Related papers: Effectful Applicative Bisimilarity: Monads, Relato…
The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational…
We consider bisimulation-invariant monadic second-order logic over various classes of finite transition systems. We present several combinatorial characterisations of when the expressive power of this fragment coincides with that of the…
There has been a growing interest in recent years in modelling multiple modalities (or views) of data to for example, understand the relationship between modalities or to generate missing data. Multi-view autoencoders have gained…
Matching estimators for average treatment effects are widely used in the binary treatment setting, in which missing potential outcomes are imputed as the average of observed outcomes of all matches for each unit. With more than two…
In this paper, we take a pervasively effectful (in the style of ML) typed lambda calculus, and show how to extend it to permit capturing pure expressions with types. Our key observation is that, just as the pure simply-typed lambda calculus…
Bidirectional transformations (bx) have primarily been modeled as pure functions, and do not account for the possibility of the side-effects that are available in most programming languages. Recently several formulations of bx that use…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
Bisimulation metrics provide a robust and accurate approach to study the behavior of nondeterministic probabilistic processes. In this paper, we propose a logical characterization of bisimulation metrics based on a simple probabilistic…
In this paper we present {\em refinement modal logic}. A refinement is like a bisimulation, except that from the three relational requirements only `atoms' and `back' need to be satisfied. Our logic contains a new operator 'all' in addition…
Traditional approaches to modelling parallelism and algebraic structure in lambda calculi often rely on monads$\unicode{x2013}$as in Moggi's framework$\unicode{x2013}$or on rich categorical structures such as biproducts$\unicode{x2013}$as…
Adversarial computations are a widely studied class of computations where resource-bounded probabilistic adversaries have access to oracles, i.e., probabilistic procedures with private state. These computations arise routinely in several…
In this paper we prove that any lambda-term that is strongly normalising for beta-reduction is also strongly normalising for beta,assoc-reduction. assoc is a call-by-value rule that has been used in works by Moggi, Joachimsky, Espirito…
A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory. The method is illustrated by the examples possessing the structure typical of many problems in applied mathematics. Good numerical…
Normal form bisimilarities are a natural form of program equivalence resting on open terms, first introduced by Sangiorgi in call-by-name. The literature contains a normal form bisimilarity for Plotkin's call-by-value $\lambda$-calculus,…
We prove bilinear inequalities for differential operators in $\mathbb{R}^2$. Such type inequalities turned out to be useful for anisotropic embedding theorems for overdetermined systems and the limiting order summation exponent. However,…
The two Girard translations provide two different means of obtaining embeddings of Intuitionistic Logic into Linear Logic, corresponding to different lambda-calculus calling mechanisms. The translations, mapping A -> B respectively to !A -o…
In categorical realizability, it is common to construct categories of assemblies and categories of modest sets from applicative structures. These categories have structures corresponding to the structures of applicative structures. In the…
We construct relative abelian categories in the sense of MacLane for models of algebraic systems in (co)complete abelian categories. As an example, we consider an analogue of Hochschild-Mitchell cohomology for the functor of Yoneda…
An approximate relativistic two-component Hamiltonian for use in molecular electronic structure calculations is derived in the form of a sum of fixed atom-centered kinetic and spin-orbit operators added to the non-relativistic Hamiltonian.…
The $\lambda$-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the…