Pragmatic Aspects of Type-Directed Partial Evaluation

Type-directed partial evaluation stems from the residualization of static values in dynamic contexts, given their type and the type of their free variables. Its algorithm coincides with the algorithm for coercinga subtype value into a supertype value, which itself coincides withBerger and Schwichtenberg's normalization algorithm for the simply typed lambda-calculus. Type-directed partial evaluation thus can be used to specialize a compiled, closed program, given its type.Since Similix, let-insertion is a cornerstone of partial evaluators for call-by-value procedural languages with computational effects (such as divergence). It prevents the duplication of residual computations, and more generally maintains the order of dynamic side effects in the residual program. This article describes the extension of type-directed partial evaluationto insert residual let expressions. This extension requires theuser to annotate arrow types with effect information. It is achieved by delimiting and abstracting control, comparably to continuation-based specialization in direct style. It enables type-directed partial evaluation of programs with effects (e.g., a definitional lambda-interpreter for an imperative language) that are in direct style. The residual programsare in A-normal form. A simple corollary yields CPS (continuation-passing style) terms instead. We illustrate both transformations with two interpreters for Paulson's Tiny language, a classical example in partial evaluation