use a regex or not?

[Joost Jacob]

I am looking for a function that takes an input string
and a pattern, and outputs a dictionary.

# @param s str, lowercase letters
# @param p str, lowercase and uppercase letters
# @return dict
def fill(s, p):
    d = {}
    ....
    return d

String s has characters from the lowercase letters.
String p is a pattern, a string of characters from the
lowercase and uppercase letters.  The idea is to match
s with p, where lowercase letters have to match
exactly, and to fill variables (with an uppercase
letter name) with the rest of s.  The variables are
collected in a dictionary with the resulting bindings.
A variable that occurs in more than one place in p must
bind to the same substring of s.

Tests:

>>> fill('ab', p='aA')
{'A': 'b'}
>>> fill('ab', p='Ab')
{'A': 'a'}
>>> fill('bb', p='Ab')      # no match
{}
>>> fill('aa', p='Aa')
{'A': 'a'}
>>> fill('aa', p='Ab')      # no match
{}
>>> fill('abb', p='aA')
{'A': 'bb'}
>>> fill('aba', p='aAa')
{'A': 'b'}
>>> fill('abb', p='aAa')    # no match
{}
>>> fill('abab', p='aAaA')  # A-matches must be equal
{'A': 'b'}
>>> fill('abac', p='aAaA')  # no match
{}
>>> fill('abac', p='aAaB')
{'A': 'b', 'B': 'c'}

Can you do it?  Is trying a solution with a regex a
good idea?