Glam

Gnarwhal's Lambda Calculus Interpreter

About

A simple lambda calculus playground
Either use the interactive shell or execute a script file

The shell

The interactive shell is so bad :(

Enter any valid expression and it will attempt to beta-reduce it. Or rather, I hope it beta-reduces it. I don't have any formal training, so I could have missed some gotchas when implementing reduction.

Shell commands are prefixed by a \
Current shell commands include:

• \q, \quit, \exit -> Exit the shell
• \exec [script] -> Execute a script file
• \help -> List shell commands

The syntax

The syntax used tries to be faithful to true lambda calculus. There are two main modifications.

1. The λ symbol is not easy to type on any mainstream keyboard layouts that I'm familiar with, so > has been added as an alternative. λ is still accepted however.
2. Variable names are not exclusively single symbols; they are strings of symbols. As such all variables must be whitespace separated.

Variable names can be any sequence of symbols that don't include the reserved symbols λ, >, ., (, ), and whitespace characters.

Lambda functions can only take a single input, but nested lambdas can be syntactically shortened to what look like multi-parameter lambdas. See examples below.

Examples

Variable syntax
var

Lambda syntax
>var.expr

Nested lambda syntax
>x.>y.>z.expr
>x y z.expr

Ordering with parentheses
(>x y.z) w

What is the Lambda Calculus?

Nope. Nope nope nope nope nope. This is usually the part of the README.md where I try and give a bit of insight into the inspiration behind a project. But this time? I'm not even gonna try and explain it. I'll say one thing about it and then you're on your own. The Lambda Calculus is a formal system of mathematics that can be used to perform any computation. Yes that is exactly like turing machines. They are equivalent.

Obligatory future plans section

• Comments
• Naming of expressions
• Show beta-reduction steps
• Multiline expressions

Etymology

Naming is hard

Gnarwhal + Lambda

The irony is that Glam is quite far from glamorous. It is most kludgy. I suppose maybe that's something to work for. Have Glam live up to it's name. Or just change it's name because it's bad.