Re: [isabelle] Huanhuan Zhang



Jasmin Blanchette wrote:
> Dear Mr. 张,
> 
> > I usually use "by simp" "by auto" "by arith" in my proof. But I do not know what exactly they mean or what they contains. Can anyone tell me which documents I can read in order to know these? I am now reading Isabelle/HOL a proof assistant for higher order logic and at the same time learn to use Isar.
> 
> Some very partial information about the proof methods can be found here:
> 
> http://www.cs.miami.edu/~tptp/CASC/J5/SystemDescriptions.html#Isabelle-HOL---2009-2
> 
> I hope other readers of the mailing list can complete the information -- e.g., arith is not mentioned.

The method "arith" is a combination of decision procedures for
arithmetic.  In its standard setup, it first tries Fourier-Motzkin
elimination (for naturals, integers, or reals; see [1] for an
overview), and if that fails, it tries a quantifier elimination
procedure for Presburger arithmetic (e.g., see [2]).  More decision
procedures may also be added.

Regards,
Sascha

[1] http://en.wikipedia.org/wiki/Fourier-Motzkin_elimination
[2] http://en.wikipedia.org/wiki/Presburger_arithmetic





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