C. Parent. Developing certified programs in the system Coq: The program tactic. BRA Workshop Types for Proofs and Programs, May 93.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....have been found, which do not correspond to intuitionistic ones. 4.11 Developing certified program This section is devoted to powerful tools that Coq provides to develop certified programs. We just mention below the main features of those tools and refer the reader to chapter 14 and references [72, 73] for more details and examples. 60 4.11.1 Realizer Fwterm. This command associates the term Fwterm to the current goal. The Fwterm s syntax is described in the chapter 14. It is an extension of the basic syntax for Coq s terms. The Realizer is used as a hint by the Program tactic described ....

C. Parent. Developing certified programs in the system Coq- The Program tactic. Technical Report 93-29, Ecole Normale Sup'erieure de Lyon, October 1993. Also in [6].

....section when specifying the type regexp: mixing logical and informative aspects in a single definition keeps it closer to the mathematical point of view. These two approaches may be mixed, however, in a more flexible methodology, implemented in the system Coq as the Program tactic by C. Parent [13, 14]. The idea is to keep the abstract specification S 0 , but to have the possibility to give the expected program f to construct its proof. All the informative part of the proof can be automatically constructed from f , leaving the logical goals to the user. The extraction of the final proof is ....

C. Parent. Developing certified programs in the system Coq- The Program tactic. Technical Report 93-29, Ecole Normale Sup'erieure de Lyon, October 1993. also in Proceedings of the BRA Workshop Types for Proofs and Programs, may 93.

....proof of S [p] Actually, it is possible to automatically construct some parts of using p, in such a way that there only remain some logical goals, called the proof obligations. This methodology has been implemented in the Coq Proof Assistant and is called the Program tactic; it is described in [12]. 1.3 How do they relate Even though the first approach deals with imperative programs and the second with functional ones, they may be related. Indeed, let us interpret the total correctness formula fPg p fQg for an imperative program p, as the proposition P (x) 9y:Q(y) in the CIC, where x ....

C. Parent. Developing certified programs in the system Coq -- The Program tactic. Technical Report 93-29, Ecole Normale Sup'erieure de Lyon, October 1993. Also in Proceedings of the BRA Workshop Types for Proofs and Programs, may 93.

....S holds, hence one can obtain a certified program from a proof of its specification. This facility is supported by the Coq system which provides a package which extracts an ML program from a proof term, as well as providing support for proving the specification of functions written in an ML syntax [20, 19, 21]. 2. Extracting proof texts written in a natural language: A proof term of type can be seen as an account of the proof steps involved in deriving the theorem , and Coq provides tools for extracting a proof written in a natural language from proof objects [6] 3. Independent proof checking: ....

C. Parent. Developing certified programs in the system Coq - the Program tactic. In H. Barendregt and T. Nipkow, editors, International Workshop on Types for Proofs and Programs, volume 806 of Lecture Notes in Computer Science, pages 291--312. Springer-Verlag, May 1993.

....and constructive type theories but instead focus on the practical application of these ideas. Some steps have been taken towards such a connection. Howe has developed a modified semantics for Nuprl to allow HOL theorems to be used within Nuprl proofs [6] Coq s Program tactic, described in [11, 12], provides automatic assistance for program verification. The approach described there can be viewed as the inverse of the program extraction process and is related to the discussion below in section 3.1. Another comparison of a constructive proof with its classical counterpart can be found in ....

C. Parent. Developing certified programs in the system Coq- The Program tactic. In H. Barendregt and T. Nipkow, editors, Types For Proofs and Programs, volume 806 of LNCS, pages 291--312, May 1993.

....paper, we focus on the inverse problem. We want to retrieve a proof from an extracted program. Obviously, there is no hope to synthesize all the forgotten proofs but our goal is to synthesize at least the types of the missing proofs. This approach has already been formulated in a precedent paper [Par93] This previous version was only an empirical explanation of a tactic implemented in Coq. In this paper, we present a more rigorous explanation. In fact, logical informations can be retrieved from a program and the main part of the proof can be reconstructed. A recurrence in the program ....

....restrictions on the proof system have to be made. Given a program p that is exactly a trace of a proof P , it can be proved that the generated logical lemmas have a proof in P . This method is the basis of an effective heuristic method corresponding to a tactic in the Coq system described in [Par93] This heuristic method considers strong extracted programs and synthesizes types by unification from the initial specification. The plan is in three main parts. First, we present the Calculus of Inductive Constructions and the extraction of [PM89b] Secondly, we show the weak extraction, why and ....

