In order to simplify the compilation process, many compilers for higher-order languages use the continuation-passing style (CPS) transformation in a first phase to generate an intermediate representation of the source program. The salient aspect of this intermediate form is that all procedures take an argument that represents the rest of the computation (the “continuation”). Since the nai¨ve CPS transformation considerably increases the size of programs, CPS compilers perform reductions to produce a more compact intermediate representation. Although often implemented as a part of the CPS transformation, this step is conceptually a second phase. Finally, code generators for typical CPS compilers treat continuations specially in order to optimize the interpretation of continuation parameters.

Abstract An extension of ML with continuation primitives similar to those found in Scheme is considered. A number of alternative type systems are discussed, and several programming examples are given. A continuation-based operational semantics is defined for a small, purely functional language, and the soundness of the Damas–Milner polymorphic type assignment system with respect to this semantics is proved. The full Damas–Milner type system is shown to be unsound in the presence of first-class continuations. Restrictions on polymorphism similar to those introduced in connection with reference types are shown to suffice for soundness.

An extension of Standard ML with continuation primitives similar to those found in Scheme is considered.A number of alternative type systems are discussed, and several programming examples are given.The semantics of type assignment for a small, purely functional fragment of the language is presented, for which both a Milner-style soundness theorem and an observational soundness theorem may be established.