Related papers: Monadic Expressions and their Derivatives [extende…
We develop a technique for generalising from data in which models are samplers represented as program text. We establish encouraging empirical results that suggest that Markov chain Monte Carlo probabilistic programming inference techniques…
One way of interpreting a left Kan extension is as taking a kind of "partial colimit", whereby one replaces parts of a diagram by their colimits. We make this intuition precise by means of the "partial evaluations" sitting in the so-called…
We investigate the behavior of extension monads, introduced in the 1990s by the second author, in terms of structure results for infinitely many finitary operations and common constructions in varieties or categories of algebras.…
The aim in this paper is to give expressions for modular linear differential operators of any order. In particular, we show that they can all be described in terms of Rankin-Cohen brackets and a modified Rankin-Cohen bracket found by Kaneko…
It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To…
We extend the functorial approach to automata by Colcombet and Petri\c{s}an [arXiv:1712.07121] from the category of sets to any elementary topos with a natural number object and establish general Myhill-Nerode theorems in our setting. As a…
We propose a generic categorical framework for learning unknown formal languages of various types (e.g. finite or infinite words, weighted and nominal languages). Our approach is parametric in a monad T that represents the given type of…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
We consider the problem of modularizing control flow in a generic abstract interpretation framework. A generic abstract interpretation framework is not truly flexible if it does not allow interpreting with different path- and…
The classical subset construction for non-deterministic automata can be generalized to other side-effects captured by a monad. The key insight is that both the state space of the determinized automaton and its semantics---languages over an…
We give thread-modular non-relational value analyses as abstractions of a local trace semantics. The semantics as well as the analyses are formulated by means of global invariants and side-effecting constraint systems. We show that a…
One approach for interpreting black-box machine learning models is to find a global approximation of the model using simple interpretable functions, which is called a metamodel (a model of the model). Approximating the black-box with a…
We extend intersection types to a computational $\lambda$-calculus with algebraic operations \`a la Plotkin and Power. We achieve this by considering monadic intersections, whereby computational effects appear not only in the operational…
We present a theoretical framework for deriving the general $n$-th order Fr\'echet derivatives of singular values in real rectangular matrices, by leveraging reduced resolvent operators from Kato's analytic perturbation theory for…
This paper is the first of two articles which develop the notion of protoperads. In this one, we construct a new monoidal product on the category of reduced S-modules. We study the associated monoids, called protoperads, which are a…
Finite automata are used to encode geometric figures, functions and can be used for image compression and processing. The original approach is to represent each point of a figure in $\mathbb{R}^n$ as a convolution of its $n$ coordinates…
This paper presents a new derivative parsing algorithm for parsing expression grammars; this new algorithm is both simpler and faster than the existing parsing expression derivative algorithm presented by Moss. This new algorithm improves…
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…
As part of the author's studies on equational reasoning for monadic programs, this report focus on non-determinism monad. We discuss what properties this monad should satisfy, what additional operators and notations can be introduced to…
In this paper, we give precise mathematical form to the idea of a structure whose data and axioms are faithfully represented by a graphical calculus; some prominent examples are operads, polycategories, properads, and PROPs. Building on the…