Re: [isabelle] Proving two real^3 spaces are the same



Hi Timothy,

Am Mittwoch, den 30.03.2011, 11:05 +1300 schrieb Timothy McKenzie:
[..]
> I tested all this in Isabelle2009-2.  I haven't moved to 
> Isabelle2011 yet, because my work relies heavily on what I've just 
> described, and the following in the NEWS file for Isabelle2011 
> worried me:
> 
> * Session Multivariate_Analysis: introduced a type class for 
> euclidean space.  Most theorems are now stated in terms of 
> euclidean spaces instead of finite cartesian products.
> 
>   types
>     real ^ 'n ~>  'a::real_vector
>               ~>  'a::euclidean_space
>               ~>  'a::ordered_euclidean_space
>         (depends on your needs)
> 
>   constants
>      _ $ _        ~> _ $$ _
>      \<chi> x. _  ~> \<chi>\<chi> x. _
>      CARD('n)     ~> DIM('a)
> 
> Also note that the indices are now natural numbers and not from 
> some finite type. Finite cartesian products of euclidean spaces, 
> products of euclidean spaces the real and complex numbers are 
> instantiated to be euclidean_spaces.  INCOMPATIBILITY.

Did you try Isabelle2011? Of course the type real ^ 'n was not removed,
but for most lemmas the constant names changed. 

Either you rewrite your terms (which is mostly Search & Replace) or you
try to stay with the "real ^ 'n" constants and use the simplifier to
rewrite them at each proof (but I'm not sure how well this approach
works).

Alternatively we could try to add the real^'n version of all changed
lemmas back (by specialising the lemmas about euclidean spaces). 

When we introduced this changes I were not aware of any existing work
using Multivariate_Analysis. Hence we did not care about backwards
compatibility. But we can try to add compatibility lemmas so you can
port your work to the next Isabelle release. Is your work available
anywhere? Is it possible to take a look at it?

> Tim
> <><

Greetings,
  Johannes







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