Classical Control, Quantum Circuits and Linear Logic in Enriched Category Theory

We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for circuits, and a more powerful host language, such that the circuit language is embedded inside the host language. Our categorical semantics for the host language is standard, and involves cartesian closed categories and monads. We interpret the circuit language not in an ordinary category, but in a category that is enriched in the host category. We show that this structure is also related to linear/non-linear models. As an extended example, we recall an earlier result that the category of W*-algebras is dcpo-enriched, and we use this model to extend the circuit language with some recursive types

Functorial Data Migration

In this paper we present a simple database definition language: that of categories and functors. A database schema is a small category and an instance is a set-valued functor on it. We show that morphisms of schemas induce three "data migration functors", which translate instances from one schema to the other in canonical ways. These functors parameterize projections, unions, and joins over all tables simultaneously and can be used in place of conjunctive and disjunctive queries. We also show how to connect a database and a functional programming language by introducing a functorial connection between the schema and the category of types for that language. We begin the paper with a multitude of examples to motivate the definitions, and near the end we provide a dictionary whereby one can translate database concepts into category-theoretic concepts and vice-versa.Comment: 30 page

Functional Big-step Semantics

When doing an interactive proof about a piece of software, it is important that the underlying programming language’s semantics does not make the proof unnecessarily difficult or unwieldy. Both smallstep and big-step semantics are commonly used, and the latter is typically given by an inductively defined relation. In this paper, we consider an alternative: using a recursive function akin to an interpreter for the language. The advantages include a better induction theorem, less duplication, accessibility to ordinary functional programmers, and the ease of doing symbolic simulation in proofs via rewriting. We believe that this style of semantics is well suited for compiler verification, including proofs of divergence preservation. We do not claim the invention of this style of semantics: our contribution here is to clarify its value, and to explain how it supports several language features that might appear to require a relational or small-step approach. We illustrate the technique on a simple imperative language with C-like for-loops and a break statement, and compare it to a variety of other approaches. We also provide ML and lambda-calculus based examples to illustrate its generality

McRunjob: A High Energy Physics Workflow Planner for Grid Production Processing

McRunjob is a powerful grid workflow manager used to manage the generation of large numbers of production processing jobs in High Energy Physics. In use at both the DZero and CMS experiments, McRunjob has been used to manage large Monte Carlo production processing since 1999 and is being extended to uses in regular production processing for analysis and reconstruction. Described at CHEP 2001, McRunjob converts core metadata into jobs submittable in a variety of environments. The powerful core metadata description language includes methods for converting the metadata into persistent forms, job descriptions, multi-step workflows, and data provenance information. The language features allow for structure in the metadata by including full expressions, namespaces, functional dependencies, site specific parameters in a grid environment, and ontological definitions. It also has simple control structures for parallelization of large jobs. McRunjob features a modular design which allows for easy expansion to new job description languages or new application level tasks.Comment: CHEP 2003 serial number TUCT00

THE LINGUISTIC ANALYSIS OF THE GRAMMATICAL VARIABILITY

The actuality of the subject. Variability, and optionality is observed at all levels of the language as a universal feature of language means. One of the key features of contemporary linguistic research is the general typology of language means’ variability and focusing on issues such as functional specifications of various variants in the text. In contrast to other language levels, the problem of variability in syntax has been studied less. The complexity of the investigation of variability in the syntax field is conditioned by the dual nature of syntactic units, and their structure-content layout. The sentence as a syntactic unit changes the structural-content layout and functional aspect in the evolutionary process. Simple sentences the generally accepted communicative speech unit and generally accepted syntactic units have been widely studied in various aspects of modern linguistic studies and currently is being studied further. The simple sentence being a structural type of sentence had a long way to development in the modern English language as well as in other languages, and has come to the present situation having structural-semantic improvement through certain changes during the speech as a result of simplification in sentence models, the expression means in sentences. Until now, there is no comprehensive description of the variativity features of all syntactic models of simple sentences in the studies where the syntactic structure of the English language has been described. Still, structural-semantic features, variations emerged in the historical development process can be underlined as an important issue because of the controversial issues in the syntax with a simple sentence and this proves the relevance of the topic. All of these bring to the agenda the comparisons by analyzing the structure-semantic layout of the simple sentence in different periods of the English language, revealing the changes in the simple sentence models, sentence members, and their means of expression, word order, analyzing the causes of those changes as an actual lingvo-methodological issue. Many researchers (K.Abdullayev, S.Abdullayev, D.Yunusov, F.Veysalli, and others) have examined the problem of variativity in different types of sentences in Azerbaijani linguistics and have shown valuable works in this area. The term "variativity" is applied to describe the functionality of different language units in modern linguistics and during the discovery of its unobserved aspects. In recent decades, the concept of enhanced variativity in phonology has also contributed to extensive research in other areas of linguistics, including syntax

Modular functionals and perturbations of Nakano spaces

We settle several questions regarding the model theory of Nakano spaces left open by the PhD thesis of Pedro Poitevin \cite{Poitevin:PhD}. We start by studying isometric Banach lattice embeddings of Nakano spaces, showing that in dimension two and above such embeddings have a particularly simple and rigid form. We use this to show show that in the Banach lattice language the modular functional is definable and that complete theories of atomless Nakano spaces are model complete. We also show that up to arbitrarily small perturbations of the exponent Nakano spaces are $\aleph_0$-categorical and $\aleph_0$-stable. In particular they are stable

A consistent extension of the lambda-calculus as a base for functional programming languages

Church's lambda-calculus is modified by introducing a new mechanism, the lambda-bar operator #, which neutralizes the effect of one preceding lambda binding. This operator can be used in such a way that renaming of bound variables in any reduction sequence can be avoided, with the effect that efficient interpreters with comparatively simple machine organization can be designed. It is shown that any semantic model of the pure λ-calculus also serves as a model of this modified reduction calculus, which guarantees smooth semantic theories. The Berkling Reduction Language (BRL) is a new functional programming language based upon this modification