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A constructor-based approach for positive/negative-conditional equational specifications [chapter]

Claus-Peter Wirth, Bernhard Gramlich
1993 Lecture Notes in Computer Science  
We present a constructor-based approach for assigning appropriate semantics to algebraic speci cations given by nite sets of positive/negative-conditional equations.  ...  ) the minimum of all models that do not identify more constructor ground terms than necessary.  ...  Acknowledgement: We would like to thank Ulrich K uhler for many valuable discussions and detailed criticisms on earlier versions of this paper.  ... 
doi:10.1007/3-540-56393-8_15 fatcat:5ebvwgrgpngq3ksx5y4snpddbe

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

Claus-Peter Wirth, Bernhard Gramlich
1994 Journal of symbolic computation  
We present a constructor-based approach for assigning appropriate semantics to such speci cations.  ...  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

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

Claus-Peter Wirth
2009 arXiv   pre-print
Finally, the whole paper may also give a practically useful overview of the syntactical means for showing confluence of conditional term rewriting systems.  ...  of our syntactical separation into constructor and non-constructor symbols, we are able to present criteria for level confluence that are not criteria for shallow confluence actually and also able to  ...  A Constructor-Based Approach for Positive/Negative-Conditional Equational Specifications. J. Symbolic Computation (1994) 17, pp. 51-90, Academic Press (Elsevier).  ... 
arXiv:0902.3614v1 fatcat:fl3fyfruqjewhlbjby3iyskmoy

Conditional equational specifications of data types with partial operations for inductive theorem proving [chapter]

Ulrich Kühler, Claus-Peter Wirth
1997 Lecture Notes in Computer Science  
The language requires constructors for designating data items and admits positive/negative conditional equations as axioms in speci cations.  ...  We propose a speci cation language for the formalization of data types with partial or non-terminating operations as part of a rewrite-based framework for inductive theorem proving.  ...  Admissibility Conditions So far we have placed no restrictions on the set of positive/negative conditional equations in a speci cation with constructors.  ... 
doi:10.1007/3-540-62950-5_60 fatcat:4phcrk53ynendnmrl2lkkiwhn4

Page 5980 of Mathematical Reviews Vol. , Issue 94j [page]

1994 Mathematical Reviews  
Summary: “We present two approaches to defining the semantics for positive/negative conditional rewrite systems.  ...  {For the entire collection see MR 94b:68025.} 94j:68132 68Q42 Becker, Klaus (D-KSRL-I; Kaiserslautern) Semantics for positive /negative conditional rewrite systems.  ... 

Page 1109 of Mathematical Reviews Vol. , Issue 96b [page]

1996 Mathematical Reviews  
A positive/negative-conditional equational specification is a finite set of finitary basic sentences [M. Makkai and R.  ...  Bunder (5-WLG; Wollongong) 96b:68124 68Q65 68Q42 Wirth, Claus-Peter (D-KSRL-C; Kaiserslautern); Gramlich, Bernhard (D-KSRL-C; Kaiserslautern) A constructor-based approach to positive /negative-conditional  ... 

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

1994 Mathematical Reviews  
, Generic induction proofs (175-197); Claus-Peter Wirth and Bernhard Gramlich, A constructor-based approach for positive/negative-conditional equational specifications (198-212); Klaus Becker, Semantics  ...  for positive/negative conditional rewrite systems (213-225); Harald Ganzinger and Jiirgen Stuber, Inductive theorem proving by consistency for first-order clauses (226-241); Francois Bronsard and Uday  ... 

Page 419 of Mathematical Reviews Vol. , Issue 95a [page]

1995 Mathematical Reviews  
Zantema, Termination of term rewriting: interpretation and type elimination (23-50); Claus-Peter Wirth and Bernhard Gramlich, A constructor-based approach to positive/negative-conditional equational specifications  ...  Singh, A semantics for speech acts (47- 71); Nelson Correa, Attribute and unification grammar: a review and analysis of formalisms (73-105); John Nerbonne, A feature- based syntax/semantics interface (  ... 

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

J Strother Moore, Claus-Peter Wirth
2014 arXiv   pre-print
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  ...  Moreover, the typed (many-sorted) approach of the positive/negative-conditional equations allows the presentation of formulas in a form that is much easier to grasp for human readers than the corresponding  ... 
arXiv:1309.6226v5 fatcat:i7nzngq47zfd7its4kfynlfpti

Contents EATCS Bulletin number 61, February 1997

1997 Theoretical Computer Science  
Wirth: Positive/Negative-Conditional Equations: A Constructor-Based Framework for Specification and Inductive Theorem Proving 93 Reports on Conferences Twelfth Annual Meeting of the British Colloquium  ...  Padberg: Abstract Petri Nets: Uniform Approach and Rule-Based Refinement G. Taentzer: Parallel and Distributed Graph Transformation: P.  ... 
doi:10.1016/s0304-3975(97)84330-7 fatcat:crayjadturb5jee3g2heonaaay

Algorithms in Philosophy, Informatics and Logic. A Position Manifesto 2017

Dov M. Gabbay, Jörg H. Siekmann
2017 IfColog journal of logics and their applications (FLAP)  
We give more examples: • Consider a representation of an agent (irrespective of the exact theory used).  ...  Boyer, Alan Bundy, Catherine Goldstein, Bernhard Gramlich, Warren A.  ...  Burstall, Robert A. Kowalski, Pat Hayes, Gordon Plotkin, J Strother Moore, Mike J. C. Gordon, Robert S.  ... 
dblp:journals/flap/GabbayS17 fatcat:wvtsqquk3vhm3ohgsxn6lzc22u

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.  ...  It was a pleasure to be taught by these masters of the field.  ... 
doi:10.1016/j.jsc.2008.05.005 fatcat:zjp4ce43onbfxbt3sv5g5wndoq

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.  ...  The formal development of a system might give rise to many proof obligations. We must prove the completeness of the specification and the validity of some inductive properties.  ...  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

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

An Even Closer Integration of Linear Arithmetic into Inductive Theorem Proving

Tobias Schmidt-Samoa
2006 Electronical Notes in Theoretical Computer Science  
Successful approaches e.g. in NQTHM or ACL2 suggest a close integration scheme which augments the decision procedures with lemmas about user-defined operators.  ...  We propose an even closer integration providing feedback about the state of the decision procedure in terms of entailed formulas for three reasons: First, to provide detailed proof objects for proof checking  ...  Wirth, and the anonymous referees for helpful comments on earlier drafts of this paper.  ... 
doi:10.1016/j.entcs.2005.11.020 fatcat:nq5mi6sdofabznxf2kk74qsdci
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