Test.Properties

Documentation

symmetric :: Eq b => (t -> t -> b) -> t -> t -> Bool

f a b == f b a

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

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

antisymmetric :: Eq b => (b -> b -> b) -> b -> b -> Bool

symmetric f a b implies a == b

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

inverts :: Eq b => (b -> b1) -> (b1 -> b) -> b -> Bool

a == (g . f) a

inverts pred succ :: Int -> Bool

inverts succ pred :: Char -> Bool

involutive :: Eq b => (b -> b) -> b -> Bool

a == (f . f) a (alternatively, inverts f f)

involutive negate

involutive reverse :: String -> Bool

nonDecreasing :: Ord b => (b -> b) -> b -> Bool

a <= f a

nonDecreasing id

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

increasing :: Ord b => (b -> b) -> b -> Bool

a < f a

increasing succ :: Int -> Bool

fixes :: Eq b => (b -> b) -> b -> Bool

Alias for idempotent

idempotent :: Eq b => (b -> b) -> b -> Bool

f a == f (f a)

idempotent (const "thingy")

idempotent (*0)

idempotent (&& False)

leftId :: Eq b => (t -> b -> b) -> t -> b -> Bool

f e a == a

leftId (+) 0

rightId :: Eq b => (b -> t -> b) -> t -> b -> Bool

f a e == a

rightId (+) 0

identity :: Eq b => (b -> b -> b) -> b -> b -> Bool

leftId f e && rightId f e

identity (+) 0

associative :: Eq b => (b -> b -> b) -> b -> b -> b -> Bool

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

associative (&&)

associative (||)

associative (++)

associative (*)

monoidal :: Eq b => (b -> b -> b) -> b -> b -> b -> b -> Bool

identity f e and associative f a b c

monoidal (&&) True

monoidal (||) False

monoidal (++) []

monoidal (*) 1

isomorphic :: (Eq b, Eq b1) => (b -> b1) -> (b1 -> b) -> b -> b1 -> Bool

a == (f . g) a && b == (g . f) b

isomorphic succ (pred :: Int -> Int)

isomorphic not not

isomorphic reverse (reverse :: String -> String)

isomorphic snd (((),) :: Int -> ((),Int))

partiallyIsomorphic :: Eq b => (b -> b1) -> (b1 -> Maybe b) -> b -> Bool

Just a == (g . f) a

partiallyIsomorphic id Just

partiallyIsomorphic show readMaybe

absorptive :: Eq b => (b -> b -> b) -> (b -> b -> b) -> b -> b -> Bool

f a (g a b) == a && g a (f a b) == a

http://en.wikipedia.org/wiki/Absorption_law

absorptive (&&) (||)

absorptive min max

equalizes :: Eq b => (a -> b) -> (t -> a) -> (t -> a) -> t -> Bool

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

equalizes even (*2) (*4)

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

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 => (a -> b) -> (a -> b1) -> (b1 -> a) -> a -> 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 => (a -> b) -> (a -> a) -> a -> Bool

idempotentBy :: Eq b => (a -> b) -> (a -> a) -> a -> 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

isomorphicBy :: (Eq b, Eq b1) => (b2 -> b) -> (a -> b1) -> (b2 -> a) -> (a -> b2) -> b2 -> a -> Bool

partiallyIsomorphicBy :: Eq b => (a -> b) -> (a -> b1) -> (b1 -> Maybe a) -> a -> Bool

absorptiveBy :: Eq b => (a -> b) -> (a -> a -> a) -> (a -> a -> a) -> a -> a -> Bool

= DocTest Setup

>>> :set -XTupleSections
>>> import Text.Read (readMaybe)