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Re: [tlaplus] << >> = { }



In TLA+, tuples and sequences are functions. However, unlike in conventional presentations of ZF set theory, functions are not defined as relations (sets of pairs) but are primitive values, axiomatized by

IsAFcn(f) == f = [x \in DOMAIN f |-> f[x]]

See also Section 16.1.7 of "Specifying Systems".

In particular, << >> = { } is not provable in TLA+, nor is its negation.

Best regards,

Stephan Merz


On 04 Apr 2014, at 16:54, fl <freder...@xxxxxxxxxxx> wrote:

 
 
Sometimes the mathematics behind TLA+ puzzle me.
 
For instance in TLA+ it is possible to prove that
 
                             ASSUME NEW A PROVE << >> = [ x \in { } |-> A ]
 
So DOMAIN << >> = { } and << >> is a function.
 
If << >> is a function then << >> is a relation.
 
 
But if << >> is a function and DOMAIN << >> = { } then << >> = { }
 
 
But I can't prove << >> = { } with TLA+. Why ?
 
--
FL

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