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Abstract: this paper we investigate the interaction of notational definitions with algorithms for testing equality and unification. We propose a syntactic criterion on definitions which avoids their expansion in many cases without losing soundness or completeness with respect to fi ffi-conversion. Our setting is the dependently typed -calculus [HHP93], but, with minor modifications, our results should apply to richer type theories and logics. The question when definitions need to be expanded is... (Update)
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...so far have validated the practicality of this proof compression technique [11] for the safety policies discussed here. Current research [15] is aimed at extending and improving these methods to obtain further compression without compromising the simplicity of the trusted...
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BibTeX entry: (Update)
Frank Pfenning and Carsten Schurmann. Algorithms for equality and unification in the presence of notational definitions. In T. Altenkirch, W. Naraschewski, and B. Reus, editors, Types for Proofs and Programs. Springer-Verlag LNCS, 1998. To appear. http://citeseer.ist.psu.edu/article/pfenning98algorithms.html More
@article{ pfenning99algorithms,
author = "Frank Pfenning and Carsten Sch{\"u}rmann",
title = "Algorithms for Equality and Unification in the Presence of Notational Definitions",
journal = "Lecture Notes in Computer Science",
volume = "1657",
pages = "179--??",
year = "1999",
url = "citeseer.ist.psu.edu/article/pfenning98algorithms.html" }
Citations (may not include all citations):434 A framework for defining logics - Harper, Honsell et al. - 1993
295 PVS: A prototype verification system (context) - Owre, Rushby et al. - 1992
294 Isabelle: A Generic Theorem Prover (context) - Paulson - 1994
254 The integration of functions into logic programming: From th.. (context) - Hanus - 1994
251 A logic programming language with lambda-abstraction - Miller - 1991
191 The LEGO proof development system: A user's manual (context) - Luo, Pollack - 1992
174 A unification algorithm for typed -calculus (context) - Huet - 1975
56 Unification and anti-unification in the Calculus of Construc.. - Pfenning - 1991
37 Unification via explicit substitutions: The case of higher-o.. - Dowek, Hardin et al. - 1996
28 Deriving algorithms from type inference systems: Application.. - Hankin, Le M'etayer - 1994
7 Available as Technical Report CMU-CS (context) - Pfenning, Schurmann et al. - 1998
7 Notational definition --- a formal account (context) - Griffin - 1988
6 The Coq Proof Assistant (context) - Barras - 1998
3 Technical Report CMU-CS (context) - Cervesato, Pfenning et al. - 1997
The graph only includes citing articles where the year of publication is known.
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