Re: [stack] Combining Combinators

On 20/6/07 6:47 PM, "Christopher Diggins" <[email protected]> wrote:

> On 6/19/07, Manfred Von Thun <[email protected]> wrote:
>> On 19/6/07 1:05 AM, "William Tanksley, Jr" <[email protected]> wrote:
>> 
>>> Manfred Von Thun <[email protected]> wrote:

[..]

>> At level one there are functions which take zero level entities
>> as arguments.
> 
> In Cat this would be the set of functions with types matching: ('A 'b -> 'C)

But also binary operators such as +, <, cons and so on, also ternary
operators such as + +, ..., also operators returning several items:
+ + dup, which consumes three and yields two. I don¹t know the
upper/lower case conventions of your type notation to say whether
these cases are already included in (A b -> C). (I don¹t dare to put
in the single quotes, knowing the mess that incompatible mailers create.)

[..]

> Is:
> 
> DEFINE f = [[dip] cons] dip.
> 
> A level-3 combinator in Joy?

Let us see. f is of the form [..] dip, with quotation [..] on top.
Because of the dip, what is below the [..] will first be saved away
temporarily, and after [..] has been executed the saved part will
be restored. Suppose the saved part is 999. So the top of the stack
is 999 [..], the 999 will be saved, [..] executed, then 999 restored.
When [..] executes, it will push [dip] and then cons something, X,
which has to be on the stack, in front of the quotation [dip], giving
[X dip]. So we know that for f == [[dip] cons] dip to operate,
the top of the stack has to be 999, and below that X.

X 999 f
X 999 [[dip] cons] dip
X [[dip] cons] i 999
X [dip] cons 999
[X dip] 999

This is all we know so far from the specification of f.
But presumably the intention is that [X dip] is going to be executed
by some unspecified combinator. In that case it will push X and
then call dip. So X will have to be a quotation, say X = [Q].
Redoing the above derivation:

[Q] 999 f
[Q] 999 [[dip] cons] dip
[Q] [[dip] cons] i 999
[Q] [dip] cons 999
[[Q] dip] 999

So f has the effect of changing [Q], the second element of the stack
into [[Q] dip], leaving the top element 999 unchanged. So f changes
one quotation [Q] into another [[Q] dip], but it does not execute the
result. So it is a higher order function in the sense of yielding a
function,
a perfectly respectable and frequently used sense of higher order. Such
things are sometimes called functionals. But they are not the sort I was
concerned with, since the resulting quotation [[Q] dip] is not executed.

I should mention that a simpler function g == [[dip] cons] i == [dip] cons
would serve equally well as an example of a program transformer. The
999 and the outer dip in your f don¹t serve any purpose.

[..]

 > If you are concerned about eliminating any possibility of level-3
> combinators in Joy, can't you rewrite the definitions of the level-2
> primitives so that they accept combinators or non-combinators? I don't
> see the reason that "dip" can't accept straight values like "5" on the
> top of the stack, if "i" can accept them.

Correction: Joy does not allow any of the following:

5 i
5 dip
5 map
2 3 + i
2 3 + dip
...
[..]

> I believe it is either good to go all the way one direction or the
> other: either non-combinator values can be "evaluated" or they can't.
> As far as I can see (and I could be mistaken) Joy is somewhat
> ambiguous about what exactly can and can't be evaluated.

can or can¹t ‹ where is the ambiguity in Joy?

In Joy the combinators always expect one or more quotations:

[Q] i
[Q] dip
[Q] map
[Q1] [Q2] concat  i
[Q1] [Q2] concat dip ...

The older combinators always expect the quotation on top of the
stack. Some of the newer convenience combinators that
I have been toying with expect a numeric parameter above the
quotation:

[Q] 3 dips

would be used like this

2 3 777 888 999 [+] 3 dips ==
2 3 [+] i 777 888 999 ==
2 3  + 777 888 999
5 777 888 999

But old and new all expect a quotation

[..]
 

 - Manfred


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