L.C. Paulson. Isabelle: A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer, Berlin, 1994. 14  Home/Search   Document Not in Database   Summary   Related Articles   Check

....These logical theories are in a format that can serve as input for theorem provers, which can then be used to prove properties of the Java program, thus achieving a high level of reliability for this program. Currently the LOOP tool supports output for the theorem provers PVS [16] and Isabelle [17]. This approach to veri cation of Java has demonstrated its usefulness for instance with the proof of a non trivial invariant for the Vector class in the standard Java API [7] The LOOP tool is currently being extended to JML, so that it can be used to verify JML annotated Java source code. We ....

L.C. Paulson. Isabelle: A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer, 1994.

....and proof strategy into mathematical logic, often a very tedious task. Our approach is to implement a simple proof checker where the results from specialized verification tools can be combined to produce a complete proof. Similar to theorem proving environments such as ACL2, HOL, ISABELLE or PVS [13, 10, 19, 18], a (backwards style) proof in our proof checker is represented as a sequence of proof states. A proof state in turn is implemented by an abstract data type, and consists essentially of a formula (the claim) a list of formulas (the pending obligations) as well as some book keeping information. ....

....systems for general purpose logics such has first or higher order predicate logic: ffl The core functionality of the checker, such as the handling of proof states and theorems, is parameterized with respect to the syntax of formulas in a logic and its inference rules. In contrast to ISABELLE [19], where different object logics are embedded in the system s meta logic, we use a simpler and more general, but less formal approach: The syntax of a logic is represented by an abstract data type and a function that recognizes well formed formulas; inference rules are implemented as functions on ....

L. C. Paulson. Isabelle: A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1994.

....of formal proofs for UNITY programs has been mechanized using various theorem proving environments. Anderson s HOL UNITY [2] is an implementation of UNITY using the HOL system [6] Heyd and Cregut s CoqUNITY [8] uses Coq, and Paulson has implemented UNITY within the Isabelle environment [15, 16]. While these implementations provide assistance in proof generation for UNITY programs, they do not generate executable code. 2 The UNITY Formalism The UNITY formalism consists of both a programming language (with accompanying execution model) and a proof logic. In this paper we are primarily ....

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

....by an integrated theorem prover. The construction of formal proofs for UNITY programs has been mechanized using various theorem proving environments. Anderson s HOL UNITY [2] is an implementation of UNITY using the HOL system [6] and Paulson has implemented UNITY within the Isabelle environment [15, 16]. While these implementations provide assistance in proof generation for UNITY programs, they do not generate executable code. 2 The UNITY Formalism The UNITY formalism consists of both a programming language (with accompanying execution model) and a proof logic. We briefly describe both, though ....

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

....21 01 1998; 10:09; no v. p.3 4 F. Bartels et al. It seems to be more desirable, however, to prove domain theoretic facts once and for all and to encode these facts as type information of the underlying system. In this way, Regensburger [16] 17] extends the Hol object logic of Isabelle [14] with domain theoretic notions by employing Isabelle s type class mechanism, which permits a fine grained use of polymorphism. On the other hand, the expressiveness of type classes is restricted since dependencies between type class parameters can not be expressed. Instead of type classes, we use ....

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

....their application in software veri cation. One part of the project was the design of the Coalgebraic Class Speci cation Language ccsl [HHJT98] and the implementation of a compiler that translates ccsl speci cations into logical theories of the theorem prover pvs [ORR 96, ORSvH95] or isabelle [Pau94] The theorem prover can then be used to reason about speci cations, especially to establish re nements between speci cations and to create models. Currently commercially successful operating systems like Unix and Windows are monolithic systems of considerable size. Most of the operating system ....

....version 2 is under development. The ccsl compiler is not publicly available (this is mostly due to the lack of manpower to develop a stable version of the compiler) The ccsl compiler acts as a frontend to an existing theorem prover. Currently it supports pvs [ORR 96, ORSvH95] and isabelle [Pau94] It accepts class speci cations in ccsl, Java, and the Java annotation language JML [LBR99] The ccsl compiler translates all its input class speci cations into equivalent speci cations in the logic of the theorem prover. These can then be loaded into isabelle or pvs, together with statements ....

L. C. Paulson. Isabelle: A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer, Berlin, 1994.

....before it is passed to a tool. Still, the Workbench provides an excellent framework for hiding such technicalities, since the specifications are treated as logical objects, and the conversions will happen behind the scenes whenever possible. 4 Isabelle, HOL Z and IsaWin In short, Isabelle [23] is a generic tactical LCF theorem prover. Here, generic means that it is particularly suited for the encoding of different logics and formal methods, tactical means that it offers user programmable proof support, and the LCF design means that the prover is centred around an abstract data type ....

L. C. Paulson. Isabelle - A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer Verlag, 1994.

....object oriented languages 1 . ccsl allows the (coalgebraic) speci cation of behavioral types or classes of object oriented languages. It uses higher order logic with universal modal operators to restrict the behavior of objects. A front end to the theorem provers pvs [ORR 96] and isabelle [Pau94] compiles ccsl speci cations into the logic of these theorem provers and allows to mechanically reason about the speci cations. Categories: D.2.4 D.2.1 F.3.1 F.4.1 (ACM 98) 1 Introduction The use of coalgebras as semantics for object orientation (explicitly proposed in [Rei95] is for us the ....

