented.

The second part of the thesis is devoted to an extension of the rho-calculus,
called graph rewriting calculus (or Rg-calculus), handling terms with sharing and cycles.
The calculus over terms is naturally generalised by using unification constraints in addition to standard rho-calculus matching constraints.
The Rg-calculus is shown to be confluent over equivalence classes of terms, under
some linearity restrictions on patterns, and expressive enough to simulate
first-order term graph rewriting and cyclic lambda-calculus.
Document type :
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Contributor : Clara Bertolissi <>
Submitted on : Friday, November 18, 2005 - 1:43:51 PM
Last modification on : Friday, February 26, 2021 - 3:28:06 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:43:08 PM


  • HAL Id : tel-00011037, version 1



Clara Bertolissi. The graph rewriting calculus: properties and expressive capabilities. Other [cs.OH]. Institut National Polytechnique de Lorraine - INPL, 2005. English. ⟨tel-00011037⟩



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