Lambda Calculus with Types:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2013
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Perspectives in Logic
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXII, 833 S. Ill., graph. Darst. |
| ISBN: | 9780521766142 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV039757960 | ||
| 003 | DE-604 | ||
| 005 | 20131128 | ||
| 007 | t | ||
| 008 | 111213s2013 ad|| |||| 00||| eng d | ||
| 020 | |a 9780521766142 |c hbk |9 978-0-521-76614-2 | ||
| 035 | |a (OCoLC)712374086 | ||
| 035 | |a (DE-599)BSZ338346635 | ||
| 040 | |a DE-604 |b ger | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-473 |a DE-19 | ||
| 084 | |a ST 136 |0 (DE-625)143591: |2 rvk | ||
| 100 | 1 | |a Barendregt, Hendrik P. |d 1947- |e Verfasser |0 (DE-588)124647219 |4 aut | |
| 245 | 1 | 0 | |a Lambda Calculus with Types |c Henk Barendregt ; Wil Dekkers ; Richard Statman |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2013 | |
| 300 | |a XXII, 833 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Perspectives in Logic | |
| 650 | 0 | 7 | |a Lambda-Kalkül |0 (DE-588)4166495-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lambda-Kalkül |0 (DE-588)4166495-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Dekkers, Wil |e Verfasser |0 (DE-588)1036623866 |4 aut | |
| 700 | 1 | |a Statman, Richard |e Verfasser |0 (DE-588)1043667733 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Bamberg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024619216&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-024619216 | ||
Datensatz im Suchindex
| _version_ | 1804148668886941696 |
|---|---|
| adam_text | Contents
Preface
page
ix
Contributors
xii
Our Founders
xiii
Introduction
xv
PART I SIMPLE TYPES
λ^
1
The Simply Typed Lambda Calculus
5
1.1
The systems
λ^.
5
1.2
First properties and comparisons
19
1.3
Normal inhabitants
32
1.4
Representing data types
38
1.5
Exercises
50
Properties
55
2.1
Normalization
55
2.2
Proofs of strong normalization
64
2.3
Checking and finding types
68
2.4
Checking inhabitation
77
2.5
Exercises
86
Tools
94
3.1
Semantics of
λ_>
94
3.2
Lambda theories and term models
107
3.3
Syntactic and semantic logical relations
114
3.4
Type reducibility
136
3.5
The five canonical term-models
156
3.6
Exercises
181
ν
vi
Contents
4
Definability, unification and matching
Written with the collaboration of
Gilles Dowek 192
4.1
Undecidability of lambda-definability
192
4.2
Undecidability of unification
207
4.3
Decidability of matching of rank
3 213
4.4
Decidability of the maximal theory
230
4.5
Exercises
240
5
Extensions
Written in part with the collaboration of Marc
Bezem
243
5.1
Lambda delta
243
5.2
Surjective pairing
255
5.3 Gödel s
system T: higher-order primitive recursion
282
5.4
Spector s system B: bar recursion
303
5.5
Platek s system
У:
fixed point recursion
312
5.6
Exercises
315
6
Applications
323
6.1
Functional programming
323
6.2
Logic and proof-checking
341
6.3
Proof theory
Written with the collaboration of Silvia Ghilezan
351
6.4
Grammars, terms and types
Written with the collaboration of Michael Moortgat
363
PART II RECURSIVE TYPES
λ^
Written with the collaboration of Felice Cardone
and Mario
Coppo
377
The Systems
λ^
379
7.1
Type algebras and type assignment
379
7.2
More on type algebras
390
7.3
Recursive types via simultaneous recursion
397
7.4
Recursive types via
μ
-abstraction
407
7.5
Recursive types as trees
424
7.6
Special views on trees
437
7.7
Exercises
442
Properties of Recursive Types
451
8.1
Simultaneous recursions vs
μ
-types
451
8.2
Properties of
μ
-types
455
8.3
Properties of types defined by a simultaneous recursion
475
8.4
Exercises
490
Contents
vii
9
Properties of Terms with Types
494
9.1
First properties of
λ=
494
9.2
Finding and inhabiting types
497
9.3
Strong normalization
507
9.4
Exercises
518
10
Models
520
10.1
Interpretations of type assignments in
λ^
520
10.2
Interpreting
Τμ
and
Τ*
525
10.3
Type interpretations in systems with explicit typing
541
10.4
Exercises
547
11
Applications
554
11.1
Subtyping
554
11.2
