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Nominal Sets : Names and Symmetry in Computer Science

By: Pitts, Andrew M.
Material type: TextTextSeries: eBooks on Demand.Cambridge Tracts in Theoretical Computer Science: Publisher: Cambridge : Cambridge University Press, 2013Description: 1 online resource (292 p.).ISBN: 9781107247581.Subject(s): Compiling (Electronic computers) | Programming languages (Electronic computers) -- Semantics | Programming languages (Electronic computers) -- SyntaxGenre/Form: Electronic books.Additional physical formats: Print version:: Nominal Sets : Names and Symmetry in Computer ScienceDDC classification: 004.0151 Online resources: Click here to view this ebook.
Contents:
Cover; Contents; Preface; 0 Introduction; 0.1 Atomic names; 0.2 Support and freshness; 0.3 Abstract syntax with binders; 0.4 Name abstraction; 0.5 Orbit-finiteness; 0.6 Alternative formulations; 0.7 Prerequisites; 0.8 Notation; PART ONE THEORY; 1 Permutations; 1.1 The category of G-sets; 1.2 Products and coproducts; 1.3 Natural numbers; 1.4 Functions; 1.5 Power sets; 1.6 Partial functions; 1.7 Quotient sets; 1.8 Finite permutations; 1.9 Name symmetries; Exercises; 2 Support; 2.1 The category of nominal sets; 2.2 Products and coproducts; 2.3 Natural numbers; 2.4 Functions; 2.5 Power sets
2.6 FM-sets2.7 Failure of choice; 2.8 Partial functions; 2.9 Quotient sets; 2.10 Non-finite support; Exercises; 3 Freshness; 3.1 Freshness relation; 3.2 Freshness quantifier; 3.3 Fresh names; 3.4 Separated product; Exercises; 4 Name abstraction; 4.1 α-Equivalence; 4.2 Nominal set of name abstractions; 4.3 Concretion; 4.4 Functoriality; 4.5 Freshness condition for binders; 4.6 Generalized name abstraction; 4.7 Many sorts of names; Exercises; 5 Orbit-finiteness; 5.1 Orbits; 5.2 Atomic nominal sets; 5.3 Finitely presentable objects; 5.4 Orbit-finite subsets; 5.5 Uniformly supported subsets
Exercises6 Equivalents of; 6.1 Sets with name swapping; 6.2 Continuous G-sets; 6.3 The Schanuel topos; 6.4 Named sets; Exercises; PART TWO APPLICATIONS; 7 Inductive and coinductive definitions; 7.1 Inductively defined subsets; 7.2 Rule induction; 7.3 Equivariant rules; 7.4 Tarski's fixed-point theorem; 7.5 Equivariant fixed-points; 7.6 Coinductively defined subsets; Exercises; 8 Nominal algebraic data types; 8.1 Signatures; 8.2 α-Equivalence; 8.3 Algebraic functors; 8.4 Initial algebra semantics; 8.5 Primitive recursion; 8.6 Induction; Exercises; 9 Locally scoped names
9.1 The category of nominal restriction sets9.2 Products and coproducts; 9.3 Functions; 9.4 λν-Calculus; 9.5 Free nominal restriction sets; 9.6 ν-Calculus; 9.7 Total concretion; Exercises; 10 Functional programming; 10.1 Types of names; 10.2 Name abstraction types; 10.3 Dynamically allocated names; 10.4 Name swapping; 10.5 Freshness relation; 10.6 Name abstraction expressions; 10.7 Name abstraction patterns; 10.8 FML; 10.9 Type assignment; 10.10 Contextual equivalence; 10.11 Step-indexed logical relation; 10.12 Abstractness; 10.13 Purity; Exercises; 11 Domain theory; 11.1 Nominal posets
11.2 Discontinuity of name abstraction11.3 Uniform directed complete posets; 11.4 Recursive domain equations; 11.5 Nominal Scott domains; Exercises; 12 Computational logic; 12.1 Unification; 12.2 Term rewriting; 12.3 Logic programming; Exercises; References; Index of notation; Index
Summary: The first detailed account of the basic theory and applications of nominal sets.
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Item type Current location Call number URL Status Date due Barcode
Electronic Book UT Tyler Online
Online
QA76.7 .P384 2013 (Browse shelf) http://uttyler.eblib.com/patron/FullRecord.aspx?p=1357339 Available EBL1357339

