Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....or integrated environment for each of them. Three research groups of the tosca project, in Milano, Pisa and Udine, have been actively involved in the area of metalanguages and metamodels developing and experimenting cospan span categories, tile logic (tl) 14, 4] and logical frameworks (e.g. lf) [15, 27], respectively. We refer the reader to [13] for a comparison between the two rst metamodels. In this paper, we discuss tile logic and logical frameworks. The foundations of both metamodels are by now well established, various tools based on them are available (e.g. 19, 7] and several case ....

Pfenning, F., The practice of Logical Frameworks, in: Proc. CAAP'96, LNCS 1059 (1996), pp. 119-134.

....be the type of datatypes, such as naturals, lists, trees, booleans, etc. These types di#er from those inhabiting Prop for their constructive contents. Therefore, CC, as many similar Type Theories, can be fruitfully used as a general logic specification language, i.e. as a Logical Framework (LF) [ 8,18, 19]. In an LF, following the judgment as types paradigm, we can represent faithfully and uniformly all the relevant concepts of the inferential process in a logical system (syntactic categories, terms, variables, contexts, assertions, axiom schemata, rule schemata, instantiation, tactics, etc. ....

F. Pfenning. The practice of Logical Frameworks. In Proc. CAAP'96, LNCS 1059, pages 119--134. Springer-Verlag, April 1996.

....daunting task of implementing a specific proof assistant or integrated environment for each of them. Our research groups in Pisa and Udine have been actively involved in the area of metalanguages and metamodels developing and experimenting tile logic (tl) 13, 4] and logical frameworks (e.g. lf) [14, 26], respectively. The foundations of both metamodels are by now well established, various tools based on them are available (e.g. 18, 7] and several case studies concerning widely used calculi and programming paradigms have been carried out. The two approaches have been developed separately and ....

Pfenning, F., The practice of Logical Frameworks, in: Proc. CAAP'96, LNCS 1059 (1996), pp. 119--134.

....with n interpretations. This is therefore a rather static approach, where neither a proof theory nor a model theory is involved. All of the above mentioned approaches can be represented in Reflective Prolog, which in turn is a particular instantiation of RCL as shown in Section 6.1. Pfenning [58] calls logical frameworks a metalanguage for the specification of deductive systems, and argues that: Logical frameworks are subject to the same general design principles as other programming or specification languages. They should be as simple and uniform as possible, yet they should provide ....

F. Pfenning. The practice of logical frameworks. In H. Kirchner, editor, Trees in Algebra and Programming - CAAP '96, LNCS 1059, pages 119--134, Linkoping, Sweden, 1996. Springer--Verlag.

....can easily be done in Feferman s FS 0 . Moreover: in this framework the availability of the simplest operation suffices for having all types of inductive definitions (and corresponding inductive principles) 1 Introduction One of the most serious drawbacks of the LF style Logical Frameworks ([7, 1, 8]) is their inability to prove metatheorems about encoded systems in a direct way (if at all) Meta level reasoning is, however, very important in mathematical discourse. Many theorems concerning a mathematical theory are not theorems of the theory, but theorems about the theory. Such theorems are ....

....Moreover, the use of inductively defined classes and predicates is crucial for logical frameworks. Indeed, in [9, 10] it is 1 taken to be their characteristic feature, and Feferman s framework FS 0 ( 4] is based on this observation. It is no wonder, therefore, that in the survey paper [8] it is stated that An important challenge for logical frameworks is to reconcile induction principles with higher order syntax . The main thesis of this paper is that the concept of transitive closure is the key for understanding inductive definitions and inductive reasoning, and so the ability ....

Pfenning F., The Practice of Logical Frameworks, in H. Kirchner (ed.): Proceedings of the Colloquium on Trees in Algebra and Programming, Linkvping, Sweden, April 1996, Springer-Verlag LNCS 1059, pp. 119-134.

....semantic ideas could help there. The calculus could provide a foundation for other specification based formalisms, and we will make some specific suggestions below. 6.1. 1 Refinement Terms We would be interested to see how this calculus might be usefully combined with work on logical frameworks [Pfe96] The use of logical variables there is an example of underdeterminism. Although Lego has a richer type system than those studied here, a fragment of it could be studied using # as a metalanguage. It would be interesting to use # as a metalanguage for giving a semantics to Lego and to prove ....

Frank Pfenning. The practice of logical frameworks. In Helene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, volume 1059 of Lecture Notes in Computer Science, pages 119--134, 1996. Invited talk.

....be the type of datatypes, such as naturals, lists, trees, booleans, etc. These types di#er from those inhabiting Prop for their constructive contents. Therefore, CC, as many similar Type Theories, can be fruitfully used as a general logic specification language, i.e. as a Logical Framework (LF) [13,23,24]. In an LF, we can represent faithfully and uniformly all the relevant concepts of the inferential process in a logical system (syntactic categories, terms, variables, contexts, assertions, axiom schemata, rule schemata, instantiation, tactics, etc. 3 The Calculus of Inductive Constructions ....

