Implementing collection classes with monads

1998 ◽  
Vol 8 (3) ◽  
pp. 231-276 ◽  
Author(s):  
ERNIE G. MANES
Keyword(s):  
Category Theory ◽  
Natural Transformation ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Formal Definition ◽  
Axiomatic Theory ◽  
Finite Set ◽  
Definition Of ◽  
The Relationship

In object-oriented programming, there are many notions of ‘collection with members in X’. This paper offers an axiomatic theory of collections based on monads in the category of sets and total functions. Heuristically, the axioms defining a collection monad state that each collection has a finite set of members of X, that pure 1-element collections exist and that a collection of collections flattens to a single collection whose members are the union of the members of the constituent collections. The relationship between monads and universal algebra leads to a formal definition of collection implementation in terms of tree-processing. Ideas from elementary category theory underly the classification of collections. For example, collections can be zipped if and only if the monad's endofunctor preserves pullbacks. Or, a collection can be uniquely specified by its shape and list of data if the morphisms of the Kleisli category of the monad are all deterministic, and the converse holds for commutative monads. Again, a collection monad is ordered if the monad's functor preserves equalizers of monomorphisms (so, in particular, if collections can be zipped the monad is ordered). Every implementable monad is ordered. It is shown using the well-ordering principle that a collection monad is ordered if and only if its functor admits an appropriated list-valued natural transformation that lists the members of each collection.

scholarly journals A Category Theoretic Approach to Metaphor Comprehension: Theory of Indeterminate Natural Transformation

2020 ◽  
Author(s):  
Miho Fuyama ◽  
Hayato Saigo ◽  
Tatsuji Takahashi
Keyword(s):  
Category Theory ◽  
Natural Transformation ◽  
Mathematical Structure ◽  
Theoretic Approach ◽  
Metaphor Comprehension ◽  
Central Notion ◽  
Meaning Creation ◽  
Natural Transformations ◽  
Categories And Functors ◽  
The Relationship

We propose the theory of indeterminate natural transformation (TINT) to investigate the dynamical creation of meaning as an association relationship between images, focusing on metaphor comprehension as an example. TINT models meaning creation as a type of stochastic process based on mathematical structure and defined by association relationships, such as morphisms in category theory, to represent the indeterminate nature of structure-structure interactions between the systems of image meanings. Such interactions are formulated in terms of the so-called coslice categories and functors as structure-preserving correspondences between them. The relationship between such functors is “indeterminate natural transformation”, the central notion in TINT, which models the creation of meanings in a precise manner. For instance, metaphor comprehension is modeled by the construction of indeterminate natural transformations from a canonically defined functor, which we call the base-of-metaphor functor.

A Unified Taxonomy Framework of Trust

2011 ◽  
pp. 29-50 ◽  
Author(s):  
Weiliang Zhao ◽  
Vijay Varadharajan ◽  
George Bryan
Keyword(s):  
Trust Management ◽  
Lower Layer ◽  
Mathematical Structure ◽  
Formal Definition ◽  
Trust Relationship ◽  
Base Level ◽  
Trust Relationships ◽  
Analysis Design ◽  
Definition Of

In this chapter, we provide a formal definition of trust relationship with a strict mathematical structure that can reflect many of the commonly used notions of trust. Based on this formal definition, we propose a unified taxonomy framework of trust. Under the taxonomy framework, we discuss classification of trust. In particular, we address the base level authentication trust at the lower layer and a hierarchy of trust relationships at a higher level. We provide a set of definitions, propositions, and operations based on the relations of trust relationships. Then we define and discuss properties of trust direction and trust symmetry. We define the trust scope label in order to describe the scope and diversity of trust relationship. All the definitions about the properties of trust become elements of the unified taxonomy framework of trust. Some example scenarios are provided to illustrate the concepts in the taxonomy framework. The taxonomy framework of trust will provide accurate terms and useful tools for enabling the analysis, design, and implementation of trust. The taxonomy framework of trust is first part of research for the overall methodology of trust relationships and trust management in distributed systems.

