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A Framework for Defining Logics
 JOURNAL OF THE ASSOCIATION FOR COMPUTING MACHINERY
, 1993
"... The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of ariti ..."
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Cited by 807 (45 self)
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The Edinburgh Logical Framework (LF) provides a means to define (or present) logics. It is based on a general treatment of syntax, rules, and proofs by means of a typed calculus with dependent types. Syntax is treated in a style similar to, but more general than, MartinLof's system of arities. The treatment of rules and proofs focuses on his notion of a judgement. Logics are represented in LF via a new principle, the judgements as types principle, whereby each judgement is identified with the type of its proofs. This allows for a smooth treatment of discharge and variable occurrence conditions and leads to a uniform treatment of rules and proofs whereby rules are viewed as proofs of higherorder judgements and proof checking is reduced to type checking. The practical benefit of our treatment of formal systems is that logicindependent tools such as proof editors and proof checkers can be constructed.
Reasoning About Functional Programs in Nuprl
 In Functional Programming, Concurrency, Simulation and Automated Reasoning
, 1993
"... . There are two ways of reasoning about functional programs in the constructive type theory of the Nuprl proof development system. Nuprl can be used in a conventional programverification mode, in which functional programs are written in a familiar style and then proven to be correct. It can als ..."
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. There are two ways of reasoning about functional programs in the constructive type theory of the Nuprl proof development system. Nuprl can be used in a conventional programverification mode, in which functional programs are written in a familiar style and then proven to be correct. It can also be used in an extraction mode, where programs are not written explicitly, but instead are extracted from mathematical proofs. Nuprl is the only constructive type theory to support both of these approaches. These approaches are illustrated by applying Nuprl to Boyer and Moore's "majority" algorithm. 1 Introduction A type system for a functional programming language can be syntactic or semantic. In a syntactically typed language, such as SML 1 [25], typing is a property of the syntax of expressions. Only certain combinations of language constructs are designated "welltyped", and only welltyped expressions are given a meaning. Each welltyped expression has a type which can be derive...
Importing Isabelle Formal Mathematics into NuPRL
, 1999
"... Isabelle and NuPRL are two theorem proving environments that are written in different dialects of ML using different formula syntaxes and different logical foundations. In spite of this, they have similar sets of basic theories, representing the same mathematical concepts. ..."
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Cited by 6 (0 self)
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Isabelle and NuPRL are two theorem proving environments that are written in different dialects of ML using different formula syntaxes and different logical foundations. In spite of this, they have similar sets of basic theories, representing the same mathematical concepts.
A framework for defining logical frameworks
 University of Udine
, 2006
"... Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be ..."
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Cited by 5 (2 self)
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Replace this file with prentcsmacro.sty for your meeting, or with entcsmacro.sty for your meeting. Both can be
Some Normalization Properties of MartinLof's Type Theory, and Applications
 in Proc. 1st Internat. Conf. on Theoretical Aspects of Computer Software, Lecture Notes in Computer Science
, 1991
"... For certain kinds of applications of type theories, the faithfulness of formalization in the theory depends on intensional, or structural, properties of objects constructed in the theory. For type theories such as LF, such properties can be established via an analysis of normal forms and types. In t ..."
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For certain kinds of applications of type theories, the faithfulness of formalization in the theory depends on intensional, or structural, properties of objects constructed in the theory. For type theories such as LF, such properties can be established via an analysis of normal forms and types. In type theories such as Nuprl or MartinLof's polymorphic type theory, which are much more expressive than LF, the underlying programming language is essentially untyped, and terms proved to be in types do not necessarily have normal forms. Nevertheless, it is possible to show that for MartinLof's type theory, and a large class of extensions of it, a sufficient kind of normalization property does in fact hold in certain wellbehaved subtheories. Applications of our results include the use of the type theory as a logical framework in the manner of LF, and an extension of the proofsasprograms paradigm to the synthesis of verified computer hardware. For the latter application we point out some ...
Structure and Behaviour in Hardware Verification
 Higher Order Logic Theorem Proving and its applications, 6th International Workshop, HUG ’93, Vancouver, B.C. Canada, number 780 in Lecture
, 1993
"... In this paper we review how hardware has been described in the formal hardware verification community. Recent developments in hardware description are evaluated against the background of the use of hardware description languages, and also in relation to programming languages. The notions of structur ..."
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In this paper we review how hardware has been described in the formal hardware verification community. Recent developments in hardware description are evaluated against the background of the use of hardware description languages, and also in relation to programming languages. The notions of structure and behaviour are crucial to this discussion. 1 Introduction Hardware has long been described using hardware description languages (hdls). More recently, in the field of hardware verification logicbased notations have been used. In this paper we explore how the relationship between the structure and behaviour of circuits has been perceived over time in the formal verification field. The structure of this paper is as follows: we give our view of hdls and simulation prior to the advent of formal methods, then we comment on formal logic methods used to describe and reason about hardware. Connections with conventional programming languages are also explored. Hardware Description Languages an...
Building Proofs by Analogy via the CurryHoward Isomorphism
, 1992
"... We present a formal method for building proofs by analogy and its implementation as a proof tactic for the NuPRL proof development system. The CurryHoward Isomorphism is used to represent proof constructions in a termfunctional language and to specify analogies by transformation rules on these ter ..."
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We present a formal method for building proofs by analogy and its implementation as a proof tactic for the NuPRL proof development system. The CurryHoward Isomorphism is used to represent proof constructions in a termfunctional language and to specify analogies by transformation rules on these terms. The method has the advantage to admit complete formalization and to make use of wellknown techniques like higherorder unification.
A Reference Version of HOL
"... Abstract. The second author has implemented a reference version of the HOL logic (henceforth called gtt). This version, written in Standard ML, is as simple as possible, making as few assumptions as necessary to present the essence of HOL. This simplicity makes the implementation easy to understand, ..."
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Abstract. The second author has implemented a reference version of the HOL logic (henceforth called gtt). This version, written in Standard ML, is as simple as possible, making as few assumptions as necessary to present the essence of HOL. This simplicity makes the implementation easy to understand, to port, to develop, to change, and to informally reason about. The first author has ported gtt to another dialect of ML, and developed the parsing, prettyprinting, and typechecking support needed to take gtt beyond its initial rudimentary conception. The implementation of gtt has already been of use in developing a variant of the HOL logic. As of this writing, there are at least four or five extant implementations of the HOL logic. These have been intensively developed, in some cases over decades, which leads us to an overwhelming question: why another? In particular, why gtt? There are several answers to this, stemming from different desires and needs in the HOL community.
IS
, 2006
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. appor t de r ech er ch e