Abstract Datatypes in PVS

PVS (Prototype Verification System) is a general-purpose environment for developing specifications and proofs. This document deals primarily with the abstract datatype mechanism in PVS which generates theories containing axioms and definitions for a class of recursive datatypes. The concepts underlying the abstract datatype mechanism are illustrated using ordered binary trees as an example. Binary trees are described by a PVS abstract datatype that is parametric in its value type. The type of ordered binary trees is then presented as a subtype of binary trees where the ordering relation is also taken as a parameter. We define the operations of inserting an element into, and searching for an element in an ordered binary tree; the bulk of the report is devoted to PVS proofs of some useful properties of these operations. These proofs illustrate various approaches to proving properties of abstract datatype operations. They also describe the built-in capabilities of the PVS proof checker for simplifying abstract datatype expressions.