F. Pfenning. The practice of Logical Frameworks. In Proc. CAAP'96, number 1059 in Lecture Notes in Computer Science, pages 119--134. Springer-Verlag, April 1996.

....believe that working inside OLF greatly simplifies our proof. Of course such simplification comes at the cost of gaining familiarity with OLF. However, we feel the trade off is advantageous. Logical frameworks have generally proven themselves to be useful tools for studying programming languages [Pfe96] and we believe OLF, though still a new formalism, will likewise prove itself useful. 1.1 Overview Section 2 introduces the ordered logical framework in which we will represent our terms and transform. In section 3.2 we define direct style terms with exception raise and handle expressions, CPS ....

Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. SpringerVerlag LNCS 1059. Invited talk.

....result. Our interest is on this practical side, and a development of our work on applications of logical frameworks, i.e. formal notations providing support for the uniform implementation of different logics, based on fragments of higherorder implicational logic and suitable in particular for ND [19, 28, 30, 38]. We address the problem of how to present families of related non classical logics so as to be suitable for such implementations. The problem is not trivial: these logics are usually presented as Hilbert systems and, even if a presentation is an ND system, it is often specialized, and ....

F. Pfenning. The practice of logical frameworks. In Proceedings of CAAP'96, Linkoping, Sweden, 1996.

.... for consequences of structured specifications in Spec I (homogeneous specifications built over I) Of course, it is not very realistic to expect all the nice features of UI mentioned above to be immediately available but with the development of universal logical frameworks (see e.g. Pfenning, 1996 ] for an excellent annotated bibliography) this way of proceeding and this line of research becomes more and more important. The two assumptions about representations considered (totality and amalgamation) turn out not to be a major problem in practice. Moreover, some standard ways of building ....

Frank Pfenning. The practice of logical frameworks. In H. Kirchner, editor, Proc. 20th Coll. on Trees in Algebra and Computing CAAP'96, volume 1059 of Lecture Notes in Computer Science, pages 119-- 134. Springer Verlag, 1996.

....Sieg; c fl Kluwer Academic Publishers. simply as a practically usable notation for formal derivation, which provides the deduction theorem directly, rather than as a metatheorem. Our work is on the practical, not the philosophical, side: we are interested in exploiting logical frameworks [26, 34, 39, 41], i.e. formal notations providing support for the uniform implementation of different logics, which are particularly suitable for ND. Specifically, we address the problem of how to present families of non classical logics so that they can be implemented in a logical framework in a usable way. The ....

F. Pfenning. The practice of logical frameworks. In H. Kirchner, editor, Proceedings of CAAP'96, LNCS 1059, pages 119--134. Springer, Berlin, 1996.

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Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

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Frank Pfenning. The practice of logical frameworks. In Helene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119{ 134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

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Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

No context found.

Frank Pfenning. The practice of logical frameworks. In Helene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

No context found.

Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

No context found.

Frank Pfenning. The practice of logical frameworks. In Helene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119-- 134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

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Pfenning, Frank. (April 22-24 1996). The practice of logical frameworks. In Trees in Algebra and Programming - CAAP'96, 21st International Colloquium, volume 1059 of LNCS, pages 119-- 134, Link oping, Sweden.

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Frank Pfenning. The practice of logical frameworks. In Helene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

....hand, it provides a conceptual tool for the concise definition and rigorous reasoning about programming languages and logics; on the other hand, it significantly reduces the effort required to actually implement deductive systems. There are various styles of logical frameworks (see, for example, [Pfe96]) with different strengths and weaknesses. Our starting point is the logical framework LF [HHP93] which supports variable binding and capture avoiding substitution through higher order abstract syntax, and parametric and hypothetical judgments through dependently typed functions. In previous work, ....

Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

.... Meta Theorems in a Logical Framework A Dissertation Proposal Raymond McDowell Department of Computer and Information Science University of Pennsylvania November 1996 Dissertation Advisor: Dale Miller, University of Pennsylvania Dissertation Committee: Jean Gallier, University of Pennsylvania Carl Gunter, University of Pennsylvania Frank Pfenning, Carnegie Mellon University Val Tannen, University of Pennsylvania (chair) 1 Abstract We investigate ....

....methodology for such reasoning. To set the stage for our work, we provide a brief introduction to higher order abstract syntax and a selective overview of research in logical frameworks. We refer the reader to [35, 17] for a more comprehensive discussion of higher order abstract syntax and to [34] for a broader survey of logical frameworks. 1.1 Higher Order Abstract Syntax The key idea of higher order abstract syntax is that variable binding in the object language is represented by abstraction of the meta language. For example, consider the simple functional language whose terms are ....

[Article contains additional citation context not shown here]

Frank Pfenning. The practice of logical frameworks. In H. Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, volume 1059 of Lecture Notes in Computer Science, pages 119--134. Springer-Verlag, April 1996.

