Explicit Polymorphism and CPS Conversion,

Abstract

We study the typing properties of CPS conversion for an extension of F, with control operators. Two classes of evaluation strategies are considered, each with call-by-name and call-by-value variants. Under the "standard" strategies, constructor abstractions are values, and constructor applications can lead to non-trivial control effects. In contrast, the "ML-like" strategies evaluate beneath constructor abstractions, reflecting the usual interpretation of programs in languages based on implicit polymorphism. Three continuation passing style sub-languages are considered, one on which the standard strategies coincide, one on which the ML-like strategies coincide, and one on which all the strategies coincide. Compositional, type-preserving CPS transformation algorithms are given for the standard strategies, resulting in terms on which all evaluation strategies coincide. This has as a corollary the soundness and termination of well-typed programs under the standard evaluation strategies. A similar result is obtained for the ML-like ca-by-name strategy. In contrast, such results are obtained for the call-by value ML-like strategy only for a restricted sub-language in which constructor abstractions are limited to values.

A practical soft type system for scheme

“…This operator provides a powerful form of nonlocal control that can be used to define exceptions, build backtracking algorithms, schedule multiple threads of control, etc. Harper and Lillibridge [1993] discovered that naively combining first-class continuations with polymorphism leads to an unsound type system, just as naively combining assignment and polymorphism does. Fortunately, the same solution of restricting polymorphism to values works for both assignment and first-class continuations [Wright and Felleisen 1994].…”

Intensional analysis of quantified types

“…· · · Such type transformations [Harper and Lillibridge 1993] are conventionally expressed in a metalanguage. However, when transforming polymorphic types like ∀α : .…”