Logical Foundations of Eval/Quote Mechanisms, and the Modal Logic S4

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 rst, the S4-calculus, is based on Bierman and De Paiva's proposal, and has all desirable logical properties, except for its non-operational avor. 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 reeexive tower. Remarkably, this language was developed from purely logical principles, but nonetheless provides some operational insight into eval/quote mechanisms.

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