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tableau.hs
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tableau.hs
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{-# OPTIONS_GHC -Wno-incomplete-patterns #-}
module Main where
removeInconveniences :: String -> String
removeInconveniences " " = ""
removeInconveniences a = [e | e<-a, e /= ' ', e /= '-']
checkEnt:: Int -> Int -> String -> Int
checkEnt _ _ [] = 0
checkEnt a b (x:xs)
| x == '&' && a == b = 1
| x == '|' && a == b = 1
| x == '>' && a == b = 1
| x == '(' = checkEnt (a+1) b xs
| x == ')' = checkEnt a (b+1) xs
| otherwise = checkEnt a b xs
splitAux:: Int -> Int -> Int -> String -> Int
splitAux _ _ _ [] = error "A entrada inserida apresenta alguma inconsistência!"
splitAux a b i (x:xs)
| x == '&' && a == b+1 = i
| x == '|' && a == b+1 = i
| x == '>' && a == b+1 = i
| x == '(' = splitAux (a+1) b (i+1) xs
| x == ')' = splitAux a (b+1) (i+1) xs
| otherwise = splitAux a b (i+1) xs
isEmpty:: Node -> Bool
isEmpty Empty = True
isEmpty _ = False
data Node =
Empty
| Node {formula :: [String]
,esq :: Node
,dir :: Node
}deriving(Show)
graftTree:: Node -> Node -> Node
graftTree Empty b = b
graftTree a Empty = a
graftTree a b
| isEmpty (esq a) = Node (formula a) (esq b) (dir b)
| otherwise = Node (formula a) (graftTree (esq a) b) (graftTree (dir a) b)
makeTree:: Node -> Node
makeTree Empty = Empty
makeTree a
| length (head (formula a)) <= 2 = a
| head(head (formula a)) == '~' &&
head(tail(head (formula a))) == '(' =
case tail (head (formula a)) !! splitAux 0 0 0 (tail (head(formula a))) of
'|' -> Node (formula a ++
formula(makeTree(
Node ["~" ++ tail(take (splitAux 0 0 0 (tail (head(formula a)))) (tail (head(formula a))))]
(esq a)
(dir a))) ++
formula(makeTree(
Node ["~" ++ init(tail (drop (splitAux 0 0 0 (tail (head(formula a)))) (tail (head (formula a)))))]
(esq a)
(dir a))))
(graftTree (esq a) (esq (graftTree (makeTree( Node ["~" ++ tail(take (splitAux 0 0 0 (tail (head(formula a)))) (tail (head(formula a))))]
Empty
Empty))
(makeTree(Node ["~" ++ init(tail (drop (splitAux 0 0 0 (tail (head(formula a)))) (tail (head (formula a)))))]
Empty
Empty)))))
(graftTree (dir a) (dir (graftTree(makeTree( Node ["~" ++ tail(take (splitAux 0 0 0 (tail (head(formula a)))) (tail (head(formula a))))]
Empty
Empty))
(makeTree(Node ["~" ++ init(tail (drop (splitAux 0 0 0 (tail (head(formula a)))) (tail (head (formula a)))))]
Empty
Empty)))))
'>' -> Node (formula a ++
formula(makeTree(
Node [tail(take (splitAux 0 0 0 (tail (head(formula a)))) (tail (head(formula a))))]
(esq a)
(dir a))) ++
formula(makeTree(
Node ["~" ++ init(tail (drop (splitAux 0 0 0 (tail (head(formula a)))) (tail (head (formula a)))))]
(esq a)
(dir a))))
(graftTree (esq a) (esq (graftTree (makeTree( Node [tail(take (splitAux 0 0 0 (tail (head(formula a)))) (tail (head(formula a))))]
Empty
Empty))
(makeTree(Node ["~" ++ init(tail (drop (splitAux 0 0 0 (tail (head(formula a)))) (tail (head (formula a)))))]
Empty
Empty)))))
(graftTree (dir a) (dir (graftTree(makeTree( Node [tail(take (splitAux 0 0 0 (tail (head(formula a)))) (tail (head(formula a))))]
Empty
Empty))
(makeTree(Node ["~" ++ init(tail (drop (splitAux 0 0 0 (tail (head(formula a)))) (tail (head (formula a)))))]
Empty
Empty)))))
'&' -> Node (formula a)
(graftTree (esq a)
(makeTree(Node ["~" ++ tail(take (splitAux 0 0 0 (tail (head(formula a)))) (tail (head(formula a))))]
Empty
Empty)))
(graftTree (dir a)
(makeTree(Node ["~" ++ init(tail (drop (splitAux 0 0 0 (tail (head(formula a)))) (tail (head (formula a)))))]
Empty
Empty)))
| head(head (formula a)) == '~' && head(tail(head (formula a))) == '~' =
Node (formula a ++ formula (makeTree (Node [drop 2 (head (formula a))] (esq a) (dir a))))
(esq (makeTree (Node [drop 2 (head (formula a))] (esq a) (dir a))))
(dir (makeTree (Node [drop 2 (head (formula a))] (esq a) (dir a))))
| otherwise =
case head (formula a) !! splitAux 0 0 0 (head(formula a)) of
'&' -> Node (formula a ++
formula(makeTree(
Node [tail(take (splitAux 0 0 0 ((head(formula a)))) ((head(formula a))))]
(esq a)
(dir a))) ++
formula(makeTree(
Node [init(tail (drop (splitAux 0 0 0 ((head(formula a)))) ((head (formula a)))))]
(esq a)
(dir a))))
