Learning Lambda Calculus
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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.
logic learning online-resources lambda-calculus type-theory
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add a comment |
$begingroup$
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.
logic learning online-resources lambda-calculus type-theory
$endgroup$
add a comment |
$begingroup$
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.
logic learning online-resources lambda-calculus type-theory
$endgroup$
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.
logic learning online-resources lambda-calculus type-theory
logic learning online-resources lambda-calculus type-theory
edited Apr 17 '16 at 6:53
community wiki
4 revs, 4 users 100%
Noldorin
add a comment |
add a comment |
9 Answers
9
active
oldest
votes
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Alligator Eggs is a cool way to learn lambda calculus.
Also learning functional programming languages like Scheme, Haskell etc. will be added fun.
edited Dec 22 '18 at 18:34
Glorfindel
3,41981830
answered Aug 4 '10 at 13:06
Pratik DeogharePratik Deoghare
5,87842438
$endgroup$
$begingroup$
Hah, looks pretty funny. Maybe not the in-depth tutorial I'm looking for, but will have to check it out!
$endgroup$
– Noldorin
Aug 4 '10 at 13:18
3
$begingroup$
Looks really fun! I can use this to teach kids.
$endgroup$
– Chao Xu
Aug 4 '10 at 13:41
1
$begingroup$
Now that I call a nice model of lambda calculus! I wonder what Dana Scott has to say about this ;-)
$endgroup$
– fgp
May 27 '13 at 14:10
$begingroup$
Alligator Eggs may be a cool way to teach it, but the site assumes you already have knowledge and you're trying to teach it to others who don't.
$endgroup$
– zumalifeguard
Jul 21 '18 at 1:55
add a comment |
$begingroup$
Recommendations:
- Barendregt & Barendsen, 1984, 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.
edited Sep 28 '18 at 21:07
ProbablyJody
33
answered Jul 28 '10 at 21:05
Charles StewartCharles Stewart
3,3542229
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1
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Thanks again Charles, that looks like good material.
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– Noldorin
Jul 30 '10 at 8:21
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Out of curiosity, will learning simply and then more advanced typed versions of lambda calculus give me a pretty good coverage of the field of type theory?
$endgroup$
– Noldorin
Jul 30 '10 at 14:23
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@Noldorin - Sorry for the long delay in replying... No, or rather it depends on what you mean by "more advanced typed versions of lambda calculus" - I think it is wiser in this case to work through seminal texts, rather than thinking of mastering the relevant formal systems directly.
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– Charles Stewart
Mar 17 '17 at 8:19
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Haha, only 7 years eh... better late than never, as they say! I've learnt a lot since then, but thank you.
$endgroup$
– Noldorin
Mar 17 '17 at 21:40
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@Noldorin You could write up your own answer to this question, maybe?
$endgroup$
– Charles Stewart
Mar 19 '17 at 11:16
|
show 1 more comment
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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 effectsModified 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.
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3
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I believe that the book by Henk P. Barendregt “The Lambda Calculus, Its Syntax and Semantics” is too formal to be useful as a first textbook to learn lambda calculus. I think it is more a reference book for people working in related fields.
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– Виталий Олегович
Jun 1 '14 at 18:00
add a comment |
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I like Type Theory and Functional Programming by Simon Thompson.
answered Jul 30 '10 at 15:07
rgrigrgrig
747414
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add a comment |
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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.
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add a comment |
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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.
answered Jul 28 '10 at 15:18
Kevin H. LinKevin H. Lin
1,82311325
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1
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Thanks for the tip. I'm sure you're right in saying that it will provide an insight, though I am perhaps looking for a more theoretical approach (as Alonzo Church originally formulated it). I have some active experience in F# which should provide a basis.
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– Noldorin
Jul 28 '10 at 15:48
8
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This won't help much with understanding types.
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– Charles Stewart
Jul 28 '10 at 21:06
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@CharlesStewart I'm responding to your old comment, because I guess with the number of upvotes the original question makes for a good reference question, and your comment somehow has a rating of 7. The question indicates an interest in untyped lambda calculus, so I don't see how your comment is relevant.
