E02.hs

-----------------------------------------------------------------------------
-- |
-- Module      :  Data.Relation.Examples.E02
-- Copyright   :  (c) DD.  2012
--                (c) LFL. 2009
-- License     :  BSD-style
-- Maintainer  :  Drew Day<drewday@gmail.com>
-- Stability   :  experimental
-- Portability :  portable
--
module Data.Relation.Examples.E02 where 

import           Data.Relation 
import qualified Data.Set      as S
import           Text.Groom


-- | 
--
-- Documentation Tests
--
-- All examples in this module are tested automatically with Doctest, and pretty printed with "Text.Groom".
-- 
-- This output is provided as proof of the correctness of the REPL (@>>>@) text:
--
-- @
--   There are 12 tests, with 12 total interactions.
--   Examples: 12  Tried: 12  Errors: 0  Failures: 0
-- @



p f = putStrLn $ groom $ f

-- | Example 2:
--
-- A student x can take n classes.
--
-- * Each student must take at least 1 class
--
-- * Each class must have at least one student.

enrollment =  fromList 
         [ ("Rebeca" , "History"    )
         , ("Rebeca" , "Mathematics"  )
         , ("Rolando", "Religion"    )
         , ("Rolando", "Comunication")
         , ("Teresa" , "Religion"    )
         , ("Teresa" , "Architecture")
         , ("Antonio", "History"    )
         ]

-- ^
-- >>> p enrollment
-- Relation{domain =
--            fromList
--              [("Antonio", fromList ["History"]),
--               ("Rebeca", fromList ["History", "Mathematics"]),
--               ("Rolando", fromList ["Comunication", "Religion"]),
--               ("Teresa", fromList ["Architecture", "Religion"])],
--          range =
--            fromList
--              [("Architecture", fromList ["Teresa"]),
--               ("Comunication", fromList ["Rolando"]),
--               ("History", fromList ["Antonio", "Rebeca"]),
--               ("Mathematics", fromList ["Rebeca"]),
--               ("Religion", fromList ["Rolando", "Teresa"])]}

-------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------


rebecaenrollment = (S.singleton "Rebeca" |$> ran enrollment) enrollment 
-- ^
-- >>> p rebecaenrollment
-- fromList ["History", "Mathematics"]

takingreligion = (dom enrollment <$| S.singleton "Religion") enrollment
-- ^
-- >>> p takingreligion
-- fromList ["Rolando", "Teresa"]


-- others courses for those taking religion
others   =  (takingreligion |$> ran enrollment) enrollment
-- ^
-- >>> p others
-- fromList ["Architecture", "Comunication", "Religion"]
--





test1 =  (takingreligion <$| ran enrollment) enrollment == takingreligion
--
-- ^
-- >>> p test1
-- True

-- Exploring |> 
--
takingreligion2 = enrollment |> S.singleton "Religion"
-- ^
-- >>> p takingreligion2
-- Relation{domain =
--            fromList
--              [("Rolando", fromList ["Religion"]),
--               ("Teresa", fromList ["Religion"])],
--          range = fromList [("Religion", fromList ["Rolando", "Teresa"])]}


id1 s =  ( v1 == v2, v1 )
    where
    v1 =  (dom  enrollment |$> s) enrollment
    v2 =   ran (enrollment |>  s)
   

id2 s = ( v1 == v2, v1 )
    where
    v1 =  (dom  enrollment <$| s) enrollment
    v2 =   dom (enrollment |>  s) 


-- Exploring <|

id3 s = ( v1 == v2, v1 )
    where
    v1 =  (s       <$| ran enrollment) enrollment
    v2 =  dom (s <|  enrollment)


id4 s = ( v1 == v2, v2 )
    where
    v1 =  (s       |$> ran enrollment) enrollment
    v2 =  ran (s <|  enrollment)


religion  = S.singleton "Religion"  -- has students
teresa    = S.singleton "Teresa" -- enrolled

--
-- ^
-- >>> p religion
-- fromList ["Religion"]

t11 = id1 religion 
--
-- ^
-- >>> p t11
-- (True, fromList ["Religion"])

t12 = id2 religion 
--
-- ^
-- >>> p t12
-- (True, fromList ["Rolando", "Teresa"])


t13 = id3 teresa 
--
-- ^
-- >>> p t13
-- (True, fromList ["Teresa"])

t14 = id4 teresa 
--
-- ^
-- >>> p t14
-- (True, fromList ["Architecture", "Religion"])


id1R, id2R 
 :: (Ord a, Ord b) => S.Set b -> Relation a b -> Bool

id3R , id4R
 :: (Ord a, Ord b) => S.Set a -> Relation a b -> Bool

id1R s r = (dom r |$> s) r == ran (r |>  s)
id2R s r = (dom r <$| s) r == dom (r |>  s) 
id3R s r = (s <$| ran r) r == dom (s <| r)
id4R s r = (s |$> ran r) r == ran (s <| r)

testAll     = all id  [ id1R religion enrollment
                      , id2R religion enrollment
                      , id3R teresa   enrollment
                      , id4R teresa   enrollment
                      ]
-- ^
-- >>> p testAll
-- True