A Syntactic Theory of Dynamic Binding

Dynamic binding, which has always been associated with Lisp, is still semantically obscure to many. Although largely replaced by lexical scoping, not only does dynamic binding remain an interesting and expressive programming technique in specialised circumstances, but also it is a key notion in semantics. This paper presents a syntactic theory that enables the programmer to perform equational reasoning on programs using dynamic binding. The theory is proved to be sound and complete with respect to derivations allowed on programs in "dynamic-environment passing style". From this theory, we derive a sequential evaluation function in a context-rewriting system. Then, we exhibit the power and usefulness of dynamic binding in two different ways. First, we prove that dynamic binding adds expressiveness to a purely functional language. Second, we show that dynamic binding is an essential notion in semantics that can be used to define the semantics of exceptions. Afterwards, we further refine the evaluation function into the popular implementation strategy called deep binding. Finally, following the saying that deep binding is suitable for parallel evaluation, we present the parallel evaluation function of a future-based functional language extended with constructs for dynamic binding