Replacement rule on function of lists

Question

I have a function f whose input is two lists. I want to define a replacement rule which brings to input to a canonical ordering. I have tried the following

CanonicalOrdering = {f[a__, b__] ->Signature@a Signature@b f[Sort@a, Sort@b]}

This seems to do what I want just fine, for example

In[2]:= f[{2, 1}, {1, 2}] /. CanonicalOrdering
Out[2]= -f[{1, 2}, {1, 2}]

However I get some warnings when I first evaluate the function

In[1]:= CanonicalOrdering = {f[a__, b__] -> Signature@a Signature@b f[Sort@a, Sort@b]}

During evaluation of In[1]:= Signature::normal: Nonatomic expression 
expected at position 1 in Signature[a].

During evaluation of In[1]:= Signature::normal: Nonatomic expression 
expected at position 1 in Signature[b].

During evaluation of In[1]:= Sort::normal: Nonatomic expression expected at 
position 1 in Sort[a].

During evaluation of In[1]:= Sort::normal: Nonatomic expression expected at 
position 1 in Sort[b].

Out[1]= {f[a__, b__] -> f[Sort[a], Sort[b]] Signature[a] Signature[b]}

I'm worried that while everything is fine for simple examples issues will arise eventually. How should my code be modified to avoid any potential issues, i.e. to avoid the warnings?

Answer 1

It seems I need to use a delayed replacement rule.

CanonicalOrdering = {f[a__, b__] :>Signature@a Signature@b f[Sort@a, Sort@b]}

This works perfectly (and makes sense).