L. C. Paulson. Isabelle: A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer, Berlin, 1994.

....tests are minimal, hand tailored axiomatizations) so that these systems show a nonmonotonic characteristic in the sense that they are no longer capable of proving some theorems if further (irrelevant) axioms are added. In interactive systems, structured theories are more commonly used. Isabelle [15, 16], HOL [8] and IMPS [6, 4] for instance use a layered approach to knowledge bases (cf. little theories in IMPS [5] Theories, however, are in a sense atomic, so that for a proof one must either explicitly enter a theory and use its methods solely, or gets the sum of all theories logically ....

Lawrence C. Paulson, Isabelle, number 828 in Lecture Notes in Computer Science, Springer Verlag, 1994.

....This note presents the Coalgebraic Class Specification Language CCSL that is developed within the LOOP project 1 . CCSL allows the (coalgebraic) specification of behavioral types or classes from object oriented languages. A front end to the theorem provers PVS [ORR 96] and ISABELLE [Pau94] compiles CCSL specifications into the logic of the theorem provers and and allows to mechanically reason about the specifications. 1. Introduction The use of coalgebras as semantics for object orientation (explicitly proposed in [Rei95] is for us the most promising approach towards ....

L. C. Paulson. Isabelle: A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer, Berlin, 1994.

....of the typed lambda calculus used by Isabelle. Next the pure Isabelle system is described and it is explained how the pure Isabelle system is extended to support reasoning in HOL and ZF. 3.1 Documentation The Isabelle system is extensively documented. The main reference is the Isabelle Book [8]. This book contains most the information found in the three technical reports [9, 5, 4] References will only be made to these reports if the information cannot be found in the Isabelle book. A number of other papers and reports discuss Isabelle and related issues and will be mentioned when ....

....; m ; OE i 1 ; OE n ] OE)s ( s j OE i s) 8 Here 1 i n and s is a higher order unifier of and OE. A big machinery is connected with resolution and higher order unification. This includes schematic variables, lifting over formulae and variables etc. For the details refer to [8]. 3.4.3 Proofs It is possible to construct proofs both in a forward and backward fashion in Isabelle. Bigger proofs are however usually constructed backwards. In Isabelle, a backwards proof is done by refining a proof state, until the desired result is proved. A proof state is simply a ....

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

....components, such as editors, pretty printers, and tables for storing theorems, provide services that make the system user friendly. Alternatively, we may implement an automated deduction system for a logic by encoding it as an object logic of a logical framework, such as Twelf [10, 9] or Isabelle [8]. With this approach, we implement a deduction system by inherting all the components of the logical framework. Clearly, implementing an automated deduction system using a logical framework is easier than implementing it using a general purpose language. However, an automated deduction system ....

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

....supports a larger class of specifications, using PVS to discharge proof obligations. Since PAMELA provides its own interface, communication between PVS and another system seems to be feasible and some experience is available. Simons [12] has been working on a system to combine proofs in Isabelle [8] with documentation. The system uses the structured documentation technique introduced by Knuth [6] to allow one file to contain both the proofs and the documentation and uses programs to separate those. This solves the problem of combining several files into one document, at the expense of using ....

Lawrence C. Paulson. Isabelle: a Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer -- Berlin, 1994.

....documents. That approach is also used by FrameMaker and Word, which are not the best word processors for mathematically oriented documents, as they have problems with context switches and treat mathematical expressions as images. Simons has been working on a system to combine proofs in Isabelle[15] with documentation[19] The system uses the structured documentation technique introduced by Knuth[12] to allow one le to contain both the proofs and the documentation and uses programs to separate those. This solves the problem of combining several les into one document, at the expense of ....

Lawrence C. Paulson. Isabelle: a Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer { Berlin, 1994.

....are proved behind the scenes to support this view. It seems to be more desirable, however, to prove domain theoretic facts once and for all and to encode these facts as type information of the underlying system. In this way, Regensburger [Reg94, Reg95] extends the HOL object logic of Isabelle [Pau94] with domain theoretic notions by employing Isabelle s type class mechanism. This mechanism permits abstracting developments over mathematical structures like partial orders and domains. Instead of type classes, we use the concept of predicate subtypes to parameterize with respect to mathematical ....

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

....as function extensions and parallel extensions to recursively defined datatypes and tools. The resulting protocols for these operations therefore require the programmer to maintain more complicated invariants than in frameworks that provide native constructs for expressing extensions. Isabelle [28] is a widely used theorem prover development framework. Developers can embed (at shallow or deep levels) object logics into its core meta logic; the core prover engine then operates over the new object logics. Isabelle and our framework have different design goals. Isabelle has been crafted ....

Paulson, L. C. Isabelle : a generic theorem prover. Number 828 in Lecture Notes in Computer Science. Springer-Verlag, Berlin; New York, 1994.

