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Set theory for verification: I. From foundations to functions
 J. Auto. Reas
, 1993
"... A logic for specification and verification is derived from the axioms of ZermeloFraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the flexibility to adapt to variants of set theory. Its higherord ..."
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Cited by 51 (20 self)
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A logic for specification and verification is derived from the axioms of ZermeloFraenkel set theory. The proofs are performed using the proof assistant Isabelle. Isabelle is generic, supporting several different logics. Isabelle has the flexibility to adapt to variants of set theory. Its higherorder syntax supports the definition of new binding operators. Unknowns in subgoals can be instantiated incrementally. The paper describes the derivation of rules for descriptions, relations and functions, and discusses interactive proofs of Cantor’s Theorem, the Composition of Homomorphisms challenge [9], and Ramsey’s Theorem [5]. A generic proof assistant can stand up against provers dedicated to particular logics. Key words. Isabelle, set theory, generic theorem proving, Ramsey’s Theorem,
Selectively instantiating definitions
 In Proc. of CADE15, volume 1421 of LNAI
, 1998
"... 1 Introduction When searching for proofs of theorems which contain definitions, it is a significant problem to decide which instances of the definitions to instantiate. Often, one needs to instantiate some, but not all, of them, and if one does instantiate all of them, one can cause the search space ..."
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Cited by 16 (3 self)
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1 Introduction When searching for proofs of theorems which contain definitions, it is a significant problem to decide which instances of the definitions to instantiate. Often, one needs to instantiate some, but not all, of them, and if one does instantiate all of them, one can cause the search space to expand in a very undesirable way. This problem has been noted in [4] and [23], and treatments of it may be found in [6], [8] and [12]. We have found a partial solution to this problem; it involves making each instance of a definition accessible to the search procedure in both its instantiated and its uninstantiated form, and letting the search procedure decide which to use, with a bias in favor of the uninstantiated form. This is very effective in some cases.
Proofs and Pictures Proving the Diamond Lemma with the grover Theorem Proving System
, 1995
"... In this paper we describe a theorem proving system called grover. grover is novel in that it may be guided in its search for a proof by information contained in a diagram. There are two parts to the system: the underlying theorem prover, called &, and the graphical subsystem which examines the d ..."
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Cited by 13 (2 self)
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In this paper we describe a theorem proving system called grover. grover is novel in that it may be guided in its search for a proof by information contained in a diagram. There are two parts to the system: the underlying theorem prover, called &, and the graphical subsystem which examines the diagram and makes calls to the underlying prover on the basis of the information found there. We have used grover to prove the Diamond Lemma, a nontrivial theorem from the theory of wellfounded relations. Key words. Automated reasoning, graphical theorem proving, proof strategies. This material is based upon work supported by the National Science Foundation under award number ISI8701133. 1 INTRODUCTION 2 1 Introduction Open almost any mathematics text book and you will find, along with the familiar symbolism of mathematics and motivational text, many diagrams which are included to help the reader visualize the particular point being made. One might be tempted to conclude that mathema...
Laura: a system to debug student programs
 Arti cial Intelligence
, 1980
"... An effort to automate the debugging of real programs is presented. We discuss possible choices in conceiving a debugging system. In order to detect all the semantic errors, it must have a knowledge of what the program is intended to achieve. Strategies and results are very dependent on the way of gi ..."
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An effort to automate the debugging of real programs is presented. We discuss possible choices in conceiving a debugging system. In order to detect all the semantic errors, it must have a knowledge of what the program is intended to achieve. Strategies and results are very dependent on the way of giving this knowledge. In the LAURA system that we have designed, the program's task is given by means of a 'program model'. Automatic debugging is then viewed as a comparison of programs. The main characteristics of LAURA are the representation f programs by graphs, which gets rid of many syntactical variations, the use of program transformations, realized on the graphs, and its heuristic strategy to identify step by step the elements of the graphs. It has been tested with about a hundred programs written by students to solve eight different problems in various fields. It is able to recognize correct programs even if their structures are very different from the structure of the program model. It is also able to express exact diagnostics of errors, or at least to localize them. It could be an effective tool for students programmers.
