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Abstract: We formalise natural deduction for first-order logic in the proof assistant Coq, using De Bruijn indices for variable binding. The main judgement we model is of the form Gamma |- d [:] phi, stating that d is a proof term of formula phi under hypotheses Gamma (Update)
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BibTeX entry: (Update)
@article{ hend:02,
author = {Dimitri Hendriks},
title = {Proof Reflection in {C}oq},
journal = {Journal of Automated Reasoning},
year = 2002,
volume = 29,
number = 3,
pages = {277--307},
url = {citeseer.ist.psu.edu/hendriks02proof.html},
url = {http://www.cs.vu.nl/~diem/publication/pdf/prfx.pdf} }
Citations (may not include all citations):116 Ideas and results in proof theory (context) - Prawitz - 1971
106 Lambda calculus notation with nameless dummies (context) - de Bruijn - 1972
73 a calculus of explicit substitutions which preserves strong .. (context) - Benaissa, Briaud et al. - 1996
47 The Coq Proof Assistant Reference Manual (context) - Barras - 1999
32 Pure Type Systems Formalized - McKinna, Pollack
32 The practice of logical frameworks - Pfenning - 1996
14 Termination of Higher-order Rewrite Systems (context) - Pol - 1996
8 Laboratory for the Foundations of Computer Science (context) - Altenkirch, inductive et al. - 1994
5 Constructive completeness of intuitionistic predicate logic:.. (context) - Persson - 1996
3 Une Theorie des Constructiones Inductives (context) - Werner - 1994
3 Automated Proof Construction in Type Theory using Resolution - Bezem, Hendriks et al. - 2000
2 Coq in Coq - Barras, Werner - 1997
2 Residual theory in lambda calculus (context) - Huet
1 Clausification of First-Order Formulae (context) - Hendriks - 1998
Documents on the same site (http://www.phil.uu.nl/~hendriks/): More
Automated Proof Construction in Type Theory using Resolution - Bezem, Hendriks, de Nivelle (2000) (Correct)
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