Adventures in time and space
<|reference_start|>Adventures in time and space: This paper investigates what is essentially a call-by-value version of PCF under a complexity-theoretically motivated type system. The programming formalism, ATR, has its first-order programs characterize the polynomial-time computable functions, and its second-order programs characterize the type-2 basic feasible functionals of Mehlhorn and of Cook and Urquhart. (The ATR-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 polynomial-time. The time-restricting part is an affine version of Barber and Plotkin's DILL. Two semantics are constructed for ATR. The first is a pruning of the naive denotational semantics for ATR. This pruning removes certain functions that cause otherwise feasible forms of recursion to go wrong. The second semantics is a model for ATR's time complexity relative to a certain abstract machine. This model provides a setting for complexity recurrences arising from ATR 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.<|reference_end|>
@article{danner2006adventures,
    title={Adventures in time and space},
    author={Norman Danner and James S. Royer},
    journal={Logical Methods in Computer Science, Volume 3, Issue 1 (March 12,
  2007) lmcs:2231},
    year={2006},
    doi={10.2168/LMCS-3(1:9)2007},
    archivePrefix={arXiv},
    eprint={cs/0612116},
    primaryClass={cs.LO cs.PL}
}