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Modular proofs for completeness of hierarchical term rewriting systems

M.R.K.Krishna Rao
1995 Theoretical Computer Science  
In this paper, we study modular aspects of hierarchical combinations of term rewriting systems.  ...  A property P of term rewriting systems is modular if the following holds: two rewriting systems ~o and ~?  ...  The author is grateful to the referees for many suggestions in improving the presentation very much.  ... 
doi:10.1016/0304-3975(95)00075-8 fatcat:hp5rkbjavnab3fj6fq3fuohbvu

Semi-completeness of hierarchical and super-hierarchical combinations of term rewriting systems [chapter]

M. R. K. Krishna Rao
1995 Lecture Notes in Computer Science  
In this paper, we study modular aspects of hierarchical and super hierarchical combinations of term rewriting systems.  ...  In particular, a sufficient condition for modularity of semi-completeness of hierarchical and super hierarchical combinations is proposed.  ...  Since weak-normalization is known to be modular for constructor sharing systems, this amounts to showing modularity of semi-completeness for constructor sharing systems.  ... 
doi:10.1007/3-540-59293-8_208 fatcat:algbduxhqzdfxay7bdxnyzsfs4

Modular aspects of term graph rewriting

M.R.K.Krishna Rao
1998 Theoretical Computer Science  
Term rewriting is generally implemented using graph rewriting for efficiency reasons. Graph rewriting allows sharing of common structures thereby saving both time and space.  ...  In this paper, we study modularity of the following properties in graph rewriting: (a) weak normalization, (b) strong normalization, (c) semi-completeness (confluence + weak normalization) and (d) completeness  ...  Detlef particularly gave a lot of suggestions improving the paper. Thanks also go to the referees for constructive suggestions.  ... 
doi:10.1016/s0304-3975(98)00079-6 fatcat:663tq6lhdfa37jybvn3ufc3rke

Unravelings and ultra-properties [chapter]

Massimo Marchiori
1996 Lecture Notes in Computer Science  
We introduce a new tool, called unraveling, to automatically translate a conditional term rewriting system (CTRS) into a term rewriting system (TRS).  ...  Moreover, we show how unravelings provide a valuable tool to study modularity of CTRSs, automatically giving a multitude of new results.  ...  Preliminaries We assume knowledge of the basic notions regarding conditional term rewriting systems and term rewriting systems (cf. 3, 15] ).  ... 
doi:10.1007/3-540-61735-3_7 fatcat:rgmk4g7zsjcbvluxrz2smul5py

Page 2414 of Mathematical Reviews Vol. , Issue 96d [page]

1996 Mathematical Reviews  
K. (6-TIFR-CG; Bombay) Simple termination of hierarchical combinations of term rewriting systems.  ...  Summary: “In this paper, we study modular aspects of hierarchi- cal combinations of term rewriting systems.  ... 

Modular termination of basic narrowing and equational unification

M. Alpuente, S. Escobar, J. Iborra
2010 Logic Journal of the IGPL  
via the modularity of basic narrowing (completeness and) termination.  ...  In this work, we study the modularity of termination of basic narrowing in hierarchical combinations of TRSs, which provides new algorithmic criteria to prove termination of basic narrowing.  ...  Acknowledgements We gratefully acknowledge the anonymous referees for providing many insights and extremely useful suggestions.  ... 
doi:10.1093/jigpal/jzq009 fatcat:zc5mu47hjzfrxorpojxffiup7e

Modular and incremental proofs of AC-termination

Claude Marché, Xavier Urbain
2004 Journal of symbolic computation  
Termination is a non-modular property of rewriting systems, thus it is a difficult task to discover termination proofs for rewriting systems of a large number of rules.  ...  , which apply to hierarchical combinations of rewriting systems.  ...  Acknowledgements We gratefully thank the anonymous referees for their fruitful help in improving this paper. This work is partially supported by the "ATIP-STIC CiME du CNRS".  ... 
doi:10.1016/j.jsc.2004.02.003 fatcat:rzdmdeyp5bbsbdaz3yyec2ntem

Page 3228 of Mathematical Reviews Vol. , Issue 97E [page]

1997 Mathematical Reviews  
K. (6-TIFR-CG; Bombay) Modular proofs for completeness of hierarchical term rewriting systems.  ...  In this paper, modular aspects of hierarchical combinations of term rewriting systems are studied.  ... 