(graftTree (esq a) (esq (graftTree (makeTree( Node [tail(take (splitAux 0 0 0 ((head(formula a)))) ((head(formula a))))]
Empty
Empty))
(makeTree(Node [init(tail (drop (splitAux 0 0 0 ((head(formula a)))) ((head (formula a)))))]
Empty
Empty)))))
(graftTree (dir a) (dir (graftTree(makeTree( Node [tail(take (splitAux 0 0 0 ((head(formula a)))) ((head(formula a))))]
Empty
Empty))
(makeTree(Node [init(tail (drop (splitAux 0 0 0 ((head(formula a)))) ((head (formula a)))))]
Empty
Empty)))))
'>' -> Node (formula a)
(graftTree (esq a)
(makeTree(Node ["~" ++ tail(take (splitAux 0 0 0 ((head(formula a)))) ((head(formula a))))]
Empty
Empty)))
(graftTree (dir a)
(makeTree(Node [init(tail (drop (splitAux 0 0 0 ((head(formula a)))) ((head (formula a)))))]
Empty
Empty)))
'|' -> Node (formula a)
(graftTree (esq a)
(makeTree(Node [tail(take (splitAux 0 0 0 ((head(formula a)))) ((head(formula a))))]
Empty
Empty)))
(graftTree (dir a)
(makeTree(Node [init(tail (drop (splitAux 0 0 0 ((head(formula a)))) ((head (formula a)))))]
Empty
Empty)))
printBlockAux :: Int -> String -> String
printBlockAux 0 _ = ""
printBlockAux 1 b = b ++ " "
printBlockAux a b = printBlockAux (a-1) (b ++ " ")
printBlock:: Int -> [String] -> String -> String -> IO()
printBlock _ [] _ _ = putStr ""
printBlock i f a v =
if i == length f then do
putStr a
putStrLn (head f)
printBlock i (tail f) a v
else do
putStr v
putStrLn (head f)
printBlock i (tail f) a v
drawTreeAux :: Int -> String -> String
drawTreeAux 0 _ = ""
drawTreeAux 1 b = b ++ "[----- "
drawTreeAux a b = drawTreeAux (a-1) (b ++ " ")
drawTree:: Node -> Int -> IO()
drawTree Empty andar = do
putStr (drawTreeAux andar " ")
print Empty
drawTree a andar = do
drawTree (esq a) (andar + 1)
printBlock ((div (length(formula a)) 2) + 1) (formula a) (drawTreeAux andar " ") (printBlockAux andar " ")
drawTree (dir a) (andar + 1)
findAtomsAux:: [String] -> [[String]] -> [[String]]
findAtomsAux [] v = v
findAtomsAux f v =
if length (head f) <= 2 then
findAtomsAux (tail f) [(head v) ++ [head f]]
else findAtomsAux (tail f) v
findAtoms:: Node -> [[String]] -> [[String]]
findAtoms a v
| not (isEmpty (esq a)) = findAtoms (esq a) (findAtomsAux (formula a) v) ++ findAtoms (dir a) (findAtomsAux (formula a) v)
| otherwise = findAtomsAux (formula a) v
itHasContradition:: [String] -> Bool
itHasContradition a
| length([e | e <-a, length e == 1, elem ("~" ++ e) a]) > 0 = True
| otherwise = False
evaluateTree:: [[String]] -> [Bool]
evaluateTree [] = [False]
evaluateTree a = [itHasContradition e |e<-a]
fetchInterpretation:: [String] -> [String]
fetchInterpretation [] = []
fetchInterpretation a =
if not (itHasContradition a) then
[e | e <- a, length e == 1, not(elem ("~" ++ e) a)] ++ [e | e <- a, length e == 2, not(elem (tail e) a)]
else
[]
fetchInterpretations:: [[String]] -> [[String]]
fetchInterpretations [] = []
fetchInterpretations a = [if (fetchInterpretation e) == [] then ["Ramo fechado!"] else e | e<-a]
leavesWithNoContradition:: [Bool] -> [Int] -> Int -> [Int]
leavesWithNoContradition [] _ _ = []
leavesWithNoContradition (x:xs) r c
|not x = r ++ [c] ++ leavesWithNoContradition xs r (c+1)
|x = r ++ leavesWithNoContradition xs r (c+1)
|otherwise = leavesWithNoContradition xs r (c+1)
isValid:: Node -> IO()
isValid tree = do
let idxs = (leavesWithNoContradition (evaluateTree (findAtoms tree [[]])) [] 1)
if length idxs == 0 then do putStrLn "A fórmula inserida não é falsificável!"
else do
putStr "A fórmula inserida é falsificável. Confira as interpretações da análise dos ramos que a negativam: "
print (fetchInterpretations (findAtoms tree [[]]))
tableau:: IO()
tableau = do
-- (p|(q&r))>((p|q)&(p|r))
-- a -> (a -> (b -> a))
-- b -> (a & (b & a))
-- (x&~x)|(y&~y)
putStrLn "Insira uma fórmula lógica: "
entrada <- getLine
let a = removeInconveniences (if checkEnt 0 0 entrada == 0 then
"~" ++ entrada
else
"~(" ++ entrada ++ ")")
let node = Node [a] Empty Empty
let tree = makeTree node
putStrLn "---------------------------------------------------------------------------------------------------------------------------------"
drawTree tree 0
putStrLn "---------------------------------------------------------------------------------------------------------------------------------"
isValid tree
main :: IO()
main = do
tableau