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Constraint Programming (CP) has been successfully applied to both constraint satisfaction and constraint optimization problems. A wide variety of specialized global constraints provide critical assistance in achieving a good model that can…
We show how (well-established) type systems based on non-idempotent intersection types can be extended to characterize termination properties of functional programming languages with pattern matching features. To model such programming…
There is an increasing body of literature proposing new and efficient persistent versions of concurrent data structures ensuring that a consistent state can be recovered after a power failure or a crash. Their correctness is typically…
The coalgebraic modelling of alternating automata and of probabilistic automata has long been obstructed by the absence of distributive laws of the powerset monad over itself, respectively of the powerset monad over the finite distribution…
Reasoning about array data structures is a key requirement for many applications in hardware and software verification, especially in combination with machine integers. The Satisfiability Modulo Theories (SMT) theory of extensional arrays…
Modern distributed systems often rely on so called weakly-consistent databases, which achieve scalability by sacrificing the consistency guarantee of distributed transaction processing. Such databases have been formalised in two different…
In recent research on non-monotonic logic programming, repeatedly strong equivalence of logic programs P and Q has been considered, which holds if the programs P union R and Q union R have the same answer sets for any other program R. This…
Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…
Constructions of spectra from symmetric monoidal categories are typically functorial with respect to strict structure-preserving maps, but often the maps of interest are merely lax monoidal. We describe conditions under which one can…
Recent advances have shown that scaling test-time computation enables large language models (LLMs) to solve increasingly complex problems across diverse domains. One effective paradigm for test-time scaling (TTS) involves LLM generators…
The uniform continuity theorem (UCT) states that every pointwise continuous real-valued function on the unit interval is uniformly continuous. In constructive mathematics, UCT is stronger than the decidable fan theorem (DFT); however, Loeb…
We present a framework for compositional program verification based on polynomial functors in dependent type theory. In this framework, polynomial functors serve as program interfaces, Kleisli morphisms for the free monad monad serve as…
The univalence axiom expresses the principle of extensionality for dependent type theory. However, if we simply add the univalence axiom to type theory, then we lose the property of canonicity - that every closed term computes to a…
In this paper we have found a necessary and sufficient condition for equivalence of two norms on a linear space using the theory of exponential vector space. Exponential vector space is an ordered algebraic structure which can be considered…
Linearizability is a commonly accepted consistency condition for concurrent objects. Filipovi\'{c} et al. show that linearizability is equivalent to observational refinement. However, linearizability does not permit concurrent objects to…
We extend the recently introduced setting of coherent differentiation for taking into account not only differentiation, but also Taylor expansion in categories which are not necessarily (left)additive. The main idea consists in extending…
This paper concerns the development of metatheory for extensible languages. It uses as its starting point a view that programming languages tailored to specific application domains are to be constructed by composing components from an open…
For $\mathbb Q$-factorial klt algebraically integrable adjoint foliated structures, we prove the cone theorem, the contraction theorem, and the existence of flips. Therefore, we deduce the existence of the minimal model program for such…
The model of asynchronous programming arises in many contexts, from low-level systems software to high-level web programming. We take a language-theoretic perspective and show general decidability and undecidability results for asynchronous…
We study lax functors between bicategories as a generalized concept of monads and describe generalized notions and theorems of formal monad theory for lax functors. Our first approach is to use the 2-monad whose lax algebras are lax…