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A logic of events
, 2003
"... There is a wellestablished theory and practice for creating correctbyconstruction functional programs by extracting them from constructive proofs of assertions of the form ∀x: A.∃y: B.R(x, y). There have been several efforts to extend this methodology to concurrent programs, say by using linear l ..."
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Cited by 10 (7 self)
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There is a wellestablished theory and practice for creating correctbyconstruction functional programs by extracting them from constructive proofs of assertions of the form ∀x: A.∃y: B.R(x, y). There have been several efforts to extend this methodology to concurrent programs, say by using linear logic, but there is no practice and the results are limited. In this paper we define a logic of events that justifies the extraction of correct distributed processes from constructive proofs that system specifications are achievable, and we describe an implementation of an extraction process in the context of constructive type theory. We show that a class of message automata, similar to IO automata and to active objects, are realizers for this logic. We provide a relative consistency result for the logic. We show an example of protocol derivation in this logic, and show how to embed temporal logics such as T LA+ in the event logic. 1
Proving Formally the Implementation of an Efficient gcd Algorithm for Polynomials
 in "3rd International Joint Conference on Automated Reasoning (IJCAR)", U. FURBACH, N. SHANKAR (editors). , Lecture Notes in Artificial Intelligence
"... Abstract. We describe here a formal proof in the Coq system of the structure theorem for subresultants, which allows to prove formally the correctness of our implementation of the subresultants algorithm. Up to our knowledge it is the first mechanized proof of this result. 1 ..."
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Abstract. We describe here a formal proof in the Coq system of the structure theorem for subresultants, which allows to prove formally the correctness of our implementation of the subresultants algorithm. Up to our knowledge it is the first mechanized proof of this result. 1
Providing a Formal Linkage between MDG and HOL
, 2002
"... We describe an approach for formally verifying the linkage between a symbolic state enumeration system and a theorem proving system. This involves the following three stages of proof. Firstly we prove theorems about the correctness of the translation part of the symbolic state system. It interface ..."
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Cited by 2 (2 self)
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We describe an approach for formally verifying the linkage between a symbolic state enumeration system and a theorem proving system. This involves the following three stages of proof. Firstly we prove theorems about the correctness of the translation part of the symbolic state system. It interfaces between low level decision diagrams and high level description languages. We ensure that the semantics of a program is preserved in those of its translated form. Secondly we prove linkage theorems: theorems that justify introducing a result from a state enumeration system into a proof system. Finally we combine the translator correctness and linkage theorems. The resulting new linkage theorems convert results to a high level language from the low level decision diagrams that the result was actually proved about in the state enumeration system.They justify importing lowlevel external verification results into a theorem prover. We use a linkage between the HOL system and a simplified version of the MDG system to illustrate the ideas and consider a small example that integrates two applications from MDG and HOL to illustrate the linkage theorems.
Dependent Types, Theorem Proving, and Applications for a Verifying Compiler
, 2005
"... One approach to Prof. Hoare’s challenge is to view the development of verified software from the perspective of interactive theorem provers. This idea is already commonly developed and many mediumscale software systems have been developed and verified in this manner. Developments based on HOL, ACL2 ..."
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One approach to Prof. Hoare’s challenge is to view the development of verified software from the perspective of interactive theorem provers. This idea is already commonly developed and many mediumscale software systems have been developed and verified in this manner. Developments based on HOL, ACL2, or PVS have already been described and advocated and our position stands on the same line: most powerful (higherorder) theorem proving systems already contain a programming language, programs can be developed and the correctness of these programs can be specified and verified, they can then be compiled into traditional executable code. In this sense, we already have a small scale example of a verification aware programming language. We propose to take advantage of the notion of “dependent types ” to ensure that this programming language combines powerful logical capabilities, reasonable expressive power, and practical linkage between computational content and logical annotations. Almost all mathematic developments contain algorithms. This imposes that
Verified Computer Algebra in Acl2 (Gröbner Bases Computation)
"... In this paper, we present the formal verification of a Common Lisp implementation of Buchberger's algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in the Acl2 system and shows how verified Computer Algebra can be achieved in an executable logic. ..."
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In this paper, we present the formal verification of a Common Lisp implementation of Buchberger's algorithm for computing Gröbner bases of polynomial ideals. This work is carried out in the Acl2 system and shows how verified Computer Algebra can be achieved in an executable logic.
5. New Results.............................................................................. 3
"... c t i v it y e p o r t 2007 Table of contents ..."