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Adventures in time and space

Published:11 January 2006Publication History

ABSTRACT

This paper investigates what is essentially a call-by-value version of PCF under a complexity-theoretically motivated type system. The programming formalism, ATR1, has its first-order programs characterize the poly-time computable functions, and its second-order programs characterize the type-2 basic feasible functionals of Mehlhorn and of Cook and Urquhart. (The ATR1-types are confined to levels 0, 1, and 2.) The type system comes in two parts, one that primarily restricts the sizes of values of expressions and a second that primarily restricts the time required to evaluate expressions. The size-restricted part is motivated by Bellantoni and Cook's and Leivant's implicit characterizations of poly-time. The time-restricting part is an affine version of Barber and Plotkin's DILL. Two semantics are constructed for ATR1. The first is a pruning of the naïve denotational semantics for ATR1. This pruning removes certain functions that cause otherwise feasible forms of recursion to go wrong. The second semantics is a model for ATR1's time complexity relative to a certain abstract machine. This model provides a setting for complexity recurrences arising from ATR1 recursions, the solutions of which yield second-order polynomial time bounds. The time-complexity semantics is also shown to be sound relative to the costs of interpretation on the abstract machine.

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  1. Adventures in time and space

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            • Published in

              cover image ACM Conferences
              POPL '06: Conference record of the 33rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages
              January 2006
              432 pages
              ISBN:1595930272
              DOI:10.1145/1111037
              • cover image ACM SIGPLAN Notices
                ACM SIGPLAN Notices  Volume 41, Issue 1
                Proceedings of the 2006 POPL Conference
                January 2006
                421 pages
                ISSN:0362-1340
                EISSN:1558-1160
                DOI:10.1145/1111320
                Issue’s Table of Contents

              Copyright © 2006 ACM

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              New York, NY, United States

              Publication History

              • Published: 11 January 2006

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