Logical Foundations of Eval/Quote Mechanisms, and the Modal Logic S4 (1997)
| Venue: | IN PRESS S1570-8683(05)00043-1/FLA AID:71 Vol.•••(•••) [DTD5] P.12 (1-12) JAL:m1a v 1.40 Prn:15/07/2005; 8:08 jal71 by:SL p. 12 12 N. Alechina, D. Shkatov / Journal of Applied Logic |
| Citations: | 5 - 0 self |
BibTeX
@TECHREPORT{Goubault-larrecq97logicalfoundations,
author = {Jean Goubault-larrecq},
title = {Logical Foundations of Eval/Quote Mechanisms, and the Modal Logic S4},
institution = {IN PRESS S1570-8683(05)00043-1/FLA AID:71 Vol.•••(•••) [DTD5] P.12 (1-12) JAL:m1a v 1.40 Prn:15/07/2005; 8:08 jal71 by:SL p. 12 12 N. Alechina, D. Shkatov / Journal of Applied Logic},
year = {1997}
}
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Abstract
Starting from the idea that cut elimination is the precise meaning of program execution, we design two languages of constructions for the minimal logic S4, yielding -calculi with idealized versions of Lisp's eval and quote. The first, the S4 -calculus, is based on Bierman and De Paiva's proposal, and has all desirable logical properties, except for its non-operational flavor. The second, the evQ-calculus, is more complicated, but has a clear operational meaning: it is a tower of interpreters in the style of Lisp's reflexive tower. Remarkably, this language was developed from purely logical principles, but nonetheless provides some operational insight into eval/quote mechanisms. 1 Introduction Let's consider two dual questions. The first is: is there a proofs-as-programs, formulasas -types correspondence for the modal logic S4? There is one between minimal and intuitionistic logics and - calculi [How80], and also for classical logic [Gri90] or linear logic [Abr93], so why not S4? A...
