Extracting constructive content from classical logic via control-like reductions (1993) [26 citations — 1 self]
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by Franco Barbanera, Stefano Berardi
In Bezem and Groote [12
ftp://lambda.di.unito.it/pub/stefano/ExtractingConstructiveContentFrom.ps.gz
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@INPROCEEDINGS{Barbanera93extractingconstructive,author = {Franco Barbanera and Stefano Berardi},
title = {Extracting constructive content from classical logic via control-like reductions},
booktitle = {In Bezem and Groote [12},
year = {1993},
pages = {45--59},
publisher = {Springer-Verlag}
}
Years of Citing Articles
Abstract:
Abstract. Recently there has been much interest in the problem of finding the computational content of classical reasoning. One of the most appealing directions for the computer scientist to tackle such a problem is the relation which has been established between classical logic and lambda calculi with control operators, like Felleisen's control operator C. In this paper we introduce a typed lambda calculus with the C operator corresponding to Peano Arithmetic, and a set of reduction rules related to the ones of the usual control calculi with C. We show how these rules, which are proved to be strongly normalizing, can be used to extract witnesses from proofs of \Sigma 0 1 sentences in
Citations
| 208 | The revised report on the syntactic theories of sequential control and state – Felleisen, Hieb - 1992 |
| 184 | λµ-calculus: An algorithmic interpretation of classical natural deduction – Parigot - 1992 |
| 164 | A formulae-as-types notion of control – Griffin - 1990 |
| 64 | Extracting Constructive Content from Classical Proofs – Murthy - 1990 |
| 51 | Reasoning with continuations – Felleisen, Friedman, et al. - 1986 |
| 34 | Classically and intuitionistically provably recursive functions – Friedman |
| 13 | Mathematical significance of consistency proofs – Kreisel - 1958 |
| 10 | Continuations and simple types: A strong normalization result – Barbanera, Berardi - 1992 |
| 3 | A constructive valuation interpretation for classical logic and its use in witness extraction – Barbanera, Berardi - 1992 |
| 3 | Validity and normalizability of proofs in 1-st and 2-nd order classical and intuitionistic logic – Prawitz - 1981 |
| 2 | A new Constructive Logic – Girard - 1991 |
| 1 | A Game-theoric semantic of Classical Logic – Coquand - 1992 |
