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Theory Interpretation in Simple Type Theory
 HIGHERORDER ALGEBRA, LOGIC, AND TERM REWRITING, VOLUME 816 OF LECTURE NOTES IN COMPUTER SCIENCE
, 1993
"... Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself. This paper presents a method for theory interpretation in a version of simple type theory, called lutins, which admit ..."
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Cited by 37 (17 self)
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Theory interpretation is a logical technique for relating one axiomatic theory to another with important applications in mathematics and computer science as well as in logic itself. This paper presents a method for theory interpretation in a version of simple type theory, called lutins, which admits partial functions and subtypes. The method is patterned on the standard approach to theory interpretation in rstorder logic. Although the method is based on a nonclassical version of simple type theory, it is intended as a guide for theory interpretation in classical simple type theories as well as in predicate logics with partial functions.
PDS  A ThreeDimensional Data Structure for Proof Plans
 PROC. OF ACIDCA'2000
, 2000
"... We present a new data structure that enables to store threedimensional proof objects in a proof development environment. The aim is to handle calculus level proofs as well as abstract proof plans together with information of their correspondences in a single structure. This enables not only differe ..."
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Cited by 35 (9 self)
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We present a new data structure that enables to store threedimensional proof objects in a proof development environment. The aim is to handle calculus level proofs as well as abstract proof plans together with information of their correspondences in a single structure. This enables not only different means of the proof development environment (e.g., rule and tacticbased theorem proving, or proof planning) to act directly on the same proof object but it also allows for easy presentation of proofs on different levels of abstraction. However, the threedimensional structure requires adjustment of the regular techniques for addition and deletion of proof lines and backtracking of the proof planner.
Cryptographically Sound Theorem Proving
 In Proc. 19th IEEE CSFW
, 2006
"... We describe a faithful embedding of the DolevYao model of Backes, Pfitzmann, and Waidner (CCS 2003) in the theorem prover Isabelle/HOL. This model is cryptographically sound in the strong sense of reactive simulatability/UC, which essentially entails the preservation of arbitrary security proper ..."
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Cited by 33 (10 self)
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We describe a faithful embedding of the DolevYao model of Backes, Pfitzmann, and Waidner (CCS 2003) in the theorem prover Isabelle/HOL. This model is cryptographically sound in the strong sense of reactive simulatability/UC, which essentially entails the preservation of arbitrary security properties under active attacks and in arbitrary protocol environments. The main challenge in designing a practical formalization of this model is to cope with the complexity of providing such strong soundness guarantees. We reduce this complexity by abstracting the model into a sound, lightweight formalization that enables both concise property specifications and efficient application of our proof strategies and their supporting proof tools. This yields the first toolsupported framework for symbolically verifying security protocols that enjoys the strong cryptographic soundness guarantees provided by reactive simulatability/UC. As a proof of concept, we have proved the security of the NeedhamSchroederLowe protocol using our framework.
Towards Selfverification of HOL Light
 In International Joint Conference on Automated Reasoning
, 2006
"... Abstract. The HOL Light prover is based on a logical kernel consisting of about 400 lines of mostly functional OCaml, whose complete formal verification seems to be quite feasible. We would like to formally verify (i) that the abstract HOL logic is indeed correct, and (ii) that the OCaml code does c ..."
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Cited by 30 (0 self)
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Abstract. The HOL Light prover is based on a logical kernel consisting of about 400 lines of mostly functional OCaml, whose complete formal verification seems to be quite feasible. We would like to formally verify (i) that the abstract HOL logic is indeed correct, and (ii) that the OCaml code does correctly implement this logic. We have performed a full verification of an imperfect but quite detailed model of the basic HOL Light core, without definitional mechanisms, and this verification is entirely conducted with respect to a settheoretic semantics within HOL Light itself. We will duly explain why the obvious logical and pragmatic difficulties do not vitiate this approach, even though it looks impossible or useless at first sight. Extension to include definitional mechanisms seems straightforward enough, and the results so far allay most of our practical worries. 1 Introduction: quis custodiet ipsos custodes? Mathematical proofs are subjected to peer review before publication, but there
Symbolic Computation: Computer Algebra and Logic
 FRONTIERS OF COMBINING SYSTEMS, APPLIED LOGIC SERIES
, 1996
"... In this paper we present our personal view of what should be the next step in the development of symbolic computation systems. The main point is that future systems should integrate the power of algebra and logic. We identify four gaps between the future ideal and the systems available at present: t ..."
