Part III no instance for show

template.hs

@@ -24,7 +24,7 @@ lookUp k ks
 
 checkSat :: BDD -> Env -> Bool
 checkSat (_, []) _
-  = false
+  = False
 checkSat (root, nodes) env
   = checkSat' nodes env (lookUp root nodes)
   where
@@ -36,42 +36,103 @@ checkSat (root, nodes) env
       | lookUpEnv 
           = checkSat' nodeList env (lookUp r nodeList)
       | otherwise 
-          = checkSat' nodeList env (lookUP l nodeList)  
+          = checkSat' nodeList env (lookUp l nodeList)  
           where 
             lookUpEnv = lookUp i env
            
 sat :: BDD -> [[(Index, Bool)]]
-sat 
-  = undefined
-
+sat (_, [])
+  = []
+sat (root, nodes)
+  = (sat' [(root', False)] (lookUp root nodes))
+      ++ (sat' [(root', True)] (lookUp root nodes))
+  where
+    (root', _, _) = lookUp root nodes
+    sat' env (i, l, r)
+      | (fOrT && r == 0) || (not(fOrT) && l == 0)
+          = [] 
+      | (fOrT && r == 1) || (not(fOrT) && l == 1)
+          = [env]
+      | fOrT
+          = (sat' (env ++ [(i', False)]) (lookUp r nodes))
+              ++ (sat' (env ++ [(i', True)]) (lookUp r nodes))
+      | otherwise -- missing one condition !!!
+          = (sat' (env ++ [(i', False)]) (lookUp l nodes))
+              ++ (sat' (env ++ [(i', True)]) (lookUp l nodes))
+          where
+            fOrT = lookUp i env
+            (i', _, _) = lookUp r nodes
 ------------------------------------------------------
 -- PART II
 
 simplify :: BExp -> BExp
-simplify 
-  = undefined
-
+simplify (Not (Prim a))
+  = Prim (not(a))
+simplify (Not i)
+  = Not i
+simplify (Or (Prim a) (Prim b))
+  = Prim (a || b)
+simplify (Or a b)
+  = Or a b 
+simplify (And (Prim a) (Prim b))
+  = Prim (a && b)
+simplify (And a b)
+  = And a b
+  
 restrict :: BExp -> Index -> Bool -> BExp
-restrict 
-  = undefined
+restrict (Prim a) _ _
+  = Prim a
+restrict (IdRef i) index bool
+  | i == index = Prim bool
+  | otherwise  = IdRef i
+restrict (Not a) index bool
+  = simplify (Not (restrict a index bool))
+restrict (Or a b) index bool
+  = simplify (Or (restrict a index bool) (restrict b index bool))
+restrict (And a b) index bool
+  = simplify (And (restrict a index bool) (restrict b index bool))  
 
 ------------------------------------------------------
 -- PART III
-
 -- Pre: Each variable index in the BExp appears exactly once
 --     in the Index list; there are no other elements
 -- The question suggests the following definition (in terms of buildBDD')
 -- but you are free to implement the function differently if you wish.
 buildBDD :: BExp -> [Index] -> BDD
-buildBDD 
-  = undefined
-
+buildBDD e xs 
+  = buildBDD' e 2 xs
+  
 -- Potential helper function for buildBDD which you are free
 -- to define/modify/ignore/delete/embed as you see fit.
 buildBDD' :: BExp -> NodeId -> [Index] -> BDD
-buildBDD' 
-  = undefined
-
+buildBDD' (Prim e) firstID []
+  | e = (1, [])
+  | otherwise = (0, [])
+buildBDD' e firstID (i:is)
+  = (firstID, (buildBDD'' e firstID (i:is)))
+  where
+    buildBDD'' :: BExp -> NodeId -> [Index] -> [BDDNode]
+    buildBDD'' exp id [lastID]
+      = [(id, (lastID, primToInt(restrict exp lastID False), 
+                       primToInt(restrict exp lastID True)))]
+    buildBDD'' exp id (x:xs)
+      = (buildBDD'' boolValueLeft nextIndexLeft xs)
+          ++ (buildBDD'' boolValueRight nextIndexRight xs) 
+             ++ [(id, (x, nextIndexLeft, nextIndexRight))]     
+      where
+        boolValueLeft = restrict exp x False
+        boolValueRight = restrict exp x True
+        nextIndexLeft = 2 * id
+        nextIndexRight = 2 * id + 1
+       
+primToInt :: BExp -> Int
+primToInt (Prim bool)
+  | bool = 1
+  | otherwise = 0
+  
+instance Show([Index] -> BDD) where
+         showList = [()]
+         
 ------------------------------------------------------
 -- PART IV
 

