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An Overview of Rewrite Rule Laboratory (RRL)
 J. of Computer and Mathematics with Applications
, 1995
"... RRL (Rewrite Rule Laboratory) was originally developed as an environment for experimenting with automated reasoning algorithms for equational logic based on rewrite techniques. It has now matured into a fullfledged theorem prover which has been used to solve hard and challenging mathematical proble ..."
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RRL (Rewrite Rule Laboratory) was originally developed as an environment for experimenting with automated reasoning algorithms for equational logic based on rewrite techniques. It has now matured into a fullfledged theorem prover which has been used to solve hard and challenging mathematical problems in automated reasoning literature as well as a research tool for investigating the use of formal methods in hardware and software design. We provide a brief historical account of development of RRL and its descendants, give an overview of the main capabilities of RRL and conclude with a discussion of applications of RRL. Key words. RRL, rewrite techniques, equational logic, discrimination nets 1 Introduction The theorem prover RRL (Rewrite Rule Laboratory) is an automated reasoning program based on rewrite techniques. The theorem prover has implementations of completion procedures for generating a complete set of rewrite rules from an equational axiomatization, associativecommutative mat...
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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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,
Comparing mathematical provers
 In Mathematical Knowledge Management, 2nd Int’l Conf., Proceedings
, 2003
"... Abstract. We compare fifteen systems for the formalizations of mathematics with the computer. We present several tables that list various properties of these programs. The three main dimensions on which we compare these systems are: the size of their library, the strength of their logic and their le ..."
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Cited by 28 (0 self)
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Abstract. We compare fifteen systems for the formalizations of mathematics with the computer. We present several tables that list various properties of these programs. The three main dimensions on which we compare these systems are: the size of their library, the strength of their logic and their level of automation. 1
A Comparison of PVS and Isabelle/HOL
 Theorem Proving in Higher Order Logics, number 1479 in Lect. Notes Comp. Sci
, 1998
"... . There is an overwhelming number of different proof tools available and it is hard to find the right one for a particular application. Manuals usually concentrate on the strong points of a proof tool, but to make a good choice, one should also know (1) which are the weak points and (2) whether the ..."
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. There is an overwhelming number of different proof tools available and it is hard to find the right one for a particular application. Manuals usually concentrate on the strong points of a proof tool, but to make a good choice, one should also know (1) which are the weak points and (2) whether the proof tool is suited for the application in hand. This paper gives an initial impetus to a consumers' report on proof tools. The powerful higherorder logic proof tools PVS and Isabelle are compared with respect to several aspects: logic, specification language, prover, soundness, proof manager, user interface (and more). The paper concludes with a list of criteria for judging proof tools, it is applied to both PVS and Isabelle. 1 Introduction There is an overwhelming number of different proof tools available (e.g. in the Database of Existing Mechanised Reasoning Systems one can find references to over 60 proof tools [Dat]). All have particular applications that they are especially suited ...
Interaction with the BoyerMoore Theorem Prover: A Tutorial Study Using the ArithmeticGeometric Mean Theorem
, 1994
"... ..."
Fast Tacticbased Theorem Proving
 TPHOLs 2000, LNCS 1869
, 2000
"... Theorem provers for higherorder logics often use tactics to implement automated proof search. Tactics use a generalpurpose metalanguage to implement both generalpurpose reasoning and computationally intensive domainspecific proof procedures. The generality of tactic provers has a performance pe ..."
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Cited by 10 (4 self)
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Theorem provers for higherorder logics often use tactics to implement automated proof search. Tactics use a generalpurpose metalanguage to implement both generalpurpose reasoning and computationally intensive domainspecific proof procedures. The generality of tactic provers has a performance penalty; the speed of proof search lags far behind specialpurpose provers. We present a new modular proving architecture that significantly increases the speed of the core logic engine.
A Ramsey Theorem in BoyerMoore Logic
 Journal of Automated Reasoning
, 1995
"... We use the BoyerMoore Prover, Nqthm, to verify the ParisHarrington version of Ramsey's Theorem. The proof we verify is a modification of the one given by Ketonen and Solovay. The Theorem is not provable in Peano Arithmetic, and one key step in the proof requires ffl 0 induction. x0. Introduct ..."
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We use the BoyerMoore Prover, Nqthm, to verify the ParisHarrington version of Ramsey's Theorem. The proof we verify is a modification of the one given by Ketonen and Solovay. The Theorem is not provable in Peano Arithmetic, and one key step in the proof requires ffl 0 induction. x0. Introduction. The most wellknown formalizations of finite mathematics are PA (Peano Arithmetic) and PRA (Primitive Recursive Arithmetic). In both, the "intended" domain of discourse is the set of natural numbers. PA is formalized in standard firstorder logic, and contains the induction schema, which can apply to arbitrary firstorder formulas. The logic of PRA allows only quantifierfree formulas, which are thought of as being universally quantified, and PRA has the induction scheme for quantifierfree formulas, expressed as a proof rule. Also, for each primitive recursive function f , PRA contains a function symbol for f and has the recursive definition of f as an axiom. Clearly, PRA is much weaker tha...
Formalization of Graph Search Algorithms and Its Applications
, 1998
"... This paper describes a formalization of a class of fixedpoint problems on graphs and its applications. This class captures several wellknown graph theoretical problems such as those of shortest path type and for data flow analysis. An abstract solution algorithm of the fixedpoint problem is forma ..."
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Cited by 8 (0 self)
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This paper describes a formalization of a class of fixedpoint problems on graphs and its applications. This class captures several wellknown graph theoretical problems such as those of shortest path type and for data flow analysis. An abstract solution algorithm of the fixedpoint problem is formalized and its correctness is proved using a theorem proving system. Moreover, the validity of the A* algorithm, considered as a specialized version of the abstract algorithm, is proved by extending the proof of the latter. The insights we obtained through these formalizations are described. We also discuss the extension of this approach to the verification of model checking algorithms.
Verification of a signature architecture with HOLZ
 In Formal Methods, LNCS
, 2005
"... Abstract. We report on a case study in using HOLZ, an embedding of Z in higherorder logic, to specify and verify a security architecture for administering digital signatures. We have used HOLZ to formalize and combine both dataoriented and processoriented architectural views. Afterwards, we for ..."
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Abstract. We report on a case study in using HOLZ, an embedding of Z in higherorder logic, to specify and verify a security architecture for administering digital signatures. We have used HOLZ to formalize and combine both dataoriented and processoriented architectural views. Afterwards, we formalized temporal requirements in Z and carried out verification in higherorder logic. The same architecture has been previously verified using the SPIN model checker. Based on this, we provide a detailed comparison of these two different approaches to formalization (infinite state with rich data types versus finite state) and verification (theorem proving versus model checking). Contrary to common belief, our case study suggests that Z is well suited for temporal reasoning about process models with rich data. Moreover, our comparison highlights the advantages of this approach and provides evidence that, in the hands of experienced users, theorem proving is neither substantially more timeconsuming nor more complex than model checking. 1