The Lambda Lambda-Bar calculus: a dual calculus for unconstrained strategies

Abstract

We present a calculus which combines a simple, CCS-like representation of finite behaviors, with two dual binders λ and λ¯. Infinite behaviors are obtained through a syntactical fixed-point operator, which is used to give a translation of λ-terms. The duality of the calculus makes the roles of a function and its environment symmetrical. As usual, the environment is allowed to call a function at any given point, each time with a different argument. Dually, the function is allowed to answer any given call, each time with a different behavior. This grants terms in our language the power of functional references.