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– Doug Spoonwood
Nov 5 '16 at 14:35
1
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@DougSpoonwood Untyped lambda calculus is just one thing the question asks for. Mostly the question is after information about typed lambda calculus.
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– Charles Stewart
Dec 8 '16 at 11:55
add a comment |
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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.
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add a comment |
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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
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add a comment |
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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.
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add a comment |
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9 Answers
9
active
oldest
votes
9 Answers
9
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Alligator Eggs is a cool way to learn lambda calculus.
Also learning functional programming languages like Scheme, Haskell etc. will be added fun.
edited Dec 22 '18 at 18:34
Glorfindel
3,41981830
answered Aug 4 '10 at 13:06
Pratik DeogharePratik Deoghare
5,87842438
$endgroup$
$begingroup$
Hah, looks pretty funny. Maybe not the in-depth tutorial I'm looking for, but will have to check it out!
$endgroup$
– Noldorin
Aug 4 '10 at 13:18
3
$begingroup$
Looks really fun! I can use this to teach kids.
$endgroup$
– Chao Xu
Aug 4 '10 at 13:41
1
$begingroup$
Now that I call a nice model of lambda calculus! I wonder what Dana Scott has to say about this ;-)
$endgroup$
– fgp
May 27 '13 at 14:10
$begingroup$
Alligator Eggs may be a cool way to teach it, but the site assumes you already have knowledge and you're trying to teach it to others who don't.
$endgroup$
– zumalifeguard
Jul 21 '18 at 1:55
add a comment |
$begingroup$
Alligator Eggs is a cool way to learn lambda calculus.
Also learning functional programming languages like Scheme, Haskell etc. will be added fun.
edited Dec 22 '18 at 18:34
Glorfindel
3,41981830
answered Aug 4 '10 at 13:06
Pratik DeogharePratik Deoghare
5,87842438
$endgroup$
$begingroup$
Hah, looks pretty funny. Maybe not the in-depth tutorial I'm looking for, but will have to check it out!
$endgroup$
– Noldorin
Aug 4 '10 at 13:18
3
$begingroup$
Looks really fun! I can use this to teach kids.
$endgroup$
– Chao Xu
Aug 4 '10 at 13:41
1
$begingroup$
Now that I call a nice model of lambda calculus! I wonder what Dana Scott has to say about this ;-)
$endgroup$
– fgp
May 27 '13 at 14:10
$begingroup$
Alligator Eggs may be a cool way to teach it, but the site assumes you already have knowledge and you're trying to teach it to others who don't.
$endgroup$
– zumalifeguard
Jul 21 '18 at 1:55
add a comment |
$begingroup$
Alligator Eggs is a cool way to learn lambda calculus.
Also learning functional programming languages like Scheme, Haskell etc. will be added fun.
edited Dec 22 '18 at 18:34
Glorfindel
3,41981830
answered Aug 4 '10 at 13:06
Pratik DeogharePratik Deoghare
5,87842438
$endgroup$
Alligator Eggs is a cool way to learn lambda calculus.
Also learning functional programming languages like Scheme, Haskell etc. will be added fun.
edited Dec 22 '18 at 18:34
Glorfindel
3,41981830
answered Aug 4 '10 at 13:06
Pratik DeogharePratik Deoghare
5,87842438
edited Dec 22 '18 at 18:34
Glorfindel
3,41981830
edited Dec 22 '18 at 18:34
Glorfindel
3,41981830
edited Dec 22 '18 at 18:34
Glorfindel
3,41981830
3,41981830
answered Aug 4 '10 at 13:06
Pratik DeogharePratik Deoghare
5,87842438
answered Aug 4 '10 at 13:06
Pratik DeogharePratik Deoghare
5,87842438
answered Aug 4 '10 at 13:06
Pratik DeogharePratik Deoghare
5,87842438
5,87842438
$begingroup$
Hah, looks pretty funny. Maybe not the in-depth tutorial I'm looking for, but will have to check it out!
$endgroup$
– Noldorin
Aug 4 '10 at 13:18
3
$begingroup$
Looks really fun! I can use this to teach kids.
$endgroup$
– Chao Xu
Aug 4 '10 at 13:41
1
$begingroup$
Now that I call a nice model of lambda calculus! I wonder what Dana Scott has to say about this ;-)
$endgroup$
– fgp
May 27 '13 at 14:10
$begingroup$
Alligator Eggs may be a cool way to teach it, but the site assumes you already have knowledge and you're trying to teach it to others who don't.
