Abstract

This thesis attempts to make precise the structure inherent in Continuation Passing Style (CPS). We emphasize that CPS translates λ-calculus into a very basic calculus that does not have functions as primitive. We give an abstract categorical presentation of continuation semantics by taking the continuation type constructor ¬ (or cont in Standard ML of New Jersey) as primitive. This constructor on types extends to a contravariant functor on terms which is adjoint to itself on the left; restricted to the subcategory of those programs that do not manipulate the current continuation, it is adjoint to itself on the right. The motivating example of such a category is built from (equivalence classes of typing judgements for) continuation passing style (CPS) terms. The categorical approach suggests a notion of effect-free term as well as some operators for manipulating continuations. We use these for writing programs that illustrate our categorical approach and refute some conjectures about control effects. A call-by-value λ-calculus with the control operator callcc can be interpreted. Arrow types are broken down into continuation types for argument/resultcontinuations pairs, reflecting the fact that CPS compiles functions into a special case of continuations. Variant translation are possible, among them “lazy ” callby-name, which can be derived by way of argument thunking, and a genuinely call-by-name transform. Specialising the semantics to the CPS term model allows a rational reconstruction of various CPS transforms.

Citations