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推理“项等价”的能力--也就是说，当一个程序等价于另一个程序时。 优化编译器试图用另一个执行速度更快的等效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，搜索具有最低成本的等价计划，定理证明器需要推断表达式之间的等价性以证明数学方程。 检验两个表达式的等价性是计算机科学中的基本问题之一。 该项目的创新之处在于通过使用一种称为相等饱和的技术来构建一个新的检查等价性的框架。 等式饱和不是将一个项重写为一个新项并忘记旧项，而是将所有等价项保持在一个单一的紧凑表示中。 该项目的影响是开发新的等价性检查技术，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，来影响它们。等式饱和依赖于使用E-Graph对一组表达式的紧凑表示，其中等价表达式被分组到E-Class中，各个运算符由E-Node表示。 该方法的核心是在一组指定的规则和等式下对给定表达式的闭包进行不动点计算。 该项目追求三个目标。 第一个推力扩展了平等饱和与Datatrance规则。 该项目利用了这样一个事实，即数据库是一种查询语言，也是基于一个定点语义，并建立了一个新的框架，允许数据库规则与平等断言相结合，在一个统一的方式。 在第二个推力的项目进行了理论研究的条件，确保终止平等饱和。 这个问题已经在各个方面独立研究了长期重写社区，追逐社区和树自动机社区;该项目将这些理论结果适用于等式饱和。 最后，在第三个推力中，该项目创建了新的优化技术，以改善其性能。 这些优化将受到数据库查询优化技术的启发，例如最坏情况下的最佳连接，半朴素评估和多查询优化。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.