Re: [stack] peg: a lazy, non-deterministic concatenative language

"dustin.deweese" <[email protected]> Sun, 22 Apr 2012 21:09:07 -0000
Newsgroups	gmane.comp.lang.concatenative
Message-ID	<[email protected]>
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--- In [email protected], "William Tanksley, Jr" <wtanksleyjr@.=
..> wrote:

> A stack meets that requirement by imposing a total ordering of all of
> its contents at all times. I think it's fair to say that an
> accumulator does as well (consider a language over matrices or quantum
> mechanical operators instead of over the integers). If the only
> possible data structure must impose a total ordering, then a stack is
> the only possibility. BUT... does peg impose a total ordering? Doesn't
> the nondeterminism hint that there's something other than a total
> ordering?

The stack for any particular execution path has a total ordering.  You coul=
d use non-determinism to make the stack appear only partially-ordered, thou=
gh, with an expression such as:

1 2 3 [] [swap] \/ $

> > 2. Concatenation must be performed on the Cartesian products of the res=
ults of evaluation of the sub-expressions
>=20
> You MIGHT mean composition rather than concatenation. Is that the case?
>=20

The second rule wasn't worded very well.  I tried to make it more precise:

2. The composition of two sub-expressions is equivalent to concatenating ea=
ch of the Cartesian products of the results of evaluating the sub-expressio=
ns individualy.

See this wiki page (https://github.com/HackerFoo/peg/wiki/Properties-of-Peg=
) for an example, as well as other information on the properties of Peg you=
 might find interesting.


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--- In <a href="mailto:concatenative%40yahoogroups.com">[email protected]</a>, &quot;William Tanksley, Jr&quot; &lt;wtanksleyjr@...&gt; wrote:<br>
<br>
&gt; A stack meets that requirement by imposing a total ordering of all of<br>
&gt; its contents at all times. I think it's fair to say that an<br>
&gt; accumulator does as well (consider a language over matrices or quantum<br>
&gt; mechanical operators instead of over the integers). If the only<br>
&gt; possible data structure must impose a total ordering, then a stack is<br>
&gt; the only possibility. BUT... does peg impose a total ordering? Doesn't<br>
&gt; the nondeterminism hint that there's something other than a total<br>
&gt; ordering?<br>
<br>
The stack for any particular execution path has a total ordering.  You could use non-determinism to make the stack appear only partially-ordered, though, with an expression such as:<br>
<br>
1 2 3 [] [swap] \/ $<br>
<br>
&gt; &gt; 2. Concatenation must be performed on the Cartesian products of the results of evaluation of the sub-expressions<br>
&gt; <br>
&gt; You MIGHT mean composition rather than concatenation. Is that the case?<br>
&gt; <br>
<br>
The second rule wasn't worded very well.  I tried to make it more precise:<br>
<br>
2. The composition of two sub-expressions is equivalent to concatenating each of the Cartesian products of the results of evaluating the sub-expressions individualy.<br>
<br>
See this wiki page (<a href="https://github.com/HackerFoo/peg/wiki/Properties-of-Peg">https://github.com/HackerFoo/peg/wiki/Properties-of-Peg</a>) for an example, as well as other information on the properties of Peg you might find interesting.<br>
<br>
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