....and computing an optimal set of competitive strategies for the training set. If the training set was representative for the domain, then the computed strategies will also perform well on the whole domain. Concrete applications we envisage are interactive proof systems like ILF [ea97] Isabelle [Pau94] or KIV [Rei92] which use or intend to use automated theorem provers as subroutines. This paper is organized as follows. After some general remarks on strategy parallelism and related approaches in Section 2 we present the strategy allocation problem in Section 3. The Sections 4 and 5 describe ....

Larry C. Paulson. Isabelle: A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science (LNCS). Springer-Verlag, 1994.

....In this paper we have continued our investigations into a Variable Typed Logic of Effects that began in [34, 23, 35, 37, 24] In particular we presented an axiomatization of the base first order theory. In [21] we described an encoding of this logic into the generic proof assistant Isabelle [43]. Encoding the syntax and proof theory of the logic was a relatively painless procedure. Especially when compared with the contortions required for logics of the Hoare and Dynamic ilk [36, 1] Since the semantics of the underlying mk calculus is operational, and the semantics of the logic is ....

Lawrence C. Paulson. Isabelle, A Generic Theorem Prover. Number 82 in Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1994.

....usually carry out multiple steps of inference and use heuristics to determine the inferences to employ. A tactic may construct an entire proof or a portion of a proof. Tactics were first used with the LCF interactive proof system [9] Most interactive theorem provers in existence today use tactics [5, 8, 6, 20, 7, 11]. We believe that parallelism will improve the performance of interactive theorem provers. Previous research has shown employing parallelism in automatic theorem provers has lead to significant speedups. For instance, the parallel version of Otter [14] Roo [13, 24] has near linear speedups for ....

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

....coding theory and Section 5 presents the mechanised proofs. Section 6 reviews important details of the implementation and conclusions follow in Section 7. 2. Interface between Isabelle and Sumit The interface we present is between the prover Isabelle and the computer algebra library Sumit. See [Paulson, 1994] and [Bronstein, 1996a, Bronstein, 1996b] respectively. Clemens Ballarin and Lawrence C. Paulson Extending Provers by Computer Algebra 3 2.1. Isabelle Isabelle is a natural deduction style theorem prover. Proofs are carried out interactively by applying tactics to the proof state and so ....

Lawrence C. Paulson. Isabelle: a generic theorem prover. Number 828 in Lecture Notes in Computer Science. Springer-Verlag, 1994.

....to coding theory and Section 5 presents the mechanised proofs. Section 6 reviews important details of the implementation and conclusions follow in Section 7. 2. Interface between Isabelle and Sumit The interface we present is between the prover Isabelle and the computer algebra library Sumit. See [Paulson, 1994] and [Bronstein, 1996a, Bronstein, 1996b] respectively. Clemens Ballarin and Lawrence C. Paulson Extending Provers by Computer Algebra 3 2.1. Isabelle Isabelle is a natural deduction style theorem prover. Proofs are carried out interactively by applying tactics to the proof state and so ....

Lawrence C. Paulson. Isabelle: a generic theorem prover. Number 828 in Lecture Notes in Computer Science. Springer-Verlag, 1994.

....coding theory and section 5 presents the mechanised proofs. Section 6 reviews important details of the implementation and in section 7 we draw conclusions. 2 Interface between Isabelle and Sumit The interface we present is between the prover Isabelle and the computer algebra library Sumit. See [Paulson, 1994] and [Bronstein, 1996] respectively. 2.1 Isabelle Isabelle is a natural deduction style theorem prover. Proofs are carried out interactively by the user by applying tactics to the proof state and so replacing subgoals by simpler ones until all the subgoals are proved. Isabelle provides tactics ....

Lawrence C. Paulson. Isabelle: a generic theorem prover. Number 828 in Lecture Notes in Computer Science. Springer-Verlag, 1994.

....[14, 8, 10] which is a widely used commercial tool environment that supports a range of development activities, including source level execution debugging and code generation to C . We try to combine the benefits of this toolset with the benefits of the generic theorem prover Isabelle 3 [15] in a single system. Constructing a theorem prover for VDMSL from scratch is a far too time consuming task, and systems like Isabelle are designed to allow fast construction of theorem provers for new logics. Our intended use of the combined tool is mainly for proving type consistency proof ....

....treat the subset supported in Mural, plus let expressions, cases expressions, patterns, enumerated expression, quote types and the character type. 3 Isabelle and VDM LPF The theorem proving component of the proof support tool consists of an instantiation of the generic theorem prover Isabelle [15] with the Logic of Partial Functions (LPF) 5, 7] This instantiation supports a subset of the ISO standard for the VDM SL ASCII notation by exploiting distinguishing features of Isabelle for defining new logics. This section gives an overview of the Isabelle based proof component and motivates ....

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L. C. Paulson. Isabelle: A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer-Verlag, Berlin, 1994.

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L.C. Paulson. Isabelle: A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer, Berlin, 1994. 14

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L.C. Paulson. Isabelle: A Generic Theorem Prover. Number 828 in Lecture Notes in Computer Science. Springer, 1994.

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