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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$\begingroup$ I suspect it'd help to distinguish typed and untyped lambda calculus, since they're quite different subjects. $\endgroup$– BlaisorbladeCommented Mar 30, 2015 at 0:52
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7 Answers
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There is, of course, the very famous book by Barendregt,
- The Lambda Calculus, Its Syntax and Semantics (Studies in Logic and the Foundations of Mathematics, Volume 103). Revised Edition, North-Holland, 1985. (link to vendor)
which doesn't require much background except for the usual mathematical maturity. This is mostly about the untyped lambda calculus. He also has some introductory notes here.
answered Jul 2, 2011 at 16:29
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$\begingroup$ Link to the notes is broken - would it be possible to update it. $\endgroup$– user85079Commented Jan 9, 2016 at 14:54
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$\begingroup$ @Mika'il The link to the notes works absolutely fine for me. $\endgroup$ Commented Jan 9, 2016 at 15:44
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$\begingroup$ The link to book now returns 404 not found. $\endgroup$ Commented Mar 16, 2017 at 2:49
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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.
answered Jul 2, 2011 at 19:32
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$\begingroup$ Plus it has exercises and some of them have solutions. $\endgroup$ Commented Aug 14, 2013 at 8:41
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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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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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$\begingroup$ The link in this answer no longer works but the same text can be found here: irif.fr/~krivine/articles/Lambda.pdf - and in some other places. $\endgroup$ Commented Mar 10, 2023 at 7:45
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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
answered Jul 2, 2011 at 19:49
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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.
answered Jul 2, 2011 at 16:47
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Proof and Types is a good place to learn about the Curry-Howard isomorphism.
answered Oct 21, 2011 at 0:25