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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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I suspect it'd help to distinguish typed and untyped lambda calculus, since they're quite different subjects. – Blaisorblade Mar 30 '15 at 0:52
up vote 6 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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Link to the notes is broken - would it be possible to update it. – Mika'il Jan 9 at 14:54
@Mika'il The link to the notes works absolutely fine for me. – Todd Trimble Jan 9 at 15:44
Thanks Todd. I was getting a forbidden access before. – Mika'il Jan 9 at 16:33

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

Another excellent book is "Lambda-calculus, types and models" Ellis Horwood (1993) by Jean-Louis Krivine

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

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