Well. You are aware of Computed Columns in SQL Server. In a similar way you can also use Computed Parameters. Consider the following procedure.

Create procedure test
(
	@datetime datetime,
	@date date = @datetime
)
as
	select @datetime as date_with_time, @date as date_only

When you execute the procedure you get this result

EXEC '2001-10-18 12:45:22.000'

date_with_time          date_only
----------------------- ----------
2001-10-18 12:45:22.000 2001-10-18

As you see the parameter accepts the value supplied for @datetime and convert it to date datatype. 
When you supply value for @date, it will ignore the value of @datetime, the default value for it

EXEC '2001-10-18 12:45:22.000','2012-01-22 19:15:12.000'

date_with_time          date_only
----------------------- ----------
2001-10-18 12:45:22.000 2012-01-22

However it is not possible to use an expression for the computed paramters 
ie @date date=dateadd(day,10,@datetime) will not work. You should be aware of this when you use paramers
this way.