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Proof Terms for Simply Typed Higher Order Logic
 IN THEOREM PROVING IN HIGHER ORDER LOGICS, 13TH INTERNATIONAL CONFERENCE, VOLUME 1869 OF LNCS
, 2000
"... This paper presents proof terms for simply typed, intuitionistic higher order logic, a popular logical framework. Unificationbased algorithms for the compression and reconstruction of proof terms are described and have been implemented in the theorem prover Isabelle. Experimental results confir ..."
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Cited by 35 (8 self)
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This paper presents proof terms for simply typed, intuitionistic higher order logic, a popular logical framework. Unificationbased algorithms for the compression and reconstruction of proof terms are described and have been implemented in the theorem prover Isabelle. Experimental results confirm the effectiveness of the compression scheme.
A Trustworthy Proof Checker
 IN ILIANO CERVESATO, EDITOR, WORKSHOP ON THE FOUNDATIONS OF COMPUTER SECURITY
, 2002
"... ProofCarrying Code (PCC) and other applications in computer security require machinecheckable proofs of properties of machinelanguage programs. The main advantage of the PCC approach is that the amount of code that must be explicitly trusted is very small: it consists of the logic in which predic ..."
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Cited by 29 (7 self)
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ProofCarrying Code (PCC) and other applications in computer security require machinecheckable proofs of properties of machinelanguage programs. The main advantage of the PCC approach is that the amount of code that must be explicitly trusted is very small: it consists of the logic in which predicates and proofs are expressed, the safety predicate, and the proof checker. We have built a minimal proof checker, and we explain its design principles, and the representation issues of the logic, safety predicate, and safety proofs. We show that the trusted computing base (TCB) in such a system can indeed be very small. In our current system the TCB is less than 2,700 lines of code (an order of magnitude smaller even than other PCC systems) which adds to our confidence of its correctness.
Verification of the MDG Components Library in HOL
, 1998
"... The MDG system is a decision diagram based verification tool, primarily designed for hardware verification. It is based on Multiway decision diagramsan extension of the traditional ROBDD approach. In this paper we describe the formal verification of the component library of the MDG system, using ..."
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Cited by 7 (6 self)
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The MDG system is a decision diagram based verification tool, primarily designed for hardware verification. It is based on Multiway decision diagramsan extension of the traditional ROBDD approach. In this paper we describe the formal verification of the component library of the MDG system, using HOL. The hardware component library, whilst relatively simple, has been a source of errors in an earlier developmental version of the MDG system. Thus verifying these aspects is of real utility towards the verification of a decision digram based verification system. This work demonstrates how machine assisted proof can be of practical utility when applied to a small focused problem.
OpenTheory: Package Management for Higher Order Logic Theories
"... Interactive theorem proving has grown from toy examples to major projects formalizing mathematics and verifying software, and there is now a critical need for theory engineering techniques to support these efforts. This paper introduces the OpenTheory project, which aims to provide an effective pack ..."
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Cited by 5 (3 self)
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Interactive theorem proving has grown from toy examples to major projects formalizing mathematics and verifying software, and there is now a critical need for theory engineering techniques to support these efforts. This paper introduces the OpenTheory project, which aims to provide an effective package management system for logical theories. The OpenTheory article format allows higher order logic theories to be exported from one theorem prover, compressed by a standalone tool, and imported into a different theorem prover. Articles naturally support theory interpretations, which is the mechanism by which theories can be cleanly transferred from one theorem prover context to another, and which also leads to more efficient developments of standard theories.
Dependency Graphs for Interactive Theorem Provers
, 2000
"... We propose tools to visualize large proof developments as graphs of theorems and definitions where edges denote the dependency between two theorems. In particular, we study means to limit the size of graphs. Experiments have been done with the Coq theorem prover [DFH + 93] and the GraphViz [EGKN] an ..."
