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tautGen.hs
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tautGen.hs
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import System.IO;
import System.Environment;
data Prop = Const Bool
| Var Char
| Not Prop
| And Prop Prop
| Or Prop Prop
| Imply Prop Prop
| Equi Prop Prop
instance Show Prop where
show (Const v) = show v
show (Var c) = [c]
show (Not p) = "~"++ right
where right = if rightNeedParen then "("++show p++")" else show p
rightNeedParen = rightPrec <= opPrec
rightPrec = priority p
opPrec = priority (Not p)
show (And l r) = left ++"&"++ right
where left = if leftNeedParen then "(" ++ show l ++ ")" else show l
right = if rightNeedParen then "(" ++ show r ++ ")" else show r
leftNeedParen = (leftPrec < opPrec) || ((leftPrec == opPrec) && not (isAnd l))
rightNeedParen = (rightPrec < opPrec ) || ((rightPrec == opPrec) && not (isAnd r))
leftPrec = priority l
rightPrec = priority r
opPrec = priority (And l r)
show (Or l r) = left ++"|"++ right
where left = if leftNeedParen then "(" ++ show l ++ ")" else show l
right = if rightNeedParen then "(" ++ show r ++ ")" else show r
leftNeedParen = (leftPrec < opPrec) || ((leftPrec == opPrec) && not (isOr l))
rightNeedParen = (rightPrec < opPrec) || ((rightPrec == opPrec) && not (isOr r))
leftPrec = priority l
rightPrec = priority r
opPrec = priority (Or l r)
show (Imply l r) = left ++">"++ right
where left = if leftNeedParen then "(" ++ show l ++ ")" else show l
right = if rightNeedParen then "(" ++ show r ++ ")" else show r
leftNeedParen = leftPrec < opPrec || ((leftPrec == opPrec) && not (isImply l))
rightNeedParen = rightPrec < opPrec || ((rightPrec == opPrec) && not (isImply r))
leftPrec = priority l
rightPrec = priority r
opPrec = priority (Imply l r)
show (Equi l r) = left ++"#"++ right
where left = if leftNeedParen then "(" ++ show l ++ ")" else show l
right = if rightNeedParen then "(" ++ show r ++ ")" else show r
leftNeedParen = leftPrec < opPrec || ((leftPrec == opPrec) && not (isEqui l))
rightNeedParen = rightPrec < opPrec || ((rightPrec == opPrec) && not (isEqui r))
leftPrec = priority l
rightPrec = priority r
opPrec = priority (Equi l r)
isAnd :: Prop -> Bool
isAnd (And _ _) = True
isAnd _ = False
isOr :: Prop -> Bool
isOr (Or _ _) = True
isOr _ = False
isImply :: Prop -> Bool
isImply (Imply _ _) = True
isImply _ = False
isEqui :: Prop -> Bool
isEqui (Equi _ _) = True
isEqui _ = False
priority :: Prop -> Int
priority (Var _) = 3
priority (Not _) = 2
priority (Imply _ _) = 1
priority (Equi _ _) = 1
priority (And _ _) = 1
priority (Or _ _) = 1
type Substitution = Pair Char Bool
type Pair var value = [(var,value)]
find :: Eq k => k -> Pair k v -> v
find k t = head [v | (k',v) <- t, k == k']
evaluate :: Substitution -> Prop -> Bool
evaluate _ (Const b) = b
evaluate s (Var x) = find x s
evaluate s (Not p) = not (evaluate s p)
evaluate s (And p q) = evaluate s p && evaluate s q
evaluate s (Or p q) = evaluate s p || evaluate s q
evaluate s (Imply p q) = evaluate s p <= evaluate s q
evaluate s (Equi p q) = evaluate s p == evaluate s q
variables :: Prop -> [Char]
variables (Const _) = []
variables (Var x) = [x]
variables (Not p) = variables p
variables (And p q) = variables p ++ variables q
