Array theory, logic and the Nial language

A logical description of arrays is developed, indicating that it is possible to incorporate array data structures into a theory that builds on the conventional theory of lists. This theory provides a basis for the functional programming language Nial. An emphasis in the development of Nial has been to explore ways to integrate the logic programming paradigm with the functional-programming and array-handling capabilities of the language. By providing a logical basis for array theory, the authors have provided a formal basis for the development of a semantics for logic programming with arrays in Nial.<>