Meyer and Wand established that the type of a term in the simply typed-calculus may be related in a straightforward manner to the type of its call-by-value CPS transform. This typing property maybe extended to Scheme-like continuation-passing primitives, from which the soundness of these extensions follows. We study the extension of these results to the Damas-Milner polymorphic type assignment system under both the call-by-value and call-by-name interpretations. We obtain CPS transforms for the call-by-value interpretation, provided that the polymorphic let is restricted to values, and for the call-by-name interpretation with no restrictions. We prove that there is no call-by-value CPS transform for the full Damas-Milner language that validates the Meyer-Wand typing property and is equivalent to the standard call-by-value transform up to-conversion. 1

Submitted for publication to Information and Computation. A summary of this paper appeared in TACS '97.

this document. Reports of further bugs, as well as design suggestions, are welcome. 2 Tutorial

. There have traditionally been two approaches to modelling environments, one by use of ønite products in Cartesian closed categories, the other by use of the base categories of indexed categories with structure. Recently, there have been more general deønitions along both of these lines: the ørst generalising from Cartesian to symmetric premonoidal categories, the second generalising from indexed categories with speciøed structure to -categories. The added generality is not of the purely mathematical kind; in fact it is necessary to extend semantics from the logical calculi studied in, say, Type Theory to more realistic programming language fragments. In this paper, we establish an equivalence between these two recent notions. We then use that equivalence to study semantics for continuations. We give three category theoretic semantics for modelling continuations and show the relationships between them. The ørst is given by a continuations monad. The second is based on a symmetric prem...

This paper is concerned with the relationship between-calculus and ��-calculus. The-calculus talks about functions and their applicative behaviour. This contrasts with the ��-calculus, that talks about processes and their interactive behaviour. Application is a special form of interaction, and therefore functions can be seen as a special form of processes. We study how the functions of the-calculus (the computable functions) can be represented as ��-calculus processes. The ��-calculus semantics of a language induces a notion of equality on the terms of that language. We therefore also analyse the equality among functions that is induced by their representation as ��-calculus processes. This paper is intended as a tutorial. It however contains some original contributions. The main ones are: the use of well-known Continuation Passing Style transforms to derive the encodings into ��-calculus and prove their correctness; the encoding of typed-calculi.