Cover; Contents; Preface; 0 Introduction; 0.1 Atomic names; 0.2 Support and freshness; 0.3 Abstract syntax with binders; 0.4 Name abstraction; 0.5 Orbit-finiteness; 0.6 Alternative formulations; 0.7 Prerequisites; 0.8 Notation; PART ONE THEORY; 1 Permutations; 1.1 The category of G-sets; 1.2 Products and coproducts; 1.3 Natural numbers; 1.4 Functions; 1.5 Power sets; 1.6 Partial functions; 1.7 Quotient sets; 1.8 Finite permutations; 1.9 Name symmetries; Exercises; 2 Support; 2.1 The category of nominal sets; 2.2 Products and coproducts; 2.3 Natural numbers; 2.4 Functions; 2.5 Power sets

2.6 FM-sets2.7 Failure of choice; 2.8 Partial functions; 2.9 Quotient sets; 2.10 Non-finite support; Exercises; 3 Freshness; 3.1 Freshness relation; 3.2 Freshness quantifier; 3.3 Fresh names; 3.4 Separated product; Exercises; 4 Name abstraction; 4.1 α-Equivalence; 4.2 Nominal set of name abstractions; 4.3 Concretion; 4.4 Functoriality; 4.5 Freshness condition for binders; 4.6 Generalized name abstraction; 4.7 Many sorts of names; Exercises; 5 Orbit-finiteness; 5.1 Orbits; 5.2 Atomic nominal sets; 5.3 Finitely presentable objects; 5.4 Orbit-finite subsets; 5.5 Uniformly supported subsets

Exercises6 Equivalents of; 6.1 Sets with name swapping; 6.2 Continuous G-sets; 6.3 The Schanuel topos; 6.4 Named sets; Exercises; PART TWO APPLICATIONS; 7 Inductive and coinductive definitions; 7.1 Inductively defined subsets; 7.2 Rule induction; 7.3 Equivariant rules; 7.4 Tarski's fixed-point theorem; 7.5 Equivariant fixed-points; 7.6 Coinductively defined subsets; Exercises; 8 Nominal algebraic data types; 8.1 Signatures; 8.2 α-Equivalence; 8.3 Algebraic functors; 8.4 Initial algebra semantics; 8.5 Primitive recursion; 8.6 Induction; Exercises; 9 Locally scoped names

9.1 The category of nominal restriction sets9.2 Products and coproducts; 9.3 Functions; 9.4 λν-Calculus; 9.5 Free nominal restriction sets; 9.6 ν-Calculus; 9.7 Total concretion; Exercises; 10 Functional programming; 10.1 Types of names; 10.2 Name abstraction types; 10.3 Dynamically allocated names; 10.4 Name swapping; 10.5 Freshness relation; 10.6 Name abstraction expressions; 10.7 Name abstraction patterns; 10.8 FML; 10.9 Type assignment; 10.10 Contextual equivalence; 10.11 Step-indexed logical relation; 10.12 Abstractness; 10.13 Purity; Exercises; 11 Domain theory; 11.1 Nominal posets

11.2 Discontinuity of name abstraction11.3 Uniform directed complete posets; 11.4 Recursive domain equations; 11.5 Nominal Scott domains; Exercises; 12 Computational logic; 12.1 Unification; 12.2 Term rewriting; 12.3 Logic programming; Exercises; References; Index of notation; Index

The first detailed account of the basic theory and applications of nominal sets.

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