Two algorithms in search of a type system
| dc.creator | Danner, Norman | |
| dc.creator | Royer, James S. | |
| dc.date | 2007-10-03 | |
| dc.date | 2008-04-18 | |
| dc.date.accessioned | 2026-07-07T09:33:03Z | |
| dc.date.available | 2026-07-07T09:33:03Z | |
| dc.description | The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable (ATR types are confined to levels 0, 1, and 2). A limitation of the original version of ATR is that the only directly expressible recursions are tail-recursions. Here we extend ATR so that a broad range of affine recursions are directly expressible. In particular, the revised ATR 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 ATR to show that these new recursion schemes do not lead out of the realm of feasibility. | |
| dc.description | 30 pages. Final version to appear in Theory of Computing Systems | |
| dc.identifier | https://arxiv.org/abs/0710.0824 | |
| dc.identifier | http://arxiv.org/abs/0710.0824 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158998 | |
| dc.subject | Logic in Computer Science | |
| dc.subject | Programming Languages | |
| dc.subject | F.3.3; F.1.3 | |
| dc.title | Two algorithms in search of a type system | |
| dc.type | text |