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This article presents GenSQL, a probabilistic programming system for querying probabilistic generative models of database tables. By augmenting SQL with only a few key primitives for querying probabilistic models, GenSQL enables complex Bayesian inference workflows to be concisely implemented. GenSQL’s query planner rests on a unified programmatic interface for interacting with probabilistic models of tabular data, which makes it possible to use models written in a variety of probabilistic programming languages that are tailored to specific workflows. Probabilistic models may be automatically learned via probabilistic program synthesis, hand-designed, or a combination of both. GenSQL is formalized using a novel type system and denotational semantics, which together enable us to establish proofs that precisely characterize its soundness guarantees. We evaluate our system on two case real-world studies—an anomaly detection in clinical trials and conditional synthetic data generation for a virtual wet lab—and show that GenSQL more accurately captures the complexity of the data as compared to common baselines. We also show that the declarative syntax in GenSQL is more concise and less error-prone as compared to several alternatives. Finally, GenSQL delivers a 1.7-6.8x speedup compared to its closest competitor on a representative benchmark set and runs in comparable time to hand-written code, in part due to its reusable optimizations and code specialization. 

We propose a novel approach to soundly combining linear types with multi-shot effect handlers. Linear type systems statically ensure that resources such as file handles and communication channels are used exactly once. Effect handlers provide a rich modular programming abstraction for implementing features ranging from exceptions to concurrency to backtracking. Whereas conventional linear type systems bake in the assumption that continuations are invoked exactly once, effect handlers allow continuations to be discarded (e.g. for exceptions) or invoked more than once (e.g. for backtracking). This mismatch leads to soundness bugs in existing systems such as the programming language Links, which combines linearity (for session types) with effect handlers. We introduce control-flow linearity as a means to ensure that continuations are used in accordance with the linearity of any resources they capture, ruling out such soundness bugs. We formalise the notion of control-flow linearity in a System F-style core calculus Feff∘, equipped with linear types, an effect type system, and effect handlers. We define a linearity-aware semantics in order to formally prove that Feff∘ preserves the integrity of linear values in the sense that no linear value is discarded or duplicated. In order to show that control-flow linearity can be made practical, we adapt Links based on the design of Feff∘, in doing so fixing a long-standing soundness bug. Finally, to better expose the potential of control-flow linearity, we define an ML-style core calculus Qeff∘, based on qualified types, which requires no programmer provided annotations, and instead relies entirely on type inference to infer control-flow linearity. Both linearity and effects are captured by qualified types. Qeff∘ overcomes a number of practical limitations of Feff∘, supporting abstraction over linearity, linearity dependencies between type variables, and a much more fine-grained notion of control-flow linearity.