The Resource Iteration theories : the equational logic of iterative processes, Stephen L. Bloom, Zoltán Ésik

Iteration theories : the equational logic of iterative processes, Stephen L. Bloom, Zoltán Ésik

Label
Iteration theories : the equational logic of iterative processes
Title
Iteration theories
Title remainder
the equational logic of iterative processes
Statement of responsibility
Stephen L. Bloom, Zoltán Ésik
Creator
Contributor
Subject
Genre
Language
eng
Member of
Cataloging source
DLC
http://library.link/vocab/creatorDate
1940-
http://library.link/vocab/creatorName
Bloom, Stephen L.
Illustrations
illustrations
Index
no index present
LC call number
QA76.9.M35
LC item number
I56 1993
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1951-
http://library.link/vocab/relatedWorkOrContributorName
Ésik, Zoltán
http://library.link/vocab/subjectName
  • Computer science
  • Iterative methods (Mathematics)
  • Logic, Symbolic and mathematical
  • matrice itérative
  • logique Floyd-Hoare
  • sémantique algébrique
  • point fixe
  • processus itératif
  • itération
  • Informatique
  • Itération (Mathématiques)
  • Logique symbolique et mathématique
  • Computer science
  • Iterative methods (Mathematics)
  • Logic, Symbolic and mathematical
  • Programmeertalen
  • Semantiek
  • Wiskundige logica
  • Symbolische logica
  • Iteratief oplossen
  • Programacao de computadores
  • Logique symbolique et mathématique
  • Informatique
  • Itération (mathématiques)
  • Fixpunkt <Datensicherung>
Label
Iteration theories : the equational logic of iterative processes, Stephen L. Bloom, Zoltán Ésik
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. [621]-630)
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
1. Mathematical Motivation. 2. Why Iteration Theories? 3. Suggestions for the Impatient Reader. 4. A Disclaimer. 5. Numbering -- 1. Preliminary Facts. 1. Sets and Functions. 2. Posets. 3. Categories. 4. 2-Categories. 5. [Sigma]-Trees -- 2. Varieties and Theories. 1. [Sigma]-Algebras. 2. Terms and Equations. 3. Theories. 4. The Theory of a Variety -- 3. Theory Facts. 1. Pairing and Separated Sum. 2. Elementary Properties of TH. 3. Theories as N x N-Sorted Algebras. 4. Special Coproducts. 5. Matrix and Matricial Theories. 6. Pullbacks and Pushouts of Base Morphisms. 7. 2-Theories -- 4. Algebras. 1. T-algebras. 2. Free Algebras in T[superscript [flat]]. 3. Subvarieties of T[superscript [flat]]. 4. The Categories TH and VAR -- 5. Iterative Theories. 1. Ideal Theories. 2. Iterative Theories Defined. 3. Properties of Iteration in Iterative Theories. 4. Free Iterative Theories -- 6. Iteration Theories. 1. Iteration Theories Defined. 2. Other Axiomatizations of Iteration Theories. 3. Theories with a Functorial Dagger. 4. Pointed Iterative Theories. 5. Free Iteration Theories. 6. Constructions on Iteration Theories. 7. Feedback Theories. 8. Summary of the Axioms -- 7. Iteration Algebras. 1. Definitions. 2. Free Algebras in T[actual symbol not reproducible]. 3. The Retraction Lemma. 4. Some Categorical Facts. 5. Properties of T[actual symbol not reproducible]. 6. A Characterization Theorem. 7. Strong Iteration Algebras -- 8. Continuous Theories. 1. Ordered Algebraic Theories. 2. [omega]-Continuous Theories. 3. Rational Theories. 4. Initiality and Iteration in 2-Theories. 5. [omega]-Continuous 2-Theories -- 9. Matrix Iteration Theories. 1. Notation. 2. Properties of the Star Operation. 3. Matrix Iteration Theories Defined. 4. Presentations in Matrix Iteration Theories. 5. The Initial Matrix Iteration Theory. 6. An Extension Theorem. 7. Matrix Iteration Theories of Regular Sets -- 10. Matricial Iteration Theories. 1. From Dagger to Star and Omega, and Back. 2. Matricial Iteration Theories Defined. 3. Examples. 4. Additively Closed Subiteration Theories. 5. Presentations in Matricial Iteration Theories. 6. The Initial Matricial Iteration Theory. 7. The Extension Theorem. 8. Additively Closed Theories of Regular Languages. 9. Closed Regular [omega]-Languages -- 11. Presentations. 1. Presentations in Iteration Theories. 2. Simulations of Presentations. 3. Coproducts Revisited -- 12. Flowchart Behaviors. 1. Axiomatizing Sequacious Functions. 2. Axiomatizing Partial Functions. 3. Diagonal Theories. 4. Sequacious Functions with Predicates. 5. Partial Functions with Predicates -- 13. Synchronization Trees. 1. Theories of Synchronization Trees. 2. Grove Iteration Theories. 3. Axiomatizing Synchronization Trees. 4. Bisimilarity -- 14. Floyd-Hoare Logic. 1. Guards. 2. Partial Correctness Assertions. 3. The Standard Example. 4. Rules for Partial Correctness. 5. Soundness. 6. The Standard, Example, Continued. 7. A-Floyd-Hoare Calculus for Iteration Theories. 8. The Standard Example, Again. 9. Completeness. 10. Examples
