Related papers: Sum and Tensor of Quantitative Effects
We study Abramsky's applicative bisimilarity abstractly, in the context of call-by-value $\lambda$-calculi with algebraic effects. We first of all endow a computational $\lambda$-calculus with a monadic operational semantics. We then show…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ''conformal vertex algebra'' or even more generally,…
The coexistence relation of quantum effects is a fundamental structure, describing those pairs of experimental events that can be implemented in a single setup. Only in the simplest case of qubit effects an analytic characterization of…
A quadratic algebra is a homogeneous algebra generated by its elements of degree 1. Manin has endowed the category of quadratic algebras with two tensor products. These structures have been adapted to operads by Ginsburg and Kapranov.…
This dissertation is concerned with the study of program equivalence and algebraic effects as they arise in the theory of programming languages. Algebraic effects represent impure behaviour in a functional programming language, such as…
As a generalization of the classical killing-contractible-complexes lemma, we present algebraic Morse theory via homological perturbation lemma, in a form more general than existing presentations in the literature. Two-sided Anick…
There are several ways to define program equivalence for functional programs with algebraic effects. We consider two complementing ways to specify behavioural equivalence. One way is to specify a set of axiomatic equations, and allow proof…
Computational effects may often be interpreted in the Kleisli category of a monad or in the coKleisli category of a comonad. The duality between monads and comonads corresponds, in general, to a symmetry between construction and…
We describe a simple machinery which translates results on algebraic sums of sets of reals into the corresponding results on their cartesian product. Some consequences are: 1. The product of a meager/null-additive set and a strong measure…
Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…
This paper studies the quantitative refinements of Abramsky's applicative similarity and bisimilarity in the context of a generalisation of Fuzz, a call-by-value $\lambda$-calculus with a linear type system that can express programs…
The development of compositional distributional models of semantics reconciling the empirical aspects of distributional semantics with the compositional aspects of formal semantics is a popular topic in the contemporary literature. This…
A fundamental result by L. Solomon in algebraic combinatorics and representation theory states that Mackey formulas for products of characters of a symmetric group, or equivalently the computation of tensor products of representations…
We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic…
Geometric Algebra and Calculus are mathematical languages encoding fundamental geometric relations that theories of physics seem to respect. We propose criteria given which statistics of expressions in geometric algebra are computable in…
Taking a quotient roughly means changing the notion of equality on a given object, set or type. In a quantitative setting, equality naturally generalises to a distance, measuring how much elements are similar instead of just stating their…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
The classical Hennessy-Milner theorem is an important tool in the analysis of concurrent processes; it guarantees that any two non-bisimilar states in finitely branching labelled transition systems can be distinguished by a modal formula.…