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Abstract: We present an algorithm for verifying that some specified arguments of an inductively defined relation in a dependently typed λ-calculus are uniquely determined by some other arguments. We prove it correct and also show how to exploit this uniqueness information in coverage checking, which allows us to verify that a definition of a function or relation covers all possible cases. In combination, the two algorithms significantly extend the power of the meta-reasoning facilities of the... (Update)
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3.2: Verifying Uniqueness in a Logical Framework - Anderson, Pfenning (2004) (Correct)
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BibTeX entry: (Update)
Anderson, Penny, & Pfenning, Frank. (2004). Verifying uniqueness in a logical framework. International Conference on Theorem Proving in Higher-Order Logics. Appel, Andrew W. (2001). Foundational proof-carrying code. IEEE Symposium on Logic in Computer Science. http://citeseer.ist.psu.edu/article/anderson04verifying.html More
@inproceedings{ anderson04verifying,
author = "Penny Anderson and Frank Pfenning",
title = "Verifying uniqueness in a logical framework",
booktitle = "International Conference on Theorem Proving in Higher-Order Logics",
year = "2004",
url = "citeseer.ist.psu.edu/article/anderson04verifying.html" }
Citations (may not include all citations):434 A framework for defining logics - Harper, Honsell et al. - 1993
136 System description: Twelf --- a meta-logical framework for d.. - Pfenning, Schurmann - 1999
96 An algorithm for testing conversion in type theory (context) - Coquand - 1991
79 Pattern matching with dependent types (context) - Coquand - 1992
47 Logical frameworks - Pfenning - 2001
38 Extensional Concepts in Intensional Type Theory (context) - Hofmann - 1995
37 Unification via explicit substitutions: The case of higher-o.. - Dowek, Hardin et al. - 1996
35 On equivalence and canonical forms in the LF type theory - Harper, Pfenning - 2003
27 Mode and termination checking for higher-order logic program.. - Rohwedder, Pfenning - 1996
26 Information and Computation (context) - Pfenning, elimination et al. - 2000
25 Toward a foundational typed assembly language - Crary - 2003
18 Dependently Typed Functional Programs and their Proofs - McBride - 1999
15 Automating the Meta Theory of Deductive Systems (context) - Schurmann - 2000
14 The groupoid model refutes uniqueness of identity proofs (context) - Hofmann, Streicher - 1994
12 Algorithms for equality and unification in the presence of n.. - Pfenning, Schurmann - 1998
11 Termination and reduction checking for higher-order logic pr.. - Pientka - 2083
8 Recursion for higher-order encodings (context) - Schurmann - 2001
7 A coverage checking algorithm for LF - Schurmann, Pfenning - 2003
6 Primitive recursion for higherorder abstract syntax (context) - Schurmann, Despeyroux et al. - 2001
5 A type-theoretic approach to induction with higher-order enc.. (context) - Schurmann - 2001
4 A modal lambda calculus with iteration and case constructs - Despeyroux, Leleu - 1998
4 Boxes go bananas: Encoding higher-order abstract syntax with.. (context) - Washburn, Weirich - 2003
2 Delphin -- toward functional programming with logical framew.. (context) - Schurmann - 2004
2 A metalogical approach to foundational certified code - Crary, Sarkar - 2003
2 Factoring pure logic programs (context) - Poswolsky, Schurmann - 2003
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Compiler Verification in LF - Hannan, Pfenning (1992) (Correct)
Meta-Programming with Names and Necessity - Nanevski, Pfenning (2002) (Correct)
Elf: A Meta-Language for Deductive Systems (System Description) - Pfenning (Correct)
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