@inproceedings{60ac57b0b82045b19efadeacb51c696a,
title = "Building decision procedures in the calculus of inductive constructions",
abstract = "It is commonly agreed that the success of future proof assistants will rely on their ability to incorporate computations within deduction in order to mimic the mathematician when replacing the proof of a proposition P by the proof of an equivalent proposition P' obtained from P thanks to possibly complex calculations. In this paper, we investigate a new version of the calculus of inductive constructions which incorporates arbitrary decision procedures into deduction via the conversion rule of the calculus. The novelty of the problem in the context of the calculus of inductive constructions lies in the fact that the computation mechanism varies along proof-checking: goals are sent to the decision procedure together with the set of user hypotheses available from the current context. Our main result shows that this extension of the calculus of constructions does not compromise its main properties: confluence, subject reduction, strong normalization and consistency are all preserved.",
keywords = "Calculus of inductive constructions, Decision procedures, Theorem provers",
author = "Fr{\'e}d{\'e}ric Blanqui and Jouannaud, \{Jean Pierre\} and Strub, \{Pierre Yves\}",
year = "2007",
month = jan,
day = "1",
doi = "10.1007/978-3-540-74915-8\_26",
language = "English",
isbn = "9783540749141",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "328--342",
booktitle = "Computer Science Logic - 21st International Workshop, CSL 2007 and 16th Annual Conference of the EACSL, Proceedings",
note = "21st International Workshop on Computer Science Logic, CSL 2007 and 16th Annual Conference of the European Association for Computer Science Logic, EACSL ; Conference date: 11-09-2007 Through 15-09-2007",
}