Matías Toro

Practical SQL engines differ in subtle ways in their handling of typing constraints and implicit type casts. These issues, usually not considered in formal accounts of SQL, directly affect the portability of queries between engines. To address this problem, we present a formal typing semantics for SQL, named TRAF , that explicitly captures both static and dynamic type behavior. The system TRAF is expressed in terms of abstract operators that provide the necessary leeway to systematically model the type and cast behavior of different SQL engines (PostgreSQL, MS SQL Server, MySQL, SQLite, and Oracle). We show that this formalism provides formal guarantees for the handling of types. We identify practical conditions under which engine instantiations satisfy type safety and type soundness. In this regard, TRAF can serve as an explicit and testable account of typing in existing engines, potentially guide their evolution, and provide a formal basis to study type-aware query optimizations and design provably-correct query translators. We also test the adequacy of the formalism by implementing TRAF in Python for these five engines and testing it with synthetic queries, SQLancer++- generated queries, and adapted Spider and Calcite benchmark queries.

Efficiently supporting sound gradual typing in a language with structural types is challenging. To date, the Grift compiler is the only close-to-the-metal implementation of gradual typing in this setting, exploiting coercions for runtime checks, and further extended with monotonic references for efficient access to statically-typed data structures. On the language design and semantics side, the Abstracting Gradual Typing (AGT) methodology has proven fruitful to elucidate existing designs and to innovate by deriving gradualizations of a wide variety of typing disciplines and language features. Grounded in abstract interpretation, the Curry-Howard inspired runtime semantics of AGT is based on the notion of evidence for consistent judgments that evolve during reduction, monitoring the plausibility of well-typedness. While expressive and versatile, it is unclear whether such evidence-based semantics are a viable route to realize an efficient implementation of gradual typing. In this work, we explore this question by designing, implementing, and evaluating an evidence-based compiler, called GrEv. We explain how to bridge the gap between the formal semantics and the GrEv compiler implementation, and identify novel monotonic semantics. We empirically evaluate the performance of GrEv on the Grift benchmark suite. The results show that an evidence-based compiler can be competitive with, and even faster than, a coercion-based compiler, exhibiting more stability across configurations on the static-to-dynamic spectrum. In addition to enriching the space of gradual typing compilers, this work opens a direct door to exploring efficient implementations of the many advanced gradual typing disciplines formally derived with AGT in the literature.

Graph databases have become an important data management technology across various domains, including biology, sociology, industry (e.g. fraud detection, supply chain management, financial services), and investigative journalism, due to their ability to efficiently store and query large-scale knowledge graphs and networks. Recently, the Graph Query Language (GQL) was introduced as a new ISO standard providing a unified framework for querying graphs. However, this initial specification lacks a formal type system for query validation. As a result, queries can fail at runtime due to type inconsistencies or produce empty results without prior warning. Solving this issue could have great benefits for users in writing correct queries, especially when handling large datasets. To address this gap, we introduce a formal type model for a core fragment of GQL extended with property-based filtering and imprecise types both in the schema and the queries. This model, named FPPC, enables static detection of semantically incorrect and stuck queries, improving user feedback. We establish key theoretical properties, including emptiness (detecting empty queries due to type mismatches) and type safety (guaranteeing that well-typed queries do not fail at runtime). Additionally, we prove a gradual guarantee, ensuring that removing type annotations either does not introduce static type errors or only increases the result set. By integrating imprecision into GQL, FPPC offers a flexible solution for handling schema evolution and incomplete type information. This work contributes to making GQL more robust, improving both its usability and its formal foundation.

Gradual typing has long been advocated as a means to bridge the gap between static and dynamic typing disciplines, enabling a range of use cases such as the gradual migration of existing dynamically typed code to more statically typed code, as well as making advanced static typing disciplines more accessible. To assess whether a given gradual language can effectively support these use cases, several formal properties have been proposed, most notably the refined criteria set forth by Siek et al. One criterion asserts that the dynamic extreme of the spectrum should be expressible in the gradual language, formalized by the existence of an adequate embedding from the corresponding dynamic language. We observe that the existing dynamic embedding criterion does not capture the desirable property of being able to ascribe embedded code to a static type that it semantically satisfies, and ensure reliable interactions with other components within the gradual language. Specifically, we introduce the notion of robustness for gradual terms, meaning that when interacting with any gradual context, runtime failures that may occur ought to be caused by the context, not by the robust term itself. We then formulate the robust dynamic embedding criterion: if a dynamic component semantically satisfies a given static type, then its embedding subsequently ascribed to that static type should be a robust term. We demonstrate that robust dynamic embedding is not implied by any existing metatheoretical property from the literature, and is not upheld by various existing gradual languages. We show that robust dynamic embedding is achievable with a gradualized simply-typed language. All the results are formalized in the Rocq proof assistant. This novel criterion complements the set of criteria for gradual languages and opens several venues for further exploration, in particular for typing disciplines that enforce rich semantic properties.

Programming language mechanisms with a type-directed semantics are nowadays common and widely used. Such mechanisms include gradual typing, type classes, implicits and intersection types with a merge operator . While sharing common challenges in their design and having complementary strengths, type-directed mechanisms have been mostly independently studied. This paper studies a new calculus, called λ M ★ , which combines two type-directed mechanisms: gradual typing and a merge operator based on intersection types. Gradual typing enables a smooth transition between dynamically and statically typed code, and is available in languages such as TypeScript or Flow. The merge operator generalizes record concatenation to allow merges of values of any two types. Recent work has shown that the merge operator enables modelling expressive OOP features like first-class traits/classes and dynamic inheritance with static type-checking. These features are not found in mainstream statically typed OOP languages, but they can be found in dynamically or gradually typed languages such as JavaScript or TypeScript. In λ M ★ , by exploiting the complementary strengths of gradual typing and the merge operator, we obtain a foundation for modelling gradually typed languages with both first-class classes and dynamic inheritance. We study a static variant of λ M ★ (called λ M ); prove the type-soundness of λ M ★ ; show that λ M ★ can encode gradual rows and all well-typed terms in the GTFL ≲ typing criteria. The dynamic gradual guarantee (DGG) is challenging due to the possibility of ambiguity errors. We establish a variant of the DGG using a semantic notion of precision based on a step-indexed logical relation.

Language support for differentially private programming is both crucial and delicate. While elaborate program logics can be very expressive, type-system-based approaches using linear types tend to be more lightweight and amenable to automatic checking and inference, and in particular in the presence of higher-order programming. Since the seminal design of Fuzz , which is restricted to ϵ-differential privacy in its original design, significant progress has been made to support more advanced variants of differential privacy, like (ϵ, δ )-differential privacy. However, supporting these advanced privacy variants while also supporting higher-order programming in full has proven to be challenging. We present Jazz , a language and type system that uses linear types and latent contextual effects to support both advanced variants of differential privacy and higher-order programming. Latent contextual effects allow delaying the payment of effects for connectives such as products, sums, and functions, yielding advantages in terms of precision of the analysis and annotation burden upon elimination, as well as modularity. We formalize the core of Jazz , prove it sound for privacy via a logical relation for metric preservation, and illustrate its expressive power through a number of case studies drawn from the recent differential privacy literature.