Theorem Proving with Definitions
, 1989
"... This paper analyses a technique (called Gazing) for unfolding de nitions on the basis of a global plan built in an abstract space. Gazing's logical properties are studied inside a formal framework which relies on a more general theory of abstraction. Some experimental results con rming the theo ..."
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Cited by 7 (5 self)
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This paper analyses a technique (called Gazing) for unfolding de nitions on the basis of a global plan built in an abstract space. Gazing's logical properties are studied inside a formal framework which relies on a more general theory of abstraction. Some experimental results con rming the theoretical ones are also presented.
A tableau calculus for quantifierfree set theoretic formulae
 In Proceedings, International Conference on Theorem Proving with Analytic Tableaux and Related Methods, Oisterwijk, The Netherlands, LNCS 1397
, 1998
"... Abstract. Set theory is the common language of mathematics. Therefore, set theory plays an important rôle in many important applications of automated deduction. In this paper, we present an improved tableau calculus for the decidable fragment of set theory called multilevel syllogistic with singlet ..."
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Abstract. Set theory is the common language of mathematics. Therefore, set theory plays an important rôle in many important applications of automated deduction. In this paper, we present an improved tableau calculus for the decidable fragment of set theory called multilevel syllogistic with singleton (MLSS). Furthermore, we describe an extension of our calculus for the bigger fragment consisting of MLSS enriched with free (uninterpreted) function symbols (MLSSF). 1
Theorem Proving with Denitions
"... This paper analyses a technique (called Gazing) for unfolding denitions on the basis of a global plan built in an abstract space. Gazing's logical properties are studied inside a formal framework which relies on a more general theory of abstraction. Some experimental results conrming the theor ..."
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Cited by 1 (0 self)
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This paper analyses a technique (called Gazing) for unfolding denitions on the basis of a global plan built in an abstract space. Gazing's logical properties are studied inside a formal framework which relies on a more general theory of abstraction. Some experimental results conrming the theoretical ones are also presented. 1
A Decidable Tableau Calculus for a Fragment of Set Theory With Iterated Membership
 II. Optimization and Complexity Issues. Journal of Automated Reasoning
, 1997
"... this paper we give a decision procedure and a decidable tableau calculus for the extension of Multilevel Syllogistic ..."
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this paper we give a decision procedure and a decidable tableau calculus for the extension of Multilevel Syllogistic
Mathematical Theorem Proving, from Muscadet0 to Muscadet4∗,
, 2014
"... Abstract: This paper presents the ideas and the choices which have been made throughout the development of the Muscadet theorem prover. We will first see the principles and main ideas which lead to a first prover in the context of the time, influenced by a famous paper by Woody Bledsoe. This program ..."
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Abstract: This paper presents the ideas and the choices which have been made throughout the development of the Muscadet theorem prover. We will first see the principles and main ideas which lead to a first prover in the context of the time, influenced by a famous paper by Woody Bledsoe. This program used natural methods and was applied to set theory. It was then rewritten as a knowledge basedsystem where an inference engine applied rules, given or automatically built by metarules which expressed general or specific mathematical knowledge. It has been applied to some difficult problems. In order to allow more flexibility for expressing knowledge, it has been rewritten in Prolog, allowing the knowledge to be more or less declarative or procedural. To work with the TPTP Library the system had to work without knowing anything about mathematics except predicate calculus. All mathematical concepts had to be defined with mathematical statements, and the membership relation handled as any other binary relation. To avoid translating knowledge to TPTP syntax, TPTP syntax has been used (this unfortunately forbade the use of some abbreviations mathematicians are comfortable with). Last but not least, the relevant trace has been extracted to give a proof easily read by anyone, except in the case of failure, when all steps may be displayed to understand (manually) the reasons for the failure. Muscadet has participated to CASC competitions. The results show its complementarity with regard to resolutionbased provers. 1
MUSCADET version 4.1 User's Manual
"... 2.2. Power set of the intersection of two sets...................................................................................3 3. From Muscadet1 to Muscadet4........................................................................................................4 ..."
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2.2. Power set of the intersection of two sets...................................................................................3 3. From Muscadet1 to Muscadet4........................................................................................................4