List Superstructures and Semantics of Iterators

Abstract

Based on the GES (Goncharov–Ershov–Sviridenko) theory of list superstructures [1, 2], we study the semantics of iterators which is used in the object iterated programming language Libretto [3]. We note that Libretto also allows us to give a strong logic interpretation and can be used for constructing and managing object oriented databases [4]. One of the main difficulties is to organize nondeterministic computations related to input collections of elements satisfying a certain condition. Iterators can be represented as a realization of bounded existential quantifier ∃x ∈ M.F (x). A basic “intrinsic” iterator in Libretto is responsible for the strategy of depthfirst search. However, there are other iterators simulating more delicate strategies for looking for solutions related, for example, with methods of constraint satisfaction [5]. In particular, it is of interest to consider iterators simulating semantic programming on finite domains [6]. Based on the Σ-definability of inductive definitions [7, 8] in the GES theory, it is possible to model recursive descriptions without additional constructions like fixed point operators. In this paper, we use this property of the GES theory coming back to the theory of admissible sets [9].