Derivation and computation: taking the Curry-Howard correspondence seriously
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2000
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge tracts in theoretical computer science
51 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXV, 384 S. |
| ISBN: | 0521771730 |
Internformat
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| 245 | 1 | 0 | |a Derivation and computation |b taking the Curry-Howard correspondence seriously |c Harold Simmons |
| 250 | |a 1. publ. | ||
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| 300 | |a XXV, 384 S. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge tracts in theoretical computer science |v 51 | |
| 650 | 7 | |a Bewijstheorie |2 gtt | |
| 650 | 4 | |a Curry-Howard, Isomorphisme de | |
| 650 | 4 | |a Lambda-calcul | |
| 650 | 7 | |a Lambda-calculus |2 gtt | |
| 650 | 7 | |a Mechanisering |2 gtt | |
| 650 | 4 | |a Preuve, Théorie de la | |
| 650 | 7 | |a Typentheorie |2 gtt | |
| 650 | 4 | |a Types, Théorie des | |
| 650 | 4 | |a Curry-Howard isomorphism | |
| 650 | 4 | |a Lambda calculus | |
| 650 | 4 | |a Proof theory | |
| 650 | 4 | |a Type theory | |
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Datensatz im Suchindex
| _version_ | 1804128008031698944 |
|---|---|
| adam_text | Titel: Derivation and computation
Autor: Simmons, Harold
Jahr: 2000
Contents
Introduction xi
Preview xv
I Development and Exercises 1
1 Derivation Systems 3
1.1 Introduction 3
Exercises 8
1.2 Generalities 8
Exercises 14
1.3 The Systems H and N 14
Exercises 18
1.4 Some algorithms on derivations 19
Exercises 24
2 COMPUTATION MECHANISMS 27
2.1 Introduction 27
Exercises 28
2.2 Combinator terms 29
Exercises 31
2.3 Combinator reduction 31
Exercises 35
2.4 A-terms 37
Exercises 40
2.5 A-reduction 40
Exercises 43
2.6 Intertranslatability 43
Exercises 45
2.7 Confluence and normalization 45
Exercises 47
3 The Typed Combinator Calculus 48
3.1 Introduction 48
Exercises 50
v
vi Contents
3.2 Derivation . 50
Exercises 52
3.3 Annotation and deletion 53
Exercises 57
3.4 Computation 57
Exercises 60
3.5 Subject reduction • 60
Exercises 65
4 The Typed A-calculus 67
4.1 Introduction 67
Exercises • 68
4.2 Derivation • 68
Exercises . • 70
4.3 Annotation and deletion • 71
Exercises . ¦ 75
4.4 Substitution ¦ 75
Exercises • 77
4.5 Computation . 78
Exercises 80
4.6 Subject reduction 80
Exercises 81
5 Substitution Algorithms 82
5.1 Introduction 82
Exercises 85
5.2 Pormal replacements 86
Exercises 89
5.3 The generic algorithm 89
Exercises 91
5.4 The mechanistic algorithm 92
Exercises 95
5.5 Some properties of Substitution 95
Exercises 98
6 Applied A-calculi 100
6.1 Introduction 100
Exercises 102
6.2 Derivation 102
Exercises 105
6.3 Type synthesis . 106
Exercises 111
6.4 Mutation 111
Exercises 120
6.5 Computation 122
Exercises 125
Contents vii
6.6 Type inhabitation 125
Exercises 128
6.7 Subject reduction 129
Exercises 135
7 Multi-recursive Arithmetic 137
7.1 Introduction 137
Exercises 140
7.2 The specifics of AG 140
Exercises 143
7.3 Forms of recursion and induction 144
Exercises 148
7.4 Small jump Operators 150
Exercises 158
7.5 The multi-recursive hierarchies 159
Exercises 163
7.6 The extent of AG 164
Exercises 165
7.7 Naming in AG 166
Exercises 169
8 Ordinals and Ordinal Notations 170
8.1 Introduction 170
Exercises 170
8.2 Ordinal arithmetic 170
Exercises 174
8.3 Fundamental sequences 174
Exercises 177
8.4 Some particular ordinals 177
Exercises 183
8.5 Ordinal notations 183
Exercises 188
9 Higher Order Recursion 189
9.1 Introduction 189
Exercises 192
9.2 The long iterator 193
Exercises 196
9.3 Limit creation and lifting 196
Exercises 198
9.4 Paxameterized ordinal iterators 198
Exercises 201
9.5 How to name ordinal iterates 202
Exercises 205
9.6 The GODS 206
Exercises 211
vüi Contents
II Solutions 213
A Derivation Systems 215
A.l Introduction 215
A.2 Generalities 216
A.3 The Systems H and N . 219
A.4 Some algorithms on derivations 225
B Computation Mechanisms 234
B.l Introduction 234
B.2 Combinator terms 237
B.3 Combinator reduction 237
B.4 A-terms 242
B.5 A-reduction 244
B.6 Intertranslatability 246
B.7 Confluence and normalization 247
C The Typed Combinator Calculus 249
