A functional logic for higher level reasoning about computation

In many areas of computation and reasoning, the value of an expression may depend on an implicit parameter, which may for example represent a program state, or time, or a possible world. In this paper we describe a formal first order logic which captures a general notion of expressions which depend on an implicit parameter. Both semantics and syntax are discussed. An important application of the logic, used as a running example, is to provide a basis for unifying the Hoare logic of procedural programs with the mathematically powerful techniques of classical logic and set theory. It is, however, beyond the scope of this paper to develop this application fully