Add initial HW code for HW 5.

KarelState.hs

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+-- | This module defines the state of a running Karel program.
+module KarelState where
+
+import Prelude hiding (Either(..))
+import KarelSyntax
+
+
+--
+-- * Positions and directions
+--
+
+-- | A cartesian coordinate, representing a position in the world.
+type Pos = (Int,Int)
+
+-- | Get the position next to the given position, offset by one square
+--   in the indicated *cardinal* direction.
+neighbor :: Card -> Pos -> Pos
+neighbor North (x,y) = (x,y+1)
+neighbor South (x,y) = (x,y-1)
+neighbor East  (x,y) = (x+1,y)
+neighbor West  (x,y) = (x-1,y)
+
+-- | Get a cardinal direction relative to the current one.
+cardTurn :: Dir -> Card -> Card
+cardTurn Front c     = c
+cardTurn Back  North = South
+cardTurn Back  South = North
+cardTurn Back  East  = West
+cardTurn Back  West  = East
+cardTurn Left  North = West
+cardTurn Left  South = East
+cardTurn Left  East  = North
+cardTurn Left  West  = South
+cardTurn Right North = East
+cardTurn Right South = West
+cardTurn Right East  = South
+cardTurn Right West  = North
+
+
+--
+-- * World state
+--
+
+-- | The state of the world is represented by a function that returns
+--   for each position:
+--    * Nothing, if the position is a wall
+--    * Just k, if the position is clear and has k beepers
+--   You can assume k is always >= 0.
+type World = Pos -> Maybe Int
+
+-- | Is the given position clear?
+isClear :: Pos -> World -> Bool
+isClear p w = w p /= Nothing
+
+-- | Is there a beeper at the given position?
+hasBeeper :: Pos -> World -> Bool
+hasBeeper p w = maybe False (>0) (w p)
+
+-- | Increment the number of beepers at the given position.
+incBeeper :: Pos -> World -> World
+incBeeper p w = \q -> if p == q 
+                         then case w q of
+                                Nothing -> Just 1
+                                Just i  -> Just (i+1)
+                         else w q
+
+-- | Decrement the number of beepers at the given position. Note that this
+--   function can yield a world with negative beepers, so you should make
+--   sure to only decrement the beepers at a position after first checking
+--   to make sure there is at least one beeper there (using `hasBeeper`).
+decBeeper :: Pos -> World -> World
+decBeeper p w = \q -> if p == q then fmap (subtract 1) (w q) else w q
+
+
+--
+-- * Robot state
+--
+
+-- | The state of the robot is represented by a triple containing:
+--    * the current position
+--    * the current facing (cardinal direction)
+--    * the number of beepers in the beeper bag
+type Robot = (Pos,Card,Int)
+
+
+-- ** Robot position
+
+-- | The robot's position.
+getPos :: Robot -> Pos
+getPos (p,_,_) = p
+
+-- | Get a position relative to the robot's current facing and position.
+relativePos :: Dir -> Robot -> Pos
+relativePos d (p,c,_) = neighbor (cardTurn d c) p
+
+-- | Set the robot's position.
+setPos :: Pos -> Robot -> Robot
+setPos p (_,c,b) = (p,c,b)
+
+-- | Update the robot's position using an update function.
+updatePos :: (Pos -> Pos) -> Robot -> Robot
+updatePos f (p,c,b) = (f p,c,b)
+
+
+-- ** Robot facing
+
+-- | The robot's facing (cardinal direction).
+getFacing :: Robot -> Card
+getFacing (_,c,_) = c
+
+-- | Set the robot's facing.
+setFacing :: Card -> Robot -> Robot
+setFacing c (p,_,b) = (p,c,b)
+
+-- | Update the robot's facing using an update function.
+updateFacing :: (Card -> Card) -> Robot -> Robot
+updateFacing f (p,c,b) = (p,f c,b)
+
+
+-- ** Beeper bag
+
+-- | The number of beepers in the beeper bag.
+getBag :: Robot -> Int
+getBag (_,_,b) = b
+
+-- | Is the beeper bag empty?
+isEmpty :: Robot -> Bool
+isEmpty (_,_,b) = b <= 0
+
+-- | Increment the number of beepers in the bag.
+incBag :: Robot -> Robot
+incBag (p,c,b) = (p,c,b+1)
+
+-- | Decrement the number of beepers in the bag.
+decBag :: Robot -> Robot
+decBag (p,c,b) = (p,c,b-1)
+
+
+--
+-- * Statement results
+--
+
+-- | The result of executing a statement.
+-- 
+--     * OK: The statement executed successfully, so return the updated state
+--       of the world and the robot. OK to execute the next statement.
+--
+--     * Done: Produced only by the Shutdown statement. This returns the final
+--       state of the robot. No further statements should be executed.
+--
+--     * Error: An error occurred. Includes a string for reporting error messages.
+--       No further statements should be executed.
+--
+data Result = OK    World Robot
+            | Done  Robot
+            | Error String
+
+instance Show Result where
+  show (OK _ r)  = "OK: " ++ show r
+  show (Done r)  = "Done: " ++ show r
+  show (Error s) = "Error: " ++ s
+
+-- | Applies a function to the result if its an OK, otherwise returns
+--   the result unchanged.
+onOK :: (World -> Robot -> Result) -> Result -> Result
+onOK f (OK w r) = f w r
+onOK _ result   = result