One argument

An attempt at a language for Racket which supports one-argument λ and function application with only one argument, for playing with trivial λ-calculus things.

This is very much prototype code: it’s intended entirely as something to play with λ-calculus and emphatically not for any serious use. Signifiantly I am not sure if the normal-order languages are semantically correct: they certainly were not and may still not be.

raco pkg install will install it. There are some examples in examples.

The languages

There are four languages, all available via #lang.

oa/normal/pure (aka oa/normal)

This is a normal-order language in which λ takes just one argument, which is not in parenthesis. So the identity function is (λ x x), for instance.


This is a normal-order language which supports ‘fancy’ λ:

In addition function application is fancified: (f x y) is ((f x) y) and so on.

oa/applicative/pure (aka oa/applicative)

This is an applicative-order language with the same syntax as oa/normal/pure.


This is an applicative-order language with the same syntax as oa/normal/fancy.

Additional syntax

All the languages support a simple version of define: (define identity (λ x x)) defines identity to have the value (λ x x) for instance. There is no fancy syntax for define.

All the languages support a tiny subset of rackunit:

Additionally there are no changes to the reader, so it will happily read numbers and so on. The only operation is λ however.


The printer is modified to try to print things which have been given names with define in a useful way: it prints their names and the canonical source code if they are functions. This is a bit ad-hoc. As an example of this:

In oa/normal/pure:

> (λ x x)
> (define identity (λ x x))
> identity
{identity}: (λ x x)
> (define another identity)
> another
{another identity}: (λ x x)
> identity
{another identity}: (λ x x)

In oa/normal/fancy:

> (λ (x y) x)
> (define true (λ (x y) x))
> true
{true}: (λ x (λ y x))

There are three possibly-useful environment variables:

There should be some better way of controlling these parameters.