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Abstract: We give a detailed, informal proof of the Church-Rosser property for the untyped -calculus and show its representation in LF. The proof is due to Tait and Martin-Lof and is based on the notion of parallel reduction. The representation employs higher-order abstract syntax and the judgments-as-types principle and takes advantage of term reconstruction as it is provided in the Elf implementation of LF. Proofs of meta-theorems are represented as higher-level judgments which relate sequences of... (Update)
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BibTeX entry: (Update)
Frank Pfenning. A proof of the Church-Rosser theorem and its representation in a logical framework. Journal of Automated Reasoning. To appear. A preliminary version is available as Carnegie Mellon Technical Report CMU-CS-92-186, September 1992. http://citeseer.ist.psu.edu/pfenning92proof.html More
@article{ pfenning93proof,
author = "Frank Pfenning",
title = "A Proof of the {Church-Rosser} Theorem and its Representation in a Logical Framework",
journal = "Journal of Automated Reasoning",
year = "1993",
url = "citeseer.ist.psu.edu/pfenning92proof.html" }
Citations (may not include all citations):729 The Lambda-Calculus: Its Syntax and Semantics (context) - Barendregt - 1980
283 Theoretical Computer Science (context) - Plotkin, call-by-value et al. - 1975
259 Combinatory Logic (context) - Curry, Feys - 1958
210 Logic programming in the LF logical framework - Pfenning - 1991
166 An overview of Prolog (context) - Nadathur, Miller - 1988
54 Specifying and Implementing Theorem Provers in a Higher-Orde.. (context) - Felty - 1989
47 Natural semantics and some of its meta-theory in Elf - Michaylov, Pfenning - 1991
40 ACM monograph series (context) - Boyer, Moore et al. - 1979
40 Compiler verification in LF - Hannan, Pfenning - 1992
39 Natural deduction as higher-order resolution - Paulson - 1986
38 Constructive mathematics and computer programming (context) - Martin-Lof - 1980
35 Lambda-calculus notation with nameless dummies: a tool for a.. (context) - de Bruijn - 1972
33 A mechanical proof of the Church-Rosser theorem (context) - Shankar - 1988
32 Implementing the meta-theory of deductive systems - Pfenning, Rohwedder - 1992
31 What is a model of the lambda calculus (context) - Meyer - 1982
29 Transactions of the American Mathematical Society (context) - Church, Rosser et al. - 1936
25 Investigating a Proof-Theoretic Meta-Language for Functional.. (context) - Hannan - 1991
13 Systems of polymorphic type assignment in LF (context) - Harper - 1990
11 The relation between computational and denotational properti.. (context) - Wadsworth - 1976
6 An implementation of the Elf core language in Standard ML (context) - Pfenning - 1991
3 Available as Technical Report CMU-CS (context) - Harper, Honsell et al. - 1987
The graph only includes citing articles where the year of publication is known.
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