J. Gallier. Constructive Logics. Part I: A Tutorial on Proof Systems and Typed -calculi. Theoretical Computer Science, 110(2):249-239, 1993. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Strong Normalisation of Cut-Elimination in Classical Logic - Urban, Bierman (1999) (3 citations) (Correct)
....for LK tq [6, 15] However we do not need their colour annotations. The problem of non termination of cut elimination occurs in both intuitionistic logic and classical logic. One example of a non terminating reduction sequence in intuitionistic logic is given in [20] for classical logic [6] and [9] give the following example: A A A A A A A; A L A A A ContrR A A A A A; A A A R A A A ContrL A A A A Cut where a commuting cut needs to be eliminated. There are two possible reductions: either the cut can be permuted upwards in the left proof branch or in the right proof branch. If one is ....
J. Gallier. Constructive Logics. Part I: A Tutorial on Proof Systems and Typed -calculi. Theoretical Computer Science, 110(2):249-239, 1993.
Cut Rules and Explicit Substitutions - Vestergaard, Wells (1999) (3 citations) (Correct)
....2 ) denote new syntactic constructs rather than the results of meta level substitutions. Generally in this approach, rewriting corresponds to the cut propagation of the cut elimination procedure. The results we present in this paper follow this approach. One example of this approach is by Gallier [20], who gives a term assignment for a system similar to LJ. Some example rewrite rules are given, but there is no detailed study and no comparison with the explicit substitution literature. In another example, Pfenning [40, 39] represents a cut elimination proof in Elf. A second example of this ....
Jean Gallier. Constructive logics, Part I: A tutorial on proof systems and typed -calculi. Theoretical Computer Science, 110:249-339, 1993. Elsevier Science Publishers.
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