Related papers: Modular implicits
Instead of a monolithic programming language trying to cover all features of interest, some programming systems are designed by combining together simpler languages that cooperate to cover the same feature space. This can improve usability…
In this paper we enrich the orthomodular structure by adding a modal operator, following a physical motivation. A logical system is developed, obtaining algebraic completeness and completeness with respect to a Kripke-style semantic founded…
As originally proposed, type classes provide overloading and ad-hoc definition, but can still be understood (and implemented) in terms of strictly parametric calculi. This is not true of subsequent extensions of type classes. Functional…
In this paper, we present an approach to define the semantics for object-oriented modeling languages. One important property of this semantics is to support underspecified and incomplete models. To this end, semantics is given as predicates…
We extend prior work on class-morphing to provide a more expressive pattern-based compile-time reflection language. Our MorphJ language offers a disciplined form of metaprogramming that produces types by statically iterating over and…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
Let $\Lambda$ be a basic finite dimensional algebra over an algebraically closed field, presented as a path algebra modulo relations; further, assume that $\Lambda$ is graded by lengths of paths. The paper addresses the classifiability, via…
Recent advances in programming languages study and design have established a standard way of grounding computational systems representation in category theory. These formal results led to a better understanding of issues of control and…
On classes of functions defined on R^2n we introduce abstract composition laws modelled after the pseudodifferential product of symbols. We attach to these composition laws modulation mappings and spaces with useful algebraic and…
We describe derived moduli functors for a range of problems involving schemes and quasi-coherent sheaves, and give cohomological conditions for them to be representable by derived geometric n-stacks. Examples of problems represented by…
In this work we define formal grammars in terms of free monoidal categories, along with a functor from the category of formal grammars to the category of automata. Generalising from the Booleans to arbitrary semirings, we extend our…
Modal types -- types that are derived from proof systems of modal logic -- have been studied as theoretical foundations of metaprogramming, where program code is manipulated as first-class values. In modal type systems, modality corresponds…
Several queries and scores have recently been proposed to explain individual predictions over ML models. Given the need for flexible, reliable, and easy-to-apply interpretability methods for ML models, we foresee the need for developing…
In this note, we investigate some topological properties of probabilistic modular spaces.
Modal dependence logics are modal logics defined on the basis of team semantics and have the downward closure property. In this paper, we introduce sound and complete deduction systems for the major modal dependence logics, especially those…
We present a generic programming framework for OCAML which makes it possible to implement extensible transformations for a large scale of type definitions. Our framework makes use of objectoriented features of OCAML, utilising late binding…
We prove a closed formula for the derivative, of any order, of a implicit function, in terms of some binomial building blocks, and explain the combinatorics behind the coefficients appearing in the formula.
Mathematical models are increasingly used in both academia and the pharmaceutical industry to understand how phenotypes emerge from systems of molecular interactions. However, their current construction as monolithic sets of equations…
Formal language techniques have been used in the past to study autonomous dynamical systems. However, for controlled systems, new features are needed to distinguish between information generated by the system and input control. We show how…
Language-conditioned policies allow robots to interpret and execute human instructions. Learning such policies requires a substantial investment with regards to time and compute resources. Still, the resulting controllers are highly…