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module Ex12_QBF2 where
 
import DTC
import Ex12_QBF1
 
data Disjunction a = Disjunction a a
data ExistQuantor a = ExistQuantor a
 
instance Functor Disjunction where
        fmap f (Disjunction x y) = Disjunction (f x) (f y)
instance Functor ExistQuantor where
        fmap f (ExistQuantor a) = ExistQuantor (f a)
        
instance EvalBQF Disjunction where
        evalFormula (Disjunction x y) = x || y
instance EvalBQF ExistQuantor where
        evalFormula (ExistQuantor e) = e
 
disj :: (Disjunction :<: f) => Mu f -> Mu f -> Mu f
disj x y = inject (Disjunction x y)
 
exists :: (ExistQuantor :<: f) => Mu f -> Mu f
exists x = inject (ExistQuantor x)

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