-- Evaluate expressions made of additions and good and bad bits.
-- Sergio Antoy and Michael Hanus
-- Thu Mar  3 16:27:55 PST 2011

-- The value of expressions containing "bad" bits is false.
-- The value of expressions containing only "good" bits is true.
-- The actual value is returned in the second argument of "value".

data Bit = Zero | One

data Expr = Add Expr Expr | Good Bit | Bad Bit

add Zero x = x
add One Zero = One
add One One = Zero

value (Add x y) (add vx vy) = value x vx && value y vy
value (Good x) y | x =:= y = True
value (Bad _) _ = False

test1 | value (Add (Good One) (Good One)) x = x where x free
test2 | value (Add (Good One) (Bad One)) x = x where x free
test3 | value (Add (Good One) (Add (Good One) (Good One))) x = x where x free