SHF: Medium: Next Generation Equality Saturation by way of Datalog

所有编程技术（包括优化编译器、查询优化器、定理证明器和模型检查器）面临的一个共同挑战是对“术语等价”进行推理的能力——也就是说，当一个程序与另一个程序等价时。优化编译器寻求用另一个执行速度更快的等效指令序列替换一个指令序列。结构化查询语言（SQL）查询优化器从查询计划开始，以最低的成本搜索等价计划，定理证明者需要推断表达式之间的等价，以证明数学方程。检验两个表达式的等价性是计算机科学的基本问题之一。该项目的新颖之处在于，通过使用一种称为“相等饱和”的技术，建立了一个检验相等性的新框架。而不是将一个项重写为一个新的项并忘记旧的项，相等饱和将所有等价项保存在一个单一的，紧凑的表示中。该项目的影响是开发检查等价性的新技术，通过提高编译器、查询优化器和定理证明器的推理和优化表达式的能力，这些技术将影响编译器、查询优化器和定理证明器。等式饱和依赖于使用E-Graph的一组表达式的紧凑表示，其中等价表达式被分组到e类中，单个操作符由e - node表示。该方法的核心是在一组指定规则和相等条件下对给定表达式的闭包进行定点计算。该项目有三个重点。第一个推力用Datalog规则扩展了相等饱和。该项目利用了数据表是一种基于固定点语义的查询语言这一事实，并构建了一个新的框架，该框架允许数据表规则以统一的方式与相等断言相结合。在第二个推力中，该项目对确保终止相等饱和的条件进行了理论研究。改写界、追逐界、树自动机界对这一问题进行了多方面的独立研究；本项目将这些理论结果应用于相等饱和。最后，在第三个推力中，该项目创建了新的均匀饱和度优化技术，以提高其性能。这些优化将受到数据库查询优化技术的启发，例如最坏情况最优连接、半幼稚求值和多查询优化。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

A common challenge faced by all programming technology, including optimizing compilers, query optimizers, theorem provers, and model checkers, is the ability to reason about "term equivalence" -- that is, when one program is equivalent to another. Optimizing compilers seek to replace one sequence of instructions with another equivalent sequence that executes faster. Structured Query Language (SQL) query optimizers start from a query plan and search for an equivalent plan with lowest cost, and theorem provers need to infer equivalences between expressions to prove mathematical equations. Checking the equivalence of two expressions is one of the fundamental problems in computer science. The project's novelties are building a new framework for checking equivalence, by using a technique called equality saturation. Instead of rewriting a term to a new one and forgetting the old one, equality saturation keeps all equivalent terms in a single, compact representation. The project's impacts are developing new technology for checking equivalence that will impact compilers, query optimizers, and theorem provers, by improving their ability to reason about, and to optimize expressions.Equality saturation relies on a compact representation of a set of expressions using an E-Graph, where equivalent expressions are grouped into E-Classes, and individual operators are represented by E-Nodes. At the core of the approach is a fixpoint computation of the closure of a given expression under a specified set of rules and under equality. The project pursues three thrusts. The first thrust extends equality saturation with Datalog rules. The project exploits the fact that datalog is a query language that is also based on a fixpoint semantics, and builds a novel framework that allows datalog rules to be combined with equality assertions, in a unified way. In the second thrust the project conducts a theoretical investigation of the conditions that ensure termination of equality saturation. This problem has been studied independently under various aspects by the term rewriting community, the chase community, and the tree automata community; this project adapts those theoretical results to equality saturation. Finally, in the third thrust, the project creates new optimization techniques for equality saturation in order to improve its performance. These optimizations will be inspired by database query optimization techniques, such as worst-case optimal joins, semi-naive evaluation, and multiquery optimization.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.