An Object-Oriented Class Library for Medical Software Development

1996 ◽  
Vol 35 (04/05) ◽  
pp. 343-347
Author(s):  
E. E. McColligan ◽  
K. C. O’Kane
Keyword(s):  
Medical Record ◽  
Rapid Development ◽  
Object Oriented ◽  
Object Oriented Programming ◽  
Message Processing ◽  
Class Library ◽  
File Access ◽  
Medical Software ◽  
High Level ◽  
The Relationship

Abstract:The objective of this research is the development of a Medical Object Library (MOL) consisting of reusable, inheritable, portable, extendable C++ classes that facilitate rapid development of medical software at reduced cost and increased functionality. The result of this research is a library of class objects that range in function from string and hierarchical file handling entities to high level, procedural agents that perform increasingly complex, integrated tasks. A system built upon these classes is compatible with any other system similarly constructed with respect to data definitions, semantics, data organization and storage. As new objects are built, they can be added to the class library for subsequent use. The MOL is a toolkit of software objects intended to support a common file access methodology, a unified medical record structure, consistent message processing, standard graphical display facilities and uniform data collection procedures. This work emphasizes the relationship that potentially exists between the structure of a hierarchical medical record and procedural language components by means of a hierarchical class library and tree structured file access facility. In doing so, it attempts to establish interest in and demonstrate the practicality of the hierarchical medical record model in the modern context of object oriented programming.

Atomistic Modeling of Point and Extended Defects in Crystalline Materials

1998 ◽  
Vol 532 ◽  
Author(s):  
Martin Jaraiz ◽  
Lourdes Pelaz ◽  
Emiliano Rubio ◽  
Juan Barbolla ◽  
George H. Gilmer ◽  
...  
Keyword(s):  
Defect Formation ◽  
Kinetic Monte Carlo ◽  
Object Oriented ◽  
Deep Submicron ◽  
Object Oriented Programming ◽  
Extended Defects ◽  
Crystalline Materials ◽  
Monte Carlo Simulation Technique ◽  
Definition Of ◽  
Reaction Equations

ABSTRACTAtomistic process modeling, a kinetic Monte Carlo simulation technique, has the interest of being both conceptually simple and extremely powerful. Instead of reaction equations it is based on the definition of the interactions between individual atoms and defects. Those interactions can be derived either directly from molecular dynamics or first principles calculations, or from experiments. The limit to its use is set by the size dimensions it can handle, but the level of performance achieved by even workstations and PC's, together with the design of efficient simulation schemes, has revealed it as a good candidate for building the next generation of process simulators, as an extension of existing continuum modeling codes into the deep submicron size regime. Over the last few years it has provided a unique insight into the atomistic mechanisms of defect formation and dopant diffusion during ion implantation and annealing in silicon. Object-oriented programming can be very helpful in cutting software development time, but care has to be taken not to degrade performance in the critical inner calculation loops. We discuss these techniques and results with the help of a fast object-oriented atomistic simulator recently developed.

SPECIFICATION OF SOFTWARE ARCHITECTURE

2000 ◽  
Vol 10 (01) ◽  
pp. 69-95 ◽  
Author(s):  
MARK J. GERKEN
Keyword(s):  
Software Architecture ◽  
Category Theory ◽  
Formal Definition ◽  
The Past ◽  
Algebraic Specifications ◽  
Software Specifications ◽  
Architecture Theory ◽  
Definition Of ◽  
Semantic Compatibility ◽  
Use Category

Over the past several years, software architecture representation and analysis has become an active area of research. However, most approaches to software architecture representation and analysis have been informal. We postulate that through formality, the term "architecture" can be precisely defined and important properties of systems, such as semantic compatibility between connected entities, can be investigated with precision. In this paper, we use category theory and algebraic specifications to develop a formal definition of architecture and show how architecture theory can be used in the construction of software specifications.

