ShowTasksCompletedToday

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