X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=lambda_evaluator.mdwn;h=d39086fd257131bb012c1fa5f71191c387c23927;hp=a137e53f090485792996f4b5771a3973a2a274b8;hb=HEAD;hpb=0b30246623a65bf32b611078db138ada6872ddc1 diff --git a/lambda_evaluator.mdwn b/lambda_evaluator.mdwn deleted file mode 100644 index a137e53f..00000000 --- a/lambda_evaluator.mdwn +++ /dev/null @@ -1,138 +0,0 @@ -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 - - - - - -
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- - - - -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. -