Dimensions
24 cm.
Extent
xv, 630 pages
Isbn
9780387563787
Lccn
93018445
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
  • (OCoLC)27640709
  • (OCoLC)ocm27640709
Label
Iteration theories : the equational logic of iterative processes, Stephen L. Bloom, Zoltán Ésik
Publication
Bibliography note
Includes bibliographical references (p. [621]-630)
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
1. Mathematical Motivation. 2. Why Iteration Theories? 3. Suggestions for the Impatient Reader. 4. A Disclaimer. 5. Numbering -- 1. Preliminary Facts. 1. Sets and Functions. 2. Posets. 3. Categories. 4. 2-Categories. 5. [Sigma]-Trees -- 2. Varieties and Theories. 1. [Sigma]-Algebras. 2. Terms and Equations. 3. Theories. 4. The Theory of a Variety -- 3. Theory Facts. 1. Pairing and Separated Sum. 2. Elementary Properties of TH. 3. Theories as N x N-Sorted Algebras. 4. Special Coproducts. 5. Matrix and Matricial Theories. 6. Pullbacks and Pushouts of Base Morphisms. 7. 2-Theories -- 4. Algebras. 1. T-algebras. 2. Free Algebras in T[superscript [flat]]. 3. Subvarieties of T[superscript [flat]]. 4. The Categories TH and VAR -- 5. Iterative Theories. 1. Ideal Theories. 2. Iterative Theories Defined. 3. Properties of Iteration in Iterative Theories. 4. Free Iterative Theories -- 6. Iteration Theories. 1. Iteration Theories Defined. 2. Other Axiomatizations of Iteration Theories. 3. Theories with a Functorial Dagger. 4. Pointed Iterative Theories. 5. Free Iteration Theories. 6. Constructions on Iteration Theories. 7. Feedback Theories. 8. Summary of the Axioms -- 7. Iteration Algebras. 1. Definitions. 2. Free Algebras in T[actual symbol not reproducible]. 3. The Retraction Lemma. 4. Some Categorical Facts. 5. Properties of T[actual symbol not reproducible]. 6. A Characterization Theorem. 7. Strong Iteration Algebras -- 8. Continuous Theories. 1. Ordered Algebraic Theories. 2. [omega]-Continuous Theories. 3. Rational Theories. 4. Initiality and Iteration in 2-Theories. 5. [omega]-Continuous 2-Theories -- 9. Matrix Iteration Theories. 1. Notation. 2. Properties of the Star Operation. 3. Matrix Iteration Theories Defined. 4. Presentations in Matrix Iteration Theories. 5. The Initial Matrix Iteration Theory. 6. An Extension Theorem. 7. Matrix Iteration Theories of Regular Sets -- 10. Matricial Iteration Theories. 1. From Dagger to Star and Omega, and Back. 2. Matricial Iteration Theories Defined. 3. Examples. 4. Additively Closed Subiteration Theories. 5. Presentations in Matricial Iteration Theories. 6. The Initial Matricial Iteration Theory. 7. The Extension Theorem. 8. Additively Closed Theories of Regular Languages. 9. Closed Regular [omega]-Languages -- 11. Presentations. 1. Presentations in Iteration Theories. 2. Simulations of Presentations. 3. Coproducts Revisited -- 12. Flowchart Behaviors. 1. Axiomatizing Sequacious Functions. 2. Axiomatizing Partial Functions. 3. Diagonal Theories. 4. Sequacious Functions with Predicates. 5. Partial Functions with Predicates -- 13. Synchronization Trees. 1. Theories of Synchronization Trees. 2. Grove Iteration Theories. 3. Axiomatizing Synchronization Trees. 4. Bisimilarity -- 14. Floyd-Hoare Logic. 1. Guards. 2. Partial Correctness Assertions. 3. The Standard Example. 4. Rules for Partial Correctness. 5. Soundness. 6. The Standard, Example, Continued. 7. A-Floyd-Hoare Calculus for Iteration Theories. 8. The Standard Example, Again. 9. Completeness. 10. Examples
Dimensions
24 cm.
Extent
xv, 630 pages
Isbn
9780387563787
Lccn
93018445
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
Other physical details
illustrations
System control number
  • (OCoLC)27640709
  • (OCoLC)ocm27640709

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