A Lambda Calculus Satellite:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
College Publications
[2022]
|
| Schriftenreihe: | Studies in logic
volume 94 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 582 Seiten |
| ISBN: | 9781848904156 |
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Datensatz im Suchindex
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| adam_text | CONTENTS Contents Acknowledgements xv About λ-calculus 1 About this book 13 General notations 23 I Preliminaries 1 The λ-calculus in a nutshell 29 1.1 The λ-calculus — Its syntax............ 29 1.2 Properties of reduction........................ 37 1.3 RuS and consequences ........................ 51 2 Böhm trees and variations 2.1 2.2 2.3 2.4 3 Theories and models of λ-calculus 3.1 3.2 II 57 About coinduction................................ 57 Numerical sequences and trees .... 63 Böhm(-Iike) trees................................ 64 Variations of Böhm trees.................... 70 79 The lattice of λ-theories....................... 79 Denotational models............................. 86 Optimal lambda reduction. 6 Infinitary lambda calculus 6.1 6.2 6.3 6.4 7 Starlings 7.1 7.2 7.3 7.4 7.5 7.6 7.7 III 163 The infinitary λ-calculus................... 163 Relative computability...................... 175 Restoring confluence........................... 180 Extensional infinitary λ-calculi .... 189 199 The S-fragment of CL......................201 Normalization.................................. 206 Infinite reductions ........... .................. 211 Head-normalization is decidable . . . 220 The word problem for S ................... 223 Non-normalizing patterns................ 228 Translating S-terms into λ-calculus . 231 Conversion 8 Perpendicular Lines Property 239 107 4.1 Planes and cyclic reductions.............. 109 4.2 Recurrent terms and the Plane Pro perty ................................................... 112 5 Families of redoxes.............................. 120
Extraction.......................................... 125 The labeled λ-calculus ..................... 140 Optimal reductions........................... 153 Sharing graphs.....................................161 8.1 Validity of PLP in Λ4(λ}................ 241 8.2 Л4(В), Μ°(ΰ) μ PLP........................242 8.3 Invalidity of PLP in A40 (λ)................ 243 Reduction 4Leaving a ^-reduction plane 5.1 5.2 5.3 5.4 5.5 117 9 Bijectivity and invertibility in λη 9.1 9.2 9.3 251 Equi-unsolvability............................... 255 Invertibility in Μ°(λη)...................... 266 Partial characterizationsof L/Rinvertibility............................................ 271
CONTENTS IV xiii Theories 10 Sensible theories 15 Church algebras for A-calculus 293 10.1 The range property fails in Ή .... 295 10.2 The FPP fails in sensible theories . . 305 11 The kite 311 11.1 Degrees of extensionality for Böhm trees ............................................. 313 11.2 H^ satisfies the ω-rule ....................... 318 11.3 Characterizing Ή+................................ 327 11.4 A characterization of βη.................... 335 V Models 12 Ordered models and theories 347 12.1 Inequational theories and ordered models................................................. 348 12.2 Extensional orders on Böhm trees . . 352 VI Open Problems 16 Open Problems 367 13.1 Intersection type systems.................... 370 13.2 Filter models in logical form.............. 379 13.3 Filter models: some case-studies . . . 389 14 Relational models 399 14.1 The class of relational graph models . 401 14.2 Tensor type assignment systems . · . 407 14.3 çNPR — A case study.......................418 14.4 Rgms in logical form .......................... 427 14.5 Relational graph theories.................... 429 463 16.1 Reduction and conversion................... 463 16.2 Models and theories............................ 470 16.3 λ(Η)ω in the analytical hierarchy . . 476 16.4 Illative Combinatory Logic.................481 VII Appendix A Mathematical background 13 Filter models 435 15.1 Algebras and Boolean products . . . 438 15.2 Church algebras.................................. 441 15.3 Easiness in universal algebra............. 447 15.4 Applications to λ-calculus models and
theories................................ 450 15.5 The main semantics are hugely in complete .............................................. 456 A.l A.2 A.3 A.4 The lean notation for A-terms .... A summary of category theory .... A summary of domain theory .... A summary of universal algebra . . . 489 491 495 501 509 References 550 Indices 551 Index of definitions..................................... 552 Index of names........................................... 565 Index of symbols ........................................ 572
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| adam_txt |
