Related papers: Linearization via Rewriting (Long Version)
In this note, we provide some categorical perspectives on the relativization construction arising from quantum measurement theory in the presence of symmetries and occupying a central place in the operational approach to quantum reference…
We revisit parallel-innermost term rewriting as a model of parallel computation on inductive data structures and provide a corresponding notion of runtime complexity parametric in the size of the start term. We propose automatic techniques…
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
We present a linear functional calculus with both the safety guarantees expressible with linear types and the rich language of combinators and composition provided by functional programming. Unlike previous combinations of linear typing and…
In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. All three calculi enable explicit…
Prior knowledge has been shown very useful to address many natural language processing tasks. Many approaches have been proposed to formalise a variety of knowledge, however, whether the proposed approach is robust or sensitive to the…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
Topics models, such as LDA, are widely used in Natural Language Processing. Making their output interpretable is an important area of research with applications to areas such as the enhancement of exploratory search interfaces and the…
We propose a $\lambda$-calculus-style formal language, called the $\mu$-syntax, as a lightweight representation of the structure of cyclic operads. We illustrate the rewriting methods behind the formalism by giving a complete step-by-step…
In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, $n$ variables, the four field operations and radical extractions). We…
This paper deals with model transformation based on attributed graph rewriting. Our contribution investigates a single pushout approach for applying the rewrite rules. The computation of graph attributes is obtained through the use of typed…
A version of the situation calculus in which situations are represented as first-order terms is presented. Fluents can be computed from the term structure, and actions on the situations correspond to rewrite rules on the terms. Actions that…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
We positively answer the question A.1.6 in J. Klop's "Ustica Notes": "Is there a recursive normalizing one-step reduction strategy for micro $\lambda$-calculus?" Micro $\lambda$-calculus refers to an implementation of the $\lambda$-calculus…
Formal explainability guarantees the rigor of computed explanations, and so it is paramount in domains where rigor is critical, including those deemed high-risk. Unfortunately, since its inception formal explainability has been hampered by…
Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…
We extend the diagrammatic calculus of syllogisms introduced in our previous paper to the general case of n-term syllogisms, showing that the valid ones are exactly those whose conclusion follows by calculation. Moreover, by pointing out…
Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix value functions. An important source of linearizations are the so called Fiedler…
Recently, deep architectures, such as recurrent and recursive neural networks have been successfully applied to various natural language processing tasks. Inspired by bidirectional recurrent neural networks which use representations that…
Focusing, introduced by Jean-Marc Andreoli in the context of classical linear logic, defines a normal form for sequent calculus derivations that cuts down on the number of possible derivations by eagerly applying invertible rules and…