On 18 Sep 2014, at 02:47, buynnnm...@yahoo.co.jp wrote:
> Dear Alexander Konovalov,
>
> Thank you very much for your description with some execution examples!
>
> I tried to run Copy and paste the example of you.It's very interesting.
>
> I have not read the document you taught me yet, but I understand the point.
> I think that is similar to polymorphism of object-oriented programming
> languages.
Yes, precisely! This is dynamic polymorphism. The method selected depends on
types of all arguments, and objects may change their type during their lifetime.
For example, if there is a faster algorithm for a group for which it is known
that is has some attribute X, you may install a generic method for IsGroup and
a specific for IsGroup and HasX. Then for a group without X a generic method
will be called, while for the group for which X is known a specific method will
be called. This will not automatically enforce the calculation of X which may
be expensive.
This may be seen in the method that implements the Feit–Thompson theorem from
my mail yesterday:
InstallImmediateMethod( IsSolvableGroup, IsGroup and HasSize, 10,
function( G )
G:= Size( G );
if IsInt( G ) and G mod 2 = 1 then
return true;
fi;
TryNextMethod();
end );
- it will be applied (automatically, since it is *immediate*) only if the Size
is already known, what is checked with HasSize.
You might be interested in the following paper which describes this in more
details:
@inproceedings{Breuer:1998:GTS:281508.281540,
author = {Breuer, Thomas and Linton, Steve},
title = {The GAP 4 Type System: Organising Algebraic Algorithms},
booktitle = {Proceedings of the 1998 International Symposium on Symbolic and
Algebraic Computation},
series = {ISSAC '98},
year = {1998},
isbn = {1-58113-002-3},
location = {Rostock, Germany},
pages = {38--45},
numpages = {8},
url = {http://doi.acm.org/10.1145/281508.281540},
doi = {10.1145/281508.281540},
acmid = {281540},
publisher = {ACM},
address = {New York, NY, USA},
}
Best wishes
Alexander
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