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Cited by 2 (0 self)
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We propose tools to visualize large proof developments as graphs of theorems and definitions where edges denote the dependency between two theorems. In particular, we study means to limit the size of graphs. Experiments have been done with the Coq theorem prover [DFH + 93] and the GraphViz [EGKN] and daVinci [FW98] graph visualization suites.
The Importance of Proof Maintenance and Reengineering
 In Proc. Int. Workshop on Higher Order Logic Theorem Proving and Its Applications
, 1995
"... Our work on the verification of real hardware designs using HOL has resulted in very large proof scripts. Consequently, problems were encountered that are not an issue in smaller verification efforts. In particular, we have found that the maintainability of proofs is of paramount importance. There a ..."
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Cited by 1 (0 self)
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Our work on the verification of real hardware designs using HOL has resulted in very large proof scripts. Consequently, problems were encountered that are not an issue in smaller verification efforts. In particular, we have found that the maintainability of proofs is of paramount importance. There are many reasons why proof scripts in LCF style theorem provers may be reused. This can be in order to maintain and understand old proofs as well as to speed the creation of new ones. Consequently, proofs should be written in styles that ease their maintainability and make them easier to reuse. Furthermore, proof tools and interfaces should be designed with proof reuse as well as proof creation in mind. Many of the problems could be prevented from occurring in the first place with suitable support. 1 Introduction The recent Fairisle switching fabric verification project [3] entailed using HOL [5] to verify real hardware designs. The resulting proofs consist of several hundred theories, the s...
Sequent Style Proof Terms for HOL
"... Abstract. In this work we present proof terms for a Gentzen sequent style presentation of HOL. Existing implementations of proof terms for HOL are natural deduction style systems. Sequent style proof terms have many advantages over natural deduction style proof terms. For example, we can translate p ..."
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Abstract. In this work we present proof terms for a Gentzen sequent style presentation of HOL. Existing implementations of proof terms for HOL are natural deduction style systems. Sequent style proof terms have many advantages over natural deduction style proof terms. For example, we can translate proof terms directly into tactics, which we can execute at the tactic level of HOL implementations. We describe several applications of our work, such as an implementation of theory interpretation, and an approach to optimising proof terms by rewriting. 1
Representation and Validation of Mechanically Generated Proofs Final Report
"... Introduction The goal of this project was to demonstrate the feasibility of the independent and trusted validation of the proofs generated by existing theorem provers. Our intention was to design, implement and formally verify a proof checking program for HOL [5] generated proofs. A proof checker ..."
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Introduction The goal of this project was to demonstrate the feasibility of the independent and trusted validation of the proofs generated by existing theorem provers. Our intention was to design, implement and formally verify a proof checking program for HOL [5] generated proofs. A proof checker can be much simpler than a full theorem prover such as HOL as it is only concerned with checking existing proofs rather than searching for or generating them. Our work has clearly demonstrated the feasibility of this approach. In particular, the main achievements of the project are as follows. ffl We have developed a computer representation suitable for communicating large, formal, machine generated proofs. ffl We have modified the HOL system to allow primitive inference proofs to be recorded in the above format. ffl We have formalised, within the HOL theorem proving system, theories of higherorder logic, Hilb
Composable Packages for Higher Order Logic Theories
"... Interactive theorem proving is tackling ever larger formalization and verification projects, and there is a critical need for theory engineering techniques to support these efforts. One such technique is effective package management, which has the potential to simplify the development of logical the ..."
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Interactive theorem proving is tackling ever larger formalization and verification projects, and there is a critical need for theory engineering techniques to support these efforts. One such technique is effective package management, which has the potential to simplify the development of logical theories by precisely checking dependencies and promoting reuse. This paper introduces a domainspecific language for defining composable packages of higher order logic theories, which is designed to naturally handle the complex dependency structures that often arise in theory development. The package composition language functions as a module system for theories, and the paper presents a welldefined semantics for the supported operations. Preliminary tests of the package language and its toolset have been made by packaging the theories distributed with the HOL Light theorem prover. This experience is described, leading to some initial theory engineering discussion on the ideal properties of a reusable theory. 1