The last few years have seen a renewed interest in continuations for expressing advanced control structures in programming languages, and new models such as Abstract Continuations have been proposed to capture these dimensions. This article investigates an alternative formulation, exploiting the latent expressive power of the standard continuation-passing style (CPS) instead of introducing yet other new concepts. We build on a single foundation: abstracting control as a hierarchy of continuations, each one modeling a specific language feature as acting on nested evaluation contexts. We show how iterating the continuation-passing conversion allows us to specify a wide range of control behavior. For example, two conversions yield an abstraction of Prologstyle backtracking. A number of other constructs can likewise be expressed i...

This thesis presents a formalism for reasoning about continuations in a categorical setting. It points out how values and continuations ca n be seen as categorically dual concepts, and that this symmetry extends to not only data types, but also control structures, evaluation strategies and higher-order constructs. The central idea is a view of continuations as a declarative concept, rather than an imperative one, and the implicat ions of this make up the spine of the presentation. A symmetrical extension of the typed *-calculus is introduced, where values and continuations are treated as opposites, permitting a mirror-image syntax for dual categorical concepts like products and coproducts. An implementable semantic description and a static type system for this calculus are given. A purely categorical description of the language is also obtained, through a correspondence with a system of combinatory logic, similar to a cartesian closed category, but with a completely symmetrical set of axioms. Finally, a number of possible practical applications and directions for further research are suggested.

Condensed graphs are proposed as an intermediate representation for functional and imperative languages. This representation may be executed on a variety of architectures, implementing a multilevel Condensed Graphs abstract machine. This machine incorporates characteristics and feedback information of its underlying architecture and guides dynamic topological transformations of the representation so as to optimize execution. These transformations can add or remove parallelism and change evaluation orders.