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Abstract: We construct two -like calculi with explicit substitutions isomorphic to two Gentzen style logical deduction (sequent calculus) logics and constructive proofs of their Hauptsatze. We thus expound the view, that cut elimination under the Curry-Howard Correspondence is propagation of explicit substitutions. By seeing the constructed calculi as non-overlapping term rewriting systems (i.e., without critical pairs), we strengthen the Hauptsatze through an equivalence result between weak innermost... (Update)
Context of citations to this paper: More
...allows abstractions on non nested patterns. Fundamental properties such as confluence and strong normalization are not studied. In [38], Vestergaard studies the correspondence between calculi with explicit substitutions (without patterns) in de Bruijn notation and...
.... for explicit substitution see, e.g. 14] It would be interesting to investigate this in greater detail this has been done recently [113]. 7.7.1. Exercise. Give sequent calculus proofs for the formulas of Example 2.2. To prove the odd numbered formulas use only sequents...
Cited by: More
Lectures on the Curry-Howard Isomorphism - Sørensen, Urzyczyn (1998) (Correct)
Pattern Matching as Cut Elimination - Cerrito, Kesner (1999) (Correct)
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1.5: Cut Rules and Explicit Substitutions - Vestergaard, Wells (1999) (Correct)
0.4: Lambda-Calculi With Explicit Substitutions And Weak.. - Ferreira, Kesner, Puel (1996) (Correct)
0.4: Confluence of Extensional and Non-Extensional λ-calculi.. - Kesner (Correct)
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BibTeX entry: (Update)
R. Vestergaard. The cut rule and explicit substitutions, 1998. Draft. http://citeseer.ist.psu.edu/article/vestergaard98cut.html More
@article{ vestergaard01cut,
author = "Rene Vestergaard and Joe B. Wells",
title = "Cut rules and explicit substitutions",
journal = "Mathematical Structures in Computer Science",
volume = "11",
number = "1",
pages = "131-168",
year = "2001",
url = "citeseer.ist.psu.edu/article/vestergaard98cut.html" }
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