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Rewrite rules are critical in equality saturation, an increasingly popular technique in optimizing compilers, synthesizers, and verifiers. Unfortunately, developing high-quality rulesets is difficult and error-prone. Recent work on automatically inferring rewrite rules does not scale to large terms or grammars, and existing rule inference tools are monolithic and opaque. Equality saturation users therefore struggle to guide inference and incrementally construct rulesets. As a result, most users still manually develop and maintain rulesets. This paper proposes Enumo, a new domain-specific language for programmable theory exploration. Enumo provides a small set of core operators that enable users to strategically guide rule inference and incrementally build rulesets. Short Enumo programs easily replicate results from state-of-the-art tools, but Enumo programs can also scale to infer deeper rules from larger grammars than prior approaches. Its composable operators even facilitate developing new strategies for ruleset inference. We introduce a new fast-forwarding strategy that does not require evaluating terms in the target language, and can thus support domains that were out of scope for prior work. We evaluate Enumo and fast-forwarding across a variety of domains. Compared to state-of-the-art techniques, enumo can synthesize better rulesets over a diverse set of domains, in some cases matching the effects of manually-developed rulesets in systems driven by equality saturation.
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Rewrite rule inference using equality saturation
Many compilers, synthesizers, and theorem provers rely on rewrite rules to simplify expressions or prove equivalences. Developing rewrite rules can be difficult: rules may be subtly incorrect, profitable rules are easy to miss, and rulesets must be rechecked or extended whenever semantics are tweaked. Large rulesets can also be challenging to apply: redundant rules slow down rule-based search and frustrate debugging. This paper explores how equality saturation, a promising technique that uses e-graphs to apply rewrite rules, can also be used to infer rewrite rules. E-graphs can compactly represent the exponentially large sets of enumerated terms and potential rewrite rules. We show that equality saturation efficiently shrinks both sets, leading to faster synthesis of smaller, more general rulesets. We prototyped these strategies in a tool dubbed Ruler. Compared to a similar tool built on CVC4, Ruler synthesizes 5.8× smaller rulesets 25× faster without compromising on proving power. In an end-to-end case study, we show Ruler-synthesized rules which perform as well as those crafted by domain experts, and addressed a longstanding issue in a popular open source tool.
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- Award ID(s):
- 1749570
- PAR ID:
- 10330235
- Date Published:
- Journal Name:
- Proceedings of the ACM on Programming Languages
- Volume:
- 5
- Issue:
- OOPSLA
- ISSN:
- 2475-1421
- Page Range / eLocation ID:
- 1 to 28
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)An e-graph efficiently represents a congruence relation over many expressions. Although they were originally developed in the late 1970s for use in automated theorem provers, a more recent technique known as equality saturation repurposes e-graphs to implement state-of-the-art, rewrite-driven compiler optimizations and program synthesizers. However, e-graphs remain unspecialized for this newer use case. Equality saturation workloads exhibit distinct characteristics and often require ad-hoc e-graph extensions to incorporate transformations beyond purely syntactic rewrites. This work contributes two techniques that make e-graphs fast and extensible, specializing them to equality saturation. A new amortized invariant restoration technique called rebuilding takes advantage of equality saturation's distinct workload, providing asymptotic speedups over current techniques in practice. A general mechanism called e-class analyses integrates domain-specific analyses into the e-graph, reducing the need for ad hoc manipulation. We implemented these techniques in a new open-source library called egg. Our case studies on three previously published applications of equality saturation highlight how egg's performance and flexibility enable state-of-the-art results across diverse domains.more » « less
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Roy, Sudeepa; Kara, Ahmet (Ed.)Recent work in programming languages developed an approach to term rewritings based on equality saturation (EqSat), which, instead of applying destructively the rewrite rules, maintains all equivalent expressions in a structure called an E-graph. This paper describes two surprising connections between EqSat and databases, going both ways. On one hand equality saturation can be viewed as a query evaluation problem, with great benefits. On the other hand, most sophisticated SQL query optimizers are based on the Volcano/Cascades framework which, we explain, is a variant of EqSat.more » « less
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Equality saturation is a program optimization technique based on non-destructive rewriting and a form of abstract interpretation called e-class analysis. Existing e-class analyses are pessimistic and therefore typically imprecise when analyzing cyclic programs, such as those in SSA form. We show that a straightforward optimistic variant of e-class analysis can result in unsoundness, due to a subtlety in how e-graphs represent programs. We propose an abstract interpretation algorithm that circumvents this issue and can optimistically analyze e-graphs during equality saturation. This results in a unified algorithm for optimistic analysis and non-destructive rewriting. We implement a prototype abstract interpreter and equality saturation tool for SSA programs. Our tool exhibits precision improvements over pure abstract interpretation (without rewriting) and pessimistic e-class analysis on example programs. Additionally, its performance is comparable to existing abstract interpretation and e-class analysis techniques.more » « less
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Regular expressions are pervasive in modern systems. Many real world regular expressions are inefficient, sometimes to the extent that they are vulnerable to complexity-based attacks, and while much research has focused on detecting inefficient regular expressions or accelerating regular expression matching at the hardware level, we investigate automatically transforming regular expressions to remove inefficiencies. We reduce this problem to general expression optimization, an important task necessary in a variety of domains even beyond compilers, e.g., digital logic design, etc. Syntax-guided synthesis (SyGuS) with a cost function can be used for this purpose, but ordered enumeration through a large space of candidate expressions can be prohibitively expensive. Equality saturation is an alternative approach which allows efficientconstruction and maintenance of expression equivalence classes generated by rewrite rules, but the procedure may not reach saturation, meaning global minimality cannot be confirmed. We present a new approach called rewrite-guided synthesis (ReGiS), in which a unique interplay between SyGuS and equality saturation-based rewriting helps to overcome these problems, resulting in an efficient, scalable framework for expression optimization.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1145/3485496
