Hi!
On Wed, May 28, 2014 at 11:54:22AM +0200, Vincent Delecroix wrote:
> Hi Christian,
>
> 2014-05-28 11:32 UTC+02:00, Christian Stump <christian.st...@gmail.com>:
> >> It seems that actually nobody read my initial post on that thread... so
> >> let me repeat
> >
> > I did -- but didn't really have any qualified contribution...
> >
> >> But the semantic has to be implemented at the level of maps not at the
> >> level of methods.
> >
> > could you explain what you mean there (maybe using your example of the
> > number of descents of a permutation).
>
> A method ( = a Python function) is not a Sage Map ( = a Python object
> that model a mathematical function). I would like first to convert the
> method into a map
> {{{
> from sage.categories.map import Map
> class NumberOfDescents(Map):
> def __init__(self):
> Map.__init__(Permutations(), NonNegativeIntegers())
>
> def _call_(self, p):
> return Integer(p.number_of_descents())
> }}}
> The above example is already non-trivial since it specifies a domain
> and a codomain (which is different from the parent of the image of an
> element):
> {{{
> sage: nod = NumberOfDescents()
> sage: p = Permutation([3,2,1])
> sage: nod(p)
> 3
> sage: nod(p).parent() is NN
> False
> }}}
> The second step would be to think how to add semantic to the map. Part
> of is already managed by the axioms/categories (for example a Morphism
> between GradedSets preserve the grading). But there is nothing for
> injectivity/surjectivity or more subtle properties.
For whatever it's worth: in MuPAD, it was possible to add type
annotations on a method; typically to specify the domain and codomain:
abs := proc(x: Dom::Integer): Dom::Integer
begin
return(x)
end
We were using this extensively for:
- Dynamic type checking in debug mode
- Retrieving the domain or codomain, typically when constructing new
functions from existing ones (e.g. in module_morphism)
- ...
Python 3 will allow to add similar annotations. In the mean time we
could possibly stuff such annotations to glorify methods:
sage: def f(x): return abs(x)
sage: f.domain=ConstantFunction(ZZ)
sage: f.codomain=ConstantFunction(NN)
sage: f(-3)
3
sage: f.domain()
Integer Ring
sage: f.codomain()
Non negative integer semiring
Anyway, just food for thoughts; it's not like there is a clear plan in
this direction.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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