2.1 KiB
untyped-lambda-calculus
A simple implementation of the untyped lambda calculus as an exercise.
This implementation lacks many features necessary to be useful,
for example let bindings, built-in functions, binding free variables, or a good REPL.
This project purely exists as an exercise and is not intended for general use.
I will make useful programming languages in the future, but this is not one of them.
Usage
Type in your expression at the prompt: >> .
The result of the evaluation of that expression will then be printed out.
Exit the prompt with Ctrl-C (or however else you kill a program in your terminal).
Bound variables will be printed followed by a number representing the number of binders between it and its definition for disambiguation.
Example session
>> let D = (\x. x x) in let F = (\f. f (f y)) in D (F ())
y y
>> let T = (\f x. f (f x)) in (\f x. T (T (T (T T))) f x) () y
y
>> \x. \y. y x
\x. \y. y:0 x:1
>> ^C
Notation
Conventional Lambda Calculus notation applies,
with the exception that variable names are mmultiple characters long,
and \ is used in lieu of λ for convenience.
- Variable names are alphanumeric, beginning with a letter.
- Outermost parentheses may be dropped:
M Nis equivalent to(M N). - Applications are left-associative:
M N Pmay be written instead of((M N) P). - The body of an abstraction extends as far right as possible:
\x. M Nmeans\x.(M N)and not ``(\x. M) N`. - A sequence of abstractions may be contracted:
\foo. \bar. \baz. Nmay be abbreviated as\foo bar baz. N. - Variables may be bound using let expressions:
let x = N in Mabbreviates(\x. N) M.
Violations of convention
- I use spaces to separate variables in abstractions instead of commas because I think it looks better.
Additional extensions to notation
Since \x. x is the left identity of applications and application syntax is left-associative,
I (syntactically) permit unary and nullary applications so that () is \x. x, and (x) is x.
On the same principle, the syntax of a lambda of no variables \. e is e.