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Abstract: The purpose of this paper is to give an exposition of material dealing with constructive logic, typed -calculi, and linear logic. The emergence in the past ten years of a coherent eld of research often named \logic and computation" has had two major (and related) e ects: rstly, it has rocked vigorously the world of mathematical logic; secondly, it has created a new computer science discipline, which spans from what is traditionally called theory of computation, to programming language... (Update)
Context of citations to this paper: More
.... an elementary proof system can easily be determined by adopting inference rules of classical sequent calculi (for instance, cf. Gal93] This facilitates a quick implementation by means of a generic theorem prover like Isabelle [Pau90] First, we informally present the...
...with no cuts. Full explanations of cut elimination can be found in Girard, Lafont and Taylor s book [GLT89] and Gallier s tutorial [Gal93] To a logician, the important property of sequent calculus is that in all the rules in the logic except cut, the formulas appearing...
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BibTeX entry: (Update)
J. Gallier. Constructive logics part I: A tutorial on proof systems and typed - calculi. Theoretical Computer Science, 110(2):249--339, March 1993. http://citeseer.ist.psu.edu/gallier03constructive.html More
@article{ gallier93constructive,
author = "Jean H. Gallier",
title = "Constructive Logics Part I: A Tutorial on Proof Systems and Typed gamma-Calculi",
journal = "Theoretical Computer Science",
volume = "110",
number = "2",
pages = "249-339",
year = "1993",
url = "citeseer.ist.psu.edu/gallier03constructive.html" }
Citations (may not include all citations):982 Theoretical Computer Science (context) - Girard - 1987
343 Introduction to Metamathematics (context) - Kleene - 1952
259 Combinatory Logic (context) - Curry, Feys - 1974
233 Computational interpretation of linear logic - Abramsky - 1990
233 The formulae-as-types notion of construction (context) - Howard - 1980
146 Investigations into logical deduction (context) - Gentzen - 1969
137 Introduction to Combinators and -Calculus (context) - Hindley, Seldin - 1986
116 Ideas and results in proof theory (context) - Prawitz - 1971
83 volume 7 of Cambridge Tracts in Theoretical Computer Science (context) - Girard, Lafont et al. - 1989
72 Logic for Computer Science (context) - Gallier - 1986
72 A new constructive logic: classical logic (context) - Girard - 1991
61 Une extension de l'interpretation de Godel a l'analyse (context) - Girard - 1971
58 a proof-theoretical study (context) - Prawitz - 1965
47 Constructivism in Mathematics: An Introduction (context) - Troelstra, van Dalen - 1988
46 Proof Theory and Logical Complexity (context) - Girard - 1987
42 A realizability interpretation of the theory of species (context) - Tait - 1975
33 Logic and Structure (context) - van Dalen - 1980
32 The correspondence between cut-elimination and normalization (context) - Zucker - 1974
30 Proof theory: some applications of cut-elimination (context) - Schwichtenberg - 1977
28 Intensional interpretation of functionals of nite type (context) - Tait - 1967
22 Contraction-free sequent calculi for intuitionistic logic (context) - Dyckho - 1992
21 Normal derivability in classical logic (context) - Tait - 1968
19 Linearizing intuitionistic implication - Lincoln, Scedrov et al. - 1991
15 Bounds for cut-elimination in intuitionistic propositional l.. (context) - Hudelmaier - 1989
14 Etudes et recherches en informatique (context) - Krivine, types et al. - 1990
13 elimination des coupures de l'arithmetique d'ordre superie.. (context) - Girard, etation - 1972
10 and Proof Theory (context) - Stenlund, Lambda - 1972
7 an interpretation of second-order quanti cation in rst-order.. (context) - Pitts - 1992
3 volume 67 of Translations of Mathematical Monographs (context) - Dragalin, introduction et al. - 1988
3 volume 103 of Studies in Logic (context) - Barendregt, Calculus - 1984
1 egles admissibles en calcul propositionnel intuitionniste (context) - Rozi - 1992
1 Privately circulated manuscript (context) - Martin-L, intuitionistic et al. - 1972
1 A new algorithm for derivability in the constructive proposi.. (context) - Vorob'ev - 1970
1 On Girard's \candidats de reductibilites (context) - Gallier - 1990
1 volume 81 of Studies in Logic (context) - Takeuti - 1975
1 volume 28 of CSLI Lecture Notes (context) - Ungar, cut-elimination et al. - 1992
1 The derivability problem in the constructive propositional c.. (context) - Vorob'ev - 1952
The graph only includes citing articles where the year of publication is known.
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