The HOL4 Description manual has a section on the simplifier.  And yes, it 
should preserve the probability of goals because at the top level, it is only 
capable of replacing equals with equals. 

Michael

On 17/03/2013, at 10:46, Vincent Aravantinos <[email protected]> 
wrote:

> Hi list,
> 
> I have two questions about the simplifier (in HOL Light and/or HOL4):
> 
> 1. Is there a recent paper/documentation explaining the internals of the 
> simplifier?
>   (I know of the seminal paper by Larry Paulson, but there are quite 
> many improvements which have been achieved since then;
>   the notion of congruence, in particular, is essential in the current 
> simplifier - at least in HOL Light;
>   it seems the nowadays simplifier is the result of a lot of work by 
> Don Syme but a (quick) look at his publications did not yield any 
> satisfactory result)
> 
> 2. Am I right that the simplifier can only achieve *invertible* 
> transformations of the goal?
>   i.e., if the simplifier turns a goal G1 into a goal G2, then G2 is 
> provable iff G1 is.
> 
> Thanks,
> V.
> 
> -- 
> Vincent ARAVANTINOS - PostDoctoral Fellow - Concordia University, Hardware
> Verification Group
> http://users.encs.concordia.ca/~vincent/
> 
> 
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