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18
leanCoP: Lean ConnectionBased Theorem Proving
 UNIVERSITY OF KOBLENZ
, 2000
"... The Prolog program "prove(M,I) : append(Q,[CR],M), "+member(,C), append(Q,R,S), prove([!],[[!C]S],[],I). prove([],,,). prove([LC],M,P,I) : (N=L; L=N) ? (member(N,P); append(Q,[DR],M), copyterm(D,E), append(A,[NB],E), append(A,B,F), (D==E ? append(R,Q,S); length(P,K), ..."
Abstract

Cited by 19 (7 self)
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The Prolog program "prove(M,I) : append(Q,[CR],M), "+member(,C), append(Q,R,S), prove([!],[[!C]S],[],I). prove([],,,). prove([LC],M,P,I) : (N=L; L=N) ? (member(N,P); append(Q,[DR],M), copyterm(D,E), append(A,[NB],E), append(A,B,F), (D==E ? append(R,Q,S); length(P,K), K!I, append(R,[DQ],S)), prove(F,S,[LP],I)), prove(C,M,P,I)." implements a theorem prover for classical firstorder (clausal) logic which is based on the connection calculus. It is sound, complete (if one more line is added), and demonstrates a comparatively strong performance.
The Nuprl Proof Development System, Version 5: Reference Manual and User’s Guide
, 2002
"... This manual is a reference manual for version 5 of the Nuprl proof development system. As the Nuprl system is constantly under development, this manual will always be incomplete. In particular, it is missing information about recent advanced features of the system and about certain extensions of Nup ..."
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Cited by 8 (3 self)
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This manual is a reference manual for version 5 of the Nuprl proof development system. As the Nuprl system is constantly under development, this manual will always be incomplete. In particular, it is missing information about recent advanced features of the system and about certain extensions of Nuprl’s type theory that are currently being added to the system. More recent information and the system itself can be found at the Nuprl web pages
MetaPRL  A Modular Logical Environment
, 2003
"... MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive ..."
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Cited by 8 (2 self)
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MetaPRL is the latest system to come out of over twenty five years of research by the Cornell PRL group. While initially created at Cornell, MetaPRL is currently a collaborative project involving several universities in several countries. The MetaPRL system combines the properties of an interactive LCFstyle tacticbased proof assistant, a logical framework, a logical programming environment, and a formal methods programming toolkit. MetaPRL is distributed under an opensource license and can be downloaded from http://metaprl.org/. This paper provides an overview of the system focusing on the features that did not exist in the previous generations of PRL systems.
ConnectionBased Proof Search in Propositional BI Logic
 In 18th Int
, 2002
"... We present a connectionbased characterization of propositional BI (logic of bunched implications), a logic combining linear and intuitionistic connectives. This logic, with its sharing interpretation, has been recently used to reason about mutable data structures and needs proof search methods. Our ..."
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Cited by 7 (6 self)
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We present a connectionbased characterization of propositional BI (logic of bunched implications), a logic combining linear and intuitionistic connectives. This logic, with its sharing interpretation, has been recently used to reason about mutable data structures and needs proof search methods. Our connectionbased characterization for BI is based on standard notions but involves, in a specic way, labels and constraints in order to capture the interactions between connectives during the proofsearch. As BI is conservative w.r.t. intuitionistic logic and multiplicative intuitionistic linear logic, we deduce, by some restrictions, new connectionbased characterizations and methods for both logics.
JProver: Integrating connectionbased theorem proving into interactive proof assistants
 IJCAR’01, volume 2083 of LNAI
, 2001
"... Abstract. JProver is a firstorder intuitionistic theorem prover that creates sequentstyle proof objects and can serve as a proof engine in interactive proof assistants with expressive constructive logics. This paper gives a brief overview of JProver’s proof technique, the generation of proof objec ..."
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Cited by 6 (2 self)
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Abstract. JProver is a firstorder intuitionistic theorem prover that creates sequentstyle proof objects and can serve as a proof engine in interactive proof assistants with expressive constructive logics. This paper gives a brief overview of JProver’s proof technique, the generation of proof objects, and its integration into the Nuprl proof development system. 1
Connectiondriven inductive theorem proving
 Studia Logica
"... Abstract. We present a method for integrating ripplingbased rewriting into matrixbased theorem proving as a means for automating inductive specification proofs. The selection of connections in an inductive matrix proof is guided by symmetries between induction hypothesis and induction conclusion. ..."
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Cited by 4 (2 self)
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Abstract. We present a method for integrating ripplingbased rewriting into matrixbased theorem proving as a means for automating inductive specification proofs. The selection of connections in an inductive matrix proof is guided by symmetries between induction hypothesis and induction conclusion. Unification is extended by decision procedures and a rippling/reverserippling heuristic. Conditional substitutions are generated whenever a uniform substitution is impossible. We illustrate the integrated method by discussing several inductive proofs for the integer square root problem as well as the algorithms extracted from these proofs.
FDL: A prototype formal digital library. PostScript document on website
, 2002
"... Digital Library (FDL). We designed the system and assembled the prototype as part of a ..."
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Cited by 3 (3 self)
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Digital Library (FDL). We designed the system and assembled the prototype as part of a
Labelled Modal Sequents
 In Areces and de Rijke [AdR99]. Use Your Logic 7
, 2000
"... In this paper we present a new labelled sequent calculus for modal logic. The proof method works with a more "liberal" modal language which allows inferential steps where di#erent formulas refer to different labels without moving to a particular world and there computing if the consequence holds. Wo ..."
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Cited by 2 (0 self)
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In this paper we present a new labelled sequent calculus for modal logic. The proof method works with a more "liberal" modal language which allows inferential steps where di#erent formulas refer to different labels without moving to a particular world and there computing if the consequence holds. Worldpaths can be composed, decomposed and manipulated through unification algorithms and formulas in different worlds can be compared even if they are subformulas which do not depend directly on the main connective. Accordingly, such a sequent system can provide a general definition of modal consequence relation. Finally, we briefly sketch a proof of the soundness and completeness results.
Matrixbased Inductive Theorem Proving
 TABLEAUX2000, LNAI 1847
, 2000
"... We present an approach to inductive theorem proving that integrates ripplingbased rewriting into matrixbased logical proof search. ..."
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Cited by 2 (2 self)
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We present an approach to inductive theorem proving that integrates ripplingbased rewriting into matrixbased logical proof search.