[Article contains additional citation context not shown here]

C. Parent. Developing certified programs in the system Coq - The Program tactic. In H. Barendregt and T. Nipkow, editors, Types For Proofs and Programs, volume 806 of LNCS, pages 291--312, May 1993.

....have been found, which do not correspond to intuitionnistic ones. 4.10 Developing certified program This section is devoted to powerful tools that Coq provides to develop certified programs. We just mention below the main features of those tools and refer the reader to chapter 12 and references [60, 61] for more details and examples. 4.10.1 Realizer Fwterm. This command associates the term Fwterm to the current goal. The Fwterm s syntax is described in the chapter 12. It is an extension of the basic syntax for Coq s terms. The Realizer is used as a hint by the Program tactic described below. ....

C. Parent. Developing certified programs in the system Coq- The Program tactic. Technical Report 93-29, Ecole Normale Sup'erieure de Lyon, October 1993. Also in Proceedings of the BRA Workshop Types for Proofs and Programs, may 93.

....It would be nice to consider more natural programs, that is, programs with fewer specifications. In fact, we would like the programmer to write F Ind programs and the method to use unification to retrieve subspecifications. This is the goal of a tactic implemented in Coq and presented in [Par93, Par95b, Par95a] This heuristic approach should follow the same method as the deterministic method, but the use of unification introduces non determinism. Nevertheless, we introduce annotations in F Ind programs that the heuristic method could use and that allow keeping a certain notion of ....

....method, but the use of unification introduces non determinism. Nevertheless, we introduce annotations in F Ind programs that the heuristic method could use and that allow keeping a certain notion of completeness. We describe some heuristics and optimizations. We refer the reader to [Par93, Par95a] for further details. A notion of typing is always necessary since we want to be able to check if the program and its specification are coherent (for this, we need to compare the type of the program and the specification) This typing is a little different from 2. We define in definition ....

[Article contains additional citation context not shown here]

C. Parent. Developing certified programs in the system Coq - The Program tactic. In H. Barendregt and T. Nipkow, editors, Types For Proofs and Programs, volume 806 of LNCS, pages 291--312, May 1993.

....Inductive Constructions [Coq85, Coq89] and a particular implementation that is the Coq system [CCF 94] Programs can be extracted from proofs, but an other possible way is to synthesize proofs from programs. This consists in inverting the program extraction of [PM89a] and has been detailed in [Par93, Par95a, Par95b] given a specification and a functional program, it is possible to reconstruct a proof of the specification whose algorithmic contents corresponds to the given program. This problem is clearly undecidable. The best way is to generate proof obligations on atomic parts of the ....

C. Parent. Developing certified programs in the system Coq - The Program tactic. In H. Barendregt and T. Nipkow, editors, Types For Proofs and Programs, volume 806 of LNCS, pages 291--312, May 1993.

....It contains a specification language and a programming language. By the Curry Howard isomorphism , a proof can be represented by a typed term whose type is the proposition that it proves. In the Calculus of Inductive Constructions, the specification of a program is regarded as a proposition. In [Par93] we described an implemented method that generates proof obligations from a program and a specification. Here, we give a theoretical description of this method. More precisely, a new extraction function called the weak extraction is defined. The strong extraction applies on terms and types. It ....

....restrictions on the proof system have to be made. Given a program p that is exactly a trace of a proof P , it can be proved that the generated logical lemmas have a proof in P . This method is the basis of an effective heuristic method corresponding to a tactic in the Coq system described in [Par93, Par95] This heuristic method considers strong extracted programs and synthesizes types by unification from the initial specification. The plan is in three main parts. First, we present the Calculus of Inductive Constructions and the extraction of [PM89b] Secondly, we show the weak extraction, ....

[Article contains additional citation context not shown here]

C. Parent. Developing certified programs in the system Coq - The Program tactic. In H. Barendregt and T. Nipkow, editors, Types For Proofs and Programs, volume 806 of LNCS, pages 291--312, May 1993.

No context found.

C. Parent. Developing certified programs in the system Coq: The program tactic. BRA Workshop Types for Proofs and Programs, May 93.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC