Test.Properties

Synopsis

• symmetric :: Eq b => (t -> t -> b) -> t -> t -> Bool
• antisymmetric :: Eq b => (b -> b -> b) -> b -> b -> Bool
• inverts :: Eq b => (b -> b1) -> (b1 -> b) -> b -> Bool
• involutive :: Eq b => (b -> b) -> b -> Bool
• nonDecreasing :: Ord b => (b -> b) -> b -> Bool
• increasing :: Ord b => (b -> b) -> b -> Bool
• fixes :: Eq b => (b -> b) -> b -> Bool
• idempotent :: Eq b => (b -> b) -> b -> Bool
• leftId :: Eq b => (t -> b -> b) -> t -> b -> Bool
• rightId :: Eq b => (b -> t -> b) -> t -> b -> Bool
• identity :: Eq b => (b -> b -> b) -> b -> b -> Bool
• associative :: Eq b => (b -> b -> b) -> b -> b -> b -> Bool
• monoidal :: Eq b => (b -> b -> b) -> b -> b -> b -> b -> Bool
• equalizes :: Eq b => (a -> b) -> (t -> a) -> (t -> a) -> t -> Bool
• eqBy :: Eq b => (a -> b) -> a -> a -> Bool
• leqBy :: Ord b => (a -> b) -> a -> a -> Bool
• leBy :: Ord b => (a -> b) -> a -> a -> Bool
• symmetricBy :: Eq b => (a -> b) -> (t -> t -> a) -> t -> t -> Bool
• antisymmetricBy :: Eq b => (t -> b) -> (t -> t -> t) -> t -> t -> Bool
• invertsBy :: Eq b => (s -> b) -> (s -> b1) -> (b1 -> s) -> s -> Bool
• involutiveBy :: Eq b => (b1 -> b) -> (b1 -> b1) -> b1 -> Bool
• nonDecreasingBy :: Ord b => (a -> b) -> (a -> a) -> a -> Bool
• increasingBy :: Ord b => (a -> b) -> (a -> a) -> a -> Bool
• fixesBy :: Eq b => (s -> b) -> (s -> s) -> s -> Bool
• idempotentBy :: Eq b => (s -> b) -> (s -> s) -> s -> Bool
• associativeBy :: Eq b => (a -> b) -> (a -> a -> a) -> a -> a -> a -> Bool
• monoidalBy :: Eq b => (a -> b) -> (a -> a -> a) -> a -> a -> a -> a -> Bool
• leftIdBy :: Eq b => (a -> b) -> (t -> a -> a) -> t -> a -> Bool
• rightIdBy :: Eq b => (a -> b) -> (a -> t -> a) -> t -> a -> Bool
• identityBy :: Eq b => (t -> b) -> (t -> t -> t) -> t -> t -> Bool

Documentation

f a b == f b a

symmetric (==) :: Int -> Int -> Bool

symmetric (+)  :: Int -> Int -> Bool

antisymmetric (-) :: Int -> Int -> Bool

a == (g . f) a

inverts pred succ :: Int -> Bool

inverts succ pred :: Char -> Bool

involutive negate

involutive reverse :: String -> Bool

a <= f a

nonDecreasing id

nonDecreasing (\x -> if even x then x else succ x)

a < f a

increasing succ :: Int -> Bool

f a == f (f a)

idempotent (const "thingy")

idempotent (*0)

idempotent (&& False)

f e a == a

leftId (+) 0

f a e == a

rightId (+) 0

leftId f e && rightId f e

identity (+) 0

f a (f b c) == f (f a b) c

associative (&&)

associative (||)

associative (++)

associative (*)

monoidal (&&) True

monoidal (||) False

monoidal (++) []

monoidal (*) 1

eq (f a) == eq (g a)

equalizes even (*2) (*4)

equalizes (const [4]) (take 7) (take 12)