Sender: info-hol-request@edu.uidaho.cs.ted
Errors-To: info-hol-request@edu.uidaho.cs.ted
From: David Shepherd <des@com.inmos>
Message-Id: <7314.9201151058@frogland.inmos.co.uk>
Subject: Re: Why sets?
To: chou@edu.ucla.cs
Date: Wed, 15 Jan 92 10:58:30 GMT
In-Reply-To: <9201151029.AA10795@maui.cs.ucla.edu>; from "chou@cs.ucla.edu" at Jan 15, 92 2:29 am

chou@cs.ucla.edu has said:
> I was browsing through library "sets" and this occurred to me:
> Why do we need sets at all?  Why can't we just use the predicates?
> What is the advantage of having a new type (*)set?  And when should
> I use (*)set and when should I use (* -> bool)?

to help distinguish between something that is intuitively a function
from * to bool and something that is a set.

e.g. consider a statement that for a sets which meet some validity requirement
then another condition holds for all their members. the two formulations are

! (values:*->bool) . (valid values) ==> (! v. (values v) ==> (condition v))

and

! (values:(*)set) . (valid values) ==> (! v. (v IN values) ==> (condition v))

While they are both effectively the same the second is more intuitive.

Also by making sets a new type it can add to type security -- i.e. it
forces you to apply the charateristic function of a set to a value and
not just the set which makes what your doing explicit.

after all you could always dispense with all the types except for :bool and
:ind ... but things would get pretty unreadable!


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