```-- | Format W3C Date and Time strings.
module Data.Time.W3C.Format
( format
)
where

import Data.Convertible
import Data.Fixed
import Data.Time
import Data.Time.W3C.Types

-- | Format W3C Date and Time string from anything convertible to
-- 'W3CDateTime' type. The most obvious acceptable type is the
-- 'W3CDateTime' itself.
format :: Convertible t W3CDateTime => t -> String
format = format' . convert
where
format' (W3CDateTime year Nothing Nothing Nothing Nothing Nothing Nothing)
= show4 year

format' (W3CDateTime year (Just month) Nothing Nothing Nothing Nothing Nothing)
= concat [show4 year, "-", show2 month]

format' (W3CDateTime year (Just month) (Just day) Nothing Nothing Nothing Nothing)
= concat [show4 year, "-", show2 month, "-", show2 day]

format' (W3CDateTime year (Just month) (Just day) (Just hour) (Just minute) Nothing (Just tz))
= concat [ show4 year
, "-"
, show2 month
, "-"
, show2 day
, "T"
, show2 hour
, ":"
, show2 minute
, showTZ tz
]

format' (W3CDateTime year (Just month) (Just day) (Just hour) (Just minute) (Just second) (Just tz))
= concat [ show4 year
, "-"
, show2 month
, "-"
, show2 day
, "T"
, show2 hour
, ":"
, show2 minute
, ":"
, case properFraction second :: (Int, Pico) of
(int, 0   ) -> show2 int
(int, frac) -> show2 int ++ tail (showFixed True frac)
, showTZ tz
]

format' w = error ("Invalid W3C Date and Time: " ++ show w)

show4 :: Integral i => i -> String
show4 i
| i >= 0 && i < 10    = "000" ++ show i
| i >= 0 && i < 100   = "00"  ++ show i
| i >= 0 && i < 1000  = "0"   ++ show i
| i >= 0 && i < 10000 = show i
| otherwise          = error ("show4: the integer i must satisfy 0 <= i < 10000: " ++ show i)

show2 :: Integral i => i -> String
show2 i
| i >= 0 && i < 10  = "0" ++ show i
| i >= 0 && i < 100 = show i
| otherwise         = error ("show2: the integer i must satisfy 0 <= i < 100: " ++ show i)

showTZ :: TimeZone -> String
showTZ tz
= case timeZoneMinutes tz of
offset | offset <  0 -> '-' : showTZ' (negate offset)
| offset == 0 -> "Z"
| otherwise   -> '+' : showTZ' offset
where
showTZ' offset
= let h = offset `div` 60
m = offset - h * 60
in
concat [show2 h, ":", show2 m]
```