$endgroup$
– zumalifeguard
Jul 21 '18 at 1:55
add a comment |
$begingroup$
Hah, looks pretty funny. Maybe not the in-depth tutorial I'm looking for, but will have to check it out!
$endgroup$
– Noldorin
Aug 4 '10 at 13:18
3
$begingroup$
Looks really fun! I can use this to teach kids.
$endgroup$
– Chao Xu
Aug 4 '10 at 13:41
1
$begingroup$
Now that I call a nice model of lambda calculus! I wonder what Dana Scott has to say about this ;-)
$endgroup$
– fgp
May 27 '13 at 14:10
$begingroup$
Alligator Eggs may be a cool way to teach it, but the site assumes you already have knowledge and you're trying to teach it to others who don't.
$endgroup$
– zumalifeguard
Jul 21 '18 at 1:55
$begingroup$
Hah, looks pretty funny. Maybe not the in-depth tutorial I'm looking for, but will have to check it out!
$endgroup$
– Noldorin
Aug 4 '10 at 13:18
$begingroup$
Hah, looks pretty funny. Maybe not the in-depth tutorial I'm looking for, but will have to check it out!
$endgroup$
– Noldorin
Aug 4 '10 at 13:18
3
3
$begingroup$
Looks really fun! I can use this to teach kids.
$endgroup$
– Chao Xu
Aug 4 '10 at 13:41
$begingroup$
Looks really fun! I can use this to teach kids.
$endgroup$
– Chao Xu
Aug 4 '10 at 13:41
1
1
$begingroup$
Now that I call a nice model of lambda calculus! I wonder what Dana Scott has to say about this ;-)
$endgroup$
– fgp
May 27 '13 at 14:10
$begingroup$
Now that I call a nice model of lambda calculus! I wonder what Dana Scott has to say about this ;-)
$endgroup$
– fgp
May 27 '13 at 14:10
$begingroup$
Alligator Eggs may be a cool way to teach it, but the site assumes you already have knowledge and you're trying to teach it to others who don't.
$endgroup$
– zumalifeguard
Jul 21 '18 at 1:55
$begingroup$
Alligator Eggs may be a cool way to teach it, but the site assumes you already have knowledge and you're trying to teach it to others who don't.
$endgroup$
– zumalifeguard
Jul 21 '18 at 1:55
add a comment |
$begingroup$
Recommendations:
- Barendregt & Barendsen, 1984, 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.
edited Sep 28 '18 at 21:07
ProbablyJody
33
answered Jul 28 '10 at 21:05
Charles StewartCharles Stewart
3,3542229
$endgroup$
1
$begingroup$
Thanks again Charles, that looks like good material.
$endgroup$
– Noldorin
Jul 30 '10 at 8:21
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Out of curiosity, will learning simply and then more advanced typed versions of lambda calculus give me a pretty good coverage of the field of type theory?
$endgroup$
– Noldorin
Jul 30 '10 at 14:23
$begingroup$
@Noldorin - Sorry for the long delay in replying... No, or rather it depends on what you mean by "more advanced typed versions of lambda calculus" - I think it is wiser in this case to work through seminal texts, rather than thinking of mastering the relevant formal systems directly.
$endgroup$
– Charles Stewart
Mar 17 '17 at 8:19
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Haha, only 7 years eh... better late than never, as they say! I've learnt a lot since then, but thank you.
$endgroup$
– Noldorin
Mar 17 '17 at 21:40
$begingroup$
@Noldorin You could write up your own answer to this question, maybe?
$endgroup$
– Charles Stewart
Mar 19 '17 at 11:16
|
show 1 more comment
$begingroup$
Recommendations:
- Barendregt & Barendsen, 1984, 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.
edited Sep 28 '18 at 21:07
ProbablyJody
33
answered Jul 28 '10 at 21:05
Charles StewartCharles Stewart
3,3542229
$endgroup$
1
$begingroup$
Thanks again Charles, that looks like good material.
