Lambda-Dropping: Transforming Recursive Equations into Programs with Block Structure

Abstract

Lambda-lifting a block-structured program transforms it into a set of recursive equations. We present the symmetric transformation: lambda-dropping. Lambda-dropping a set of recursive equations restores block structure and lexical scope.<br /> <br />For lack of block structure and lexical scope, recursive equations must carry around all the parameters that any of their callees might possibly need. Both lambda-lifting and lambda-dropping thus require one to compute Def/Use paths:<ul><li>for lambda-lifting: each of the functions occurring in the path of a free variable is passed this variable as a parameter;</li><li>for lambda-dropping: parameters which are used in the same scope as their definition do not need to be passed along in their path.</li></ul>A program whose blocks have no free variables is scope-insensitive. Its blocks are then free to float (for lambda-lifting) or to sink (for lambda-dropping) along the vertices of the scope tree.<br /> <br />Our primary application is partial evaluation. Indeed, many partial evaluators for procedural programs operate on recursive equations. To this end, they lambda-lift source programs in a pre-processing phase. But often, partial evaluators [automatically] produce residual recursive equations with dozens of parameters, which most compilers do not handle efficiently. We solve this critical problem by lambda-dropping residual programs in a post-processing phase, which significantly improves both their compile time and their run time.<br /> <br /> Lambda-lifting has been presented as an intermediate transformation in compilers for functional languages. We study lambda-lifting and lambda-dropping per se, though lambda-dropping also has a use as an intermediate transformation in a compiler: we noticed that lambda-dropping a program corresponds to transforming it into the functional representation of its optimal SSA form. This observation actually led us to substantially improve our PEPM '97 presentation of lambda-dropping.<br /><br />Superseded by BRICS-RS-99-27.