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35
Integrating Gandalf and HOL
 Theorem Proving in Higher Order Logics: TPHOLs ’99, LNCS 1690
, 1999
"... Gandalf is a firstorder resolution theoremprover, optimized for speed and specializing in manipulations of large clauses. In this paper I describe GANDALF TAC, a HOL tactic that proves goals by calling Gandalf and mirroring the resulting proofs in HOL. This call can occur over a network, and a ..."
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Cited by 44 (2 self)
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Gandalf is a firstorder resolution theoremprover, optimized for speed and specializing in manipulations of large clauses. In this paper I describe GANDALF TAC, a HOL tactic that proves goals by calling Gandalf and mirroring the resulting proofs in HOL. This call can occur over a network, and a Gandalf server may be set up servicing multiple HOL clients. In addition, the translation of the Gandalf proof into HOL fits in with the LCF model and guarantees logical consistency.
More ChurchRosser Proofs (in Isabelle/HOL)
 Journal of Automated Reasoning
, 1996
"... The proofs of the ChurchRosser theorems for fi, j and fi [ j reduction in untyped calculus are formalized in Isabelle/HOL, an implementation of Higher Order Logic in the generic theorem prover Isabelle. ..."
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Cited by 39 (4 self)
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The proofs of the ChurchRosser theorems for fi, j and fi [ j reduction in untyped calculus are formalized in Isabelle/HOL, an implementation of Higher Order Logic in the generic theorem prover Isabelle.
LEOII — A cooperative automatic theorem prover for higherorder logic
 In Fourth International Joint Conference on Automated Reasoning (IJCAR’08), volume 5195 of LNAI
, 2008
"... Abstract. LEOII is a standalone, resolutionbased higherorder theorem prover designed for effective cooperation with specialist provers for natural fragments of higherorder logic. At present LEOII can cooperate with the firstorder automated theorem provers E, SPASS, and Vampire. The improved pe ..."
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Cited by 35 (23 self)
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Abstract. LEOII is a standalone, resolutionbased higherorder theorem prover designed for effective cooperation with specialist provers for natural fragments of higherorder logic. At present LEOII can cooperate with the firstorder automated theorem provers E, SPASS, and Vampire. The improved performance of LEOII, especially in comparison to its predecessor LEO, is due to several novel features including the exploitation of term sharing and term indexing techniques, support for primitive equality reasoning, and improved heuristics at the calculus level. LEOII is implemented in Objective Caml and its problem representation language is the new TPTP THF language. 1
TPS: A TheoremProving System for Classical Type Theory
, 1996
"... . This is description of TPS, a theoremproving system for classical type theory (Church's typed #calculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a comb ..."
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Cited by 16 (0 self)
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. This is description of TPS, a theoremproving system for classical type theory (Church's typed #calculus). TPS has been designed to be a general research tool for manipulating wffs of first and higherorder logic, and searching for proofs of such wffs interactively or automatically, or in a combination of these modes. An important feature of TPS is the ability to translate between expansion proofs and natural deduction proofs. Examples of theorems that TPS can prove completely automatically are given to illustrate certain aspects of TPS's behavior and problems of theorem proving in higherorder logic. AMS Subject Classification: 0304, 68T15, 03B35, 03B15, 03B10. Key words: higherorder logic, type theory, mating, connection, expansion proof, natural deduction. 1. Introduction TPS is a theoremproving system for classical type theory ## (Church's typed #calculus [20]) which has been under development at Carnegie Mellon University for a number years. This paper gives a general...
Symbolic and parametric model checking of discretetime markov Chains
 In Proc. of ICTAC’04, Springer LNCS 3407
, 2004
"... daws at cs.ru.nl Abstract. We present a languagetheoretic approach to symbolic model checking of PCTL over discretetime Markov chains. The probability with which a path formula is satisfied is represented by a regular expression. A recursive evaluation of the regular expression yields an exact rat ..."
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Cited by 16 (0 self)
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daws at cs.ru.nl Abstract. We present a languagetheoretic approach to symbolic model checking of PCTL over discretetime Markov chains. The probability with which a path formula is satisfied is represented by a regular expression. A recursive evaluation of the regular expression yields an exact rational value when transition probabilities are rational, and rational functions when some probabilities are left unspecified as parameters of the system. This allows for parametric model checking by evaluating the regular expression for different parameter values, for instance, to study the influence of a lossy channel in the overall reliability of a randomized protocol. 1
Type Inference Verified: Algorithm W in Isabelle/HOL
, 1997
"... This paper presents the first machinechecked verification of Milner's type inference algorithm W for computing the most general type of an untyped term enriched with letexpressions. This term language is the core of most typed functional programming languages and is also known as MiniML. We ..."
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Cited by 15 (1 self)
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This paper presents the first machinechecked verification of Milner's type inference algorithm W for computing the most general type of an untyped term enriched with letexpressions. This term language is the core of most typed functional programming languages and is also known as MiniML. We show how to model all the concepts involved, in particular types and type schemes, substitutions, and the thorny issue of "new" variables. Only a few key proofs are discussed in detail. The theories and proofs are developed in Isabelle/HOL, the HOL instantiation of the generic theorem prover Isabelle.
Traces of I/OAutomata in Isabelle/HOLCF
 TAPSOFT'97: THEORY AND PRACTICE OF SOFTWARE DEVELOPMENT, VOLUME 1214 OF LNCS
, 1997
"... This paper presents a formalization of finite and infinite sequences in domain theory carried out in the theorem prover Isabelle. The results ..."
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Cited by 14 (5 self)
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This paper presents a formalization of finite and infinite sequences in domain theory carried out in the theorem prover Isabelle. The results
Mechanical Verification of Distributed Algorithms in HigherOrder Logic
 The Computer Journal
, 1995
"... this paper we explain how to do so using HOLan interactive proof assistant for higherorder logic developed by Gordon and others [18]. First, we describe how to build an infrastructure in HOL that supports reasoning about distributed algorithms, including formal theories of predicates, temporal l ..."
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Cited by 12 (1 self)
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this paper we explain how to do so using HOLan interactive proof assistant for higherorder logic developed by Gordon and others [18]. First, we describe how to build an infrastructure in HOL that supports reasoning about distributed algorithms, including formal theories of predicates, temporal logic, labeled transition systems, simulation of programs, translation of properties, and graphs. Then we demonstrate, via an example, how to use the powerful intuition about events and causality to guide and structure correctness proofs of distributed algorithms. The example used is the verification of PIF (propagation of information with feedback), which is a simple but typical distributed algorithm due to Segall [33]. 1 INTRODUCTION
Treating partiality in a logic of total functions
 THE COMPUTER JOURNAL
, 1997
"... The need to use partial functions arises frequently in formal descriptions of computer systems. However, most proof assistants are based on logics of total functions. One way to address this mismatch is to invent and mechanize a new logic. Another is to develop practical workarounds in existing sett ..."
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Cited by 10 (0 self)
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The need to use partial functions arises frequently in formal descriptions of computer systems. However, most proof assistants are based on logics of total functions. One way to address this mismatch is to invent and mechanize a new logic. Another is to develop practical workarounds in existing settings. In this paper we take the latter course: we survey and compare methods used to support partiality in a mechanization of a higher order logic featuring only total functions. The techniques we discuss are generally applicable and are illustrated by relatively large examples.