HackyLambdas is the final project for Lambda Calculus by Ian Wold and Paul Yon.
I used the Sprache parser to parse the lambda terms. The lambda calculus is very left-recursive, so I got around this by using Sprache's operator capabilities to parse the functions and applications - viewing the period and the space as operators allows one to hackily get around the left recursion in the grammar. Surely there's a better way, but this is the fun way.
HackyLambdas can do several things. First, it can beta-reduce and compute typing constraints for simply typed lambda calculus terms. In place of a lambda, a backslash is used. For example, one could input the following:
>: (\x.x) y
And HackyLambdas will beta-reduce it, as well as compute the typing constraints on the term.
You can define terms with HackyLambdas:
>: true = \a.\b.a
You can type in integers, and they will be translated into Church-encoded numerals automagically:
HackyLambdas can convert any LC term to its corresponding DeBruijn notation:
>: debruijn db>: \x.x
And HackyLambdas can check for alpha-equivalence between any two terms
>: alpha a1>: \x.x a2>: \y.y