$endgroup$
– Noldorin
Jul 30 '10 at 8:21
$begingroup$
Out of curiosity, will learning simply and then more advanced typed versions of lambda calculus give me a pretty good coverage of the field of type theory?
$endgroup$
– Noldorin
Jul 30 '10 at 14:23
$begingroup$
@Noldorin - Sorry for the long delay in replying... No, or rather it depends on what you mean by "more advanced typed versions of lambda calculus" - I think it is wiser in this case to work through seminal texts, rather than thinking of mastering the relevant formal systems directly.
$endgroup$
– Charles Stewart
Mar 17 '17 at 8:19
$begingroup$
Haha, only 7 years eh... better late than never, as they say! I've learnt a lot since then, but thank you.
$endgroup$
– Noldorin
Mar 17 '17 at 21:40
$begingroup$
@Noldorin You could write up your own answer to this question, maybe?
$endgroup$
– Charles Stewart
Mar 19 '17 at 11:16
|
show 1 more comment
$begingroup$
Recommendations:
- Barendregt & Barendsen, 1984, 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.
edited Sep 28 '18 at 21:07
ProbablyJody
33
answered Jul 28 '10 at 21:05
Charles StewartCharles Stewart
3,3542229
$endgroup$
Recommendations:
- Barendregt & Barendsen, 1984, 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.
edited Sep 28 '18 at 21:07
ProbablyJody
33
answered Jul 28 '10 at 21:05
Charles StewartCharles Stewart
3,3542229
edited Sep 28 '18 at 21:07
ProbablyJody
33
edited Sep 28 '18 at 21:07
ProbablyJody
33
edited Sep 28 '18 at 21:07
ProbablyJody
33
33
answered Jul 28 '10 at 21:05
Charles StewartCharles Stewart
3,3542229
answered Jul 28 '10 at 21:05
Charles StewartCharles Stewart
3,3542229
answered Jul 28 '10 at 21:05
Charles StewartCharles Stewart
3,3542229
3,3542229
1
$begingroup$
Thanks again Charles, that looks like good material.
$endgroup$
– Noldorin
Jul 30 '10 at 8:21
$begingroup$
Out of curiosity, will learning simply and then more advanced typed versions of lambda calculus give me a pretty good coverage of the field of type theory?
$endgroup$
– Noldorin
Jul 30 '10 at 14:23
$begingroup$
@Noldorin - Sorry for the long delay in replying... No, or rather it depends on what you mean by "more advanced typed versions of lambda calculus" - I think it is wiser in this case to work through seminal texts, rather than thinking of mastering the relevant formal systems directly.
$endgroup$
– Charles Stewart
Mar 17 '17 at 8:19
$begingroup$
Haha, only 7 years eh... better late than never, as they say! I've learnt a lot since then, but thank you.
$endgroup$
– Noldorin
Mar 17 '17 at 21:40
$begingroup$
@Noldorin You could write up your own answer to this question, maybe?
$endgroup$
– Charles Stewart
Mar 19 '17 at 11:16
|
show 1 more comment
1
$begingroup$
Thanks again Charles, that looks like good material.
$endgroup$
– Noldorin
Jul 30 '10 at 8:21
$begingroup$
Out of curiosity, will learning simply and then more advanced typed versions of lambda calculus give me a pretty good coverage of the field of type theory?
$endgroup$
– Noldorin
Jul 30 '10 at 14:23
$begingroup$
@Noldorin - Sorry for the long delay in replying... No, or rather it depends on what you mean by "more advanced typed versions of lambda calculus" - I think it is wiser in this case to work through seminal texts, rather than thinking of mastering the relevant formal systems directly.
$endgroup$
– Charles Stewart
Mar 17 '17 at 8:19
$begingroup$
Haha, only 7 years eh... better late than never, as they say! I've learnt a lot since then, but thank you.
$endgroup$
– Noldorin
Mar 17 '17 at 21:40
$begingroup$
@Noldorin You could write up your own answer to this question, maybe?
$endgroup$
– Charles Stewart
Mar 19 '17 at 11:16
1
1
$begingroup$
Thanks again Charles, that looks like good material.
$endgroup$
– Noldorin
Jul 30 '10 at 8:21
$begingroup$
Thanks again Charles, that looks like good material.
