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View all- Valarcher P(2008)A complete characterization of primitive recursive intensional behavioursRAIRO - Theoretical Informatics and Applications10.1051/ita:200705342:1(69-82)Online publication date: 18-Jan-2008
Sequential algorithms, deterministic parallelism, and intensional expressiveness
Authors: 
Stephen Brookes and Denis DancanetAuthors Info & Claims
Stephen Brookes and Denis DancanetAuthors Info & ClaimsJanuary 1995
Pages 13 - 24
Abstract
We call language L1 intensionally more expressive than L2 if there are functions which can be computed faster in L1 than in L2. We study the intensional expressiveness of several languages: the Berry-Curien programming language of sequential algorithms, CDS0, a deterministic parallel extension to it, named CDSP, and various parallel extensions to the functional programming language PCF. The paper consists of two parts.
In the first part, we show that CDS0 can compute the minimum of two numbers n and p in unary representation in time O(min(n,p)). However, it cannot compute a “natural” version of this function. CDSP allows us to compute this function, as well as functions like parallel-or. This work can be seen as an extension of the work of Colson with primitive recursive algorithms to the setting of sequential algorithms.
In the second part, we show that deterministic parallelism adds intensional expressiveness, settling a “folk” conjecture from the literature in the negative. We show that CDSP is more expressive intensionally than CDS0. We also study three parallel extensions to PCF: parallel-or (por) and parallel conditionals on booleans (pifο) and integers (pifι). The situation is more complicated there: pifι is still more expressive than both pifο and por. However, pifι still is not as expressive as the deterministic query construct of CDSP. Thus, we identify a hierarchy of intensional expressiveness for deterministic parallelism.
References
[1]
G. Berry, Programming with concrete data structures and sequential algorithms, in: Proc. A CM Conf. on Functional Programming Languages and Computer Architecture, 1981, 49-57.
[2]
G. Berry and P.-L. Curien, Sequential algorithms on concrete data structures, Theoretical Computer Science 20 (1985) 265-321.
[3]
G. Berry and P.-L. Curien, The kernel of the applicative language CDS: Theory and practice, in: M. Nivat and J.C. Reynolds, eds., Algebraic Methods #n Semantics (Cambridge University Press, 1985) 35-87.
[4]
S. Brookes and S. Geva, Computational Comonads and Intensional Semantics, in: M. Fourman, P. Johnstone, and A. Pitts, eds., Applications of Categories in Computer Science, LMS Lecture Notes 177 (Cambridge University Press, 1992) 1-44.
[5]
S Brookes and S. Geva, Towards a theory of parallel algorithms on concrete data structures, Theoretical Computer Science 101 (1992) 177-221.
[6]
R Cartwright, P.-L. Curien, M. Felleisen, Fully abstract semantics for observably sequential languages, to appear in Information and Computation.
[7]
L Colson, About Primitive Recursive Algorithms, in: Proc. International Colloquium on Automata, Languages, and Programming, 1989, 194-206.
[8]
L Colson, Reprdsentation intentionelle d'algorithmes dans les syst#mes fonctioneUes: une dtude de cas, Th#se de Doctorat, Universit# Paris VII (1991).
[9]
T Coquand, Une preuve directe du Th#or#me d'Ultime Obstination, Comptes Rendus de l'Acaddmie des Sciences, March 1992.
[10]
T fI. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms (MIT Press, 1990).
[11]
P.-L. Curien, Categomcal Combinators, Sequential Algorithms, and Functional Programming (Birkh#user, 1993).
[12]
D.J. Gurr, Semantic Frameworks for Complexity, Doctoral Thesis, University of Edinburgh, Technical Report ECS-LFCS-91-130, January 1991.
[13]
J.E. tIopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation (Addison-Wesley, 1979).
[14]
J. Hughes and A. Ferguson, A loop-detecting interpreter for lazy, higher-order programs, in: Proc. Glasgow Workshop on Functional Languages, 1992.
[15]
G. Kahn and G.D. Plotkin, Concrete Domains, Theoretical Computer Science 121 (1993).
[16]
S.C. Kleene, Introduction to Metamathematics (North- Holland, 1952).
[17]
R. Milner, M. Tofte, and R. Harper, The definition of Standard ML (MIT Press, 1990).
[18]
G.D. Plotkin, LCF considered as a programming language, Theoretical Computer Science 5 (1977) 223-56.
[19]
M. Rosendahl, Automatic complexity analysis, in: Proc. A CM Conf. on Functional Programming Languages and Computer Architecture, 1989, 144-156.
[20]
A. Stoughton, Interdefinability of parallel operations in PCF, Theoretical Computer Science 79 (1991) 357-8.
Index Terms
- Sequential algorithms, deterministic parallelism, and intensional expressiveness
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Published: 25 January 1995
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POPL95: 22nd ACM Symposium on Principles of Programming Languages
January 23 - 25, 1995
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View all- Valarcher P(2008)A complete characterization of primitive recursive intensional behavioursRAIRO - Theoretical Informatics and Applications10.1051/ita:200705342:1(69-82)Online publication date: 18-Jan-2008
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