Type-Directed Partial Evaluation

Abstract

<p>We present a strikingly simple partial evaluator, that is type-directed and reifies a compiled program into the text of a residual, specialized program. Our partial evaluator is concise (a few lines) and it handles the flagship examples of offline monovariant partial evaluation. Its source programs are constrained in two ways: they must be closed and monomorphically typable. Thus dynamic free variables need to be factored out in a ``dynamic initial environment´´. Type-directed partial evaluation uses no symbolic evaluation for specialization, and naturally processes static computational effects.</p><p>Our partial evaluator is the part of an offline partial evaluator that residualizes static values in dynamic contexts. Its restriction to the simply typed lambda-calculus coincides with Berger and Schwichtenberg's ``inverse of the evaluation functional´´ (LICS'91), which is an instance of normalization in a logical setting. As such, type-directed partial evaluation essentially achieves lambda-calculus normalization. We extend it to produce specialized programs that are recursive and that use disjoint sums and computational effects. We also analyze its limitations: foremost, it does not handle inductive types.</p><p>This paper therefore bridges partial evaluation and lambda-calculus normalization through higher-order abstract syntax, and touches upon parametricity, proof theory, and type theory (including subtyping and coercions), compiler optimization, and run-time code generation (including decompilation). It also offers a simple solution to denotational semantics-based compilation and compiler generation.</p><p>Proceedings of POPL96, the 1996 ACM Symposium on Principles of Programming Languages (to appear).</p>