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Cited by 30 (3 self)
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In this paper we present our personal view of what should be the next step in the development of symbolic computation systems. The main point is that future systems should integrate the power of algebra and logic. We identify four gaps between the future ideal and the systems available at present: the logic, the syntax, the mathematics, and the prover gap, respectively. We discuss higher order logic without extensionality and with set theory as a subtheory as a logic frame for future systems and we propose to start from existing computer algebra systems and proceed by adding new facilities for closing the syntax, mathematics, and the prover gaps. Mathematica seems to be a particularly suitable candidate for such an approach. As the main technique for structuring mathematical knowledge, mathematical methods (including algorithms), and also mathematical proofs, we underline the practical importance of functors and show how they can be naturally embedded into Mathematica.
The TPS theorem proving system
 9th International Conference on Automated Deduction, Argonne, Illinois
, 1988
"... TPS is a theorem proving system for first and higherorder logic which runs in Common Lisp and can operate in automatic, semiautomatic, and interactive modes. As its logical language TPS uses the typed Acalculus [6], in which most theorems of mathematics can be expressed very directly. TPS can be ..."
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Cited by 28 (5 self)
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TPS is a theorem proving system for first and higherorder logic which runs in Common Lisp and can operate in automatic, semiautomatic, and interactive modes. As its logical language TPS uses the typed Acalculus [6], in which most theorems of mathematics can be expressed very directly. TPS can be used to search for an expansion proof [10, 11] of a theorem, which represents in a nonredtmdant way the basic combinatorial information required to construct a proof of
An integrated proof language for imperative programs
 In PLDI’09
"... We present an integrated proof language for guiding the actions of multiple reasoning systems as they work together to prove complex correctness properties of imperative programs. The language operates in the context of a program verification system that uses multiple reasoning systems to discharge ..."
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Cited by 28 (5 self)
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We present an integrated proof language for guiding the actions of multiple reasoning systems as they work together to prove complex correctness properties of imperative programs. The language operates in the context of a program verification system that uses multiple reasoning systems to discharge generated proof obligations. It is designed to 1) enable developers to resolve key choice points in complex program correctness proofs, thereby enabling automated reasoning systems to successfully prove the desired correctness properties; 2) allow developers to identify key lemmas for the reasoning systems to prove, thereby guiding the reasoning systems to find an effective proof decomposition; 3) enable multiple reasoning systems to work together productively to prove a single correctness property by providing a mechanism that developers can use to divide the property into lemmas, each of which is suitable for
Proof Transformations in HigherOrder Logic
, 1987
"... We investigate the problem of translating between different styles of proof systems in higherorder logic: analytic proofs which are well suited for automated theorem proving, and nonanalytic deductions which are well suited for the mathematician. Analytic proofs are represented as expansion proofs, ..."
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Cited by 27 (6 self)
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We investigate the problem of translating between different styles of proof systems in higherorder logic: analytic proofs which are well suited for automated theorem proving, and nonanalytic deductions which are well suited for the mathematician. Analytic proofs are represented as expansion proofs, H, a form of the sequent calculus we define, nonanalytic proofs are represented by natural deductions. A nondeterministic translation algorithm between expansion proofs and Hdeductions is presented and its correctness is proven. We also present an algorithm for translation in the other direction and prove its correctness. A cutelimination algorithm for expansion proofs is given and its partial correctness is proven. Strong termination of this algorithm remains a conjecture for the full higherorder system, but is proven for the firstorder fragment. We extend the translations to a nonanalytic proof system which contains a primitive notion of equality, while leaving the notion of expansion proof unaltered. This is possible, since a nonextensional equality is definable in our system of type theory. Next we extend analytic and nonanalytic proof systems and the translations between them to include extensionality. Finally, we show how the methods and notions used so far apply to the problem of translating expansion proofs into natural deductions. Much care is taken to specify this translation in a