Re: [stack] Is this language concatenative?

On Sun, 29 Apr 2007, Michael Nedzelsky wrote:

> Consider the following example. Is this language concatenative?

A couple of comments...

  * There is the lexical level and the grammatical level, and care must
    be taken not to confuse the two. eg. The number token
    "-2.1e-10" is not postfix concatenative.

  * In Joy [ and ] seem to have a special status. Namely the
    concatenative property only seems to work if you treat [ and ] and
    everything between a matching pair as a single entity.

  * Chris says, "The semantics of a concatenative language are that
    each term is a state function (e.g. from a set of stacks to a set
    of stacks), and the concatenation of two terms implies the
    composition of those functions."

    I'm not convinced the word "stack" needs to appear in the
    definition at all.

    Any fragment of a concatenative language is a function mapping a
    set X onto itself. In Joy X is the set of stacks. I'm not convinced
    that is the only valid domain for concatenative languages.

    I would also hypothesize a family of languages where "string
    concatenation represents XXX" where XXX is some other useful
    mathematical operation apart from functional composition.

    Conversely another family exists where "functional composition is
    represented by SOME TRIVIAL OPERATION ON FAMILIAR PRIMITIVE
    DATATYPE". eg. List append, tree join...

    Of course the whole thing can be generalized in both directions to
    create families of languages where "BASIC MATHEMATICAL OPERATIONS
    are represented by TRIVIAL OPERATIONS on FAMILIAR PRIMITIVE
    DATATYPES".

    So one could compile..
    * a long list of all basic and interesting  mathematical operations
    * and there algebraic properties
      and then
    * another list of primitive datatypes and
    * basic operations on those datatypes and
      the algebraic properties
    and overlay the two wherever the algebras match and create a new language.

    And then select from that vast family those languages (that language?) which
    affords the greatest simplifications.

    The answer may well be "represent functional composition by string
    concatenation", ie. Joy.



Ok, so let me distill this wild lateral thinking down a bit....

Question 1:

   Is "string concatenation" or "functional composition" or the
   representation by one of the other the fundamental thing about
   concatenative languages? Or is the broader concept "isomorphisms
   between algebras of higher mathematical constructs and algebras of
   primitive computer datatypes lead to
   (deceptive?|interesting?|useful?) simplifications"


Question 1b :

   Can you propose an interesting "non-von thunnian" language (like a
   non-euclidean space) where we either....

     * Use other primitive datatype / operation instead of strings and
       concatenation..

     * Or represent some other basic mathematical operation by concatenation.

       Candidates I can think of off the top of my head is
       * multiplication "ab === a * b"
       * convolution

and / or

     * operates non-trivially and interestingly on something other than stacks.


Question 2:

   Are stacks the only meaningful domain and range for the functions we
   are composing?



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