Does peer tutoring in kindergarten exist? Thinking around the tutoring concept.

2019 ◽  
Vol X (4 (29)) ◽  
pp. 63-84
Author(s):  
Aneta Babiuk-Massalska
Keyword(s):  
Nervous System ◽  
Preschool Child ◽  
Social Experiences ◽  
The Other ◽  
Older Children ◽  
Student Relationship ◽  
Definition Of ◽  
The Relationship

The article reviews the definitions of the tutoring concept in preschoolers relationships. Can we qualify the relationships of preschool children in learning situations as tutoring? Or maybe a different name would be more suitable for them? Preschoolers are used to learning in a different way than adults and older children. They prefer learning mimicking or playing. They obtain knowldge occasionally an unintentionally. In turn, definitions of tutoring quite precisely contain formulated fortifications that a little child is not able to meet yet. Immaturity of the nervous system limit the level and length of attention span of little child and relatively small, compared to school children and adults number of social experiences can seriously hamper the classification of situations in which children learn from each other as tutoring. While the generally understood master-student relationship, associated with tutoring, is quite often noticeable during childhood collaboration and play in which one child can do more than the other, the more detailed assumptions of tutoring are not as accessible to the observer. For example, it is difficult to talk about the regularity or planned nature of children's relationships. The definition of tutoring also sets specific expectations regarding the teacher's skills, among which are: high interpersonal competences, commitment to the relationship with the mentee, professionalism and responsibility. From a preschool child who would play the role of a teacher, it is difficult to demand fluent speech, not to mention professionalism and regularity. A preschool child, who just start to learn numbers, is often unable to orient himself in time, which makes it difficult or even impossible to plan and systematize his activities. Little child needs adult help in this area.

Reviews of the Literature

1955 ◽  
Vol 14 (1) ◽  
pp. 34-36
Keyword(s):  
Natural Resources ◽  
Urban Society ◽  
Formal Definition ◽  
Underlying Assumption ◽  
The Core ◽  
Legal Structure ◽  
Political Ideologies ◽  
Central Bond ◽  
Definition Of

This book is meant as an overview of the rapidly increasing literature on "those social roles which arise from the classification of men by the work they do." The core of his problem, Professor Caplow states, is the interplay of such factors as "the availability of natural resources, political ideologies, and the legal structure … with the more or less predictable consequences of the division of labor" (e.g. size, specialization, and rationalization). His underlying assumption, he says, is Durkheim's: occupation is the central bond of solidarity in modern urban society. Neither the formal definition of task nor the underlying assumption are pursued systematically—and, in fact, occupational groupings are later seen as subordinate to "more fundamental affiliations based on kinship, locality, religion, property, and status." (p. 182).

scholarly journals COMPARISON OF PARSING METHODS FOR THE ANALISYS OF A NATURAL LANGUAGE SENTENCE

2021 ◽  
Vol 10 (34) ◽  
Author(s):  
A.N SAK ◽  
◽  
E.V BESSONOVA ◽  
Keyword(s):  
Neural Networks ◽  
Natural Language ◽  
Machine Translation ◽  
Convolutional Neural Networks ◽  
Object Oriented ◽  
Important Task ◽  
Object Oriented Programming ◽  
Parts Of Speech ◽  
Translation Systems

When constructing machine translation systems, an important task is to represent data using graphs, where words act as vertices, and relations between words in a sentence act as edges. One of these tasks at the first stage of the analysis is the classification of words as parts of speech, and at the next stage of the analysis to determine the belonging of words to the sentence members’ classes. The article discusses methods of parsing both on the basis of rules determined in advance by means of traditional object-oriented programming, and on the basis of analysis by means of graph convolutional neural networks with their subsequent training. Online dictionaries act as a thesaurus.

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