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The problem of automatically proving the equality of terms over recursive functions and inductive data types is challenging, as such proofs often require auxiliary lemmas which must themselves be proven. Previous attempts at lemma discovery compromise on either efficiency or efficacy.Goal-directedapproaches are fast but limited in expressiveness, as they can only discover auxiliary lemmas which entail their goals.Theory explorationapproaches are expressive but inefficient, as they exhaustively enumerate candidate lemmas. We introducee-graph guided lemma discovery, a new approach to finding equational proofs that makes theory exploration goal-directed. We accomplish this by using e-graphs and equality saturation to efficiently construct and compactly represent the space ofallgoal-oriented proofs. This allows us to explore only those auxiliary lemmasguaranteedto help make progress on some of these proofs. We implemented our method in a new prover called CCLemma and compared it with three state-of-the-art provers across a variety of benchmarks. CCLemma performs consistently well on two standard benchmarks and additionally solves 50% more problems than the next best tool on a new challenging set. 

The Rust type system guarantees memory safety and data-race freedom. However, to satisfy Rust's type rules, many familiar implementation patterns must be adapted substantially. These necessary adaptations complicate programming and might hinder language adoption. In this paper, we demonstrate that, in contrast to manual programming, automatic synthesis is not complicated by Rust's type system, but rather benefits in two major ways. First, a Rust synthesizer can get away with significantly simpler specifications. While in more traditional imperative languages, synthesizers often require lengthy annotations in a complex logic to describe the shape of data structures, aliasing, and potential side effects, in Rust, all this information can be inferred from the types, letting the user focus on specifying functional properties using a slight extension of Rust expressions. Second, the Rust type system reduces the search space for synthesis, which improves performance. In this work, we present the first approach to automatically synthesizing correct-by-construction programs in safe Rust. The key ingredient of our synthesis procedure is Synthetic Ownership Logic, a new program logic for deriving programs that are guaranteed to satisfy both a user-provided functional specification and, importantly, Rust's intricate type system. We implement this logic in a new tool called RusSOL. Our evaluation shows the effectiveness of RusSOL, both in terms of annotation burden and performance, in synthesizing provably correct solutions to common problems faced by new Rust developers. 

We present Lifty, a domain-specific language for data-centric applications that manipulate sensitive data. A Lifty programmer annotates the sources of sensitive data with declarative security policies, and the language statically and automatically verifies that the application handles the data according to the policies. Moreover, if verification fails, Lifty suggests a provably correct repair, thereby easing the programmer burden of implementing policy enforcing code throughout the application. The main insight behind Lifty is to encode information flow control using liquid types, an expressive yet decidable type system. Liquid types enable fully automatic checking of complex, data dependent policies, and power our repair mechanism via type-driven error localization and patch synthesis. Our experience using Lifty to implement three case studies from the literature shows that (1) the Lifty policy language is sufficiently expressive to specify many real-world policies, (2) the Lifty type checker is able to verify secure programs and find leaks in insecure programs quickly, and (3) even if the programmer leaves out all policy enforcing code, the Lifty repair engine is able to patch all leaks automatically within a reasonable time.