Re: [stack] What does "concatenative" actually mean?

On Mar 6, 2009, at 9:13 PM, Christopher Diggins wrote:

>> Let me clarify: Quotation is just a higher order function. When you
>> apply it to a function, you get a new function. This is a very simple
>> and straightforward operation.
>
> You don't apply quotation to a function. You quote a term (i.e. an
> expression). This creates a new term. When a quoted term is evaluated
> it creates a function.

There's no reason you have to view it that way. Viewing it as a simple  
function gives you a few clear way of understanding its semantics.

> A higher-order function takes a function as input and/or returns a  
> function as output at run-time.

I never was taught in math class that functions only get run at run- 
time. You're talking about an implementation detail. If you have a  
higher order function applied to a constant argument, you can reduce  
it whenever you like.

> The only difference between lambda abstractions and quotations is  
> that lambda abstractions allow (but do not require) the usage of  
> named variables.

Lambda abstractions *do* require the usage of named variables. That's  
what lambda does -- introduce variables. You seem to be confusing  
lambda calculus with Lisp.

Lambda is not a function. Quotation, on the other hand, is  
understandable as a function. This is very much a good thing and not  
something to be lost or confused by equating it with lambda. What  
quotation does is *much* simpler than what lambda does.

> In a quotation, there is always exactly one implied variable, a  
> stack (at least in Joy and Cat).

That's not an implied variable. I'm not even sure what an "implied  
variable" would be. There's either a variable present that is  
eliminated via substitution as part of an application or there isn't.  
It's true that you can express the semantics of a function in a  
concatenative language using lambda calculus, but that's just  
equivalent to saying that lambda calculus is turing complete.

Quotation does not introduce any variables, "implied" or otherwise.

- John