A Tutorial on Specifying Data Structures in Maude

This tutorial describes the equational specification of a series of typical data structures in Maude. We start with the well-known stacks, queues, and lists, to continue with binary and search trees. Not only are the simple versions considered but also advanced ones such as AVL and 2-3-4 trees. The operator attributes available in Maude allow the specification of data based on constructors that satisfy some equational properties, like concatenation of lists which is associative and has the empty list as identity, as opposed to the free constructors available in other functional programming languages. Moreover, the expressive version of equational logic in which Maude is based, namely membership equational logic, allows the faithful specification of types whose data are defined not only by means of constructors, but also by the satisfaction of additional properties, like sorted lists or search trees. In the second part of the paper we describe the use of an inductive theorem prover, the ITP, which itself is developed and integrated in Maude by means of the powerful metalevel and metalanguage features offered by the latter, to prove properties of the data structures. This is work in progress because the ITP is still under development and, as soon as the data gets a bit complex, the proof of their properties gets even more complex.