CONTENTS Contents Acknowledgements xv About λ-calculus 1 About this book 13 General notations 23 I Preliminaries 1 The λ-calculus in a nutshell 29 1.1 The λ-calculus — Its syntax. 29 1.2 Properties of reduction. 37 1.3 RuS and consequences . 51 2 Böhm trees and variations 2.1 2.2 2.3 2.4 3 Theories and models of λ-calculus 3.1 3.2 II 57 About coinduction. 57 Numerical sequences and trees . 63 Böhm(-Iike) trees. 64 Variations of Böhm trees. 70 79 The lattice of λ-theories. 79 Denotational models. 86 Optimal lambda reduction. 6 Infinitary lambda calculus 6.1 6.2 6.3 6.4 7 Starlings 7.1 7.2 7.3 7.4 7.5 7.6 7.7 III 163 The infinitary λ-calculus. 163 Relative computability. 175 Restoring confluence. 180 Extensional infinitary λ-calculi . 189 199 The S-fragment of CL.201 Normalization. 206 Infinite reductions . . 211 Head-normalization is decidable . . . 220 The word problem for S . 223 Non-normalizing patterns. 228 Translating S-terms into λ-calculus . 231 Conversion 8 Perpendicular Lines Property 239 107 4.1 Planes and cyclic reductions. 109 4.2 Recurrent terms and the Plane Pro perty . 112 5 Families of redoxes. 120
Extraction. 125 The labeled λ-calculus . 140 Optimal reductions. 153 Sharing graphs.161 8.1 Validity of PLP in Λ4(λ}. 241 8.2 Л4(В), Μ°(ΰ) μ PLP.242 8.3 Invalidity of PLP in A40 (λ). 243 Reduction 4Leaving a ^-reduction plane 5.1 5.2 5.3 5.4 5.5 117 9 Bijectivity and invertibility in λη 9.1 9.2 9.3 251 Equi-unsolvability. 255 Invertibility in Μ°(λη). 266 Partial characterizationsof L/Rinvertibility. 271
CONTENTS IV xiii Theories 10 Sensible theories 15 Church algebras for A-calculus 293 10.1 The range property fails in Ή . 295 10.2 The FPP fails in sensible theories . . 305 11 The kite 311 11.1 Degrees of extensionality for Böhm trees . 313 11.2 H^ satisfies the ω-rule . 318 11.3 Characterizing Ή+. 327 11.4 A characterization of βη. 335 V Models 12 Ordered models and theories 347 12.1 Inequational theories and ordered models. 348 12.2 Extensional orders on Böhm trees . . 352 VI Open Problems 16 Open Problems 367 13.1 Intersection type systems. 370 13.2 Filter models in logical form. 379 13.3 Filter models: some case-studies . . . 389 14 Relational models 399 14.1 The class of relational graph models . 401 14.2 Tensor type assignment systems . · . 407 14.3 çNPR — A case study.418 14.4 Rgms in logical form . 427 14.5 Relational graph theories. 429 463 16.1 Reduction and conversion. 463 16.2 Models and theories. 470 16.3 λ(Η)ω in the analytical hierarchy . . 476 16.4 Illative Combinatory Logic.481 VII Appendix A Mathematical background 13 Filter models 435 15.1 Algebras and Boolean products . . . 438 15.2 Church algebras. 441 15.3 Easiness in universal algebra. 447 15.4 Applications to λ-calculus models and
theories. 450 15.5 The main semantics are hugely in complete . 456 A.l A.2 A.3 A.4 The lean notation for A-terms . A summary of category theory . A summary of domain theory . A summary of universal algebra . . . 489 491 495 501 509 References 550 Indices 551 Index of definitions. 552 Index of names. 565 Index of symbols . 572 |
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| index_date | 2024-07-03T22:03:13Z |
| indexdate | 2024-07-10T09:51:40Z |
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| isbn | 9781848904156 |
| language | English |
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| publisher | College Publications |
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| series | Studies in logic |
| series2 | Studies in logic |
| spelling | Barendregt, Hendrik P. 1947- Verfasser (DE-588)124647219 aut A Lambda Calculus Satellite London College Publications [2022] © 2022 XVI, 582 Seiten txt rdacontent n rdamedia nc rdacarrier Studies in logic volume 94 Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Lambda-Kalkül (DE-588)4166495-4 gnd rswk-swf Beweistheorie (DE-588)4145177-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s Lambda-Kalkül (DE-588)4166495-4 s Beweistheorie (DE-588)4145177-6 s DE-604 Manzoneto, Giulio 19XX- Sonstige (DE-588)1293528552 oth Studies in logic volume 94 (DE-604)BV022429273 94 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034236464&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barendregt, Hendrik P. 1947- A Lambda Calculus Satellite Studies in logic Mathematische Logik (DE-588)4037951-6 gnd Lambda-Kalkül (DE-588)4166495-4 gnd Beweistheorie (DE-588)4145177-6 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4166495-4 (DE-588)4145177-6 |
| title | A Lambda Calculus Satellite |
| title_auth | A Lambda Calculus Satellite |
| title_exact_search | A Lambda Calculus Satellite |
| title_exact_search_txtP | A Lambda Calculus Satellite |
| title_full | A Lambda Calculus Satellite |
| title_fullStr | A Lambda Calculus Satellite |
| title_full_unstemmed | A Lambda Calculus Satellite |
| title_short | A Lambda Calculus Satellite |
| title_sort | a lambda calculus satellite |
| topic | Mathematische Logik (DE-588)4037951-6 gnd Lambda-Kalkül (DE-588)4166495-4 gnd Beweistheorie (DE-588)4145177-6 gnd |
| topic_facet | Mathematische Logik Lambda-Kalkül Beweistheorie |
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