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I have some background in set theory and automata and I am looking for a good place to start with lambda calculus.

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7 Answers 7

up vote 5 down vote accepted

There is, of course, the very famous book by Barendregt, which doesn't require much background except for the usual mathematical maturity. He also has some introductory notes here.

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Proof and Types is a good place to learn about the Curry-Howard isomorphism.

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Another excellent book is "Lambda-calculus, types and models" Ellis Horwood (1993) by Jean-Louis Krivine http://www.pps.jussieu.fr/~krivine/articles/Lambda.pdf

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The best books that I've found are:

  • Very basic: Hankin, An introduction to the lambda calculus for computer scientists.
  • Advanced: Sorensen and Urzyczyn, Lectures on the Curry-Howard isomorphism.
  • Advanced: Hindley, Basic simple type theory.
  • The Bible: Barendregt, The lambda calculus: its syntax and semantics.
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I really enjoy Types and Programming Languages by Benjamin C. Pierce. We used this for a course on the lambda calculus, and I felt this was a great way for a mathematician to learn the subject

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An introductory book that seems very nice to me is Lambda-Calculus and Combinators. An introduction by J. Roger Hindley and Jonathan P. Seldin.

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Plus it has exercises and some of them have solutions. –  Trismegistos Aug 14 '13 at 8:41

Stoy's book:

Joseph E. Stoy, Denotational Semantics: The Scott-Strachey Approach to Programming Language Semantics. MIT Press, Cambridge, Massachusetts, 1977

Is a classic, and highly recommended.

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