On Thursday, July 17, 2014 10:35:32 PM UTC-7, Robert Bradshaw wrote:
> I'm not sure multimethods alone are enough to solve issues with Sage's
> type system (e.g. coercion, where the result of a+b may happen in a
> completely new domain) but they could certainly help.
>
Indeed. If you want multiple dispatch in python you can have it:
class multi_dispatch(object):
def __init__(self):
self.dispatch = []
def register_function(self,signature,function):
self.dispatch.append( (signature,function) )
def register(self,*signature):
def register_decorator(function):
self.register_function(signature,function)
return function
return register_decorator
def __call__(self,*args):
for sig in self.dispatch:
if len(args) == len(sig) and all(isinstance(a,b) for a,b in zip(
args,sig[0])):
return sig[1](*args)
raise TypeError("Signature not implemented")
With this it is now quite straightforward to write multiple dispatch at the
cost of using a decorator:
T = multi_dispatch()
@T.register(int,int)
def int_int(a,b):
return "called with integers (%d,%d)"%(a,b)
@T.register(int,float)
def int_float(a,b):
return "called with integer and float (%d,%f)"%(a,b)
@T.register(float,float)
def float_float(a,b):
return "called with floats (%f,%f)"%(a,b)
You can then just call T:
>>> T(1,2)
'called with integers (1,2)'
>>> T(1,2.0)
'called with integer and float (1,2.000000)'
>>> T(1.0,2.0)
'called with floats (1.000000,2.000000)'
>>> T(1.0,2)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "dispatch.py", line 15, in __call__
raise TypeError("Signature not implemented")
TypeError: Signature not implemented
The key is in optimizing the signature lookup (and the kind of lookup can
definitely be refined a *lot* in the above implementation--linear search by
registration order is probably not optimal) and finding a useful way of
describing signatures and properly prioritizing which signature should get
precedence (if you think C3 is complicated for multiple inheritance, brace
yourself for multiple dispatch).
In a dynamically typed language, multiple dispatch has a rather high cost.
LISP MOP implementations have a lot of experience. In the end it's just a
little helper tool, though. It doesn't really do things you can't otherwise
do.
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