A question regarding JAW88

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Eric Macaulay

May 4, 2020, 2:15:08 AM5/4/20
to Calculational Mathematics
Hi Jeremy,

Would it be fair to view

!=    {...}

as a proof of ¬[¬(P=Q)] ?


Jeremy Weissmann

May 4, 2020, 8:09:13 AM5/4/20
to calculationa...@googlegroups.com
Well, that would mean “somewhere P == Q”, no?  Which roughly means that for some point  x  in the underlying space, we have  P.x == Q.x . 

I believe my notation was indicating that the equality was dependent on the scalar context.  For example, for punctual, conjunctive  f ,  we can calculate:

|[ Context:  x => y

!=   {  x == x /\ y ,  f  is punctual  }
     f.(x /\ y)
==  {  f is conjunctive  } 
     f.x /\ f.y


which allows us to conclude:

    [ (x => y)  =>  (f.x => f.y) ]     ,

or that  f  is punctually monotonic. There’s no way to carry out that first step using the conventions in Chapter 4 (I believe) of Dijkstra and Scholten’s  Predicate Calculus and Program Semantics .

It’s been a long, long time since I wrote those JAWs but I’ll re-read the note and let me know if you have more questions. 


On May 4, 2020, at 02:15, Eric Macaulay <elih...@gmail.com> wrote:

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