Pure, Applied and Typed
Chapman and Hall/CRC – 2011 – 357 pages
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.
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
Elementary Combinatory Logic. Main Theorems. Systems of Arithmetic. Connection to λ-Calculi. (In)Equational Combinatory Logic. Models. Dual and Symmetric Combinatory Logic. Combinators in Applications. Typed Combinatory Logic. Appendix.
Katalin Bimbo is an assistant professor in the Department of Philosophy at the University of Alberta in Edmonton, Canada.