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Syntactic Confluence Criteria for Positive/Negative-Conditional Term Rewriting Systems [article]

Claus-Peter Wirth
2009 arXiv   pre-print
We study the combination of the following already known ideas for showing confluence of unconditional or conditional term rewriting systems into practically more useful confluence criteria for conditional  ...  Finally, the whole paper may also give a practically useful overview of the syntactical means for showing confluence of conditional term rewriting systems.  ...  Positive/Negative Conditional Rewriting. 1 st CTRS 1987, LNCS 308, pp. 129-143, Springer. Deepak Kapur, David R. Musser, Paliath Narendran (1988).  ... 
arXiv:0902.3614v1 fatcat:fl3fyfruqjewhlbjby3iyskmoy

Conservative Extension in Positive/Negative Conditional Term Rewriting with Applications to Software Renovation Factories [chapter]

Wan Fokkink, Chris Verhoef
1999 Lecture Notes in Computer Science  
We transpose a conservative extension theorem from structural operational semantics to conditional term rewriting.  ...  The result is useful for the development of software renovation factories, and for modular specification of abstract data types.  ...  A (positive/negative) conditional term rewriting system (CTRS) is a set of positive/negative conditional rewrite rules.  ... 
doi:10.1007/978-3-540-49020-3_7 fatcat:jp2ban237fc2denhpp3fw6chvi

A Constructor-Based Approach to Positive/Negative-Conditional Equational Specifications

Claus-Peter Wirth, Bernhard Gramlich
1994 Journal of symbolic computation  
the fundamental results for positive-conditional rewrite systems.  ...  We study algebraic speci cations given by nite sets R of positive/negative-conditional equations (i. e. universallyquanti ed rst-orderimplicationswith a single equation in the succedent and a conjunction  ...  , J urgen Avenhaus and Klaus Becker for fruitful discussions, and Klaus Madlener and R udiger Lunde for useful hints.  ... 
doi:10.1006/jsco.1994.1004 fatcat:icf2mgkryzgqnoxunmndaqv6ee

Shallow confluence of conditional term rewriting systems

Claus-Peter Wirth
2009 Journal of symbolic computation  
Recursion can be conveniently modeled with left-linear positive/ negative-conditional term rewriting systems, provided that nontermination, non-trivial critical overlaps, non-right-stability, nonnormality  ...  For such systems we present novel sufficient criteria for shallow confluence and arrive at the first decidable confluence criterion admitting nontrivial critical overlaps.  ...  For Acl2 cf. e.g. Kaufmann et al. (2000) . And for the school of explicit induction, to which these systems belong, cf. the handbook articles of Bundy (1999) and Walther (1994) .  ... 
doi:10.1016/j.jsc.2008.05.005 fatcat:zjp4ce43onbfxbt3sv5g5wndoq

Automation of Mathematical Induction as part of the History of Logic [article]

J Strother Moore, Claus-Peter Wirth
2014 arXiv   pre-print
For most of our illustrative examples in this article, however, we will use the higher flexibility and conceptual adequacy of positive/negative-conditional rewrite systems.  ...  relation after addition of the new positive/negative-conditional equations for the f k , assuming any arbitrary model M of all (positive/negative-conditional) equations with free constructors to be given  ... 
arXiv:1309.6226v5 fatcat:i7nzngq47zfd7its4kfynlfpti

The Automation of Proof by Mathematical Induction [chapter]

Alan Bundy
2001 Handbook of Automated Reasoning  
Thus mathematical induction is a key enabling technology for the use of formal methods in information technology.  ...  Mathematical induction is required for reasoning about objects or events containing repetition, e.g. computer programs with recursion or iteration, electronic circuits with feedback loops or parameterized  ...  The axioms of such a specification spec = (sig, E, A) are positive/negative conditional equations, they define new operators on top of a fixed built-in algebra A.  ... 
doi:10.1016/b978-044450813-3/50015-1 fatcat:y2m3e2cjjfhf5nvs734xddyxqi

Page 1365 of Mathematical Reviews Vol. 26, Issue Index [page]

Mathematical Reviews  
Weiermann, Andreas see Rathjen, Michael, 94j:03120 Wirth, Claus-Peter (with Gramlich, Bernhard) A constructor-based approach for positive /negative-conditional equational specifications.  ...  A parallel completion procedure for term rewriting systems. (English summary) (see 94f:68008) Zantema, H. Termination of term rewriting by interpretation.  ... 

Using induction and rewriting to verify and complete parameterized specifications

Adel Bouhoula
1996 Theoretical Computer Science  
In software engineering there is a growing demand for formal methods for the specification and validation of software systems.  ...  In this framework, many provers have been developed, However they require much user interaction even for simple proof tasks.  ...  Acknowledgements I am grateful to Michael Rusinowitch, Hrlrne Kirchner, Toby Walsh, Peter Padawitz and Jiirgen Avenhaus for many fruitful discussions.  ... 
doi:10.1016/s0304-3975(96)80708-0 fatcat:53ewk2m25jgvpkby6w2cbwwaim