Related papers: Cyclic Shift in the Lambek Calculus
A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…
For spaces of analytic functions defined on an open set in $\mathbb{C}^n$ that satisfy certain nice properties, we show that operators that preserve shift-cyclic functions are necessarily weighted composition operators. Examples of spaces…
Lambek calculus is a logical foundation of categorial grammar, a linguistic paradigm of grammar as logic and parsing as deduction. Pentus (2010) gave a polynomial-time algorithm for determ- ining provability of bounded depth formulas in the…
The intrinsic treatment of binding in the lambda calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs, types, and programs. Supporting such a data structure in an implementation…
We collect and organise known results and add some new ones of the following nature: if A is a bounded operator in a Hilbert or Banach space, does there exist a nonconstant polynomial p(z) such that p(A) is "simpler", "nicer" than A. The…
In this project, a rather complete proof-theoretical formalization of Lambek Calculus (non-associative with arbitrary extensions) has been ported from Coq proof assistent to HOL4 theorem prover, with some improvements and new theorems.…
A comparison of Landin's form of lambda calculus with Church's shows that, independently of the lambda calculus, there exists a mechanism for converting functions with arguments indexed by variables to the usual kind of function where the…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
The notions of chaos and frequent hypercyclicity enjoy an intimate relationship in linear dynamics. Indeed, after a series of partial results, it was shown by Bayart and Rusza in 2015 that for backward weighted shifts on…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…
We show that Willwacher's cyclic formality theorem can be extended to preserve natural Gravity operations on cyclic multivector fields and cyclic multidifferential operators. We express this in terms of a homotopy Gravity quasi-isomorphism…
We investigate the relationship between finite terms in {\lambda}-letrec, the {\lambda}-calculus with letrec, and the infinite {\lambda}-terms they express. We say that a lambda-letrec term expresses a lambda-term if the latter can be…
Every language recognized by the Lambek calculus with brackets is context-free. This is shown by combining an observation by J\"ager with an entirely straightforward adaptation of the method Pentus used for the original Lambek calculus. The…
In this paper, we study the cyclicity of the shift operator $S$ acting on a Banach space $\X$ of analytic functions on the open unit disc $\D$. We develop a general framework where a method based on a corona theorem can be used to show that…
Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity Criterion. As an application we characterize upper…
We consider the cyclic closure of a language, and its generalisation to the operators $C^k$ introduced by Brandst\"adt. We prove that the cyclic closure of an indexed language is indexed, and that if $L$ is a context-free language then…
We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift…
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…