Lambda Shell

Simple shell for evaluating lambda expressions

About the Lambda Shell

The Lambda Shell is a feature-rich shell environment and command-line tool for evaluating terms of the pure, untyped lambda calculus. The Lambda Shell builds on the shell creation framework Shellac, and showcases most of Shellac's features.

• Evalutate lambda terms directly from the shell prompt using normal or applicative order. In normal order, one can evaluate to normal form, head normal form, or weak head normal form.
• Define aliases for lambda terms using a top level, non-recursive 'let' construct.
• Show traces of term evaluation, or dump the trace to a file
• Count the number of reductions when evaluating terms
• Test two lambda terms for beta-equivalance (that is; if two terms, when evaluated to normal form, are alpha equivalant).
• Programs can be entered from the command line (using the -e option) or piped into stdin (using the -s option).
• Perform continuation passing style (CPS) transforms on terms before evaluation using the double bracked syntax, e.g., [[ five ]].

License

The Lambda Shell is licensed under the GNU GPL version 2. See the LICENSE file for details.

Sample session

The Lambda Shell, version 0.3
Copyright 2005-2006, Robert Dockins


The Lambda Shell comes with ABSOLUTELY NO WARRANTY; for details
type ':nowarranty'.  This is free software, and you are welcome to
redistribute it under certain conditions; type ':gpl'
for details

> (\x y. x) (\a. a) (\b. b)
\a. a
> :load prelude.lam
> :show four
four = succ three
> four
\f x. f (f (f (f x)))
> mul two three
\f x. f (f (f (f (f (f x)))))
> let x = plus six two
> x == eight
equal
> x == nine
not equal
> one
\f x. f x
> [[ one ]]
\f k. k (\x k_0. f x k_0)
> :showcount
showcount on
> sub seven two
\f x. f (f (f (f (f x))))
<<90 reductions>>
> let l = insertSort (cons two (cons three (cons one nil)))
> index zero l
one
<<463 reductions>>
> index one l
two
<<2135 reductions>>
> index two l
three
<<5720 reductions>>
> :quit