Repetitive Reduction Patterns in Lambda Calculus with letrec (Work in Progress)

TL;DR

This paper introduces an optimization for lambda calculus with letrec that predicts and reduces repetitive redex patterns, improving the efficiency of recursive function execution in functional programming languages.

Contribution

It develops an analysis to identify and eliminate repetitive redex patterns caused by sharing constructs like letrec, enhancing compiler optimization techniques.

Findings

Redundant beta-reductions in recursive functions can be predicted and eliminated.

The analysis effectively identifies binders with repetitive reduction patterns.

Potential integration into existing compilers to improve execution efficiency.

Abstract

For the lambda-calculus with letrec we develop an optimisation, which is based on the contraction of a certain class of 'future' (also: virtual) redexes. In the implementation of functional programming languages it is common practice to perform beta-reductions at compile time whenever possible in order to produce code that requires fewer reductions at run time. This is, however, in principle limited to redexes and created redexes that are 'visible' (in the sense that they can be contracted without the need for unsharing), and cannot generally be extended to redexes that are concealed by sharing constructs such as letrec. In the case of recursion, concealed redexes become visible only after unwindings during evaluation, and then have to be contracted time and again. We observe that in some cases such redexes exhibit a certain form of repetitive behaviour at run time. We describe an analysis for identifying binders that give rise to such repetitive reduction patterns, and eliminate them by a sort of predictive contraction. Thereby these binders are lifted out of recursive positions or eliminated altogether, as a result alleviating the amount of beta-reductions required for each recursive iteration. Both our analysis and simplification are suitable to be integrated into existing compilers for functional programming languages as an additional optimisation phase. With this work we hope to contribute to increasing the efficiency of executing programs written in such languages.