Computable models:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Springer
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 240 S. |
| ISBN: | 9781848820517 |
Internformat
MARC
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| 245 | 1 | 0 | |a Computable models |c Raymond Turner |
| 264 | 1 | |a London |b Springer |c 2009 | |
| 300 | |a XI, 240 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Computable functions | |
| 650 | 4 | |a Model theory | |
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Datensatz im Suchindex
| _version_ | 1804139309971800064 |
|---|---|
| adam_text | Contents
1
What is a Computable Model?
.................................. 1
1.1
Mathematical Models
..................................... 1
1.2
Specifications, Programs, and Models
....................... 2
1.3
Data Types and Programming Languages
..................... 3
1.4
Theories of Data
......................................... 4
1.5
Recursive Models
........................................ 5
1.6
Intensional Models
....................................... 6
1.7
A Logical Foundation for Specification
...................... 7
1.8
Implementable Models
.................................... 7
1.9
The Logical Setting
....................................... 8
References
.................................................... 9
2
Typed Predicate Logic
.......................................... 11
2.1
Judgments and Contexts
................................... 11
2.2
Structural Rules
.......................................... 13
2.3
Types
................................................... 13
2.4
Relations and Functions
................................... 15
2.5
Equality
................................................ 15
2.6
Prepositional Rules
....................................... 16
2.7
Quantifier Rules
.......................................... 17
2.8
TPL Derivations
......................................... 18
2.9
Type Inference
........................................... 20
References
.................................................... 23
3
Data Types
.................................................... 25
3.1
Booleans
................................................ 25
3.2
Products
................................................ 27
3.3
Stacks
.................................................. 29
3.4
Terms
.................................................. 30
3.5
Numbers
................................................ 30
3.6
Lists
................................................... 32
3.7
A Type of Types
......................................... 33
iii
Contents
3.8
Theories of Data Types
.................................... 33
References
.................................................... 35
4
Definability
................................................... 37
4.1
Semidecidable Relations
................................... 38
4.2
Decidable Relations
...................................... 39
References
.................................................... 41
5
Specification
.................................................. 43
5.1
A Logical Perspective
..................................... 44
5.2
Some Specifications
...................................... 45
5.3
Operations on Schema
.................................... 48
5.4
Conservative Extensions
................................... 51
References
.................................................... 52
6
Functions
..................................................... 53
6.1
Totality and Functionality
.................................. 53
6.2
Functional Application
.................................... 54
6.3
Explicit Functions
........................................ 57
6.4
The Elimination of Application
............................. 59
References
.................................................... 62
7
Preconditions
................................................. 63
7.1
Specifications with Preconditions
........................... 63
7.2
Totality and Functionality
.................................. 65
7.3
Functional Application
.................................... 67
7.4
Application Elimination
................................... 69
7.5
Partial Functions
......................................... 69
References
.................................................... 70
8
Natural Numbers
.............................................. 71
8.1
A Theory of Numbers
..................................... 71
8.2
Numerical Specification
................................... 74
8.3
Recursive Specifications
................................... 79
8.4
Enriched Arithmetic
...................................... 82
8.5
Arithmetic Interpretation
.................................. 83
References
.................................................... 84
9
Typed Set Theory
.............................................. 85
9.1
CST
.................................................... 85
9.2
Elementary Properties
..................................... 88
9.3
Subsets and Extensionality
................................. 89
9.4
New Sets from Old
....................................... 90
9.5
Set-Theoretic Relations
................................... 97
Contents jx
9.6
Arithmetic
Interpretation..................................100
References
................................................... 102
10 Systems
Modeling
.............................................1
03
10.1
The Requirements
........................................
ЮЗ
10.2
The State
...............................................104
10.3
Operations
..............................................107
10.4
A Mathematical Model
....................................108
References
....................................................
Ill
11
A Type of Types
...............................................113
11.1
The Type type
...........................................114
11.2
Dependent Types
.........................................115
11.3
Dependent Specifications
..................................116
11.4
Polymorphic Specifications
................................117
11.5
Polymorphic Set Theory
...................................
