93 lines
No EOL
3.3 KiB
Haskell
93 lines
No EOL
3.3 KiB
Haskell
module Main where
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import FOLSyntax ( Formula(Conj, Neg, Impl), Term(..) )
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import Parser ( parseFormula )
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import Resolution ( CNF, doResolution )
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import Normalforms
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( makeNNF,
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renameBinders,
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makePNF,
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makeSkolem,
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makeCNF,
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makeClauseSet )
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{-
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To prove a formula we:
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1. Construct `Neg phi`
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2. Transform `Neg phi` to a clause list
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3. doResolution on clause list
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-}
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proveFormula :: Formula -> Either () CNF
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proveFormula form = doResolution . makeClauseSet . makeCNF . makeSkolem . makePNF . renameBinders . makeNNF $ Neg form
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-- unification examples
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terma1 :: Term
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terma1 = Fun "f" [Var "x", Fun "g" [Var "y"]]
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termb1 :: Term
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termb1 = Fun "f" [Fun "g" [Var "z"], Var "z"]
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terma2 :: Term
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terma2 = Fun "f" [Var "x", Fun "g" [Var "x"], Fun "h" [Var "y"]]
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termb2 :: Term
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termb2 = Fun "f" [Fun "k" [Var "y"], Fun "g" [Var "z"], Var "z"]
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terma3 :: Term
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terma3 = Fun "f" [Var "x", Fun "g" [Var "x"]]
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termb3 :: Term
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termb3 = Fun "f" [Var "z", Var "z"]
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-- NNF example from gloin
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formula1 :: Formula
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formula1 = parseFormula "!((A () \\/ !B()) /\\ (C ()))"
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-- PNF and skolem example from gloin
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formula2 :: Formula
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formula2 = parseFormula "forall x. (forall y. L(y,x)) -> exists y.M(x,y)"
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-- Resolution example from gloin script
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formula3 :: Formula
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formula3 = parseFormula "P(a()) /\\ (forall x. P(x) -> P(f(x))) -> (exists x. P(f(f(x)))) "
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-- Resolution example from gloin exercises (sheet 11, ex 5) [already in CNF]
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formula4 :: Formula
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formula4 = parseFormula "((S(f(x), y)) \\/ (S(y, z)) \\/ (P(y))) /\\ (!(S(f(f(x)), x))) /\\ (!P(f(z)))"
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-- now a big example, sheet 11, exercise 6: Drogenschmuggel, this doesn't work yet but I'm sure its just the exercise thats wrong...
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formula5 :: Formula
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formula5 = Impl (Conj phi1 (Conj phi2 phi3)) psi
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where
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phi1 = parseFormula "forall x.E(x) /\\ !I(x) -> exists y.Z(y) /\\ S(y,x)"
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phi2 = parseFormula "exists x. (D(x) /\\ E(x)) /\\ forall y. S(y,x) -> D(y)"
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phi3 = parseFormula "forall x.I(x) -> !D(x)"
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psi = parseFormula "exists x. Z(x) /\\ D(x)"
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-- aerzte und quacksalber v2
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formula6 :: Formula
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formula6 = Impl (Conj psi1 psi2) psi3
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where
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psi1 = parseFormula "forall x. D(x) -> exists y. P(y) /\\ L(y,x)"
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psi2 = parseFormula "forall x. P(x) -> forall y. Q(y) -> !L(x, y)"
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psi3 = parseFormula "forall x. D(x) -> !Q(x)"
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main :: IO ()
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main = do
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putStrLn $ "Now making NNF of formula: " ++ show formula1
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print $ makeNNF formula1
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putStrLn $ "Now making PNF of formula: " ++ show formula2
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print . makePNF . renameBinders $ makeNNF formula2
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putStrLn $ "Now making Skolemform of formula: " ++ show formula2
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print . makeSkolem . makePNF . renameBinders $ makeNNF formula2
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putStrLn $ "Now proving formula by resolution: " ++ show formula3
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case proveFormula formula3 of
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Left _ -> putStrLn "Success!"
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Right _ -> return ()
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putStrLn $ "Now Proving formula by resolution: " ++ show formula4
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case doResolution $ makeClauseSet formula4 of
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Left _ -> putStrLn "Success!"
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Right _ -> return ()
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putStrLn $ "Now Proving formula by resolution: " ++ show formula5
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case proveFormula formula5 of
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Left _ -> putStrLn "Success!"
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Right _ -> return ()
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putStrLn $ "Now Proving formula by resolution: " ++ show formula6
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case proveFormula (Neg formula6) of
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Left _ -> putStrLn "Success!"
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Right _ -> return () |