Combinators, lambda-terms and proof theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Reidel
1972
|
| Schriftenreihe: | Synthese library
[42] |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Zugl.: Uppsala, Univ., Diss., 1972 |
| Beschreibung: | 184 S. |
| ISBN: | 9027703051 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
PREFACE 5
CHAPTER 1. THE THEORY OF COMBINATORS AND THE A CALCULUS 11
1. Introduction 11
2. Informal theory of combinators 17
2.1. Combinators and combinations 17
2.2. The combinators I, B, W, C, *, *F 17
2.3. Extensionality 19
2.4. Alternative primitive combinators 20
2.5. Composite products, powers and deferred combinators 22
2.6. Truth functions 23
3. Equality and reduction 26
3.2. Combinatory terms 27
3.3. a equality 28
3.4. Functional abstraction 28
3.5. Substitution 29
3.6. Weak reduction 30
3.7. Equality 33
3.8. Strong reduction 37
4. The A calculus 41
4.1. A terms 41
4.2. Substitution 42
4.3. Equality 42
4.4. Reduction 43
4.5. (5 reduction 45
4.6. Historical remarks 46
5. Equivalence of the A calculus and the theory of combinators 47
8 CONTENTS
6. Set theoretical interpretations of combinators 51
6.1. Introduction 51
6.2. Scott s models 53
6.3. Combinatorial completeness 55
6.4. A representation result 59
6.5. Limit spaces 65
7. Illative combinatory logic and the paradoxes 67
CHAPTER 2. THE CHURCH ROSSER PROPERTY 73
1. Introduction 73
2. /{ reductions 74
3. One step reduction 76
4. Proof of main result 79
5. Generalization 84
6. Generalized weak reduction 86
CHAPTER 3. COMBINATORY ARITHMETIC 91
1. Introduction 91
2. Combinatory definability 92
3. Fixed points and numeral sequences 101
4. Undecidability results 106
CHAPTER 4. COMPUTABLE FUNCTIONALS OF FINITE TYPE 109
1. Introduction 109
2. Finite types and terms of finite types 112
3. The equation calculus 114
4. The role of the induction rule 118
5. Soundness of the axioms 120
6. Defining axioms and uniqueness rules 123
7. Reduction rules 125
8. Computability and normal form 126
9. Interpretation of types and terms 134
CHAPTER 5. PROOFS IN THE THEORY OF SPECIES 143
1. Introduction 143
CONTENTS 9
2. Formulas, terms and types 144
3. A terms and deductions 147
4. The equation calculus 151
5. Reduction and normal form 155
6. The strong normalization theorem 156
7. Interpretation of types and terms 165
BIBLIOGRAPHY 177
INDEX OF NAMES 181
INDEX OF SUBJECTS 182
|
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| bvnumber | BV001944368 |
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| discipline | Mathematik Philosophie |
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| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV001944368 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:37:40Z |
| institution | BVB |
| isbn | 9027703051 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001267387 |
| oclc_num | 221551893 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-703 DE-739 DE-355 DE-BY-UBR DE-29T DE-20 DE-19 DE-BY-UBM DE-29 DE-706 DE-M468 |
| owner_facet | DE-91G DE-BY-TUM DE-703 DE-739 DE-355 DE-BY-UBR DE-29T DE-20 DE-19 DE-BY-UBM DE-29 DE-706 DE-M468 |
| physical | 184 S. |
| publishDate | 1972 |
| publishDateSearch | 1972 |
| publishDateSort | 1972 |
| publisher | Reidel |
| record_format | marc |
| series | Synthese library |
| series2 | Synthese library |
| spelling | Stenlund, Sören 1943- Verfasser (DE-588)137291310 aut Combinators, lambda-terms and proof theory Sören Stenlund Dordrecht Reidel 1972 184 S. txt rdacontent n rdamedia nc rdacarrier Synthese library [42] Zugl.: Uppsala, Univ., Diss., 1972 Combinatory logic Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Kombinatorische Logik (DE-588)4164750-6 gnd rswk-swf Lambda-Kalkül (DE-588)4166495-4 gnd rswk-swf Metamathematik (DE-588)4074759-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Beweistheorie (DE-588)4145177-6 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kombinatorische Logik (DE-588)4164750-6 s DE-604 Metamathematik (DE-588)4074759-1 s Mathematische Logik (DE-588)4037951-6 s Mathematik (DE-588)4037944-9 s Beweistheorie (DE-588)4145177-6 s Lambda-Kalkül (DE-588)4166495-4 s Synthese library [42] (DE-604)BV000005044 42 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001267387&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stenlund, Sören 1943- Combinators, lambda-terms and proof theory Synthese library Combinatory logic Mathematische Logik (DE-588)4037951-6 gnd Kombinatorische Logik (DE-588)4164750-6 gnd Lambda-Kalkül (DE-588)4166495-4 gnd Metamathematik (DE-588)4074759-1 gnd Mathematik (DE-588)4037944-9 gnd Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4164750-6 (DE-588)4166495-4 (DE-588)4074759-1 (DE-588)4037944-9 (DE-588)4145177-6 (DE-588)4113937-9 |
| title | Combinators, lambda-terms and proof theory |
| title_auth | Combinators, lambda-terms and proof theory |
| title_exact_search | Combinators, lambda-terms and proof theory |
| title_full | Combinators, lambda-terms and proof theory Sören Stenlund |
| title_fullStr | Combinators, lambda-terms and proof theory Sören Stenlund |
| title_full_unstemmed | Combinators, lambda-terms and proof theory Sören Stenlund |
| title_short | Combinators, lambda-terms and proof theory |
| title_sort | combinators lambda terms and proof theory |
| topic | Combinatory logic Mathematische Logik (DE-588)4037951-6 gnd Kombinatorische Logik (DE-588)4164750-6 gnd Lambda-Kalkül (DE-588)4166495-4 gnd Metamathematik (DE-588)4074759-1 gnd Mathematik (DE-588)4037944-9 gnd Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Combinatory logic Mathematische Logik Kombinatorische Logik Lambda-Kalkül Metamathematik Mathematik Beweistheorie Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001267387&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005044 |
| work_keys_str_mv | AT stenlundsoren combinatorslambdatermsandprooftheory |