The principal type structures
567
11.3
Recursive types in programming languages
570
11.4
Further reading
573
11.5
Exercises
576
PART III INTERSECTION TYPES %
Written with the collaboration of
Fabio Alessi,
Mariangiola Dezani-Ciancaglini,
Furio Honsell
and Paula Seven
577
12
An Example System
579
12.1
The type assignment system AnBCD
580
12.2
The filter model T 1*00
586
12.3
Completeness of type assignment
589
13
Type Assignment Systems
591
13.1
Type theories
594
13.2
Type assignment
606
13.3
Type structures
610
13.4
Filters
614
13.5
Exercises
617
14
Basic Properties of Intersection Type Assignment
619
14.1
Inversion lemmas
622
14.2
Subject reduction and expansion
627
14.3
Exercises
634
15
Type and Lambda Structures
640
15.1
Meet semi-lattices and algebraic lattices
643
viii Contents
15.2
Natural
type structures and lambda structures
656
15.3
Type and zip structures
662
15.4
Zip and lambda structures
667
15.5
Exercises
676
16
Filter Models
680
16.1
Lambda models
683
16.2
Filter models
689
16.3
Poo models as filter models
701
16.4
Other filter models
716
16.5
Exercises
724
17
Advanced Properties and Applications
728
17.1
Realizability interpretation of types
730
17.2
Characterizing syntactic properties
735
17.3
Approximation theorems
742
17.4
Applications of the approximation theorem
757
17.5
Undecidability of inhabitation
Written with the collaboration of
Pawel
Urzyczyn
762
17.6
Exercises
786
References
791
Indices
814
Index of terms
815
Index of citations
823
Index of symbols
828
|
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| author | Barendregt, Hendrik P. 1947- Dekkers, Wil Statman, Richard |
| author_GND | (DE-588)124647219 (DE-588)1036623866 (DE-588)1043667733 |
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| author_sort | Barendregt, Hendrik P. 1947- |
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| building | Verbundindex |
| bvnumber | BV039757960 |
| classification_rvk | ST 136 |
| ctrlnum | (OCoLC)712374086 (DE-599)BSZ338346635 |
| discipline | Informatik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV039757960 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:10:48Z |
| institution | BVB |
| isbn | 9780521766142 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024619216 |
| oclc_num | 712374086 |
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| owner | DE-473 DE-BY-UBG DE-19 DE-BY-UBM |
| owner_facet | DE-473 DE-BY-UBG DE-19 DE-BY-UBM |
| physical | XXII, 833 S. Ill., graph. Darst. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series2 | Perspectives in Logic |
| spelling | Barendregt, Hendrik P. 1947- Verfasser (DE-588)124647219 aut Lambda Calculus with Types Henk Barendregt ; Wil Dekkers ; Richard Statman 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2013 XXII, 833 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Perspectives in Logic Lambda-Kalkül (DE-588)4166495-4 gnd rswk-swf Lambda-Kalkül (DE-588)4166495-4 s DE-604 Dekkers, Wil Verfasser (DE-588)1036623866 aut Statman, Richard Verfasser (DE-588)1043667733 aut Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024619216&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Barendregt, Hendrik P. 1947- Dekkers, Wil Statman, Richard Lambda Calculus with Types Lambda-Kalkül (DE-588)4166495-4 gnd |
| subject_GND | (DE-588)4166495-4 |
| title | Lambda Calculus with Types |
| title_auth | Lambda Calculus with Types |
| title_exact_search | Lambda Calculus with Types |
| title_full | Lambda Calculus with Types Henk Barendregt ; Wil Dekkers ; Richard Statman |
| title_fullStr | Lambda Calculus with Types Henk Barendregt ; Wil Dekkers ; Richard Statman |
| title_full_unstemmed | Lambda Calculus with Types Henk Barendregt ; Wil Dekkers ; Richard Statman |
| title_short | Lambda Calculus with Types |
| title_sort | lambda calculus with types |
| topic | Lambda-Kalkül (DE-588)4166495-4 gnd |
| topic_facet | Lambda-Kalkül |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024619216&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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