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A Proof of the ChurchRosser Theorem and its Representation in a Logical Framework
, 1992
"... We give a detailed, informal proof of the ChurchRosser property for the untyped lambdacalculus and show its representation in LF. The proof is due to Tait and MartinLöf and is based on the notion of parallel reduction. The representation employs higherorder abstract syntax and the judgmentsast ..."
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Cited by 36 (8 self)
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We give a detailed, informal proof of the ChurchRosser property for the untyped lambdacalculus and show its representation in LF. The proof is due to Tait and MartinLöf and is based on the notion of parallel reduction. The representation employs higherorder abstract syntax and the judgmentsastypes principle and takes advantage of term reconstruction as it is provided in the Elf implementation of LF. Proofs of metatheorems are represented as higherlevel judgments which relate sequences of reductions and conversions.
Implementing the MetaTheory of Deductive Systems
 Proceedings of the 11th International Conference on Automated Deduction
, 1992
"... . We exhibit a methodology for formulating and verifying metatheorems about deductive systems in the Elf language, an implementation of the LF Logical Framework with an operational semantics in the spirit of logic programming. It is based on the mechanical verification of properties of transformatio ..."
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Cited by 32 (9 self)
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. We exhibit a methodology for formulating and verifying metatheorems about deductive systems in the Elf language, an implementation of the LF Logical Framework with an operational semantics in the spirit of logic programming. It is based on the mechanical verification of properties of transformations between deductions, which relies on type reconstruction and schemachecking. The latter is justified by induction principles for closed LF objects, which can be constructed over a given signature. We illustrate our technique through several examples, the most extensive of which is an interpretation of classical logic in minimal logic through a continuationpassingstyle transformation on proofs. 1 Introduction Formal deductive systems have become an important tool in computer science. They are used to specify logics, type systems, operational semantics and other aspects of languages. The role of such specifications is threefold. Firstly, inference rules serve as a highlevel notation w...
Type Systems for Closure Conversions
 In The Workshop on Types for Program Analysis
, 1995
"... . We consider the problem of analyzing and proving correct simple closure conversion strategies for a higherorder functional language. We specify the conversions as deductive systems, making use of annotated types to provide constraints which guide the construction of the closures. We exploit the a ..."
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Cited by 25 (0 self)
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. We consider the problem of analyzing and proving correct simple closure conversion strategies for a higherorder functional language. We specify the conversions as deductive systems, making use of annotated types to provide constraints which guide the construction of the closures. We exploit the ability of deductive systems to specify concisely complex relationships between source terms and closureconverted terms. The resulting specifications and proofs are relatively clear and straightforward. The use of deductive systems is central to our work as we can subsequently encode these systems in the LF type theory and then code them in the Elf programming language. The correctness proofs can also be coded in this language, providing machinechecked versions of these proofs. 1 Introduction Closure conversion is the process of transforming functions containing free variables into a closures, a representation of a function that consists of a piece of code for the function and a record con...