This script will show tasks completed today, provided you have TaskPaper set to store the done date and you use date formats of YYYY-MM-DD.
on getShortDate()
set now to (current date)
set {day:d, year:y, time:t} to now
-- Calculate the month number.
copy now to b
set b's month to January
set m to (b - 2500000 - now) div -2500000
-- Short date in yyyy-mm-dd format.
tell (y * 10000 + m * 100 + d) as string
set dateString to text 1 thru 4 & "-" & text 5 thru 6 & "-" & text 7 thru 8
end tell
return dateString
end getShortDate
set theDate to getShortDate()
set searchString to "@done = \"" & theDate & "\" and project = \"Archive\""
tell application "TaskPaper"
set the search field string of the front document to searchString
end tell