Related papers: Monadic Expressions and their Derivatives
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…
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…
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…
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
This paper studies the design of programming languages with handlers of higher-order effectful operations -- effectful operations that may take in computations as arguments or return computations as output. We present and analyse a core…
Markov automata (MA) constitute an expressive continuous-time compositional modelling formalism. They appear as semantic backbones for engineering frameworks including dynamic fault trees, Generalised Stochastic Petri Nets, and AADL. Their…
Calculational abstract interpretation, long advocated by Cousot, is a technique for deriving correct-by-construction abstract interpreters from the formal semantics of programming languages. This paper addresses the problem of deriving…
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 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…
In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted…
In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…
Recent theoretical work on automatic differentiation (autodiff) has focused on characteristics such as correctness and efficiency while assuming that all derivatives are automatically generated by autodiff using program transformation, with…
With the increased interest in machine learning, and deep learning in particular, the use of automatic differentiation has become more wide-spread in computation. There have been two recent developments to provide the theoretical support…
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…
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…
Concurrent to the rapid progress in the development of neural-network based models in areas like natural language processing and computer vision, the need for creating explanations for the predictions of these black-box models has risen…
In the study of computational effects, it is important to consider the notion of computational effects with parameters. The need of such a notion arises when, for example, statically estimating the range of effects caused by a program, or…
We propose regular expressions to abstractly model and study properties of resource-aware computations. Inspired by nominal techniques -- as those popular in process calculi -- we extend classical regular expressions with names (to model…
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…
Multiset automata are a class of automata for which the symbols can be read in any order and obtain the same result. We investigate weighted multiset automata and show how to construct them from weighted regular expressions. We present…