Declarative definition of group indexed data structures and approximation of their domains

Authors:
Jean-Louis Giavitto;Olivier Michel
Affiliations:
LaMI umr 8042 du CNRS, Université d'Évry Val d'Essone, Tour Évry-2, 523 Place des terasses de l'agora, 91000 Évry, France;LaMI umr 8042 du CNRS, Université d'Évry Val d'Essone, Tour Évry-2, 523 Place des terasses de l'agora, 91000 Évry, France
Venue:
Proceedings of the 3rd ACM SIGPLAN international conference on Principles and practice of declarative programming
Year:
2001

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Abstract

We introduce a new high-level programming abstraction which extends the concept of data collection. The new construct, called GBF (for Group Based Data-Field), is based on an algebra of index sets, called a shape, and a functional extension of the array type, the field type. Shape constructions are based on group theory and put the emphasis on the logical neighborhood of the data structure elements. A field is a function from a shape to some set of values. In this study, we focus on regular neigh borhood structures and we show that arrays of any dimensions, cyclic array and trees are special kind of GBF.The recursive definitions of a GBF are then studied and we provide some elements for an implementation and some computability results in the case of recursive definition.