Tobias
On 02/06/2015 20:18, Florian Haftmann wrote:
Dear all,
recently, I stumbled (once again) over the matter of the »real« conversion.
There is an inclusion hierarchy (⊆) of numerical types
(num ⊆) nat ⊆ int ⊆ rat ⊆ real ⊆ complex
We can embed »smaller« into »bigger« types using conversions
(numeral ⊆) of_nat ⊆ of_int ⊆ of_rat ⊆ of_real
These conversions have solid generic algebraic definitions!
For historic reasons, there is also the conversion real :: 'a ⇒ real
which is overloaded and can be instantiated to arbitrary types. This
(co)conversion works in the other direction without any algebraic
foundation!
My impression is that having this conversion is a bad idea. For
illustration have a look at
http://isabelle.in.tum.de/repos/isabelle/file/3d696ccb7fa6/src/HOL/Archimedean_Field.thy#l312
which gives a wonderful generic lemma relating fraction division and
integer division:
»floor (of_int k / of_int l) = k div l«
Note that the result type of the of_int conversion is polymorphic and
can be instantiated to rat and real likewise!
In the presence of the »real« conversion, there is a second variant
»floor (real k / real l) = k div l«
which must be given separately!
For uniformity it would be much better to have »real« disappear in the
middle run. I see two potential inconveniences at the moment:
* Writing »of_foo« might demand a type annotation on its result in many
cases (n.b. operations of type foo ⇒ 'a are one of the rare cases where
explicit type annotations must be given in terms rather than at »fixes«).
* We have the existing abbreviations »real_of_foo« which have no type
ambiguity, but might seem a little bit verbose.
Anyway, the duplication seems more grivious to me than such syntax issues.
Any comments?
Florian
_______________________________________________
isabelle-dev mailing list
isabelle-...@in.tum.de
https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev
smime.p7s
Description: S/MIME Cryptographic Signature
_______________________________________________ isabelle-dev mailing list isabelle-...@in.tum.de https://mailmanbroy.informatik.tu-muenchen.de/mailman/listinfo/isabelle-dev
