A π – calculus Semantics of Logical Variables and Unification

A π–calculus semantics of terms and logical variables, environment creation visavis term copying and variable refreshing, and sequential unification is presented. The π–calculus’s object–oriented approach to modelling evolving communication structures is used to model the evolving communication environment found in concurrent logic program computations. The novelty of this semantics is that it explicitly models logic variables as active channels. These channels are referenced by π–calculus channel labels, and when used in concert with the ν restriction operator, model variable scopes and environments. Sequential unification without occurs check is modelled by traversing term expressions, and binding variables to terms as appropriate. The π–calculus is well-suited for this, as its object–oriented view of concurrency permits the modelling of the object passing and variable redirection that occurs during unification. This semantics is a central component of a more comprehensive operational semantics of concurrent logic programming languages currently being developed.