$endgroup$
– Noldorin
Jul 30 '10 at 8:21
$begingroup$
Out of curiosity, will learning simply and then more advanced typed versions of lambda calculus give me a pretty good coverage of the field of type theory?
$endgroup$
– Noldorin
Jul 30 '10 at 14:23
$begingroup$
Out of curiosity, will learning simply and then more advanced typed versions of lambda calculus give me a pretty good coverage of the field of type theory?
$endgroup$
– Noldorin
Jul 30 '10 at 14:23
$begingroup$
@Noldorin - Sorry for the long delay in replying... No, or rather it depends on what you mean by "more advanced typed versions of lambda calculus" - I think it is wiser in this case to work through seminal texts, rather than thinking of mastering the relevant formal systems directly.
$endgroup$
– Charles Stewart
Mar 17 '17 at 8:19
$begingroup$
@Noldorin - Sorry for the long delay in replying... No, or rather it depends on what you mean by "more advanced typed versions of lambda calculus" - I think it is wiser in this case to work through seminal texts, rather than thinking of mastering the relevant formal systems directly.
$endgroup$
– Charles Stewart
Mar 17 '17 at 8:19
$begingroup$
Haha, only 7 years eh... better late than never, as they say! I've learnt a lot since then, but thank you.
$endgroup$
– Noldorin
Mar 17 '17 at 21:40
$begingroup$
Haha, only 7 years eh... better late than never, as they say! I've learnt a lot since then, but thank you.
$endgroup$
– Noldorin
Mar 17 '17 at 21:40
$begingroup$
@Noldorin You could write up your own answer to this question, maybe?
$endgroup$
– Charles Stewart
Mar 19 '17 at 11:16
$begingroup$
@Noldorin You could write up your own answer to this question, maybe?
$endgroup$
– Charles Stewart
Mar 19 '17 at 11:16
|
show 1 more comment
$begingroup$
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 effectsModified 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.
$endgroup$
3
$begingroup$
I believe that the book by Henk P. Barendregt “The Lambda Calculus, Its Syntax and Semantics” is too formal to be useful as a first textbook to learn lambda calculus. I think it is more a reference book for people working in related fields.
$endgroup$
– Виталий Олегович
Jun 1 '14 at 18:00
add a comment |
$begingroup$
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 effectsModified 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.
$endgroup$
3
$begingroup$
I believe that the book by Henk P. Barendregt “The Lambda Calculus, Its Syntax and Semantics” is too formal to be useful as a first textbook to learn lambda calculus. I think it is more a reference book for people working in related fields.
$endgroup$
– Виталий Олегович
Jun 1 '14 at 18:00
add a comment |
$begingroup$
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 effectsModified 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.
$endgroup$
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 effectsModified 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.
edited Oct 23 '16 at 4:40
community wiki
2 revs, 2 users 98%
kunjan kshetri
3
$begingroup$
I believe that the book by Henk P. Barendregt “The Lambda Calculus, Its Syntax and Semantics” is too formal to be useful as a first textbook to learn lambda calculus. I think it is more a reference book for people working in related fields.
$endgroup$
– Виталий Олегович
Jun 1 '14 at 18:00
add a comment |
3
$begingroup$
I believe that the book by Henk P. Barendregt “The Lambda Calculus, Its Syntax and Semantics” is too formal to be useful as a first textbook to learn lambda calculus. I think it is more a reference book for people working in related fields.
$endgroup$
– Виталий Олегович
Jun 1 '14 at 18:00
3
3
$begingroup$
I believe that the book by Henk P. Barendregt “The Lambda Calculus, Its Syntax and Semantics” is too formal to be useful as a first textbook to learn lambda calculus. I think it is more a reference book for people working in related fields.
$endgroup$
– Виталий Олегович
Jun 1 '14 at 18:00
$begingroup$
I believe that the book by Henk P. Barendregt “The Lambda Calculus, Its Syntax and Semantics” is too formal to be useful as a first textbook to learn lambda calculus. I think it is more a reference book for people working in related fields.
