Generating compiler optimizations from proofs

Abstract

We present an automated technique for generating compiler optimizations from examples of concrete programs before and after improvements have been made to them. The key technical insight of our technique is that a proof of equivalence between the original and transformed concrete programs informs us which aspects of the programs are important and which can be discarded. Our technique therefore uses these proofs, which can be produced by translation validation or a proof-carrying compiler, as a guide to generalize the original and transformed programs into broadly applicable optimization rules.We present a category-theoretic formalization of our proof generalization technique. This abstraction makes our technique applicable to logics besides our own. In particular, we demonstrate how our technique can also be used to learn query optimizations for relational databases or to aid programmers in debugging type errors.Finally, we show experimentally that our technique enables programmers to train a compiler with application-specific optimizations by providing concrete examples of original programs and the desired transformed programs. We also show how it enables a compiler to learn efficient-to-run optimizations from expensive-to-run super-optimizers.

Relational Decomposition

“…Hints for the discovery of relational invariants may potentially arise from Amtoft et al's preconditions for conditional information flow [2], Barthe et al's product programs [10], from Rhodium's transformation rules [27], or from Tate et al's program equivalence graphs [36]. It would also be interesting to compare the expressiveness and usability of our rules for dissonant loops with the rules from translation validation [20], and to investigate how the latter can be justified in a more semantics-oriented fashion.…”

More accurate recommendations for method-level changes

“…Tate et al [37] use a proof-checker to learn transformations from examples. They can only find provably semantic-preserving transformations.…”

Provably correct peephole optimizations with alive

“…Peephole optimization patterns for a particular ISA can be generated from an ISA specification [6]. In contrast to compiler optimizations, optimized code sequences can be synthesized either with peephole pattern generation or through superoptimization [3,11,22,30,33].…”