Re: [stack] Re: Some thoughts on Object Cat

John Nowak <[email protected]> wrote:
>  Manfred Von Thun wrote:

>  > In Joy at least, the i combinator does not mean application. Joy is a
>  > concatenative language, not an applicative language. The applicative
>  > languages are the lambda calculus and the combinatory calculus,
>  > together with their descendents – just about all programming languages
>  > descend from the lambda calculus. All applicative languages  have an
>  > apply operation: apply this function to those arguments, but mostly
>  > there
>  > is no explicit symbol for that operation. Joy does not have such an
>  > operation neither explicit nor implicit.

>  Are concatenative languages not just a particular kind of applicative
>  language? It seems to me that there's no real difference between this:
>     foo = 1 2 + *
>  And this (where '1' and '2' are functions of type 'A -> A Num' as
>  above):
>     foo stack = * (+ (2 (1 stack)))

I suppose the key word in "no real difference" is "real". See
http://en.wikipedia.org/wiki/No_true_Scotsman. Clearly there's a
difference -- trivially, the two are reverses; less trivially, one of
them includes grouping operators that aren't present in the other; and
critically, those grouping operators happen to serve to distinguish
between an operator and its operands.

>  Of course, because Joy is a restricted form of applicative language,
>  you can reason about things in ways you can't in the general case.
>  Perhaps there's something more fundamental I'm missing here that makes
>  Joy non-applicative.

I think your example serves well enough, even though it doesn't
actually include an example of an operand which is not ALSO an
operator.

>  - John

-Wm

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