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E-raamat: Combinatory Logic: Pure, Applied and Typed

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(University of Alberta, Edmonton, Canada)
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Combinatory logic is one of the most versatile areas within logic that is tied to parts of philosophical, mathematical, and computational logic. Functioning as a comprehensive source for current developments of combinatory logic, this book is the only one of its kind to cover results of the last four decades. Using a reader-friendly style, the author presents the most up-to-date research studies. She includes an introduction to combinatory logic before progressing to its central theorems and proofs. The text makes intelligent and well-researched connections between combinatory logic and lambda calculi and presents models and applications to illustrate these connections.

Arvustused

For beginners, it is a compact introduction, including exercises, to the classical syntactic theory of combinators with some pointers to their models and their relation with ¿-calculus. More advanced readers may find in the book much information on the connections between combinators and non-classical and substructural logics that are now a prominent topic in several areas, from philosophical logic to theoretical computer science, information that is mostly scattered through the research literature. MATHEMATICAL REVIEWS, 2012

One of the commendable aspects of the book is its extensive and up-to-date bibliography, which deals with CL and other relevant topics in logic; it will surely aid many readers who may need to brush up on background information in the course of their study. Computing Reviews, 2012

Preface ix
1 Elements of combinatory logic 1(28)
1.1 Objects, combinators and terms
1(5)
1.2 Various kinds of combinators
6(6)
1.3 Reductions and combinatory bases
12(17)
2 Main theorems 29(24)
2.1 Church–Rosser property
29(9)
2.2 Normal forms and consistency
38(6)
2.3 Fixed points
44(8)
2.4 Second fixed point theorem and undecidability
52(1)
3 Recursive functions and arithmetic 53(40)
3.1 Primitive and partial recursive functions
54(10)
3.2 First modeling of partial recursive functions in CL
64(17)
3.3 Second modeling of partial recursive functions in CL
81(4)
3.4 Undecidability of weak equality
85(8)
4 Connections to λ-calculi 93(28)
4.1 λ-calculi: Λ
93(13)
4.2 Combinators in Λ
106(4)
4.3 Back and forth between CL and Λ
110(11)
5 (In)equational combinatory logic 121(12)
5.1 Inequational calculi
121(7)
5.2 Equational calculi
128(5)
6 Models 133(46)
6.1 Term models
134(2)
6.2 Operational models
136(12)
6.3 Encoding functions by numbers
148(7)
6.4 Domains
155(10)
6.5 Models for typed CL
165(9)
6.6 Relational models
174(5)
7 Dual and symmetric combinatory logics 179(42)
7.1 Dual combinators
179(22)
7.2 Symmetric combinators
201(9)
7.3 Structurally free logics
210(11)
8 Applied combinatory logic 221(16)
8.1 Illative combinatory logic
221(6)
8.2 Elimination of bound variables
227(10)
9 Typed combinatory logic 237(38)
9.1 Simply typed combinatory logic
237(31)
9.2 Intersection types for combinators
268(7)
Appendix 275(46)
A.1 Elements of combinatory logic
275(9)
A.2 Main theorems
284(4)
A.3 Recursive functions and arithmetic
288(4)
A.4 Connections to λ-calculi
292(2)
A.5 (In)equational combinatory logic
294(2)
A.6 Models
296(6)
A.7 Dual and symmetric combinatory logic
302(6)
A.8 Applied combinatory logic
308(4)
A.9 Typed combinatory logic
312(9)
Bibliography 321(10)
List of Symbols 331(4)
Index 335
Katalin Bimbo is an assistant professor in the Department of Philosophy at the University of Alberta in Edmonton, Canada.
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