template.hs~

@@ -24,7 +24,7 @@ lookUp k ks
 
 checkSat :: BDD -> Env -> Bool
 checkSat (_, []) _
-  = false
+  = False
 checkSat (root, nodes) env
   = checkSat' nodes env (lookUp root nodes)
   where
@@ -36,42 +36,103 @@ checkSat (root, nodes) env
       | lookUpEnv 
           = checkSat' nodeList env (lookUp r nodeList)
       | otherwise 
-          = checkSat' nodeList env (lookUP l nodeList)  
+          = checkSat' nodeList env (lookUp l nodeList)  
           where 
             lookUpEnv = lookUp i env
            
 sat :: BDD -> [[(Index, Bool)]]
-sat 
-  = undefined
-
+sat (_, [])
+  = []
+sat (root, nodes)
+  = (sat' [(root', False)] (lookUp root nodes))
+      ++ (sat' [(root', True)] (lookUp root nodes))
+  where
+    (root', _, _) = lookUp root nodes
+    sat' env (i, l, r)
+      | (fOrT && r == 0) || (not(fOrT) && l == 0)
+          = [] 
+      | (fOrT && r == 1) || (not(fOrT) && l == 1)
+          = [env]
+      | fOrT
+          = (sat' (env ++ [(i', False)]) (lookUp r nodes))
+              ++ (sat' (env ++ [(i', True)]) (lookUp r nodes))
+      | otherwise -- missing one condition !!!
+          = (sat' (env ++ [(i', False)]) (lookUp l nodes))
+              ++ (sat' (env ++ [(i', True)]) (lookUp l nodes))
+          where
+            fOrT = lookUp i env
+            (i', _, _) = lookUp r nodes
 ------------------------------------------------------
 -- PART II
 
 simplify :: BExp -> BExp
-simplify 
-  = undefined
-
+simplify (Not (Prim a))
+  = Prim (not(a))
+simplify (Not i)
+  = Not i
+simplify (Or (Prim a) (Prim b))
+  = Prim (a || b)
+simplify (Or a b)
+  = Or a b 
+simplify (And (Prim a) (Prim b))
+  = Prim (a && b)
+simplify (And a b)
+  = And a b
+  
 restrict :: BExp -> Index -> Bool -> BExp
-restrict 
-  = undefined
+restrict (Prim a) _ _
+  = Prim a
+restrict (IdRef i) index bool
+  | i == index = Prim bool
+  | otherwise  = IdRef i
+restrict (Not a) index bool
+  = simplify (Not (restrict a index bool))
+restrict (Or a b) index bool
+  = simplify (Or (restrict a index bool) (restrict b index bool))
+restrict (And a b) index bool
+  = simplify (And (restrict a index bool) (restrict b index bool))  
 
 ------------------------------------------------------
 -- PART III
-
 -- Pre: Each variable index in the BExp appears exactly once
 --     in the Index list; there are no other elements
 -- The question suggests the following definition (in terms of buildBDD')
 -- but you are free to implement the function differently if you wish.
 buildBDD :: BExp -> [Index] -> BDD
-buildBDD 
-  = undefined
-
+buildBDD e xs 
+  = buildBDD' e 2 xs
+  
 -- Potential helper function for buildBDD which you are free
 -- to define/modify/ignore/delete/embed as you see fit.
 buildBDD' :: BExp -> NodeId -> [Index] -> BDD
-buildBDD' 
-  = undefined
-
+buildBDD' (Prim e) firstID []
+  | e = (1, [])
+  | otherwise = (0, [])
+buildBDD' e firstID (i:is)
+  = (firstID, (buildBDD'' e firstID (i:is)))
+  where
+    buildBDD'' :: BExp -> NodeId -> [Index] -> [BDDNode]
+    buildBDD'' exp id [lastID]
+      = [(id, (lastID, primToInt(restrict exp lastID False), 
+                       primToInt(restrict exp lastID True)))]
+    buildBDD'' exp id (x:xs)
+      = (buildBDD'' boolValueLeft nextIndexLeft xs)
+          ++ (buildBDD'' boolValueRight nextIndexRight xs) 
+             ++ [(id, (x, nextIndexLeft, nextIndexRight))]     
+      where
+        boolValueLeft = restrict exp x False
+        boolValueRight = restrict exp x True
+        nextIndexLeft = 2 * id
+        nextIndexRight = 2 * id + 1
+       
+primToInt :: BExp -> Int
+primToInt (Prim bool)
+  | bool = 1
+  | otherwise = 0
+  
+instance Show([Index] -> BDD) where
+         showList = [()]
+         
 ------------------------------------------------------
 -- PART IV