Combinatory Logic: Pure, Applied and Typed (Discrete Mathematics and Its Applications)

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Product Description

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.

Combinatory Logic: Pure, Applied and Typed (Discrete Mathematics and Its Applications) Review

Table of contents:
1. elements of combinatory logic
2. main theorems
3. recursive functions and arithmetic
4. connections to lambda-calculi
5. (in)equational combinatory logic
6. models
7. dual and symmetric combinatory logics
8. applied combinatory logic
9. typed combinatory logic
Appendix

I have just skimmed through the book. It seems to be written in a very clear style, explaining the rationale behind the study of combo logic and its historical roots.

The author is interested in applying combo logic to the study of linear / substructural logics, whereas I'm interested in the untyped aspect of illative logic.

Ch 7 deals with duality, ie, where f(n) is the function f applied to the number n, it can be dually encoded as the number n applied to f. This is new to me.

Ch 8 deals briefly with illative combo logic.

My library doesn't have this book, so I bought it and keep it as a reference.

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