Commit 0cbdeb65 authored by daniel's avatar daniel
Browse files

part I done

parents
import Data.List
type Index = Int
data BExp = Prim Bool | IdRef Index | Not BExp | And BExp BExp | Or BExp BExp
deriving (Eq, Ord, Show)
type Env = [(Index, Bool)]
type NodeId = Int
type BDDNode = (NodeId, (Index, NodeId, NodeId))
type BDD = (NodeId, [BDDNode])
------------------------------------------------------
-- PART I
-- Pre: The item is in the given table
lookUp :: Eq a => a -> [(a, b)] -> b
lookUp x = snd . head . filter (\(u,_) -> x == u)
checkSat :: BDD -> Env -> Bool
checkSat (x, xs) l
| lookUp i l = if r == 1 || r == 0 then intToBool r else checkSat (r, xs) l
| otherwise = if q == 1 || q == 0 then intToBool q else checkSat (q, xs) l
where
(i,q,r) = lookUp x xs
intToBool 0 = False
intToBool _ = True
sat :: BDD -> [[(Index, Bool)]]
sat bdd@(rootId, nodes) = filter (checkSat bdd) allEnvs
where
indexes = reverse . nub . map (\(_, (i,_,_)) -> i) $ nodes
boolPerms 0 = []
boolPerms 1 = [[False],[True]]
boolPerms n = foldr (\x acc -> (True:x):((False:x):acc)) [] (boolPerms (n-1))
allEnvs = map (zip indexes) (boolPerms (length indexes))
{-
sat' :: BDD -> [[(Index, Bool)]]
sat' bdd@(rootId, nodes)
| q == 1 = [[]]
| q == 0 = []
| r == 1 = [[]]
| r == 0 = []
| otherwise = sat' (q, nodes) ++ sat' (r, nodes)
where
(i,q,r) = lookUp rootId nodes
-}
------------------------------------------------------
-- PART II
simplify :: BExp -> BExp
simplify
= undefined
restrict :: BExp -> Index -> Bool -> BExp
restrict
= undefined
------------------------------------------------------
-- 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
-- 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
------------------------------------------------------
-- PART IV
-- Pre: Each variable index in the BExp appears exactly once
-- in the Index list; there are no other elements
buildROBDD :: BExp -> [Index] -> BDD
buildROBDD
= undefined
------------------------------------------------------
-- Examples for testing...
b1, b2, b3, b4, b5, b6, b7, b8 :: BExp
b1 = Prim False
b2 = Not (And (IdRef 1) (Or (Prim False) (IdRef 2)))
b3 = And (IdRef 1) (Prim True)
b4 = And (IdRef 7) (Or (IdRef 2) (Not (IdRef 3)))
b5 = Not (And (IdRef 7) (Or (IdRef 2) (Not (IdRef 3))))
b6 = Or (And (IdRef 1) (IdRef 2)) (And (IdRef 3) (IdRef 4))
b7 = Or (Not (IdRef 3)) (Or (IdRef 2) (Not (IdRef 9)))
b8 = Or (IdRef 1) (Not (IdRef 1))
bdd1, bdd2, bdd3, bdd4, bdd5, bdd6, bdd7, bdd8 :: BDD
bdd1 = (0,[])
bdd2 = (2,[(4,(2,1,1)),(5,(2,1,0)),(2,(1,4,5))])
bdd3 = (5,[(5,(1,0,1))])
bdd4 = (2,[(2,(2,4,5)),(4,(3,8,9)),(8,(7,0,1)),(9,(7,0,0)),
(5,(3,10,11)),(10,(7,0,1)),(11,(7,0,1))])
bdd5 = (3,[(4,(3,8,9)),(3,(2,4,5)),(8,(7,1,0)),(9,(7,1,1)),
(5,(3,10,11)),(10,(7,1,0)),(11,(7,1,0))])
bdd6 = (2,[(2,(1,4,5)),(4,(2,8,9)),(8,(3,16,17)),(16,(4,0,0)),
(17,(4,0,1)),(9,(3,18,19)),(18,(4,0,0)),(19,(4,0,1)),
(5,(2,10,11)),(10,(3,20,21)),(20,(4,0,0)),(21,(4,0,1)),
(11,(3,22,23)),(22,(4,1,1)),(23,(4,1,1))])
bdd7 = (6,[(6,(2,4,5)),(4,(3,8,9)),(8,(9,1,1)),(9,(9,1,0)),
(5,(3,10,11)),(10,(9,1,1)),(11,(9,1,1))])
bdd8 = (2,[(2,(1,1,1))])
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