$endgroup$
– Виталий Олегович
Jun 1 '14 at 18:00
add a comment |
$begingroup$
I like Type Theory and Functional Programming by Simon Thompson.
answered Jul 30 '10 at 15:07
rgrigrgrig
747414
$endgroup$
add a comment |
$begingroup$
I like Type Theory and Functional Programming by Simon Thompson.
answered Jul 30 '10 at 15:07
rgrigrgrig
747414
$endgroup$
add a comment |
$begingroup$
I like Type Theory and Functional Programming by Simon Thompson.
answered Jul 30 '10 at 15:07
rgrigrgrig
747414
$endgroup$
I like Type Theory and Functional Programming by Simon Thompson.
answered Jul 30 '10 at 15:07
rgrigrgrig
747414
answered Jul 30 '10 at 15:07
rgrigrgrig
747414
answered Jul 30 '10 at 15:07
rgrigrgrig
747414
answered Jul 30 '10 at 15:07
rgrigrgrig
747414
747414
add a comment |
add a comment |
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
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.
answered Oct 20 '12 at 20:45
community wiki
Mikael
add a comment |
add a comment |
$begingroup$
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.
answered Jul 28 '10 at 15:18
Kevin H. LinKevin H. Lin
1,82311325
$endgroup$
1
$begingroup$
Thanks for the tip. I'm sure you're right in saying that it will provide an insight, though I am perhaps looking for a more theoretical approach (as Alonzo Church originally formulated it). I have some active experience in F# which should provide a basis.
$endgroup$
– Noldorin
Jul 28 '10 at 15:48
8
$begingroup$
This won't help much with understanding types.
$endgroup$
– Charles Stewart
Jul 28 '10 at 21:06
$begingroup$
@CharlesStewart I'm responding to your old comment, because I guess with the number of upvotes the original question makes for a good reference question, and your comment somehow has a rating of 7. The question indicates an interest in untyped lambda calculus, so I don't see how your comment is relevant.
$endgroup$
– Doug Spoonwood
Nov 5 '16 at 14:35
1
$begingroup$
@DougSpoonwood Untyped lambda calculus is just one thing the question asks for. Mostly the question is after information about typed lambda calculus.
$endgroup$
– Charles Stewart
Dec 8 '16 at 11:55
add a comment |
$begingroup$
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.
answered Jul 28 '10 at 15:18
Kevin H. LinKevin H. Lin
1,82311325
$endgroup$
1
$begingroup$
Thanks for the tip. I'm sure you're right in saying that it will provide an insight, though I am perhaps looking for a more theoretical approach (as Alonzo Church originally formulated it). I have some active experience in F# which should provide a basis.
$endgroup$
– Noldorin
Jul 28 '10 at 15:48
8
$begingroup$
This won't help much with understanding types.
$endgroup$
– Charles Stewart
Jul 28 '10 at 21:06
$begingroup$
@CharlesStewart I'm responding to your old comment, because I guess with the number of upvotes the original question makes for a good reference question, and your comment somehow has a rating of 7. The question indicates an interest in untyped lambda calculus, so I don't see how your comment is relevant.
$endgroup$
– Doug Spoonwood
Nov 5 '16 at 14:35
1
$begingroup$
@DougSpoonwood Untyped lambda calculus is just one thing the question asks for. Mostly the question is after information about typed lambda calculus.
$endgroup$
– Charles Stewart
Dec 8 '16 at 11:55
add a comment |
$begingroup$
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.
answered Jul 28 '10 at 15:18
Kevin H. LinKevin H. Lin
1,82311325
$endgroup$
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.
answered Jul 28 '10 at 15:18
Kevin H. LinKevin H. Lin
1,82311325
answered Jul 28 '10 at 15:18
Kevin H. LinKevin H. Lin
1,82311325
answered Jul 28 '10 at 15:18
Kevin H. LinKevin H. Lin
1,82311325
answered Jul 28 '10 at 15:18
Kevin H. LinKevin H. Lin
1,82311325
1,82311325
1
$begingroup$
Thanks for the tip. I'm sure you're right in saying that it will provide an insight, though I am perhaps looking for a more theoretical approach (as Alonzo Church originally formulated it). I have some active experience in F# which should provide a basis.
$endgroup$
– Noldorin
Jul 28 '10 at 15:48
8
$begingroup$
This won't help much with understanding types.
