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.

Equality saturation is an emerging technique for program and query optimization developed in the programming language community. It performs term rewriting over an E-graph, a data structure that compactly represents a program space. Despite its popularity, the theory of equality saturation lags behind the practice. In this paper, we define a fixpoint semantics of equality saturation based on tree automata and uncover deep connections between equality saturation and the chase. We characterize the class of chase sequences that correspond to equality saturation. We study the complexities of terminations of equality saturation in three cases: single-instance, all-term-instance, and all-E-graph-instance. Finally, we define a syntactic criterion based on acyclicity that implies equality saturation termination.

We propose a new synthesis algorithm that can efficiently search programs with local variables (e.g., those introduced by lambdas). Prior bottom-up synthesis algorithms are not able to evaluate programs with free local variables , and therefore cannot effectively reduce the search space of such programs (e.g., using standard observational equivalence reduction techniques), making synthesis slow. Our algorithm can reduce the space of programs with local variables. The key idea, dubbed lifted interpretation , is to lift up the program interpretation process, from evaluating one program at a time to simultaneously evaluating all programs from a grammar. Lifted interpretation provides a mechanism to systematically enumerate all binding contexts for local variables, thereby enabling us to evaluate and reduce the space of programs with local variables. Our ideas are instantiated in the domain of web automation. The resulting tool, Arborist , can automate a significantly broader range of challenging tasks more efficiently than state-of-the-art techniques including WebRobot and Helena.

We present egglog, a fixpoint reasoning system that unifies Datalog and equality saturation (EqSat). Like Datalog, egglog supports efficient incremental execution, cooperating analyses, and lattice-based reasoning. Like EqSat, egglog supports term rewriting, efficient congruence closure, and extraction of optimized terms. We identify two recent applications -- a unification-based pointer analysis in Datalog and an EqSat-based floating-point term rewriter -- that have been hampered by features missing from Datalog but found in EqSat or vice-versa. We evaluate our system by reimplementing those projects in egglog. The resulting systems in egglog are faster, simpler, and fix bugs found in the original systems.

We present a new approach to e-matching based on relational join; in particular, we apply recent database query execution techniques to guarantee worst-case optimal run time. Compared to the conventional backtracking approach that always searches the e-graph "top down", our new relational e-matching approach can better exploit pattern structure by searching the e-graph according to an optimized query plan. We also establish the first data complexity result for e-matching, bounding run time as a function of the e-graph size and output size. We prototyped and evaluated our technique in the state-of-the-art egg e-graph framework. Compared to a conventional baseline, relational e-matching is simpler to implement and orders of magnitude faster in practice.

Machine learning is increasingly applied in high-stakes decision making that directly affect people's lives, and this leads to an increased demand for systems to explain their decisions. Explanations often take the form of counterfactuals , which consists of conveying to the end user what she/he needs to change in order to improve the outcome. Computing counterfactual explanations is challenging, because of the inherent tension between a rich semantics of the domain, and the need for real time response. In this paper we present CeCo, the first system that can compute plausible and feasible counterfactual explanations in real time. At its core, CeCo relies on a genetic algorithm, which is customized to favor searching counterfactual explanations with the smallest number of changes. To achieve real-time performance, we introduce two novel optimizations: Δ-representation of candidate counterfactuals, and partial evaluation of the classifier. We compare empirically CeCo against five other systems described in the literature, and show that it is the only system that can achieve both high quality explanations and real time answers.