Two Algorithms in Search of a Type-System

The authors’ programming formalism is a version of call-by-value under a complexity-theoretically motivated type system. programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are -definable ( types are confined to levels 0, 1, and 2). A limitation of the original...

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Bibliographic Details
Published inTheory of computing systems Vol. 45; no. 4; pp. 787 - 821
Main Authors Danner, Norman, Royer, James S.
Format Journal Article
LanguageEnglish
Published New York Springer-Verlag 01.11.2009
Springer Nature B.V
Subjects
Algorithms
Computer Science
Semantics
Theory of Computation
Basic feasible functionals
Higher-type computation
Higher-type complexity
Compositional semantics
Implicit computational complexity
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Summary:The authors’ programming formalism is a version of call-by-value under a complexity-theoretically motivated type system. programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are -definable ( types are confined to levels 0, 1, and 2). A limitation of the original version of is that the only directly expressible recursions are tail-recursions. Here we extend so that a broad range of affine recursions are directly expressible. In particular, the revised can fairly naturally express the classic insertion- and selection-sort algorithms, thus overcoming a sticking point of most prior implicit-complexity-based formalisms. The paper’s main work is in refining the original time-complexity semantics for to show that these new recursion schemes do not lead out of the realm of feasibility.
ISSN:1432-4350
1433-0490
DOI:10.1007/s00224-009-9181-y