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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| Published in | Theory of computing systems Vol. 45; no. 4; pp. 787 - 821 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer-Verlag
01.11.2009
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. |
| Author | Danner, Norman Royer, James S. |
| Author_xml | – sequence: 1 givenname: Norman surname: Danner fullname: Danner, Norman email: ndanner@wesleyan.edu organization: Department of Mathematics and Computer Science, Wesleyan University – sequence: 2 givenname: James S. surname: Royer fullname: Royer, James S. organization: Department of Electrical Engineering and Computer Science, Syracuse University |
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| Cites_doi | 10.1016/S0890-5401(03)00009-9 10.1145/503272.503297 10.1017/S0956796800003889 10.1007/BF01201998 10.1145/800119.803890 10.1145/507382.507386 10.1016/0168-0072(93)90044-E 10.1137/S0097539794263452 10.1145/227234.227246 10.1006/jpdc.1994.1038 10.1145/1111037.1111053 10.1145/976706.976713 10.1145/1248648.1248652 10.1007/978-1-4684-6802-1 10.1007/978-1-4612-2566-9_11 |
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| Keywords | Basic feasible functionals Higher-type computation Higher-type complexity Compositional semantics Implicit computational complexity |
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| References | Danner, Royer (CR8) 2006 CR2 Blelloch (CR4) 1996; 39 Hofmann (CR11) 2002 Cook, Urquhart (CR7) 1993; 63 Ignjatovic, Sharma (CR13) 2004; 5 Leivant (CR17) 1995 Jones (CR14) 2001; 11 Danner, Royer (CR9) 2007; 3 Ko (CR16) 1991 Milner, Tofte, Harper, MacQueen (CR19) 1977 Bellantoni, Cook (CR3) 1992; 2 CR10 Pierce (CR20) 2002 Kapron, Cook (CR15) 1996; 25 Aehlig, Schwichtenberg (CR1) 2002; 3 Hofmann (CR12) 2003; 183 Blelloch, Chatterjee, Hardwick, Sipelstein, Zagha (CR5) 1994; 21 Chakravarty, Leshchinskiy, Jones, Keller, Marlow (CR6) 2007 Mehlhorn (CR18) 1974 M.M.T. Chakravarty (9181_CR6) 2007 N. Danner (9181_CR9) 2007; 3 B.M. Kapron (9181_CR15) 1996; 25 K. Aehlig (9181_CR1) 2002; 3 N.D. Jones (9181_CR14) 2001; 11 K. Mehlhorn (9181_CR18) 1974 D. Leivant (9181_CR17) 1995 S. Bellantoni (9181_CR3) 1992; 2 M. Hofmann (9181_CR12) 2003; 183 A. Ignjatovic (9181_CR13) 2004; 5 9181_CR2 9181_CR10 G.E. Blelloch (9181_CR5) 1994; 21 S. Cook (9181_CR7) 1993; 63 G.E. Blelloch (9181_CR4) 1996; 39 B.C. Pierce (9181_CR20) 2002 K.-I. Ko (9181_CR16) 1991 N. Danner (9181_CR8) 2006 R. Milner (9181_CR19) 1977 M. Hofmann (9181_CR11) 2002 |
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Mehlhorn – ident: 9181_CR10 – volume-title: The Definition of Standard ML (Revised) year: 1977 ident: 9181_CR19 contributor: fullname: R. Milner – volume: 3 start-page: 383 issue: 3 year: 2002 ident: 9181_CR1 publication-title: ACM Trans. Comput. Log. doi: 10.1145/507382.507386 contributor: fullname: K. Aehlig – volume-title: Types and Programming Languages year: 2002 ident: 9181_CR20 contributor: fullname: B.C. Pierce – volume: 25 start-page: 117 issue: 1 year: 1996 ident: 9181_CR15 publication-title: SIAM J. Comput. doi: 10.1137/S0097539794263452 contributor: fullname: B.M. Kapron |
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programming formalism is a version of call-by-value
under a complexity-theoretically motivated type system.
programs run in type-2 polynomial-time... 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... |
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| Title | Two Algorithms in Search of a Type-System |
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