## Theoretical Informatics and Applications Informatique Théorique et Applications Will be set by the publisher A COMPLETE CHARACTERIZATION OF PRIMITIVE RECURSIVE INTENSIONAL BEHAVIOURS

### BibTeX

@MISC{Valarcher_theoreticalinformatics,

author = {P. Valarcher},

title = {Theoretical Informatics and Applications Informatique Théorique et Applications Will be set by the publisher A COMPLETE CHARACTERIZATION OF PRIMITIVE RECURSIVE INTENSIONAL BEHAVIOURS},

year = {}

}

### OpenURL

### Abstract

Abstract. We give a complete characterization of the class of functions that are the intensional behaviours of Primitive Recursive algorithms. This class is the set of primitive recursive functions that have a null basic case of recursion. This result is obtained using the property of ultimate unarity and a geometrical approach of sequential functions on N the set of positive integers. AMS Subject Classification. — Give AMS classification codes —. 1.

### Citations

21 |
About primitive recursive algorithms
- Colson
- 1991
(Show Context)
Citation Context ...he property of ultimate unarity and a geometrical approach of sequential functions on N the set of positive integers. AMS Subject Classification. — Give AMS classification codes —. 1. Introduction In =-=[4,5]-=-, L. Colson studies the behaviour of PR algorithms and proves that there is no algorithm (in PR) that computes the minimum of two (unary) integers in time O(inf). He proves this result by studying the... |

16 |
and Pierre-Louis Curien. Domains and LambdaCalculi
- Amadio
- 1998
(Show Context)
Citation Context ...irst recall a well-known result from Theory of Domains that restricts the class of intensional behaviours (it is not a restriction of mathttP R systems but is due to the sequentiality of the language =-=[1,2]-=-). We give a geometrical approach to the class of functions that may be intensional behaviours. 4.2. Geometrical approach of intensional behaviour From results in denotational semantics, we know that ... |

11 |
System T, call-by-value and the minimum problem
- Colson, Fredholm
- 1998
(Show Context)
Citation Context ...The author has shown some new results on intensional behaviour (now called structural complexity) of other primitive recursive schemas (in [17]). In the same framework, L. Colson and D. Fredholm (see =-=[6, 13]-=-) show that call-by-value strategy (with primitive recursion over lists of integers and with primitive recursion in Keywords and phrases: Intensional behaviour, semantics, primitive recursion 1 LACL, ... |

10 | Sequential algorithms, deterministic parallelism, and intensional expressiveness
- Brookes, Dancanet
- 1995
(Show Context)
Citation Context ...BE SET BY THE PUBLISHER higher types, called system T of Goedel) does not allow to compute the good algorithm of the min function. Similar questions have been studied by S. Brookes and D. Dancanet in =-=[3]-=- and [9] with non-determinism and CDS languages. Recently, in [15], Y. Moschovakis has established a linear lower bound for the complexity of non-trivial primitive recursive program from piecewise lin... |

6 |
Generating the greatest common divisor, and limitations of primitive recursive algorithms
- Dries
(Show Context)
Citation Context ...ched in efficiency by primitive recursive programs from the same given functions. He ended by an open problem relative to the classical Euclidean algorithm (L. Van Den Dries gives a partial answer in =-=[11]-=-). And lastly, T. Crolard, S. Lacas and the author extend the result of incompletness of algorithms to imperative language in [8]. In this paper, we give a complete characterization of the intensional... |

4 | On the Expressive Power of the Loop Language
- Crolard, Lacas, et al.
- 2006
(Show Context)
Citation Context ...sical Euclidean algorithm (L. Van Den Dries gives a partial answer in [11]). And lastly, T. Crolard, S. Lacas and the author extend the result of incompletness of algorithms to imperative language in =-=[8]-=-. In this paper, we give a complete characterization of the intensional behaviour of PR algorithms: these are functions that verify the property of sequentiality [2] and with ultimate behaviours defin... |

