[isabelle-dev] Proper sign of gcd / lcm on type int

[Makarius]

On 01/06/16 21:27, Florian Haftmann wrote:
> Note that the mixed signs of PolyML.IntInf.lcm maintain the property
> 
> 	gcd a b * lcm a b = a * b
> 
> whereas the lcm in GCD.thy obeys
> 
> 	gcd a b * lcm a b = normalize a * normalize b
> 
> which emphasises the dual nature of the gcd/lcm lattice.
> 
> Both are ok in my view; ironically, lcm is used more often in
> Isabelle/ML than gcd.  Providing an lcm in the manner of HOL is trivial,
> though:
> 
> 	Integer.gcd = PolyML.gcd
> 	Integer.lcm = abs oo PolyML.lcm

These two lines are the plan. Is that a good one or a bad one?

Presently, I have used PolyML.IntInf.gcd and PolyML.IntInf.lcm for
rat.ML (see da38571dd5bd). It somehow violates our cozy Isabelle/ML
library environment to refer to structure PolyML.


BTW, AFP has special code generator setup for PolyML.IntInf.gcd here:

https://bitbucket.org/isa-afp/afp-devel/src/54c65361e6ed029f70572de89cfc5736153a0feb/thys/Gauss_Jordan/Code_Generation_IArrays_SML.thy?at=default&fileviewer=file-view-default#Code_Generation_IArrays_SML.thy-33

https://bitbucket.org/isa-afp/afp-devel/src/54c65361e6ed029f70572de89cfc5736153a0feb/thys/Echelon_Form/Examples_Echelon_Form_IArrays.thy?at=default&fileviewer=file-view-default#Examples_Echelon_Form_IArrays.thy-44

Luckily, this is only gcd and not lcm, so it coincides already.


	Makarius


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