| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Test.Properties
- 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
symmetric :: Eq b => (t -> t -> b) -> t -> t -> Bool Source
f a b == f b a
symmetric (==) :: Int -> Int -> Bool
symmetric (+) :: Int -> Int -> Bool
antisymmetric :: Eq b => (b -> b -> b) -> b -> b -> Bool Source
symmetric f a ba == b
antisymmetric (-) :: Int -> Int -> Bool
inverts :: Eq b => (b -> b1) -> (b1 -> b) -> b -> Bool Source
a == (g . f) a
inverts pred succ :: Int -> Bool
inverts succ pred :: Char -> Bool
involutive :: Eq b => (b -> b) -> b -> Bool Source
nonDecreasing :: Ord b => (b -> b) -> b -> Bool Source
a <= f a
nonDecreasing id
nonDecreasing (\x -> if even x then x else succ x)
increasing :: Ord b => (b -> b) -> b -> Bool Source
a < f a
increasing succ :: Int -> Bool
fixes :: Eq b => (b -> b) -> b -> Bool Source
Alias for idempotent
idempotent :: Eq b => (b -> b) -> b -> Bool Source
f a == f (f a)
idempotent (const "thingy")
idempotent (*0)
idempotent (&& False)
associative :: Eq b => (b -> b -> b) -> b -> b -> b -> Bool Source
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 Source
identity f eassociative f a b c
monoidal (&&) True
monoidal (||) False
monoidal (++) []
monoidal (*) 1
equalizes :: Eq b => (a -> b) -> (t -> a) -> (t -> a) -> t -> Bool Source
eq (f a) == eq (g a)
equalizes even (*2) (*4)
equalizes (const [4]) (take 7) (take 12)
symmetricBy :: Eq b => (a -> b) -> (t -> t -> a) -> t -> t -> Bool Source
antisymmetricBy :: Eq b => (t -> b) -> (t -> t -> t) -> t -> t -> Bool Source
involutiveBy :: Eq b => (b1 -> b) -> (b1 -> b1) -> b1 -> Bool Source
nonDecreasingBy :: Ord b => (a -> b) -> (a -> a) -> a -> Bool Source
increasingBy :: Ord b => (a -> b) -> (a -> a) -> a -> Bool Source
idempotentBy :: Eq b => (s -> b) -> (s -> s) -> s -> Bool Source
associativeBy :: Eq b => (a -> b) -> (a -> a -> a) -> a -> a -> a -> Bool Source
monoidalBy :: Eq b => (a -> b) -> (a -> a -> a) -> a -> a -> a -> a -> Bool Source
identityBy :: Eq b => (t -> b) -> (t -> t -> t) -> t -> t -> Bool Source