Re: [stack] are concatenative languages applicative?

On Apr 24, 2008, at 3:10 PM, John Nowak wrote:

> Apologies for starting a new thread of sorts, but the "Object Cat"
> thread already had run through three or four different topics, and it
> seems like a good idea to discuss this in such a way that it'll be
> archived properly. I'd really like an answer here.
>
> First off, let me say that I'm not particularly interested in if Joy's
> 'i' is an 'eval'. This does, as Chris pointed out, seem to get us
> bogged down in implementation details. As far as I can tell, 'eval' is
> defined to be some procedure that works on code, be that code a string
> or some more structured form of data. In a language like Cat, there's
> no such code being passed around as there is in Joy, and I don't think
> there's anyone here who would say Cat isn't concatenative.
>
> What I'm interested in is this "dequotation" rule:
>
>    [$A] i  ==  $A
>
> In other words, these are all equivalent:
>
>    1 2 [3 * *] i  ==  1 2 3 * *  ==  1 [2 3] i [* *] i
>
> An important thing to note here is that this translation is just a
> rewriting of function-level code. '$A' is a function, not a value.
> This seems fundamentally different from this rule in the combinatory
> calculus, where 'x' is a *value*, not a function:
>
>    (I x)  ==  x
>
> (William already has said essentially the same thing with respect to
> operators and operands.)
>
> I guess my questions are as follows: Are concatenative languages
> applicative, and if so, what's the equivalent of '[$A] i == $A' in the
> lambda calculus?

As I understand it, the lambda calculus form  \X.E  represents an  
abstraction
(\X) and an application (E). Seems to me a straightforward reading of  
Joy's
[foo] as an abstraction and i as being/causing an application is the  
equivalence
you seek. Joy's i and lambda calculus' dot perform the same function  
in their
respective languages.

Am I the only one here who thinks the word "function" has too many  
meanings?
--
don


> ...If such a translation cannot be given, does that mean
> concatenative languages are non-applicative? If so, is there another
> term besides "concatenative" that can be used to describe their
> properties?
>
> - John