model :: String
model | and [

            -- De FO theorie hier

            forall q (\x -> exists p (\y -> x + y > 6)),
            member p 4,
            r < 4

            -- Het outputvocabularium hier
        ] = output [("p",show p),("q",show q),("r",show r)] where
       
            -- Het vocabularium en domeinen hier
            p = subset [2,3,4]
            q = subset [4,5,6]
            r = elementOf p


-- de modellen moeten berekend worden
main = model

-- library FO functions
member (x:xs) v = x == v || member xs v
member [] _ = False

elementOf :: [a] -> a
elementOf (x:xs) = x ? elementOf xs
elementOf [] |False = error "no empty list"

subset :: [a] -> [a]
subset []     = []
subset (x:xs) = (x:subset xs) ? subset xs

forall :: [a] -> (a -> Bool) -> Bool
forall = flip all

exists :: [a] -> (a -> Bool) -> Bool
exists = flip any

output :: [(String,String)] -> String
output = unwords . (map (\(x,y) -> x ++ ":=" ++ y))