Re: [boost] [SPAM] Re: thinking algebraically (was Re: proto::or_ arity

From: Marco (mrcekets_at_[hidden])
Date: 2007-04-23 10:27:00

On Mon, 23 Apr 2007 11:11:04 +0200, Paul Giaccone <paulg_at_[hidden]>  
wrote:

> Marco wrote:

>>
>> Well, the last word is up to the author's library, however I'd be
>> surprised if the following relations were not valid:
>>
>> associativity:
>> or_< T1, or_<T2, T3> > == or_< T1, T2, T3 > == or_< or_<T1, T2,>, T3 >
>> and_< T1, and_<T2, T3> > == and_< T1, T2, T3 > == and_< and_<T1, T2,>,  
>> T3 >
>>
>
> Excuse my mathematical pedantry and going off topic. The operations or_
> and and_ are binary, not ternary. Each of the middle expressions is, by
> definition (that is, mathematical consensus), equal to at least one of
> the corresponding outer terms. One or both of the equalities in each of
> the above relations is therefore tautologous (that is, always true).
>
> The only requirement for associativity is:
>
> 	or_< T1, or_<T2, T3> > == or_< or_<T1, T2,>, T3 >          #1
> 	and_< T1, and_<T2, T3> > == and_< and_<T1, T2,>, T3 >      #2
>
>

I agree the only requirements for associativity are the equalities #1 and  
#2.
The middle term in my relations has to be seen as the demonstration (IMO)  
that associativity really holds.

Marco

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