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 re-lational 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.

Equality-Based Translation Validator for LLVM

“…Generating Proofs. As described in our follow-up work [6], after Peggy validates a transformation it can use the resulting E-PEG to generate a proof of equivalence of the two programs. This proof has already helped us determine how often axioms are useful.…”

A quantitative study of reductions in algebraic libraries

“…Another direction would be to develop more use cases of assumption to increase its benefit to symbolic computation. As inspired by recent work on axiom based verifications for Java program [12,11], it would be also interesting to see how user assumption can help verify program transformations for computer algebra code.…”

Precise reasoning with structured time, structured heaps, and collective operations

“…Our optimistic fixpoint approach is directly inspired by Lerner et al 's work on composing dataflow analyses and transformations [Lerner et al 2002]. Related work has aimed to automatically prove the correctness of compiler optimizations [Lerner et al 2003], and on generating compiler optimizations from proofs of equivalence and before/after examples [Tate et al 2010]. A related line of work models a space of possible program transformations given by equivalence rules through the notion of equality saturation, based on a program equivalence graphs (PEGs) [Tate et al 2011] as IR.…”