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Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…
We show that, when the actions of a Mazurkiewicz trace are considered not merely as atomic (i.e., mere names) but transformations from a specified type of inputs to a specified type of outputs, we obtain a novel notion of presentation for…
Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…
Substructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar,…
An advantage of scientific workflow systems is their ability to collect runtime provenance information as an execution trace. Traces include the computation steps invoked as part of the workflow run along with the corresponding data…
A combination of a finite number of linear independent states forms superposition in a way that cannot be conceived classically. Here, using the tools of resource theory of superposition, we give the conditions for a class of superposition…
Programming languages with algebraic effects often track the computations' effects using type-and-effect systems. In this paper, we propose to view an algebraic effect theory of a computation as a variable context; consequently, we propose…
We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both…
G. Plotkin and the author have worked out the equivalence between state transformer semantics and predicate transformer semantics in a domain theoretical setting for programs combining nondeterminism and probability. Works of C. Morgan and…
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…
We present extensions to a continuous-state dependency parsing method that makes it applicable to morphologically rich languages. Starting with a high-performance transition-based parser that uses long short-term memory (LSTM) recurrent…
We present a denotational semantics for higher-order probabilistic programs in terms of linear operators between Banach spaces. Our semantics is rooted in the classical theory of Banach spaces and their tensor products, but bears…
Chase algorithms are indispensable in the domain of knowledge base querying, which enable the extraction of implicit knowledge from a given database via applications of rules from a given ontology. Such algorithms have proved beneficial in…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
This invited paper presents an overview of an ongoing research program aimed at extending the Curry-Howard-Lambek correspondence to quantum computation. We explore two key frameworks that provide both logical and computational foundations…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
LLMs are increasingly used as general-purpose reasoners, but long inputs remain bottlenecked by a fixed context window. Recursive Language Models (RLMs) address this by externalising the prompt and recursively solving subproblems. Yet…
Static resource analysis determines the resource consumption (e.g., time complexity) of a program without executing it. Among the numerous existing approaches for resource analysis, affine type systems have been one dominant approach.…
Motivated by the increasing shift to multicore computers, recent work has developed language support for responsive parallel applications that mix compute-intensive tasks with latency-sensitive, usually interactive, tasks. These…