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Categories for types

Categories for types (1회 대출)

자료유형
단행본
개인저자
Crole, Roy L.
서명 / 저자사항
Categories for types / Roy L. Crole.
발행사항
Cambridge ;   New York :   Cambridge University Press ,   1993   (2002 printing)  
형태사항
xvii, 335 p. : ill. ; 24 cm.
총서사항
Cambridge mathematical textbooks
ISBN
0521450926 0521457017 (pbk.) 9780521457019 (pbk.)
서지주기
Includes bibliographical references (p. 315-319) and index.
일반주제명
Categories (Mathematics) Lambda calculus.
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008 940718s1993 enka b 001 0 eng
010 ▼a 94184387
020 ▼a 0521450926
020 ▼a 0521457017 (pbk.)
020 ▼a 9780521457019 (pbk.)
035 ▼a (KERIS)REF000006662286
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
050 0 0 ▼a QA169 ▼b .C685 1993
082 0 0 ▼a 511.3 ▼2 20
082 0 4 ▼a 512.62 ▼2 22
090 ▼a 512.62 ▼b C944c
100 1 ▼a Crole, Roy L.
245 1 0 ▼a Categories for types / ▼c Roy L. Crole.
260 ▼a Cambridge ; ▼a New York : ▼b Cambridge University Press , ▼c 1993 ▼g (2002 printing)
300 ▼a xvii, 335 p. : ▼b ill. ; ▼c 24 cm.
440 0 ▼a Cambridge mathematical textbooks
504 ▼a Includes bibliographical references (p. 315-319) and index.
650 0 ▼a Categories (Mathematics)
650 0 ▼a Lambda calculus.
945 ▼a KINS

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.62 C944c 등록번호 121173247 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차

CONTENTS
Preface = ⅹ
Advice for the Reader = xiv
1 Order, Lattices and Domains = 1
  1.1 Introduction = 1
  1.2 Ordered Sets = 2
  1.3 Basic Lattice Theory = 12
  1.4 Boolean and Heyting Lattices = 20
  1.5 Elementary Domain Theory = 24
  1.6 Further Exercises = 33
  1.7 Pointers to the Literature = 36
2 A Category Theory Primer = 37
  2.1 Introduction = 37
  2.2 Categories and Examples = 40
  2.3 Functors and Examples = 45
  2.4 Natural Transformations and Examples = 49
  2.5 Isomorphisms and Equivalences = 52
  2.6 Products and Coproducts = 55
  2.7 The Yoneda Lemma = 61
  2.8 Cartesian Closed Categories = 67
  2.9 Monics, Equalisers, Pullbacks and their Duals = 73
  2.10 Adjunctions = 77
  2.11 Limits and Colimits = 91
  2.12 Strict Indexed Categories = 106
  2.13 Further Exercises = 113
  2.14 Pointers to the Literature = 118
3 Algebraic Type Theory = 120
  3.1 Introduction = 120
  3.2 Definition of the Syntax = 121
  3.3 Algebraic Theories = 127
  3.4 Motivating a Categorical Semantics = 129
  3.5 Categorical Semantics = 132
  3.6 Categorical Models and the Soundness Theorem = 134
  3.7 Categories of Models = 137
  3.8 Classifying Category of an Algebraic Theory = 139
  3.9 The Categorical Type Theory Correspondence = 147
  3.10 Further Exercises = 151
  3.11 Pointers to the Literature = 152
4 Functional Type Theory = 154
  4.1 Introduction = 154
  4.2 Definition of the Syntax = 156
  4.3 λ x-Theories = 161
  4.4 Deriving a Categorical Semantics = 163
  4.5 Categorical Semantics = 168
  4.6 Categorical Models and the Soundness Theorem = 171
  4.7 Categories of Models = 172
  4.8 Classifying Category of a λ x-Thcory = 175
  4.9 The Categorical Type Theory Correspondence = 180
  4.10 Categorical Gluing = 185
  4.11 Further Exercises = 192
  4.12 Pointers to the Literature = 199
5 Polymorphic Functional Type Theory = 201
  5.1 Introduction = 201
  5.2 The Syntax and Equations of 2 λ x-Theories = 203
  5.3 Deriving a Categorical Semantics = 214
  5.4 Categorical Semantics and Soundness Theorems = 224
  5.5 A PER Model = 234
  5.6 A Domain Model = 241
  5.7 Classifying Hyperdoctrine of a 2 λ x-Theory = 262
  5.8 Categorical Type Theory Correspondence = 268
  5.9 Pointers to the Literature = 274
6 Higher Order Polymorphism = 275
  6.1 Introduction = 275
  6.2 The Syntax and Equations of ωλ x-Theories = 275
  6.3 Categorical Semantics and Soundness Theorems = 285
  6.4 A PER Model = 291
  6.5 A Domain Model = 292
  6.6 Classifying Hyperdoctrine of an ωλ x-Theory = 310
  6.7 Categorical Type Theory Correspondence = 313
  6.8 Pointers to the Literature = 314
Bibliography = 315
Index = 320

관련분야 신착자료

Macdonald, Alan (2021)