Can "a piece of music written to march to" be also used instead of "a piece of music written for marching to"?

Hello, how are you?

I would like to ask a question.

Expression A.
a piece of music written for marching to

Expression B.
a piece of music written to march to

Expression A is from Oxford English Learner's Dictionary, and
Expression B is what I made up.

Can Expression B be used instead of Expression A?

Thank you for the explanation and your help.