X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=code%2Flambda_evaluator.mdwn;fp=code%2Flambda_evaluator.mdwn;h=d39086fd257131bb012c1fa5f71191c387c23927;hp=0000000000000000000000000000000000000000;hb=50102e40c57ebd7aef267b201292646587766573;hpb=8d7045981a2a3c5f12fecd1608598bfdd9d678a4 diff --git a/code/lambda_evaluator.mdwn b/code/lambda_evaluator.mdwn new file mode 100644 index 00000000..d39086fd --- /dev/null +++ b/code/lambda_evaluator.mdwn @@ -0,0 +1,144 @@ +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.) + +*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)`. + +*Let*: in order to make building a more elaborate set of terms easier, it is possible to define values using `let`. +In this toy system, `let`s should only be used at the beginning of a file. If we have, for intance, + + let true = (\x (\y x)) in + let false = (\x (\y y)) in + ((true yes) no) + +the result is `yes`. + +*Comments*: anything following a semicolon to the end of the line is ignored. +Blank lines are fine. + +*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 ω) 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. + + + + +do eta-reductions too + + + + + +
+
+ + + + +Under the hood +--------------- + +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 +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: + +* Chris Barker's JavaScript lambda calculator +* [Oleg Kiselyov's Haskell lambda calculator](http://okmij.org/ftp/Computation/lambda-calc.html#lambda-calculator-haskell). +* The top-down JavaScript lexer and parser at . + +Improvements we hope to add: + +* detecting some common cases of non-normalizing terms (the problem of determining in general whether a term will normalize is undecidable) +* returning results in combinator form (the evaluator already accepts combinators as input) +* displaying reductions one step at a time +* specifying the reduction order and depth +* allow other binders such as ∀ and ∃ (though these won't be interpreted as doing anything other than binding variables) + + +Other Lambda Evaluators/Calculutors +----------------------------------- + +* [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). +* [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). + +See also: + +* [Jason Jorendorff's Try Scheme](http://tryscheme.sourceforge.net/about.html): Runs a miniature Scheme interpreter in Javascript, in your browser. +