Dynamic shape computations have become critical in modern machine learning workloads, especially in emerging large language models. The success of these models has driven the demand for their universal deployment across a diverse set of backend environments. In this paper, we present Relax, a compiler abstraction for optimizing end-to-end dynamic machine learning workloads. Relax introduces a cross-level abstraction that encapsulates computational graphs, loop-level tensor programs, and external library calls in a single representation. Relax also introduces first-class symbolic shape annotations to track dynamic shape computations globally across the program, enabling dynamic shape-aware cross-level optimizations. We build an end-to-end compilation framework using the proposed approach to optimize dynamic shape models. Experimental results on LLMs show that Relax delivers performance competitive with state-of-the-art systems across various GPUs and enables deployment of emerging models to a broader set of emerging environments, including mobile phones, embedded devices, and web browsers.

Building a trustworthy life-critical embedded system requires deep reasoning about the potential effects that sequences of machine instructions can have on full system operation. Rather than trying to analyze complete binaries and the countless ways their instructions can interact with one another — memory, side effects, control registers, implicit state, etc. — we explore a new approach. We propose an architecture controlled by a thin computational layer designed to tightly correspond with the lambda calculus, drawing on principles of functional programming to bring the assembly much closer to myriad reasoning frameworks, such as the Coq proof assistant. This approach allows assembly-level verified versions of critical code to operate safely in tandem with arbitrary code, including imperative and unverified system components, without the need for large supporting trusted computing bases. We demonstrate that this computational layer can be built in such a way as to simultaneously provide full programmability and compact, precise, and complete semantics, while still using hardware resources comparable to normal embedded systems. To demonstrate the practicality of this approach, our FPGA-implemented prototype runs an embedded medical application which monitors and treats life-threatening arrhythmias. Though the system integrates untrusted and imperative components, our architecture allows for the formal verification of multiple properties of the end-to-end system. We present a proof of correctness of the assembly-level implementation of the core algorithm in Coq, the integrity of trusted data via a non-interference proof, and a guarantee that our prototype meets critical timing requirements.

Though statistical analyses are centered on research questions and hypotheses, current statistical analysis tools are not. Users must first translate their hypotheses into specific statistical tests and then perform API calls with functions and parameters. To do so accurately requires that users have statistical expertise. To lower this barrier to valid, replicable statistical analysis, we introduce Tea, a high-level declarative language and runtime system. In Tea, users express their study design, any parametric assumptions, and their hypotheses. Tea compiles these high-level specifications into a constraint satisfaction problem that determines the set of valid statistical tests and then executes them to test the hypothesis. We evaluate Tea using a suite of statistical analyses drawn from popular tutorials. We show that Tea generally matches the choices of experts while automatically switching to non-parametric tests when parametric assumptions are not met. We simulate the effect of mistakes made by non-expert users and show that Tea automatically avoids both false negatives and false positives that could be produced by the application of incorrect statistical tests.

Deciding the equivalence of SQL queries is a fundamental problem in data management. As prior work has mainly focused on studying the theoretical limitations of the problem, very few implementations for checking such equivalences exist. In this paper, we present a new formalism and implementation for reasoning about the equivalences of SQL queries. Our formalism, U-semiring, extends SQL's semiring semantics with unbounded summation and duplicate elimination. U-semiring is defined using only very few axioms and can thus be easily implemented using proof assistants such as Lean for automated query reasoning. Yet, they are sufficient enough to enable us reason about sophisticated SQL queries that are evaluated over bags and sets, along with various integrity constraints. To evaluate the effectiveness of U-semiring, we have used it to formally verify 68 equivalent queries and rewrite rules from both classical data management research papers and real-world SQL engines, where many of them have never been proven correct before.

Building a trustworthy life-critical embedded system requires deep reasoning about the potential effects that sequences of machine instructions can have on full system operation. Rather than trying to analyze complete binaries and the countless ways their instructions can interact with one another --- memory, side effects, control registers, implicit state, etc. --- we explore a new approach. We propose an architecture controlled by a thin computational layer designed to tightly correspond with the lambda calculus, drawing on principles of functional programming to bring the assembly much closer to myriad reasoning frameworks, such as the Coq proof assistant. This approach allows assembly-level verified versions of critical code to operate safely in tandem with arbitrary code, including imperative and unverified system components, without the need for large supporting trusted computing bases. We demonstrate that this computational layer can be built in such a way as to simultaneously provide full programmability and compact, precise, and complete semantics, while still using hardware resources comparable to normal embedded systems. To demonstrate the practicality of this approach, our FPGA-implemented prototype runs an embedded medical application which monitors and treats life-threatening arrhythmias. Though the system integrates untrusted and imperative components, our architecture allows for the formal verification of multiple properties of the end-to-end system, including a proof of correctness of the assembly-level implementation of the core algorithm, the integrity of trusted data via a non-interference proof, and a guarantee that our prototype meets critical timing requirements.

We describe the metaprogramming framework currently used in Lean, an interactive theorem prover based on dependent type theory. This framework extends Lean's object language with an API to some of Lean's internal structures and procedures, and provides ways of reflecting object-level expressions into the metalanguage. We provide evidence to show that our implementation is performant, and that it provides a convenient and flexible way of writing not only small-scale interactive tactics, but also more substantial kinds of automation.

Language fuzzing is a bug-finding technique for testing compilers and interpreters, its effectiveness depends upon the ability to automatically generate valid programs in the language under test. Despite the proven success of language fuzzing, there is a severe lack of tool support for fuzzing statically-typed languages with advanced type systems because existing fuzzing techniques cannot effectively and automatically generate well-typed programs that use sophisticated types. In this work we describe how to automatically generate well-typed programs that use sophisticated type systems by phrasing the problem of well-typed program generation in terms of Constraint Logic Programming (CLP). In addition, we describe how to specifically target the typechecker implementation for testing, unlike all existing work which ignores the typechecker. We focus on typechecker precision bugs, soundness bugs, and consistency bugs. We apply our techniques to Rust, a complex, industrial-strength language with a sophisticated type system.

Fuzz testing builds confidence in compilers and interpreters. It is desirable for fuzzers to allow targeted generation of programs that showcase specific language features and behaviors. However, the predominant program generation technique used by most language fuzzers, stochastic context-free grammars, does not have this property. We propose the use of constraint logic programming (CLP) for program generation. Using CLP, testers can write declarative predicates specifying interesting programs, including syntactic features and semantic behaviors. CLP subsumes and generalizes the stochastic grammar approach.

Type feedback and type inference are two common methods used to optimize dynamic languages such as JavaScript. Each of these methods has its own strengths and weaknesses, and we propose that each can benefit from the other if combined in the right way. We explore the interdependency between these two methods and propose two novel ways to combine them in order to significantly increase their aggregate benefit and decrease their aggregate overhead. In our proposed strategy, an initial type inference pass is applied that can reduce type feedback overhead by enabling more intelligent placement of profiling hooks. This initial type inference pass is novel in the literature. After profiling, a final type inference pass uses the type information from profiling to generate efficient code. While this second pass is not novel, we significantly improve its effectiveness in a novel way by feeding the type inference pass information about the function signature, i.e., the types of the function's arguments for aspecific function invocation. Our results show significant speedups when using these low-overhead strategies, ranging from 1.2x to 4x over an implementation that does not perform type feedback or type inference based optimizations. Our experiments are carried out across a wide range of traditional benchmarks and realistic web applications. The results also show an average reduction of 23.5% in the size of the profiled data for these benchmarks.