Learning Lambda Calculus What are some good online/free resources (tutorials, guides, exercises, and the like) for learning Lambda Calculus?
Specifically, I am interested in the following areas:


*

*Untyped lambda calculus

*Simply-typed lambda calculus

*Other typed lambda calculi

*Church's Theory of Types (I'm not sure where this fits in).


(As I understand, this should provide a solid basis for the understanding of type theory.)
Any advice and suggestions would be appreciated.
 A: 
Alligator Eggs is a cool way to learn lambda calculus.
Also learning functional programming languages like Scheme, Haskell etc. will be added fun.
A: I found this iPhone app that works as an un-typed lambda calculator, it works with  successor, addition, addition with successor, multiplication, exponentiation, predecessor and subtraction operations. It shows a step by step process which might be helpful for people who are just starting with lambda calculus.
link: https://itunes.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=928503408&mt=8
A: Recommendations:

*

*Barendregt & Barendsen, 1998, Introduction to lambda-calculus;

*Girard, Lafont & Taylor, 1987, Proofs and Types;

*Sørenson & Urzyczyn, 1999, Lectures on the Curry-Howard Isomorphism.

All of these are mentioned in the LtU Getting Started thread.
A: Here are a couple of resources that will get you started:


*

*The Lambda Calculus, Its Syntax and Semantics - This is a must!

*Lecture Notes on the Lambda Calculus by Peter Selinger

*History of Lambda Calculi

*Impact of Lambda Calculus on Logic and Computer Science

*Introduction to Lambda Calculus

*Lambda Calculi with Types

*Tutorial Introduction to Lambda Calculus

*Call-by-name, call-by-value and the Lambda Calculus

*Control operators, the SECD-machine, and
the lambda-calculus.  - With effects

*Modified basic functionality in combinatory logic- H.B. Curry.

*The principal type scheme of an object in combinatory 
logic. - J. Roger Hindley. 
Since I am a computer science graduate, most of these are geared towards computer scientists rather than logicians. 
Bonus : There is a new book that has come out Semantics Engineering with PLT Redex. I haven't read it but people have told me good things about it.
I hope this helps. Please feel free to ask me any questions. Thanks.
A: Some time ago, I was surprised not to find many untyped & simply-typed lambda calculus interpreters among the answers to this question, so I started working for a while in an educational lambda calculus interpreter called Mikrokosmos (can also be used online). It implements untyped and simply typed lambda calculus (and also illustrates Curry-Howard).
Surely, you could also use some functional programming language; but at least for me, it was difficult to determine exactly which constructs of the language are lambda calculus and which are extras offered by that particular language. Haskell for instance approximately implements System-F, but I also wanted to have a simply(as simple as possible)-typed lambda calculus interpreter.
The interpreter is free software and you can integrate them on other learning materials (such as Jupyter notebooks or web pages). I have used it before to teach lambda calculus to CS students.
Please note that I am the main developer of this interpreter. I am only posting here because this same question inspired me to start the development.
A: I like Type Theory and Functional Programming by Simon Thompson.
A: It might be nice to work through Structure and Interpretation of Computer Programs, which is available online for free. This book is an introduction to computer science and the programming language Scheme, which is a flavor of the programming language Lisp, which is based on the lambda calculus. Although it is not strictly a book about the lambda calculus, it might be fun or useful to gain some hands-on and "practical" experience with the lambda calculus by reading some of this book and working through some of its exercises.
A: Lambda-Calculus and Combinators, an Introduction by J. ROGER HINDLEY and JONATHAN P. SELDIN is a great (and relatively modern) resource that doesn't assume any previous knowledge.
It is available online here.
A: 
To Dissect a Mockingbird: A Graphical Notation for the Lambda Calculus with Animated Reduction by David C Keenan is a nice complement to Alligator Eggs given above. Keenan uses Smullyan's bird metaphors from To Mock a Mockingbird and augments them with diagram notation, which aids in building intuition around combinators. The above is Y combinator in Keenan's notation.
