# The article is finally done

## Brent Kerby — 2002-06-20 03:09:31

    As promised, I did finally finish the article about the theory of

    concatenative combinators, or in other words, what you get when you reduce

    Joy down to its bare bores so far that you end up with something comparable

    to the pure combinatory logic or lambda calculus. (I haven't really

    proofread it, and it seems a bit disorganized, but it has a lot of

    information, and it seemed best to put it up now rather than delay longer

    and try to fix it up)

    It is available at http://tunes.org/~iepos/joy.html. Manfred, if you'd like

    me to put this in the Files section of the group, I can, or you can do it if

    you'd like.

    By the way, I was browsing tonight and discovered something interesting: a

    page describing two languages Iota and Jot

    (http://ling.ucsd.edu/~barker/Iota/), by Chris Barker. It starts with

    Unlambda's ideas and takes it a few steps further, to give you an idea of

    what this is :-) In, particular what he did with Jot is particularly novel;

    in essense, it is like a concatenative language with only two words, "0" and

    "1", which have these effects:

      0 == [k] [s]

      1 == cons

    What's fascinating is that you can get "s" and "k" back out, like this:

      k == 0 0 1 1 1

      s == 0 0 0 1 1 1 1 1

    In Jot's notation we write "0 0 1 1 1" as just "11100" (Jot has a prefix

    heritage, so we simply reverse the whole string from as it would be written

    in Joy). Anyhow, being able to get "s" and "k" out and having "cons" gives

    us a sort of completeness (it gives us the ability to construct a quotation

    of any applicative combinator)

    Now, the big question: can a similar or better completeness be generated

    using only two true combinators? (the above "0" is not a true combinator).

    To start, we know that the base {[], take, i, cat, dup, zap} would do it,

    except that it has 6 combinators in it instead of 2.

    - Brent

## Manfred von Thun — 2002-07-17 05:04:05

    On Wed, 19 Jun 2002, Brent Kerby wrote:

     > As promised, I did finally finish the article about the theory of

    > concatenative combinators, or in other words, what you get when you reduce

    > Joy down to its bare bores so far that you end up with something comparable

                            ^^^^^   (Freudian slip ?)

     > to the pure combinatory logic or lambda calculus. (I haven't really

    > proofread it, and it seems a bit disorganized, but it has a lot of

    > information, and it seemed best to put it up now rather than delay longer

    > and try to fix it up)

     I am VERY impressed. This is a huge piece of work. Very professional.

    Thank you very much. As soon as I can I shall go through it in detail.

     >

    > It is available at http://tunes.org/~iepos/joy.html. Manfred, if you'd like

    > me to put this in the Files section of the group, I can, or you can do it if

    > you'd like.

     Yes, please, put it in the files section. I'll also plant a link to it

    on the main Joy page.

    [.. about Jot - I followed the link from your paper]

     > - Brent

     Thanks again.

      - Manfred