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Thursday, July 30, 2020 | History

5 edition of Axiomatic Domain Theory in Categories of Partial Maps (Distinguished Dissertations in Computer Science) found in the catalog.

# Axiomatic Domain Theory in Categories of Partial Maps (Distinguished Dissertations in Computer Science)

## by Marcelo P. Fiore

• 205 Want to read
• 8 Currently reading

Written in English

Subjects:
• Analytic topology,
• Computers - General Information,
• Computers,
• Computer Books: General,
• Computer Books: Languages,
• Discrete Mathematics,
• Programming - Software Development,
• Computers / Programming / Software Development,
• Mathematics-Discrete Mathematics,
• Programming languages (Electronic computers)-,
• Programming languages (Electronic computers)--Semantics

• The Physical Object
FormatPaperback
Number of Pages254
ID Numbers
Open LibraryOL7747998M
ISBN 100521602777
ISBN 109780521602778

Axiomatic Domain Theory in Categories of Partial Maps Full Description: "First systematic account of axiomatic categorical domain theory and functional programming. The stress you have at work, your personal relationships, or many other problems you face in everyday life, all disappear when you lose yourself in a great story. Theorem (Go¨del ) If set theory without the Axiom of Choice (ZF) is consistent (i.e. does not lead to a contradiction), then set theory with the axiom of choice (ZFC) is consistent. Importance of this result: Set theory is the axiomatization of mathematics, and without AC no-one seriously doubts its truth, or at least consistency.

The aim of Axiomatic Domain Theory (ADT) is to axiomatise the structure needed on a category so that its objects can be considered to be domains (see [11, x Axiomatic Domain Theory]). Models of axiomatic domain theory are given with respect to an enrichment base provided by a model of intuitionistic linear type theory [2, 3]. These enrich-. Complete cuboidal sets in Axiomatic Domain Theory. C has all pull-backs of η 1 and η classifies partial maps with and proved representation results into categories of partial functions.

I studied category theory, is made explicit throughout the present book. My interest to the Axiomatic Method stems from my work on Euclid and extends through Hilbert and axiomatic set theories to Lawvere’s axiomatic topos theory to the Univalent Foundations of mathematics recently proposed by Vladimir Voevodsky. Marcelo P. Fiore. Axiomatic Domain Theory in Categories of Partial Maps. Cambridge University Press. Google Scholar Digital Library; Marcelo P Fiore and Gordon D Plotkin. An axiomatisation of computationally adequate domain theoretic models of FPC. In Author: VákárMatthijs, KammarOhad, StatonSam.

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### Axiomatic Domain Theory in Categories of Partial Maps (Distinguished Dissertations in Computer Science) by Marcelo P. Fiore Download PDF EPUB FB2

Axiomatic categorical domain theory is crucial for understanding the meaning of programs and reasoning about them.

This book is the first systematic account of the subject and studies mathematical structures suitable for modelling functional programming languages in an axiomatic (i.e. abstract) by: Axiomatic categorical domain theory is crucial for understanding the meaning of programs and reasoning about them.

This book is the first systematic account of the subject and studies mathematical structures suitable for modelling functional programming languages in an axiomatic (abstract) setting.

The Paperback of the Axiomatic Domain Theory in Categories of Partial Maps by Marcelo P Fiore at Barnes & Noble.

