The Semantics of Reflected Proof

The Semantics of Reflected Proof (1990)

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by Stuart Allen , Robert L. Constable , Douglas J. Howe , William E. Aitken

Venue:	IN PROC. OF FIFTH SYMP. ON LOGIC IN COMP. SCI
Citations:	85 - 11 self

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Datum	Value	Source
TITLE	The Semantics of Reflected Proof	user correction - Legacy Corrections
AUTHOR NAME	Stuart Allen	user correction
AUTHOR AFFIL	Cornell University	user correction
AUTHOR ADDR	Ithaca, NY 14853	user correction
AUTHOR NAME	Robert L. Constable	user correction
AUTHOR AFFIL	Cornell University	user correction
AUTHOR ADDR	Ithaca, NY 14853	user correction
AUTHOR NAME	Douglas J. Howe	user correction
AUTHOR AFFIL	Cornell University	user correction
AUTHOR ADDR	Ithaca, NY 14853	user correction
AUTHOR NAME	William E. Aitken	user correction
AUTHOR AFFIL	Cornell University	user correction
AUTHOR ADDR	Ithaca, NY 14853	user correction
ABSTRACT	We begin to lay the foundations for reasoning about proofs whose steps include both invocations of programs to build subproofs (tactics) and references to representations of proofs themselves (reflected proofs). The main result is the definition of a single type of proof which can mention itself, using a new technique which finds a fixed point of a mapping between metalanguage and object language. This single type contrasts with hierarchies of types used in other approaches to accomplish the same classification. We show that these proofs are valid, and that every proof can be reduced to a proof involving only primitive inference rules. We also show how to extend the results to proofs from which programs (such as tactics) can be derived, and to proofs that can refer to a library of definitions and previously proven theorems. We believe that the mechanism of reflection is fundamental in building proof development systems, and we illustrate its power with applications to automating reasoning and describing modes of computation.	user correction - Legacy Corrections
YEAR	1990	INFERENCE
VENUE	IN PROC. OF FIFTH SYMP. ON LOGIC IN COMP. SCI	user correction
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	95--197	INFERENCE
CITATIONS	28 found	ParsCit 1.0