Documented (in docstring and in ReST documentation) signatures of the match, search and (since 3.4) fullmatch methods of regex pattern object are:

match(string[, pos[, endpos]])
search(string[, pos[, endpos]])
fullmatch(string[, pos[, endpos]])

However in implementation the first keyword argument by mistake named "pattern". This looks as nonsense. The pattern is object itself, and first argument is a string. First arguments in other methods (split, findall, etc) named "string", and module-level functions have both "pattern" and "string" parameters:

match(pattern, string, flags=0)
search(pattern, string, flags=0)

I think we should fix this mistake. The "pattern" name is obviously wrong and is not match the documentation.