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.

oa/normal/fancy

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

• (λ (x) ...) is (λ x ...);
• (λ (x y) ...) is (λ x (λ y ...) and so on.

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.

oa/applicative/fancy

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:

• test-case is rackunit’s test-case; check-equiv? and
• check-not-equiv? are like check-eqv? and check-not-eqv? but they will suitably force evaluation of anything not evaluated yet.

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

Hacks

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

There are three possibly-useful environment variables:

• OA_HOLD_DEBUGGING, if defined, will cause it to tell you when forms are being ‘held’ (equivalent to delay) and ‘released’ (equivalent to force).
• OA_NO_STASH_PRINTING, if defined, will turn off all the attempted printing cleverness.
• OA_FANCY_TRACING, if defined, will cause it to trace the rewriting of forms in the fancy languages.

There should be some better way of controlling these parameters.