Second-Order Principles in Specification Languages for
Object-Oriented Programs
Bernhard Beckert, Kerry Trentelman
Within the setting of object-oriented program specification and
verification, pointers and object references can be considered as
relations between the elements of a data structure. When we specify
properties of these data structures, we often describe properties of
relations. Hence it is important to be able to talk about relations
and their properties when specifying object-oriented programs or
programs with pointers. Many interesting properties of relations such
as transitive closure, finiteness, and generatedness are not
expressible in first-order logic (FOL); hence neither are they
expressible in first-order fragments of specification languages. In
this paper we give an overview of the different ways such properties
can be expressed in various logics, with a particular emphasis on
extensions of FOL, i.e. transitive closure logic, fixed-point logic,
and first-order dynamic logic. Within the paper we also discuss which
of these extensions already are - or in fact should be - implemented
within specification languages. We feel that such a discussion is
necessary since it is often the case that when an extension of FOL is
implemented within a specification language it is done so in an ad hoc
manner.