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Re: [mizar] strict



Hi,

On Tue, 9 Jan 2007, Jesse Alama wrote:

definition
 func F2 -> doubleLoopStr equals
 coherence;
end;

there doesn't seem to be a definition of what it means to be a strict
doubleLoopStr; moreover, when I browse

http://mmlquery.mizar.org/mmlquery/fillin.php?filledfilename=phparticle.mqt&argument=article+vectsp_1

I see that there appears to be something like a definition:

definition
 let a1 be doubleLoopStr;
 attr a1 is strict;
end;

but when I browse VECTSP_1.MIZ, I don't see any definition of strict
for doubleLoopStr's.  What's going on?  What does "strict" mean?  How
can I prove that a doubleLoopStr is strict?

"strict" doesn't have its own definition as it is a special (in a way "meta" attribute) - it means that a term which has a structure type <Theta> has exactly the same selectors (fields) as introduced in the definition of the type <Theta>, so in your case only the selectors of a doubleLoopStr - any extension to that would break the "strictness". So you may think of a vector space as of a group, but it's not a "strict" group.

You don't have to worry about proving "strictness" with your definition - if you define your functor using an "aggregate" structure term explicitely enumerating all selectors, like

doubleLoopStr(# {0,1}, add2, prod2, unit2, zero2 #),

then the "strict" attribute is added automatically. This is why the definition of "strict" has a special meaning which is automatically defined separately for all structures - and it is added to the XML presentation even if it's not present in the actual miz/abs file.

Best,

Adam Naumowicz

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