C.l Introduction 249
C.2 Derivation 249
C.3 Annotation and deletion 252
C.4 Computation 256
C.5 Subject reduction 258
D The Typed A-calculus 264
D.l Introduction 264
D.2 Derivation 264
D.3 Annotation and deletion 267
D.4 Substitution 269
D.5 Computation 271
D.6 Subject reduction 275
E Substitution Algorithms 279
E.l Introduction 279
E.2 Formal replacements 281
E.3 The generic algorithm 281
E.4 The mechanistic algorithm 283
E.5 Some properties of Substitution 287
F Applied A-calculi 290
F.l Introduction 290
F.2 Derivation 290
F.3 Type synthesis 292
F.4 Mutation 297
F.5 Computation 306
F.6 Type inhabitation 308
F.7 Subject reduction 314
Contents ix
G Multi-recursive Arithmetic 318
G.l Introduction 318
G.2 The specifics of AG 319
G.3 Forms of recursion and induction 323
G.4 Small jump Operators 331
G.5 The multi-recursive hierarchies 334
G.6 The extent of AG 337
G.7 NaminginAG 340
H Ordinals and Ordinal Notations 341
H.l Introduction 341
H.2 Ordinal arithmetic 341
H.3 Fundamental sequences 345
H.4 Some particular ordinals 347
H.5 Ordinal notations 348
I Higher Order Recursion 355
1.1 Introduction 355
1.2 The long iterator 357
1.3 Limit creation and lifting 359
1.4 Parameterized ordinal iterators ¦ 360
1.5 How to name ordinal iterates 366
1.6 The GODS 368
Postview 371
BlBLIOGRAPHY 375
commonly used symbols 377
Index 379
|
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| id | DE-604.BV013246029 |
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| isbn | 0521771730 |
| language | English |
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| physical | XXV, 384 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge tracts in theoretical computer science |
| series2 | Cambridge tracts in theoretical computer science |
| spelling | Simmons, Harold 1942- Verfasser (DE-588)1016589964 aut Derivation and computation taking the Curry-Howard correspondence seriously Harold Simmons 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2000 XXV, 384 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in theoretical computer science 51 Bewijstheorie gtt Curry-Howard, Isomorphisme de Lambda-calcul Lambda-calculus gtt Mechanisering gtt Preuve, Théorie de la Typentheorie gtt Types, Théorie des Curry-Howard isomorphism Lambda calculus Proof theory Type theory Cambridge tracts in theoretical computer science 51 (DE-604)BV000754528 51 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009028110&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Simmons, Harold 1942- Derivation and computation taking the Curry-Howard correspondence seriously Cambridge tracts in theoretical computer science Bewijstheorie gtt Curry-Howard, Isomorphisme de Lambda-calcul Lambda-calculus gtt Mechanisering gtt Preuve, Théorie de la Typentheorie gtt Types, Théorie des Curry-Howard isomorphism Lambda calculus Proof theory Type theory |
| title | Derivation and computation taking the Curry-Howard correspondence seriously |
| title_auth | Derivation and computation taking the Curry-Howard correspondence seriously |
| title_exact_search | Derivation and computation taking the Curry-Howard correspondence seriously |
| title_full | Derivation and computation taking the Curry-Howard correspondence seriously Harold Simmons |
| title_fullStr | Derivation and computation taking the Curry-Howard correspondence seriously Harold Simmons |
| title_full_unstemmed | Derivation and computation taking the Curry-Howard correspondence seriously Harold Simmons |
| title_short | Derivation and computation |
| title_sort | derivation and computation taking the curry howard correspondence seriously |
| title_sub | taking the Curry-Howard correspondence seriously |
| topic | Bewijstheorie gtt Curry-Howard, Isomorphisme de Lambda-calcul Lambda-calculus gtt Mechanisering gtt Preuve, Théorie de la Typentheorie gtt Types, Théorie des Curry-Howard isomorphism Lambda calculus Proof theory Type theory |
| topic_facet | Bewijstheorie Curry-Howard, Isomorphisme de Lambda-calcul Lambda-calculus Mechanisering Preuve, Théorie de la Typentheorie Types, Théorie des Curry-Howard isomorphism Lambda calculus Proof theory Type theory |
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