variables (Or p q) = variables p ++ variables q
variables (Imply p q) = variables p ++ variables q
variables (Equi p q) = variables p ++ variables q
bools :: Int -> [[Bool]]
bools 0 = [[]]
bools n = map (False:) bss ++ map (True:) bss
where bss = bools (n-1)
removeDuplicates :: Eq a => [a] -> [a]
removeDuplicates [] = []
removeDuplicates (x:xs) = x : removeDuplicates (filter (/= x) xs)
substs :: Prop -> [Substitution]
substs p = map (zip vars) (bools (length vars))
where vars = removeDuplicates (variables p)
isTautology :: Prop -> Bool
isTautology p = and [evaluate s p | s <- substs p]
string2Prop :: [Char] -> [Prop] -> Prop
string2Prop [] subProps = head subProps
string2Prop (elem:rest) subProps
| elem == 'p' || elem == 'q' = string2Prop rest (Var elem:subProps)
| elem == '~' =
let (var, restOfList) = (head subProps, tail subProps)
in string2Prop rest (Not var:restOfList)
| elem == '&' =
let (p, q, restOfList) = getElemsStackAndPop subProps
in string2Prop rest (And p q:restOfList)
| elem == '|' =
let (p, q, restOfList) = getElemsStackAndPop subProps
in string2Prop rest (Or p q:restOfList)
| elem == '>' =
let (p, q, restOfList) = getElemsStackAndPop subProps
in string2Prop rest (Imply p q:restOfList)
| elem == '#' =
let (p, q, restOfList) = getElemsStackAndPop subProps
in string2Prop rest (Equi p q:restOfList)
getElemsStackAndPop :: [Prop] -> (Prop, Prop, [Prop])
getElemsStackAndPop stack = (head (tail stack), head stack, tail (tail stack))
checkStr :: [Char] -> [Char] -> Bool
checkStr [] checkList = length checkList == 1
checkStr (elem:rest) checkList | elem == 'p' || elem == 'q' = checkStr rest (elem:checkList)
| elem == '~' = not (null checkList) && checkStr rest checkList
| elem == '&' || elem == '|' ||
elem == '>' || elem == '#' = length checkList >= 2 && checkStr rest (tail checkList)
powerset :: [a] -> [[a]]
powerset [] = [[]]
powerset (x:xs) = [x:ps | ps <- powerset xs] ++ powerset xs
--complexity = length list ^ n
samples :: Int -> [a] -> [[a]]
samples 0 _ = [[]]
samples n xs = [ p : ps | p <- xs, ps <- samples (n - 1) xs]
changeVar :: [Char] -> [Char]
changeVar [] = []
changeVar (elem:rest) | elem == 'p' = 'q' : changeVar rest
| elem == 'q' = 'p' : changeVar rest
| otherwise = elem : changeVar rest
unique :: [[Char]] -> [[Char]]
unique [] = []
unique (x:xs) = x:unique (filter (\elem -> x /= elem && elem /= changeVar x) xs)
genTaut :: Int-> [[Char]]
genTaut n = unique [props | y<- [1..n],
z <- powerset "pq~&|>#", --genPowerset
props <- filter (\q -> checkStr q [] && isTautology (string2Prop q [])) (samples y z)]
uniqueProps :: [Prop] -> [Prop]
uniqueProps [] = []
uniqueProps (x:xs) = x:uniqueProps (filter (\elem -> show x /= show elem) xs)
gen :: [[Char]] -> [Prop] -> Int -> [Prop]
gen [] list n = uniqueProps list
gen (x:rest) list n = let prop = string2Prop x []
in if length (show prop) <= n
then
gen rest (list ++ [prop]) n
else
gen rest list n
genAllTaut :: Int -> Handle -> IO()
genAllTaut n file = do
mapM_ (hPrint file) (gen (genTaut n) [] n)
main :: IO ()
main = do
(firstArg:secArg:_) <-getArgs
fileHandle <- openFile secArg WriteMode
let n = read firstArg :: Int
genAllTaut n fileHandle
hClose fileHandle
putStrLn $ "Generation completed for n = " ++ show n