Abstract

this paper, is the analysis of notions of approximation aiming at explaining and justifying (order-theoretic) properties of categories of domains. For example, in [Fio94c, Fio94a], while studying the interaction between partiality and order-enrichment we considered contextual approximation which, in the framework we were working in, coincided with the specialisation preorder . But in the applications carried out in [FP94, Fio94a] we had to work with an axiomatised notion of approximation, instead of the aforementioned one, for the following two reasons: first, the specialisation preorder is not appropriate in categories of domains and stable functions (see [Fio94c]) and, second, we do not know of non-order-theoretic axioms making the specialisation preorder !-complete. To overcome these drawbacks another notion of approximation was to be considered. And, it was the second problem that motivated the intensional notion of approximation provided by the path relation. In fact, it is shown in [Fio94b] that under suitable axioms the path relation can be equipped with a canonical passage-to-the-limit operator appropriate for fixed-point computations; stronger axioms make this operator be given by lubs of !-chains

Citations