module Dummy where

import Prelude (undefined, Show, Eq, Ord, Bool)

import MyLogic

eq :: (A_Bool, A_Bool) -> A_Bool

le :: (A_Bool, A_Bool) -> A_Bool

ne :: (A_Bool, A_Bool) -> A_Bool

neg :: A_Bool -> A_Bool

vee :: (A_Bool, A_Bool) -> A_Bool

wedge :: (A_Bool, A_Bool) -> A_Bool

data A_Bool = A_True

| A_False

deriving (Show, Eq, Ord)

neg x

= case x of

A_False -> A_True

A_True -> A_False

wedge (x, y)

= case (x, y) of

(A_False, A_False) -> A_False

(A_True, A_False) -> A_False

(A_False, A_True) -> A_False

(A_True, A_True) -> A_True

vee (x, y) = neg (wedge (neg x, neg y))

le (x, y) = vee (neg x, y)

eq (x, y) = wedge (le (x, y), le (y, x))

ne (x, y) = wedge (vee (x, y), neg (wedge (x, y)))