The practice of logical frameworks

Pfenning, Frank

doi:10.1007/3-540-61064-2_33

Cited by 25 publications

(14 citation statements)

References 60 publications

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“…For n > 0 we proceed with a case analysis of the reduction rules that apply to Ξ (and thus to Ξθ) to show that in fact every reduct of Ξθ is reducible. Most cases follow easily from the induction hypothesis, Definition 19,and Lemmas 7,10,17,18,20,21,and 22. We show the interesting cases below.…”

Section: Lemma 23 For Any Derivationmentioning

confidence: 93%

“…Dependent typed λ-calculi have been used to specify computations in ways analogous to the logic programming setting presented here [22]. Schürmann and Pfenning [26] presented a meta-logic for such a dependent typed λ-terms that can be used to reason about higher-order deductions in ways similar to uses of F Oλ ∆IN [14].…”

Section: Applications Of F Oλ ∆Inmentioning

confidence: 99%

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Cut-elimination for a logic with definitions and induction

McDowell

Miller

2000

Theoretical Computer Science

136

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In order to reason about specifications of computations that are given via the proof search or logic programming paradigm one needs to have at least some forms of induction and some principle for reasoning about the ways in which terms are built and the ways in which computations can progress. The literature contains many approaches to formally adding these reasoning principles with logic specifications. We choose an approach based on the sequent calculus and design an intuitionistic logic F Oλ ∆IN that includes natural number induction and a notion of definition. We have detailed elsewhere that this logic has a number of applications. In this paper we prove the cut-elimination theorem for F Oλ ∆IN , adapting a technique due to Tait and Martin-Löf. This cut-elimination proof is technically interesting and significantly extends previous results of this kind.

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Section: Lemma 23 For Any Derivationmentioning

confidence: 93%

Section: Applications Of F Oλ ∆Inmentioning

confidence: 99%

Cut-elimination for a logic with definitions and induction

McDowell

Miller

2000

Theoretical Computer Science

136

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“…The principal application areas lie in the theory of programming languages and logics, reasoning about specifications, programs, and protocols, and the formalization of mathematics. We refer the interested reader to (Pfenning, 1996) for some further information on applications of logical frameworks. The handbook article (Pfenning, 2001b) provides more detailed development of LF and includes some material on meta-logical frameworks.…”

Section: Resultsmentioning

confidence: 99%

“…The type-theoretic and logic programming approaches were later combined in the Elf language (Pfenning, 1991). At this point, there was a pause in the development of new frameworks, while the potential and limitations of existing systems were explored in numerous experiments (see Pfenning (1996)). The mid-nineties saw renewed activity with implementations of frameworks based on inductive definitions such as FS 0 (Feferman, 1988;Basin and Matthews, 1996) and ALF (Altenkirch et al, 1994), partial inductive definitions (Eriksson, 1994), substructural frameworks (Miller, 1994;Cervesato and Pfenning, 1996), rewriting logic (Martì-Oliet and Meseguer, 1993), and labelled deductive systems (Gabbay, 1994).…”

Section: Introductionmentioning

confidence: 99%

Logical Frameworks—A Brief Introduction

Pfenning

2002

Proof and System-Reliability

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Abstract. A logical framework is a meta-language for the formalization of deductive systems. We provide a brief introduction to logical frameworks and their methodology, concentrating on LF. We use first-order logic as the running example to illustrate the representations of syntax, natural deductions, and proof transformations.We also sketch a recent formulation of LF centered on the notion of canonical form, and show how it affects proofs of adequacy of encodings.

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“…Tasks carried out with the help of logical frameworks include proof checking, proof search, and establishing meta-theoretic properties of deductive systems. For an overview and introduction to logical frameworks, their applications, and further pointers to the literature see [4,32,29].…”

Section: Introductionmentioning

confidence: 99%

A Current Logical Framework: The Propositional Fragment

Watkins¹,

Cervesato²,

Pfenning³

et al. 2003

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Abstract. We present the propositional fragment CLF 0 of the Concurrent Logical Framework (CLF). CLF extends the Linear Logical Framework to allow the natural representation of concurrent computations in an object language. The underlying type theory uses monadic types to segregate values from computations. This separation leads to a tractable notion of definitional equality that identifies computations differing only in the order of execution of independent steps. From a logical point of view our type theory can be seen as a novel combination of lax logic and dual intuitionistic linear logic. An encoding of a small Petri net exemplifies the representation methodology, which can be summarized as "concurrent computations as monadic expressions".

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The practice of logical frameworks

Cited by 25 publications

References 60 publications

Cut-elimination for a logic with definitions and induction

Cut-elimination for a logic with definitions and induction

Logical Frameworks—A Brief Introduction

A Current Logical Framework: The Propositional Fragment

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