Can someone recommend me a book for self study which will cover topics of logic, lambda calculus and type theory. I know about "Computability and Logic" written by Bolos but it describe recursive function as a model of computation and does no cove type theory.
If there is no singe book I would like to read some book which would build a bridge between those topics.
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I found this a valuable and concise introduction:
The Seven Virtues of Simple Type Theory by William M. Farmer.
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Being a programmer the one I am recommending is more of a programming book but does cover lambda calculus and type theory. Types and Programming Languages by Benjamin C. Pierce. I am not sure what you mean by logic in this question so I am not saying the book covers logic, but am pretty sure it will cover what you need.
For the list of lambda type systems covered see: λ-Calculus extensions: meaning of extension symbols
I found some good book on those topics. This book has exercises with solution so it is perfect for self studying. The book is "Lambda-Calculus and Combinators an Introduction" by J. Roger Hindley, Jonathan P. Seldin. Link for more info http://www.cambridge.org/us/knowledge/isbn/item1175709/?site_locale=en_US