mu
Simple untyped (and soon simply typed) lambda calculus interpreter written in Haskell.
Features:
- Bound and free variables
- Abstractions (functions)
- Function application
- Aliases to name expressions so they don't have to be typed out over and over again
- "Evaluation" through alpha conversion and beta reduction
Grammar
input ::= expr (";" expr)*
expr ::= alias | application
alias ::= ALIASIDENT ":=" application
application ::= (term)* | "(" application ")"
term ::= variable | abstraction
variable ::= VARIDENT | ALIASIDENT
abstraction ::= ("\" | "λ") VARIDENT "." application
VARIDENT ::= _any single lowercase letter_
ALIASIDENT ::= _any series of alpha numeric characters_
Whitespace after any token is ignored.
Comments can be started with --.
Examples
> ID := \x.x -- The identity function.
\x.x
> ID a
a
> AND := \p.\q.p q p -- Boolean and.
\p.\q.p q p
> TRUE := \x.\y.x -- Boolean true.
\x.\y.x
> FALSE := \x.\y.y -- Boolean false.
\x.\y.y
> AND TRUE FALSE ; AND TRUE TRUE
\x.\y.y ; \x.\y.x
Building & Running
The project can be easily built using Cabal (install via ghcup on Linux):
$ cabal build
and can also be run using
$ cabal run
This will launch a REPL in which Lambda Calculus expressions can be typed and evaluated.
The program REPL can be installed by using
$ cabal install
This way it can be executed from anywhere by just invoking the mu command.
License
Licensed under the MIT License.