A Formulae-as-Types Notion of Control (1990)
| Venue: | In Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages |
| Citations: | 206 - 0 self |
BibTeX
@INPROCEEDINGS{Griffin90aformulae-as-types,
author = {Timothy G. Griffin},
title = {A Formulae-as-Types Notion of Control},
booktitle = {In Conference Record of the Seventeenth Annual ACM Symposium on Principles of Programming Languages},
year = {1990},
pages = {47--58},
publisher = {ACM Press}
}
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Abstract
The programming language Scheme contains the control construct call/cc that allows access to the current continuation (the current control context). This, in effect, provides Scheme with first-class labels and jumps. We show that the well-known formulae-astypes correspondence, which relates a constructive proof of a formula ff to a program of type ff, can be extended to a typed Idealized Scheme. What is surprising about this correspondence is that it relates classical proofs to typed programs. The existence of computationally interesting "classical programs" --- programs of type ff, where ff holds classically, but not constructively --- is illustrated by the definition of conjunctive, disjunctive, and existential types using standard classical definitions. We also prove that all evaluations of typed terms in Idealized Scheme are finite.