.... theory Pi , relies on the judgments as types representation methodology, and has been implemented as the higher order constraint logic programming language Elf [Pfe91, Pfe94a] LF and Elf have been widely used to study logical formalisms [Pfe95] and programming languages [MP91, Pfe92] see [Pfe96] for a survey) Unfortunately, many constructs and concepts needed in common programming practice cannot be represented in a satisfactory way in meta languages based on intuitionistic logic and intuitionistic type theory, such as LF . In particular, constructs based on the notion of state as ....

Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

....hand, it provides a conceptual tool for the concise definition and rigorous reasoning about programming languages and logics; on the other hand, it significantly reduces the effort required to actually implement deductive systems. There are various styles of logical frameworks (see, for example, [Pfe96]) with different strengths and weaknesses. Our starting point is the logical framework LF [HHP93] which supports variable binding and capture avoiding substitution through higher order abstract syntax, and parametric and hypothetical judgments through dependently typed functions. In previous work, ....

Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

....for representing deductive systems which are common in the study of logics and programming languages. It allows concise encodings of many common inference systems, such as natural deduction and sequent calculi, type systems, operational semantics, compilers, abstract machines, etc. see [Pfe96] for a survey) These representations often lead directly to implementations, either via the constraint logic programming paradigm [Pfe94] or via general search using tactics and tacticals. The logical framework derives its expressive power from the use of dependent types together with ....

....[Roh94,RP96] implements meta theoretic proofs as relations whose This work was sponsored by NSF Grant CCR 9619584 1 See [DPS97] for a detailed analysis. operational reading as logic programs realizes the informal proofs. This has been applied successfully in many case studies (see [Pfe96]) but lacks automation. The second is based on reflection via a modal provability operator. At present it is unclear how this idea, developed for simple types in [DPS97] interacts with dependent types, and if it is flexible enough for many of the theorems that can be treated with ....

[Article contains additional citation context not shown here]

Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119-- 134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

....to lemmas and the restriction to reasoning only about closed expressions. We are presently extending both the meta logic M 2 and its implementation to overcome these limitations. Example Suites. Twelf has been employed for a number of experiments in the area of programming languages and logics [Pfe96]. Many of these are contained in the example suite which is distributed with the Twelf system. Some of the examples contain fully automated proofs, others only their implementations as higher level judgments. One of the most well developed case studies is Mini ML. We prove value soundness, type ....

Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

....from the meta level abstractions and we use in our logical framework representation. Since our investigation is based on a one pass CPS transformation, the language above does not contain administrative redices. In the methodology of logical frameworks using higher order abstract syntax (see [Pfe96] for a survey) expressions from an object language are represented as terms in a calculus using constants as constructors. Object language variables are represented as variables in the meta language, which means that the scope of variables bound in the object language must be delimited by ....

Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

....for representing deductive systems which are common in the study of logics and programming languages. It allows concise encodings of many common inference systems, such as natural deduction and sequent calculi, type systems, operational semantics, compilers, abstract machines, etc. see [Pfe96] for a survey) These representations often lead directly to implementations, either via the constraint logic programming paradigm [Pfe94] or via general search using tactics and tacticals. The logical framework derives its expressive power from the use of dependent types together with ....

....Grant CCR 9619584. To appear at CADE 15. logical framework can offer. The first called schema checking [Roh94,RP96] implements meta theoretic proofs as relations whose operational reading as logic programs realizes the informal proofs. This has been applied successfully in many case studies (see [Pfe96]) but lacks automation. The second is based on reflection via a modal provability operator. At present it is unclear how this idea, developed for simple types in [DPS97] interacts with dependent types, and if it is flexible enough for many of the theorems that can be treated with ....

[Article contains additional citation context not shown here]

Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

....systems, namely those dealing with state. As an example we encode a version of Mini ML with mutable references including its type system and its operational semantics, and describe how to take practical advantage of the representation of its computations. 1 Introduction A logical framework [Pfe96] is a formal meta language specifically designed to represent and reason about programming languages, logics and other formalisms that can be described as deductive systems. These frameworks consist of a meta representation language with desirable computational and representational properties, ....

Frank Pfenning. The practice of logical frameworks. In H'el`ene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134, Linkoping, Sweden, April 1996. Springer-Verlag LNCS 1059. Invited talk.

No context found.

Frank Pfenning. The practice of logical frameworks. In Helene Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, pages 119--134. LNCS 1059 Springer-Verlag, 1996.

No context found.

Pfenning, F., The practice of Logical Frameworks, in: Proc. CAAP'96, Lecture Notes in Computer Science 1059 (1996), pp. 119--134.

No context found.

Pfenning, F.: The practice of logical frameworks. In Kirchner, H., ed.: Trees in Algebra and Programming - CAAP '96. LNCS 1059, Linkoping, Sweden, Springer-- Verlag (1996) 119--134

No context found.

Frank Pfenning. The practice of logical frameworks. In H. Kirchner, editor, Proceedings of the Colloquium on Trees in Algebra and Programming, volume 1059 of Lecture Notes in Computer Science, pages 119--134, Springer-Verlag, 1996.

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