Hierarchical termination revisited

Enno Ohlebusch
2002 Information Processing Letters  
Dershowitz [2] coined the name "hierarchical termination" for this preservation, while other authors use the longer term "modularity of termination for hierarchical combinations".  ...  Among other things, term rewriting constitutes a Turing-complete computational model which is closely related to functional programming.  ...  The term rewriting system R 1 = {g(x, y) → x} is obviously C E -terminating.  ... 
doi:10.1016/s0020-0190(02)00272-7 fatcat:x5en6t4sjnfprgq2kad4qnbmeu

Modular Properties of Composable Term Rewriting Systems

Enno Ohlebusch
1995 Journal of symbolic computation  
In this paper we prove several new modularity results for unconditional and conditional term rewriting systems.  ...  Most of the known modularity results for the former systems hold for disjoint or constructor-sharing combinations. Here we focus on a more general kind of combination: so-called composable systems.  ...  Acknowledgements I am grateful to Aart Middeldorp and the referees for their comments on the paper.  ... 
doi:10.1006/jsco.1995.1036 fatcat:igpsgira6nbl7kbe3dq3euaovi

Modular properties of constructor-sharing conditional term rewriting systems [chapter]

Enno Ohlebusch
1995 Lecture Notes in Computer Science  
First, using a recent modularity result Ohl94b] for unconditional term rewriting systems (TRSs), it is shown that semi-completeness is a modular property of constructor-sharing join conditional term rewriting  ...  Second, we do not only extend results of Middeldorp Mid93] on the modularity of termination for disjoint CTRSs to constructor-sharing systems but also simplify the proofs considerably.  ...  Acknowledgements: The author thanks Aart Middeldorp for discussions about the subtleties of CTRSs.  ... 
doi:10.1007/3-540-60381-6_18 fatcat:hu3zo3sizraqdonsrrn7fv6hla

Termination for the direct sum of left-linear term rewriting systems [chapter]

Yoshihito Toyama, Jan Willem Klop, Hendrik Pieter Barendregt
1989 Lecture Notes in Computer Science  
It is shown that two term rewriting systems both are left-linear and complete if and only if the direct sum of these systems is so.  ...  A b s t r a c t The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols.  ...  properties of term rewriting systems have a modular character, where we call a property modular if its validity for a term rewriting system, hierarchically composed of some smaller term rewriting systems  ... 
doi:10.1007/3-540-51081-8_127 fatcat:k55hqevomzc2jmuocusviibwti

Page 3475 of Mathematical Reviews Vol. , Issue 94f [page]

1994 Mathematical Reviews  
With, Complete- ness and confluence of order-sorted term rewriting (393-407); Charles Hoot, Completion for constrained term rewriting systems (408-423); Harald Ganzinger and Uwe Waldmann, Termination  ...  Banach, Simple type inference for term graph rewriting systems (51-66); Aart Middel- dorp, Completeness of combinations of conditional constructor systems (82-96); Detlef Plump, Collapsed tree rewriting  ... 

Persistence Of Termination For Term Rewriting Systems With Ordered Sorts

Munehiro Iwami
2007 Zenodo  
Furthermore we give the example as application of this result. Also we obtain that completeness is persistent for this class of term rewriting systems.  ...  A property is persistent if for any many-sorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property.  ...  Also, we can not use the modularity results for composable TRSs [17] , [19] and hierarchical combinations and hierarchical combinations with common subsystem of TRSs [16] , [19] .  ... 
doi:10.5281/zenodo.1081045 fatcat:e5elhfr6knewvcjvlmo7htjere

Modularity in noncopying term rewriting

Masahito Kurihara, Azuma Ohuchi
1995 Theoretical Computer Science  
It is known that termination and completeness are not modular properties of term rewriting systems: the disjoint union of terminating (complete) term rewriting systems need not be terminating (complete  ...  In this paper, we introduce a class of "noncopying" term rewriting systems as a new, term-based formalism for a kind of graph rewriting systems, and prove that this class enjoys the modularity of termination  ...  Acknowledgements many research topics other than modularity.  ... 
doi:10.1016/0304-3975(94)00248-3 fatcat:xh57wfiflrhptngop6uvp3rdo4
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