$endgroup$
– Charles Stewart
Jul 28 '10 at 21:06
$begingroup$
@CharlesStewart I'm responding to your old comment, because I guess with the number of upvotes the original question makes for a good reference question, and your comment somehow has a rating of 7. The question indicates an interest in untyped lambda calculus, so I don't see how your comment is relevant.
$endgroup$
– Doug Spoonwood
Nov 5 '16 at 14:35
1
$begingroup$
@DougSpoonwood Untyped lambda calculus is just one thing the question asks for. Mostly the question is after information about typed lambda calculus.
$endgroup$
– Charles Stewart
Dec 8 '16 at 11:55
add a comment |
1
$begingroup$
Thanks for the tip. I'm sure you're right in saying that it will provide an insight, though I am perhaps looking for a more theoretical approach (as Alonzo Church originally formulated it). I have some active experience in F# which should provide a basis.
$endgroup$
– Noldorin
Jul 28 '10 at 15:48
8
$begingroup$
This won't help much with understanding types.
$endgroup$
– Charles Stewart
Jul 28 '10 at 21:06
$begingroup$
@CharlesStewart I'm responding to your old comment, because I guess with the number of upvotes the original question makes for a good reference question, and your comment somehow has a rating of 7. The question indicates an interest in untyped lambda calculus, so I don't see how your comment is relevant.
$endgroup$
– Doug Spoonwood
Nov 5 '16 at 14:35
1
$begingroup$
@DougSpoonwood Untyped lambda calculus is just one thing the question asks for. Mostly the question is after information about typed lambda calculus.
$endgroup$
– Charles Stewart
Dec 8 '16 at 11:55
1
1
$begingroup$
Thanks for the tip. I'm sure you're right in saying that it will provide an insight, though I am perhaps looking for a more theoretical approach (as Alonzo Church originally formulated it). I have some active experience in F# which should provide a basis.
$endgroup$
– Noldorin
Jul 28 '10 at 15:48
$begingroup$
Thanks for the tip. I'm sure you're right in saying that it will provide an insight, though I am perhaps looking for a more theoretical approach (as Alonzo Church originally formulated it). I have some active experience in F# which should provide a basis.
$endgroup$
– Noldorin
Jul 28 '10 at 15:48
8
8
$begingroup$
This won't help much with understanding types.
$endgroup$
– Charles Stewart
Jul 28 '10 at 21:06
$begingroup$
This won't help much with understanding types.
$endgroup$
– Charles Stewart
Jul 28 '10 at 21:06
$begingroup$
@CharlesStewart I'm responding to your old comment, because I guess with the number of upvotes the original question makes for a good reference question, and your comment somehow has a rating of 7. The question indicates an interest in untyped lambda calculus, so I don't see how your comment is relevant.
$endgroup$
– Doug Spoonwood
Nov 5 '16 at 14:35
$begingroup$
@CharlesStewart I'm responding to your old comment, because I guess with the number of upvotes the original question makes for a good reference question, and your comment somehow has a rating of 7. The question indicates an interest in untyped lambda calculus, so I don't see how your comment is relevant.
$endgroup$
– Doug Spoonwood
Nov 5 '16 at 14:35
1
1
$begingroup$
@DougSpoonwood Untyped lambda calculus is just one thing the question asks for. Mostly the question is after information about typed lambda calculus.
$endgroup$
– Charles Stewart
Dec 8 '16 at 11:55
$begingroup$
@DougSpoonwood Untyped lambda calculus is just one thing the question asks for. Mostly the question is after information about typed lambda calculus.
$endgroup$
– Charles Stewart
Dec 8 '16 at 11:55
add a comment |
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
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.
edited Feb 10 at 22:17
community wiki
2 revs, 2 users 80%
Mirzhan Irkegulov
add a comment |
add a comment |
$begingroup$
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
$endgroup$
add a comment |
$begingroup$
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
$endgroup$
add a comment |
$begingroup$
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
$endgroup$
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
answered Oct 14 '14 at 16:21
community wiki
NugSoth
add a comment |
add a comment |
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
add a comment |
$begingroup$
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.
$endgroup$
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.
answered Oct 28 '18 at 20:55
community wiki
Mario Román
add a comment |
add a comment |
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