module FOLSyntax where

data Term = Var String | Fun String [Term] deriving (Eq, Ord)
data Formula
    = Pred String [Term]
    | Neg Formula
    | Conj Formula Formula
    | Disj Formula Formula
    | Impl Formula Formula
    | All String Formula
    | Exists String Formula
    | T
    | F
    deriving (Eq, Ord)


instance Show Term where
    show (Var x) = x
    show (Fun f []) = f
    show (Fun f (x : xs)) = f ++ "(" ++ show x ++ foldr ((++) . (", "++) . show) ")" xs

instance Show Formula where
    show (Pred p []) = p
    show (Pred p (x : xs)) = p ++ "(" ++ show x ++ foldr ((++) . (", "++) . show) ")" xs
    show (Neg f) = "!(" ++ show f ++ ")"
    show (Conj f1 f2) = "(" ++ show f1 ++ " /\\ " ++ show f2 ++ ")"
    show (Disj f1 f2) = "(" ++ show f1 ++ " \\/ " ++ show f2 ++ ")"
    show (Impl f1 f2) = "(" ++ show f1 ++ " -> " ++ show f2 ++ ")"
    show (All x f) = "(forall " ++ x ++ ". " ++ show f ++ ")"
    show (Exists x f) = "(exists " ++ x ++ ". " ++ show f ++ ")"
    show T = "true"
    show F = "false"