FREE Shipping on $35 or more. Due to COVID, orders may be : Marcel0 Fiore, Axiomatic Domain Theory in Categories of Partial Maps (Cambridge University Press, ), ISBN 0 Domains are the mathematical structures used in denotational semantics to inter- pret programming languages and domain theory is the mathematical theory of such structures. Cambridge University Press - Axiomatic Domain Theory in Categories of Partial Maps - Marcelo P. Fiore Cambridge University Press - Axiomatic Domain Theory in Categories of Partial Maps - Marcelo P. Fiore Excerpt More information. Axiomatic categorical domain theory is crucial for understanding the meaning of programs and reasoning about them. This book is the first systematic account of the subject and studies mathematical structures suitable for modelling functional programming languages in an Axiomatic (i.e. abstract) setting. In particular, the author develops theories of partiality and recursive types and applies. Axiomatic Domain Theory in Categories of Partial Maps First systematic account of Axiomatic categorical domain theory and functional programming. 英文书摘要. 查看全文信息(Full Text Information) Axiomatic Domain Theory in Categories of Partial Maps. Semantics of Programming Languages exposes the basic motivations and philosophy underlying the applications of semantic techniques in computer science. It introduces the mathematical theory of programming languages with an emphasis on higher-order functions and type systems. Designed as a text for upper-level and graduate-level students, the mathematically sophisticated approach will also. Pages (March ) Download full issue. Previous vol/issue. Next vol/issue. Actions for selected articles. Select all / Deselect all. Download PDFs Export citations. Show all article previews Show all article previews. Receive an update when the latest issues in this journal are published. In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems.A theory is a consistent, relatively-self-contained body of knowledge which usually contains an axiomatic system and all its derived theorems. An axiomatic system that is completely described is a special kind of formal system. At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate. M.P. Fiore: Axiomatic Domain Theory in Categories of Partial Maps. Cambridge University Press Distinguished Dissertations in Computer Science, Cambridge University Press Distinguished Dissertations in Computer Science, Cited by: Axiomatic (ISBN ) is a collection of short science fiction stories by Greg stories all delve into different aspects of self and identity. The Guardian describes it as "[w]onderful mind-expanding stuff, and well-written too.". Axiomatic Domain Theory in Categories of Partial Maps (by Marcelo Fiore) If, on the other hand, you are looking to understand the connection between type theory and the Curry-Howard isomorphism, nothing beats Lectures on the Curry-Howard Isomorphism which is book in Elsevier's Studies in Logic and the Foundations of Mathematics. Kamke's Theory of Sets is also not "axiomatic" but I seem to recall learning some good stuff from it. I think it was from that one that I learned that the indices in the sequence$\aleph_0,\aleph_1,\aleph_2,\ldots$are just the ordinals, including e.g.$\omega$and$\omega+1\$ and so on, and the least uncountable ordinal, etc.

Axiomatic categorical domain theory is crucial for understanding the meaning of programs and reasoning about them. This book is the first systematic account of the subject and studies mathematical structures suitable for modelling functional programming languages in an axiomatic (i.e. abstract) setting.

Indeed, Scott’s early work on Domain Theory was semi-nal to the subsequent extensive development of the theory of continuous lattices, which also drew heavily on ideas from topology, analysis, topological algebra and category theory [GHK+80].

Partial information. This is a great (historical) discussion of axiomatic set theory. Suppes published this book in with all that that implies. Notation is old style and takes some getting used to. I'm not a set theorist but I suspect much work has been done over the last 60 years and today set theory probably doesn't look like it did to Professor by: Finally, axiomatic theories of truth can be compared with each other in a way that philosophical and semantic theories cannot, by means of the methods of interpretation and proof-theoretic reduction so that one can speak of one theory being stronger (or weaker) than another.

It combines ideas from the theory of dynamical systems and from the theory of state-based computation. Although still in its infancy, it is an active area of research that generates wide interest. Written by one of the founders of the field, this book acts as the first mature and accessible introduction to by:.

Project Euclid - mathematics and statistics online. Fiore, M., and G. Rosolini, “Two models of synthetic domain theory,” Journal of Pure and Applied Algebra, vol.

Author: Jean-Pierre Marquis.In a more narrow sense, the term "axiomatic set theory" may denote some axiomatic theory aiming at the construction of some fragment of informal ("naive") set theory.

Set theory, which was formulated aroundhad to deal with several paradoxes from its very beginning.Book: Axiomatic Domain Theory in Categories of Partial Maps. Cambridge University Press, Distinguished Dissertations in Computer Science,