Related papers: A Framework for Higher-Order Effects & Handlers
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…
Online Analytical Processing (OLAP) comprises tools and algorithms that allow querying multidimensional databases. It is based on the multidimensional model, where data can be seen as a cube, where each cell contains one or more measures…
Relational properties describe multiple runs of one or more programs. They characterize many useful notions of security, program refinement, and equivalence for programs with diverse computational effects, and they have received much…
This article begins with a study of convex effect-state spaces. We point out that such spaces are equivalent to interval effect algebras that generate an ordered linear space and possess an order-determining set of states. We then discuss…
We introduce a new nameless representation of lambda terms inspired by ordered logic. At a lambda abstraction, number and relative position of all occurrences of the bound variable are stored, and application carries the additional…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
Hybrid computation combines discrete and continuous dynamics in the form of an entangled mixture inherently present both in various natural phenomena, and in applications ranging from control theory to microbiology. The emergent behaviours…
When humans conceive how to perform a particular task, they do so hierarchically: splitting higher-level tasks into smaller sub-tasks. However, in the literature on natural language (NL) command of situated agents, most works have treated…
We present a framework, named the Montagovian generative lexicon, for computing the semantics of natural language sentences, expressed in many sorted higher order logic. Word meaning is depicted by lambda terms of second order lambda…
This paper proposes a functional foundation for model driven engineering that unifies model construction, metamodels, templates, and transformations under a single formalism: the model expression algebra. In this algebra, models are values,…
A general framework is proposed for integration of rules and external first order theories. It is based on the well-founded semantics of normal logic programs and inspired by ideas of Constraint Logic Programming (CLP) and constructive…
Higher order derivatives of functions are structured high dimensional objects which lend themselves to many alternative representations, with the most popular being multi-index, matrix and tensor representations. The choice between them…
Quantum supermaps provide a framework in which higher order quantum processes can act on lower order quantum processes. In doing so, they enable the definition and analysis of new quantum protocols and causal structures. Recently, key…
We propose a novel, operational framework to formally describe the semantics of concurrent programs running within the context of a relaxed memory model. Our framework features a "temporary store" where the memory operations issued by the…
An elegant description of the general form of order automorphisms of effect algebras has been known in the complex case. We present a much simpler proof based on the projective geometry which works also in the real case. As an application…
Basic results in combinatorial mathematics provide the foundation for a theory and calculus for reasoning about sequential behavior. A key concept of the theory is a generalization of Boolean implicant which deals with statements of the…
Text analytical tasks like word embedding, phrase mining, and topic modeling, are placing increasing demands as well as challenges to existing database management systems. In this paper, we provide a novel algebraic approach based on…
This work revisits operator learning from a spectral perspective by introducing Polar Linear Algebra, a structured framework based on polar geometry that combines a linear radial component with a periodic angular component. Starting from…