1
20
11.6
Specifications and Types
...................................122
11.7
Arithmetic Interpretation
..................................124
References
....................................................125
12
Schemata
.....................................................127
12.1
A Theory of Relations
.....................................127
12.2
A Minimal Theory
........................................130
12.3
Operations on Schemata
...................................132
12.4
Arithmetic Interpretation
..................................139
References
....................................................140
13
Separation Types
..............................................143
13.1
Theories with Separation
..................................143
13.2
Subtypes in Specification
..................................145
13.3
Preconditions and Functions
...............................146
13.4
Polymorphism and Subtypes
...............................148
13.5
The Elimination of Subtypes
...............................149
References
....................................................153
14
Recursive Schemata
............................................155
14.1
Closure and Induction
..................................... 55
14.2
Simultaneous Recursion
...................................158
14.3
Arithmetic Interpretation
..................................162
14.4
Sets and Schemata
........................................
162
References
....................................................
166
15
Inductive Types
................................................
167
15.1
The General Form
........................................
167
x
Contents
15.2
Some Inductive Types
.....................................168
15.3
Conservative Extensions
...................................170
15.4
Finite Schemata
..........................................171
References
....................................................175
16
Recursive Functions
...........................................177
16.1
General Form
............................................177
16.2
Numerical Recursion
.....................................180
16.3
Recursive Functions and Inductive Types
.....................181
References
....................................................183
17
Schema Definitions
............................................185
17.1
Schema Definitions
.......................................185
17.2
Refinement
..............................................188
17.3
Implementable Definitions
.................................191
17.4
The Limits of Refinement
..................................192
17.5
Properties of Schemata
....................................193
References
....................................................194
18
Computable Ontology
..........................................195
18.1
Implementable Models
.................................... 195
18.2
A Type of Events
......................................... 196
18.3
Arithmetic Interpretation
.................................. 197
18.4
Instants
................................................. 198
18.5
Implementation
.......................................... 199
References
.................................................... 199
19
Classes
.......................................................201
19.1
Classes and Judgments
....................................201
19.2
Class Elimination
........................................204
References
....................................................205
20
Classes of Functions
...........................................207
20.1
Function Application
.....................................207
20.2
Specifications and Function Classes
.........................209
20.3
Partial Functions
.........................................212
20.4
Polymorphism
...........................................213
References
....................................................215
21
Computable Analysis
..........................................217
21.1
Cauchy Sequences
........................................217
21.2
Operations on the Real Numbers
............................219
21.3
Implementation
..........................................220
References
....................................................222
Contents xi
22 Programming
Language Specification
............................223
22.1
The Abstract Machine
.....................................223
22.2
A Programming Language and Its Specification
...............226
22.3
Implementation
..........................................228
References
....................................................229
23
Abstract Types
................................................231
23.1
Axiomatic Specifications
..................................231
23.2
Polymorphism and Data Abstraction
.........................234
References
....................................................236
24
Conclusion
....................................................237
Index
.............................................................239
|
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| spelling | Turner, Raymond 1947- Verfasser aut Computable models Raymond Turner London Springer 2009 XI, 240 S. txt rdacontent n rdamedia nc rdacarrier Computable functions Model theory Berechenbarkeit (DE-588)4138368-0 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Berechnungstheorie (DE-588)4005581-4 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 s Berechenbarkeit (DE-588)4138368-0 s DE-604 Berechnungstheorie (DE-588)4005581-4 s 1\p DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017687927&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Turner, Raymond 1947- Computable models Computable functions Model theory Berechenbarkeit (DE-588)4138368-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd Berechnungstheorie (DE-588)4005581-4 gnd |
| subject_GND | (DE-588)4138368-0 (DE-588)4114528-8 (DE-588)4005581-4 |
| title | Computable models |
| title_auth | Computable models |
| title_exact_search | Computable models |
| title_full | Computable models Raymond Turner |
| title_fullStr | Computable models Raymond Turner |
| title_full_unstemmed | Computable models Raymond Turner |
| title_short | Computable models |
| title_sort | computable models |
| topic | Computable functions Model theory Berechenbarkeit (DE-588)4138368-0 gnd Mathematisches Modell (DE-588)4114528-8 gnd Berechnungstheorie (DE-588)4005581-4 gnd |
| topic_facet | Computable functions Model theory Berechenbarkeit Mathematisches Modell Berechnungstheorie |
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