-----------------------------------------------------------------------------
-- Copyright 2010, Open Universiteit Nederland. This file is distributed 
-- under the terms of the GNU General Public License. For more information, 
-- see the file "LICENSE.txt", which is included in the distribution.
-----------------------------------------------------------------------------
-- |
-- Maintainer  :  bastiaan.heeren@ou.nl
-- Stability   :  provisional
-- Portability :  portable (depends on ghc)
--
-----------------------------------------------------------------------------
module Domain.Math.Equation.CoverUpExercise 
   ( coverUpExercise, coverUpStrategy 
   ) where

import Common.Context
import Common.Exercise
import Common.Strategy hiding (replicate)
import Control.Monad
import Domain.Math.Data.Relation
import Domain.Math.Data.OrList
import Domain.Math.Equation.CoverUpRules
import Domain.Math.Equation.Views
import Domain.Math.Examples.DWO1
import Domain.Math.Expr
import Prelude hiding (repeat)

------------------------------------------------------------
-- Exercise

coverUpExercise :: Exercise (OrList (Equation Expr))
coverUpExercise = makeExercise 
   { exerciseId   = describe "solve an equation by covering up" $
                       newId "algebra.equations.coverup"
   , status       = Provisional
   , parser       = parseExprWith (pOrList (pEquation pExpr))
   -- , equivalence  = \_ _ -> True
   , isReady      = solvedEquations
   , extraRules   = coverUpRulesOr
   , strategy     = coverUpStrategy
   , navigation   = termNavigator
   , examples     = map (orList . return) (concat (fillInResult ++ coverUpEquations))
   }

------------------------------------------------------------
-- Strategy and rules
   
coverUpStrategy :: LabeledStrategy (Context (OrList (Equation Expr)))
coverUpStrategy = label "Cover-up" $ 
   repeat $ somewhere $ alternatives coverUpRulesOr

{-
cleanUp :: Rule (OrList (Equation Expr)) -> Rule (OrList (Equation Expr))
cleanUp = doAfter $ fmap $ fmap cleanUpExpr

cleanUpExpr :: Expr -> Expr
cleanUpExpr = transform (simplify (makeView f fromRational))
 where
   f (Negate a) = liftM negate (f a)
   f (Sqrt a)   = match rationalView a >>= rootedRational 2
   f (Sym s [Nat n, a]) | isRootSymbol s =
      match rationalView a >>= rootedRational n
   f e = match rationalView e

rootedInt :: Integer -> Integer -> Maybe Integer 
rootedInt a b = do
   guard (a > 0)
   let d = fromInteger b ** Prelude.recip (fromInteger a) :: Double
       n = round d :: Integer
   guard (n Prelude.^ a == b)
   return n
   
rootedRational :: Integer -> Rational -> Maybe Rational 
rootedRational a r = do
   x <- rootedInt a (numerator r)
   y <- rootedInt a (denominator r)
   return (fromInteger x / fromInteger y)
-}
------------------------------------------------------------
-- Testing

{-   
main = map test (concat (fillInResult ++ coverUpEquations))

test e = case apply coverUpStrategy (inContext (OrList [e])) of
            Just a | solvedList (fromContext a)  -> True
                   | otherwise -> error (show (e, a))
            _ -> error (show e) -}