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Re: ((a&&b)||c)==((a||c)&&(b||c)) is not true

• To: mathgroup at smc.vnet.net
• Subject: [mg62086] Re: ((a&&b)||c)==((a||c)&&(b||c)) is not true
• From: "Steven T. Hatton" <hattons at globalsymmetry.com>
• Date: Fri, 11 Nov 2005 02:51:49 -0500 (EST)
• References: <200511090845.DAA17387@smc.vnet.net> <dksig6$k6l$1@smc.vnet.net> <dkuvog$7rc$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Richard Fateman wrote:

> A good reason for Mathematica to fail to show that these
> are the same, is that they are in some senses different.
> 
> 
> These look like logical statements and as such they look like they
> are logically identical, but these are actually
> programs with short-circuit evaluation.
> 
> 
> Consider
> c[] := (Print[C_called]; True)
> a[] := (Print[A_called]; False)
> b[] := (Print[B_called]; True)
> (a[] && b[]) || c[]
> (a[] || c[]) && (b[] || c[])
> 
> They are different PROGRAMS.

Good observation.  There should, however, be some way to tell Mathematica to
treat them as traditional symbolic logic statements.  I don't believe that
LogicExpand will do that for me.  I'm not sure what happens with Implies,
but my observation is that it does not handle all cases.
-- 
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• References:
  • ((a&&b)||c)==((a||c)&&(b||c))
    • From: "Steven T. Hatton" <hattons@globalsymmetry.com>