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A temporal-logic approach to binding-time analysis

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1 Author(s)
Davies, R. ; Dept. of Comput. Sci., Carnegie Mellon Univ., Pittsburgh, PA, USA

The Curry-Howard isomorphism identifies proofs with typed λ-calculus terms, and correspondingly identifies propositions with types. We show how this isomorphism can be extended to relate constructive temporal logic with binding-time analysis. In particular we show how to extend the Curry-Howard isomorphism to include the O (“next”) operator from linear-time temporal logic. This yields the simply typed λO-calculus which we prove to be equivalent to a multi-level binding-time analysis like those used in partial evaluation for functional programming languages. Further, we prove that normalization in λO can be done in an order corresponding to the times in the logic, which explains why λO is relevant to partial evaluation. We then extend λO to a small functional language, Mini-MLO, and give an operational semantics for it. Finally, we prove that this operational semantics correctly reflects the binding-times in the language, a theorem which is the functional programming analog of time-ordered normalization

Published in:

Logic in Computer Science, 1996. LICS '96. Proceedings., Eleventh Annual IEEE Symposium on

Date of Conference:

27-30 Jul 1996