The sprint is tied into the dashing mechanic, after pressing the sprint button you will gradually accelerate up to +100% of your normal speed. Like so:
1 sec: +30%
2 sec: +60%
3 sec: +100%
4+ sec: You remain at +100%

As you keep sprinting the dash button will begin counting up. If you reach the limit of your Dash (6 seconds right?) or cancel the sprint before that then the Dash icon will turn red to indicate it is cooling down and begin counting down. During that period you cannot dash nor sprint.

This could lead to some interesting modifiers in armours i.e. +/-1 second to dash countdown (You can run further for longer but will have to suffer a penalty when dashing OR more often dashing and less running).

Personally I think that sprinting would render dashing obsolete since the main use for dashing (in my view) is getting out of an enemies swing. Dashing does this, yes, but renders you incapable for Y seconds. Sprinting would do the same but leave you open for a shorter time. Even a 1 or 2 second dash should be able to get you out of a Lumber's swing. I think. Haven't performed any math yet on velocities and time and all that other jazz that makes me want to break a leg. Well I have, performed math that is, but is vague as hell and I don't trust those numbers.
Oh! And it may make a mess of Devilites and Wolvers and anything else that requires lock-on since you'll be sprinting all over the place.