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16
A Compiled Implementation of Strong Reduction
"... Motivated by applications to proof assistants based on dependent types, we develop and prove correct a strong reducer and b equivalence checker for the lcalculus with products, sums, and guarded fixpoints. Our approach is based on compilation to the bytecode of an abstract machine performing weak ..."
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Cited by 92 (5 self)
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Motivated by applications to proof assistants based on dependent types, we develop and prove correct a strong reducer and b equivalence checker for the lcalculus with products, sums, and guarded fixpoints. Our approach is based on compilation to the bytecode of an abstract machine performing weak reductions on nonclosed terms, derived with minimal modifications from the ZAM machine used in the Objective Caml bytecode interpreter, and complemented by a recursive "read back" procedure. An implementation in the Coq proof assistant demonstrates important speedups compared with the original interpreterbased implementation of strong reduction in Coq.
Formalizing the LogicAutomaton Connection
"... Abstract. This paper presents a formalization of a library for automata on bit strings in the theorem prover Isabelle/HOL. It forms the basis of a reflectionbased decision procedure for Presburger arithmetic, which is efficiently executable thanks to Isabelle’s code generator. With this work, we th ..."
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Cited by 10 (1 self)
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Abstract. This paper presents a formalization of a library for automata on bit strings in the theorem prover Isabelle/HOL. It forms the basis of a reflectionbased decision procedure for Presburger arithmetic, which is efficiently executable thanks to Isabelle’s code generator. With this work, we therefore provide a mechanized proof of the wellknown connection between logic and automata theory. 1
A Reflexive Formalization of a SAT Solver in Coq
 In Proceedings of TPHOLs
, 2008
"... Abstract. We present a Coq formalization of an algorithm deciding the satisfiability of propositional formulas (SAT). This SAT solver is described as a set of inference rules in a manner that is independent of the actual representation of propositional variables and formulas. We prove soundness and ..."
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Abstract. We present a Coq formalization of an algorithm deciding the satisfiability of propositional formulas (SAT). This SAT solver is described as a set of inference rules in a manner that is independent of the actual representation of propositional variables and formulas. We prove soundness and completeness for this system, and instantiate our solver directly on the propositional fragment of Coq’s logic in order to obtain a fully reflexive tactic. Such a tactic represents a first and important step towards our ultimate goal of embedding an automated theorem prover inside the Coq system. We also extract a certified Ocaml implementation of the algorithm. 1
Experiments with Finite Tree Automata in Coq
, 2001
"... Tree automata are a fundamental tool in computer science. We report on experiments to integrate tree automata in Coq using shallow and deep reflection techniques. While shallow reflection seems more natural in this context, it turns out to give disappointing results. Deep reflection is more diffi ..."
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Cited by 6 (2 self)
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Tree automata are a fundamental tool in computer science. We report on experiments to integrate tree automata in Coq using shallow and deep reflection techniques. While shallow reflection seems more natural in this context, it turns out to give disappointing results. Deep reflection is more difficult to apply, but is more promising.
Verifying haskell programs by combining testing and proving
 In Proceedings of the Third International Conference on Quality Software
"... We propose a method for improving confidence in the correctness of Haskell programs by combining testing and proving. Testing is used for debugging programs and specification before a costly proof attempt. During a proof development, testing also quickly eliminates wrong conjectures. Proving helps u ..."
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Cited by 4 (0 self)
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We propose a method for improving confidence in the correctness of Haskell programs by combining testing and proving. Testing is used for debugging programs and specification before a costly proof attempt. During a proof development, testing also quickly eliminates wrong conjectures. Proving helps us to decompose a testing task in a way that is guaranteed to be correct. To demonstrate the method we have extended the Agda/Alfa proof assistant for dependent type theory with a tool for random testing. As an example we show how the correctness of a BDDalgorithm written in Haskell is verified by testing properties of component functions. We also discuss faithful translations from Haskell to type theory.
Experiments with finite tree automata in Coq
 In Proc. 14th Int. Conf. Theorem Proving in Higher Order Logics (TPHOL’01), volume 2152 of LNCS
, 2001
"... Abstract. Tree automata are a fundamental tool in computer science. We report on experiments to integrate tree automata in Coq using shallow and deep reflection techniques. While shallow reflection seems more natural in this context, it turns out to give disappointing results. Deep reflection is mor ..."
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Abstract. Tree automata are a fundamental tool in computer science. We report on experiments to integrate tree automata in Coq using shallow and deep reflection techniques. While shallow reflection seems more natural in this context, it turns out to give disappointing results. Deep reflection is more difficult to apply, but is more promising. 1
A High Level Reachability Analysis using Multiway Decision Graph in the HOL Theorem Prover
"... Abstract. In this paper, we provide all the necessary infrastructure to define a high level states exploration approach within the HOL theorem prover. While related work has tackled the same problem by representing primitive BDD operations as inference rules added to the core of the theorem prover, ..."
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Abstract. In this paper, we provide all the necessary infrastructure to define a high level states exploration approach within the HOL theorem prover. While related work has tackled the same problem by representing primitive BDD operations as inference rules added to the core of the theorem prover, we have based our approach on the Multiway Decision Graphs (MDGs). We define canonic MDGs as wellformed directed formulae in HOL. Then, we formalize the basic MDG operations following a deep embedding approach and we derive the correctness proof for each operation. Finally, a high level reachability analysis is implemented as a tactic that uses our MDG theory within HOL. 1
Testing and Proving in Dependent Type Theory (Part II: Verifying Haskell Programs by Combining Testing and Proving)
 CHALMERS UNIVERSITY OF TECHNOLOGY AND GOTEBORG UNIVERSITY
, 2003
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Reflecting Symbolic Model Checking in Coq
, 2000
"... We describe an implementation and a proof of correctness of a symbolic model checker for the calculus using BDDs, completely formalized in the Coq proof assistant. This gives us a certified model checker which can run as a subsystem of Coq and provides a safe way of integrating symbolic model chec ..."
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We describe an implementation and a proof of correctness of a symbolic model checker for the calculus using BDDs, completely formalized in the Coq proof assistant. This gives us a certified model checker which can run as a subsystem of Coq and provides a safe way of integrating symbolic model checking techniques inside the Coq proof assistant. Coq's extraction mechanism also gives us a certified model checker running in Caml.
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"... Mémoire de stage pour obtenir le diplome de master 2 recherche de l’université de ParisSud 11 ..."
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Mémoire de stage pour obtenir le diplome de master 2 recherche de l’université de ParisSud 11