[mercury-users] compilation problem, all, some

[David Overton]

On Fri, Jul 16, 2004 at 01:32:37PM -0700, Maurizio Colucci wrote:
> On Friday 16 July 2004 02:07, Zoltan Somogyi wrote:
> > The transliteration of the comment is the following:
> >
> > the_verb_is_visible(V, SelectedObjs) :-
> >         verb_get_requirements(V, Reqs),
> >         all [O] (
> >                 member(O, SelectedObjs)
> >         =>
> >                 member(P, Reqs),
> >                 call(P, O)
> >         ).
> 
> 
> Gosh... It was that easy :-)
> 
> I hadn't tried that because, since I had used "all [O]", I assumed I had to 
> use "some [P]". 
> 
> Instead, I notice you use "all [O]" for universal quantification, while 
> leaving the existential quantification of P implicit.
> 
> But then, what is "some" used for in Mercury? 

Explicit existential quantification is not often necessary -- the
implicit quantification usually does what you want.

You could write:

the_verb_is_visible(V, SelectedObjs) :-
        verb_get_requirements(V, Reqs),
        all [O] (
                member(O, SelectedObjs)
        =>
		some [P] (
                        member(P, Reqs),
                        call(P, O)
		)
        ).

or even

the_verb_is_visible(V, SelectedObjs) :-
        some [Reqs] (
                verb_get_requirements(V, Reqs),
                all [O] (
                        member(O, SelectedObjs)
                =>
                        some [P] (
                                member(P, Reqs),
                                call(P, O)
                        )
                )
        ).

both of which are equivalent to Zoltan's code, but much less readable.

The goal `all [X] p(X)' is really syntactic sugar for 
`not ( some [X] not p(X) )'.
In this case, the explicit quantification is necessary:
`not ( not p(X) )' would be implicitly quantified as
`not ( not ( some [X] p(X) ) )' which would then be simplified to
`some [X] p(X)'.


David
-- 
David Overton
WWW: http://www.overtons.id.au/
Mobile Phone (UK): +44 7799 344 322
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