An official website of the United States government
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 toapplyrewrite rules, can also be used toinferrewrite 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.
more »
« less
Optimizing Regular Expressions via Rewrite-Guided Synthesis
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
- Award ID(s):
- 2124010
- PAR ID:
- 10358779
- Date Published:
- Journal Name:
- 2022 31st International Conference on Parallel Architectures and Compilation Techniques (PACT)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
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
-
Nadel, Alexander; Rozier, Kristin Yvonne (Ed.)Syntax-guided synthesis (SyGuS) is a recent software synthesis paradigm in which an automated synthesis tool is asked to synthesize a term that satisfies both a semantic and a syntactic specification. We consider a special case of the SyGuS problem, where a term is already known to satisfy the semantic specification but may not satisfy the syntactic one. The goal is then to find an equivalent term that additionally satisfies the syntactic specification, provided by a context-free grammar. We introduce a novel procedure for solving this problem which leverages pattern matching and automated discovery of rewrite rules. We also provide an implementation of the procedure by modifying the SyGuS solver embedded in the cvc5 SMT solver. Our evaluation shows that our new procedure significantly outperforms the state of the art on a large set of SyGuS problems for standard SMT-LIB theories such as bit-vectors, arithmetic, and strings.more » « less
-
This paper develops a new framework for program synthesis, called semantics-guided synthesis (SemGuS), that allows a user to provide both the syntax and the semantics for the constructs in the language. SemGuS accepts a recursively defined big-step semantics, which allows it, for example, to be used to specify and solve synthesis problems over an imperative programming language that may contain loops with unbounded behavior. The customizable nature of SemGuS also allows synthesis problems to be defined over a non-standard semantics, such as an abstract semantics. In addition to the SemGuS framework, we develop an algorithm for solving SemGuS problems that is capable of both synthesizing programs and proving unrealizability, by encoding a SemGuS problem as a proof search over Constrained Horn Clauses: in particular, our approach is the first that we are aware of that can prove unrealizabilty for synthesis problems that involve imperative programs with unbounded loops, over an infinite syntactic search space. We implemented the technique in a tool called MESSY, and applied it to SyGuS problems (i.e., over expressions), synthesis problems over an imperative programming language, and synthesis problems over regular expressions.more » « less
-
Program verification and synthesis frameworks that allow one to customize the language in which one is interested typically require the user to provide a formally defined semantics for the language. Because writing a formal semantics can be a daunting and error-prone task, this requirement stands in the way of such frameworks being adopted by non-expert users. We present an algorithm that can automatically synthesize inductively defined syntax-directed semantics when given (i) a grammar describing the syntax of a language and (ii) an executable (closed-box) interpreter for computing the semantics of programs in the language of the grammar. Our algorithm synthesizes the semantics in the form of Constrained-Horn Clauses (CHCs), a natural, extensible, and formal logical framework for specifying inductively defined relations that has recently received widespread adoption in program verification and synthesis. The key innovation of our synthesis algorithm is a Counterexample-Guided Synthesis (CEGIS) approach that breaks the hard problem of synthesizing a set of constrained Horn clauses into small, tractable expression-synthesis problems that can be dispatched to existing SyGuS synthesizers. Our tool Synantic synthesized inductively-defined formal semantics from 14 interpreters for languages used in program-synthesis applications. When synthesizing formal semantics for one of our benchmarks, Synantic unveiled an inconsistency in the semantics computed by the interpreter for a language of regular expressions; fixing the inconsistency resulted in a more efficient semantics and, for some cases, in a 1.2x speedup for a synthesizer solving synthesis problems over such a language.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