4 | Programming language expressiveness and circuit complexity
- Dancanet, Brookes
- 1996
(Show Context)
Citation Context ...Y THE PUBLISHER higher types, called system T of Goedel) does not allow to compute the good algorithm of the min function. Similar questions have been studied by S. Brookes and D. Dancanet in [3] and =-=[9]-=- with non-determinism and CDS languages. Recently, in [15], Y. Moschovakis has established a linear lower bound for the complexity of non-trivial primitive recursive program from piecewise linear give... |

4 | On the asymptotic behaviour of primitive recursive algorithms. Theoretical Computer Science - David |

4 | On primitive recursive algorithms and the greatest common divisor function
- Moschovakis
- 2003
(Show Context)
Citation Context ...does not allow to compute the good algorithm of the min function. Similar questions have been studied by S. Brookes and D. Dancanet in [3] and [9] with non-determinism and CDS languages. Recently, in =-=[15]-=-, Y. Moschovakis has established a linear lower bound for the complexity of non-trivial primitive recursive program from piecewise linear given functions. His main result is that logtime programs for ... |

3 |
Sequentialite de l'evaluation formelle des lambdas-expressions
- Berry
- 1978
(Show Context)
Citation Context ...gorithms to imperative language in [8]. In this paper, we give a complete characterization of the intensional behaviour of PR algorithms: these are functions that verify the property of sequentiality =-=[2]-=- and with ultimate behaviours definable by primitive recursive schema with null basic case. The paper is organized as follow: in section 2 we present the language of PR terms as term rewriting systems... |

2 |
On lazy natural numbers with applications
- Escardo
- 1993
(Show Context)
Citation Context ...o algorithm (in PR) that computes the minimum of two (unary) integers in time O(inf). He proves this result by studying the interpretation of PR algorithms on the domain of lazy (or partial) integers =-=[12]-=-: this domain captures the way an algorithm writes on its output as a function of what it has already read on its inputs, this function is called intensional behaviour. He notices that all algorithms ... |

2 |
Computing minimum with primitive recursion over lists
- Fredholm
- 1996
(Show Context)
Citation Context ...The author has shown some new results on intensional behaviour (now called structural complexity) of other primitive recursive schemas (in [17]). In the same framework, L. Colson and D. Fredholm (see =-=[6, 13]-=-) show that call-by-value strategy (with primitive recursion over lists of integers and with primitive recursion in Keywords and phrases: Intensional behaviour, semantics, primitive recursion 1 LACL, ... |

2 |
Intensionality vs extensionality and primitive recursion
- Valarcher
- 1996
(Show Context)
Citation Context ... predecessor, closed by composition and an iteration schema. The author has shown some new results on intensional behaviour (now called structural complexity) of other primitive recursive schemas (in =-=[17]-=-). In the same framework, L. Colson and D. Fredholm (see [6, 13]) show that call-by-value strategy (with primitive recursion over lists of integers and with primitive recursion in Keywords and phrases... |

1 |
Une preuve directe du théclvorème d’ultime obstination. Compte Rendus de l’Académie des
- Coquand
- 1992
(Show Context)
Citation Context ...ur. He notices that all algorithms look ultimately at at most one of their inputs so that ultimate interpretations are unaries functions (this propety is called ultimate obstinacy). Later, T. Coquand =-=[7]-=- gives a constructive proof of this property and as side effect he gives a definition of the class of functions that are ultimatly the intensional behaviours of PR algorithms: successor function, cons... |

1 |
Contribution à l’etude du comportement intentionel des algorithmes: le cas de la récursion primitive. Thèse de doctorat, Université P
- Valarcher
- 1996
(Show Context)
Citation Context ... it’s not constructive. Let t be a term of a PR system then: Theorem 6.2. The intensional behaviour of t is ultimately unary. Proof. The proof follows the one of T. Coquand in [7]. It can be found in =-=[16]-=-. □ 7. Full characterization Corollary 7.1. Coquand [7] The ultimate intensional behaviours of PR systems are among the asymptotic behaviours of the smallest set containing constant functions, identit... |