Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....rewriting, logic programming and type checking. The generalization to higher order uni cation increases the expressiveness, the applicability and improves the level of abstraction. This explains the interest in higher order systems such as higher order logics and higherorder deduction systems [And86,Pau94,GLM97,And01,Pfe01], higher order (functional) programming languages [BMS80,Tur85,Pau91,Bar90,Bir98] higherorder logic programming languages [Mil91,HKMN95] higher order rewriting [Nip91,Klo92,DJ90] and higher order uni cation [Hue75,Dow01] It is well known that second order uni cation hence higher order uni ....

Lawrence C. Paulson. Isabelle, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

....under interactive guidance of the user. In recent years, especially interactive theorem provers based on higher order logic have matured in such a way, that real world applications have come into their reach. The most widely used verification systems of this type are probably HOL [GM93] Isabelle [Pau94] and PVS [ORR 96] Examples for real world applications include verifications dealing with the AAMP5 microprocessor [MS95] the type system of a subset of Java [NvO98] and various security protocols [BP98] The reason of the success can mainly be found in the expressiveness of higher order ....

....a theory of possibly infinite sequences, which can be used to model the communication histories of I O automata. Furthermore, we will see that a methodology is required in order to combine two of Isabelle s object logics in a fruitful manner, namely Isabelle s version of higher order logic (HOL [Pau94] and its extension to Scott s domain theory (HOLCF [MNOS98, Reg95] Sequences. The formalization of possibly infinite sequences in theorem provers based on higher order logic is an active research area [MN97, DG97, DGM97, CP96, HJ97a, Pau97] In most cases, the motivation is to provide a ....

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Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

....mega s knowledge based proof planning approach and Omega mega s multi strategy proof planner Multi. 2. 1 Knowledge Based Proof Planning Many interactive systems use tactical theorem proving to enable the application of complex and human oriented proof steps (see e.g. Nuprl [8] Isabelle [18]) Tactical theorem proving is based on the notion of a tactic which encapsulates repeatedly occurring sequences of inference steps into macro steps. Proof planning was originally conceived as an extension of tactical theorem proving to enable automated theorem proving on the level of tactics. It ....

Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer, Germany, 1994.

....in logic. The proof checker, originally implemented by inference rules, uses model checking in the later versions. Many researchers advocate semi automated techniques. This is incorporated by tools like Ehdm [RvHO91] SDVS [BILT92] PVS [COR 95] HOL [MT93] or its o#spring Isabelle [Pau94] Here the tool helps organizing and documenting the constructed proof in a reproducible way. Typically the re usage of lemmas (or libraries of them) and high level proof strategies are supported. Moreover, powerful automation can be applied in special cases that occur frequently. For example, ....

Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science (LNCS). Springer--Verlag, New York, NY, USA, 1994. 9

....that arose several times when groups, usually interested in theorem proving, realized that the idea of a deductive system was independent of the language and inference rules it was used on. This paper applies ideas from the Edinburgh Logical Framework [9] and the related Isabelle proof assistant [17]. All languages are coded in higher order logic. Categories of phrases in the grammar of a language are imitated by types of terms of the lambda calculus. The observer and the agent may use different languages. Terms of the agent s language (indicated as table) and the observer s language ....

Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

.... Factorization Theorem was mechanized in Nuprl [6] in 1986 [9] Recently, Th ery compared mechanizations in Coq [4] HOL [7] and PVS [11] of Fermat s Little Theorem [20] We have mechanized Euler Fermat s and Wilson s Theorem in the Higher Order Logic (HOL) of the generic proof assistant Isabelle [12]. The mechanization is included in the latest distribution of Isabelle [10] Substantial parts of other areas of mathematics have also been formalized in Isabelle HOL, e.g. set theory [16] The rest of this paper is organized as follows: In Section 2 we recall some basic facts of number theory ....

....note that we did not utilize Euler Fermat s Theorem. An Inductive Approach to Formalizing Notions of Number Theory Proofs 7 4 Mechanization In this section we give an overview of our mechanization in Isabelle HOL of Euler Fermat s and Wilson s Theorems. Isabelle is a generic proof assistant [12]. Various object logics have been (and can be) formalized by extending Isabelle s meta logic, which is intuitionistic higher order logic. One of the most well developed object logics is Isabelle HOL, formalizing higher order logic. Many substantial results of both mathematics and computer science ....

Lawrence C. Paulson. Isabelle, A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

....logic. The Nuprl system [CAB 86] is based on a constructive system of higher types and universes inspired by the type theories of Martin L of. The Coq system [CH85,DFH 91] also features a similar constructive type theory with impredicative type quanti cation and abstraction. Isabelle [Pau94] is a metalogical framework that uses higher order Horn clauses to represent inference rules. Prolog [NM90] is a similar metalogical framework based on the hereditary Harrop fragment of higherorder logic. There is a general impression that higher order logics are not easily automated. We get a ....

Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

....term rewriting, logic programming and type checking. The generalization to higher order uni cation increases the expressiveness, the applicability and improves the level of abstraction. This explains the interest in higher order systems such as higher order logics and higherorder deduction systems [And86,Pau94,GLM97,And01,Pfe01], higher order (functional) programming languages [BMS80,Tur85,Pau91,Bar90,Bir98] higherorder logic programming languages [Mil91,HKMN95] higher order rewriting [Nip91,Klo92,DJ90] and higher order uni cation [Hue75,Dow01] It is well known that second order uni cation hence higher order uni ....

Lawrence C. Paulson. Isabelle, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994. 45

....verify the properties established about the formal descriptions of the language. A very active team in this eld is the Bali team at University of Munich who is working on a comprehensive study of the Java language, its properties and its implementation [20, 18, 24] using the proof system Isabelle [23]. Other work has been done with the formal method B and the associated tools [3] or at Kestrel Institute using Specware [13, 25] 1.2 A few facts about Coq Coq is a proof system based on type theory [16] and more precisely on the calculus of constructions [4, 5] and its inductive extensions [6, ....

Lawrence C. Paulson and Tobias Nipkow. Isabelle : a generic theorem prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

....mega s knowledge based proof planning approach and Omega mega s multi strategy proof planner Multi. 2. 1 Knowledge Based Proof Planning Many interactive systems use tactical theorem proving to enable the application of complex and human oriented proof steps (see e.g. Nuprl [8] Isabelle [18]) Tactical theorem proving is based on the notion of a tactic which encapsulates repeatedly occurring sequences of inference steps into macro steps. Proof planning was originally conceived as an extension of tactical theorem proving to enable automated theorem proving on the level of tactics. It ....

Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer, Germany, 1994.

....each recursive function. The introduction of well founded recursion using an accessibility principle as used in this paper was described by Nordstr#m in [9] Inductive denitions and inductive types also appear in proof systems based on simply typed higher order logic, such as HOL [6] or Isabelle [13]. Camilleri and Melham provide a package to systematize the denition of inductive relations in the HOL system [8] but this is not powerful enough to describe the notion of accessibility used in this paper. Harrison [7] provides a more practical tool, powerful enough to describe the necessary ....

Lawrence C. Paulson and Tobias Nipkow. Isabelle : a generic theorem prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

....and Wilson. Most of these results have been formalized and mechanized before (most notably using the Boyer Moore Theorem Prover [2, 3, 4, 8] Part of our contribution is to give a coherent presentation of our development, which has been mechanized using the Isabelle HOL theorem proving system [7]. More interesting though, is the way we have formalized important parts of the theorems of Fermat and Wilson. Both use notions of pairing o elements of sets in a one to one manner. We have developed a generalized approach to handle these concepts. Once the machinery is in place, this seems ....

Lawrence C. Paulson. Isabelle, A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

....latter case, the semantics of the source logic is described using the base logic and the desired proof rules are derived by means of lemmas in the base logic. According also to Skakkebk[13] semantic logical frameworks, such as PVS, are to be preferred to syntactic logical ones, such as Isabelle[10], because they can potentially deliver faster results, in the sense that development time is usually shorter. To what concerns a direct syntactic support of the source logic, syntactic logical frameworks are obviously more powerful than semantic logical ones, which often demand quite a bit of ....

Lawrence C. Paulson. Isabelle: a generic theorem prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, New York, NY, USA, 1994.

....proving the theorems that expressed security properties of a system or protocol, an expert user would carefully guide the prover, producing lemmas and narrowly directing the proof search to yield results. More recent theorem proving efforts have used the HOL [GM93] PVS [ORSvH95] and Isabelle [Pau94] verification systems to express and reason about properties of security protocols. These sophisticated verification systems support specifications in higher order logic and allow the user to create custom proof strategies and tactics with which the systems can do more effective automated proof ....

Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

....verify the properties established about the formal descriptions of the language. A very active team in this eld is the Bali team at University of Munich who is working on a comprehensive study of the Java language, its properties and its implementation [15, 13, 19] using the Isabelle proof system [18]. Other work has been done with the formal method B and the associated tools [3] at Kestrel Institute using Specware [8, 20] or in Nijmegen [9, 10] using both PVS [16] and Isabelle. 2 Formalizing the language and type system 2.1 Data types The formalization we studied is based on a very ....

Lawrence C. Paulson and Tobias Nipkow. Isabelle : a generic theorem prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

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Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

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Lawrence C. Paulson. Isabelle: a generic theorem prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag Inc., New York, NY, USA, 1994. 14

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Lawrence C. Paulson and Tobias Nipkow. Isabelle : a generic theorem prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

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Lawrence Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

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Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, New York, 1994.

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Lawrence Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, 1994.

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Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer--Verlag, 1994.

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Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, New York, 1994.

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Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, Berlin, Heidelberg, 1994.

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Lawrence C. Paulson. Isabelle: A Generic Theorem Prover, volume 828 of Lecture Notes in Computer Science. Springer-Verlag, New York, 1994.

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