This lambda evaluator will allow you to write lambda terms and evaluate (that is, normalize) them, and inspect the results.
-(This won't work in Racket, because Racket doesn't even try to represent the internal structure of a function in a human-readable way.)
+(This won't work in Racket, because Racket doesn't even try to represent the internal structure of a function in a human-readable way.)
-*Lambda terms*: lambda terms are written with a backslash, thus: `((\x (\y x)) z)`.
+*Lambda terms*: lambda terms are written with a backslash, thus: `((\x (\y x)) z)`.
If you click "Normalize", the system will try to produce a normal-form lambda expression that your original term reduces to (~~>). So `((\x (\y x)) z)` reduces to `(\y z)`.
*Abbreviations*: In an earlier version, you couldn't use abbreviations. `\x y. y x x` had to be written `(\x (\y ((y x) x)))`. We've upgraded the parser though, so now it should be able to understand any lambda term that you can.
-*Constants*: The combinators `S`, `K`, `I`, `C`, `B`, `W`, `T`, `M` (aka <code>ω</code>) and `L` are pre-defined to their standard values. Also, integers will automatically be converted to Church numerals. (`0` is `\s z. z`, `1` is `\s z. s z`, and so on.)
+*Constants*: The combinators `S`, `K`, `I`, `C`, `B`, `W`, `T`, `V`, `M` (aka <code>ω</code>) and `L` are pre-defined to their standard values. Also, integers will automatically be converted to Church numerals. (`0` is `\s z. z`, `1` is `\s z. s z`, and so on.)
*Variables*: Variables must start with a letter and can continue with any sequence of letters, numbers, `_`, `-`, or `/`. They may optionally end with `?` or `!`. When the evaluator does alpha-conversion, it may change `x` into `x'` or `x''` and so on. But you should not attempt to use primed variable names yourself.
---------------
The interpreter is written in JavaScript and runs inside your browser.
-So if you decide to reduce a term that does not terminate (such as `((\x (x x)) (\x (x x)))`), it will be your
+So if you decide to reduce a term that does not terminate (such as `((\x (x x)) (\x (x x)))`), it will be your
browser that stops responding, not the wiki server.
The main code is [here](http://lambda.jimpryor.net/code/lambda.js). Suggestions for improvements welcome.
-The code is based on:
+The code is based on:
* Chris Barker's JavaScript lambda calculator
* [Oleg Kiselyov's Haskell lambda calculator](http://okmij.org/ftp/Computation/lambda-calc.html#lambda-calculator-haskell).
* [Peter Sestoft's Lambda Calculus Reducer](http://www.itu.dk/people/sestoft/lamreduce/index.html): Very nice! Allows you to select different evaluation strategies, and shows stepwise reductions.
* [Chris Barker's Lambda Tutorial](http://homepages.nyu.edu/~cb125/Lambda)
-* [Penn Lambda Calculator](http://www.ling.upenn.edu/lambda/): Pedagogical software developed by Lucas Champollion, Josh Tauberer and Maribel Romero. Linguistically oriented. Requires installing Java (Mac users will probably already have it installed).
+* The UPenn [Lambda Calculator](http://dylanbumford.com/LambdaCalculator/): Pedagogical software developed by Lucas Champollion and others. Linguistically oriented, uses types. Requires Java (many users will probably already have Java installed).
* [Mike Thyer's Lambda Animator](http://thyer.name/lambda-animator/): Graphical tool for experimenting with different reduction strategies. Also requires installing Java, and Graphviz.
* [Matt Might's Lambda Evaluator](http://matt.might.net/articles/implementing-a-programming-language/) in Scheme (R5RS and Racket).