| Safe Haskell | Safe-Inferred |
|---|---|
| Language | Haskell2010 |
Test.Invariant
- (<=>) :: Eq b => (a -> b) -> (a -> b) -> a -> Bool
- (&>) :: Testable b => (a -> Bool) -> (a -> b) -> a -> Property
- idempotent :: Eq a => (a -> a) -> a -> Bool
- pointSymmetric :: (Num a, Num b, Eq b) => (a -> b) -> a -> Bool
- reflectionSymmetric :: (Num a, Eq b) => (a -> b) -> a -> Bool
- monotonicIncreasing :: (Ord a, Ord b) => (a -> b) -> a -> a -> Bool
- monotonicIncreasing' :: (Ord a, Ord b) => (a -> b) -> a -> a -> Bool
- monotonicDecreasing :: (Ord a, Ord b) => (a -> b) -> a -> a -> Bool
- monotonicDecreasing' :: (Ord a, Ord b) => (a -> b) -> a -> a -> Bool
- involutory :: Eq a => (a -> a) -> a -> Bool
- inverts :: Eq a => (b -> a) -> (a -> b) -> a -> Bool
- commutative :: Eq b => (a -> a -> b) -> a -> a -> Bool
- associative :: Eq a => (a -> a -> a) -> a -> a -> a -> Bool
- distributesLeftOver :: Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Bool
- distributesRightOver :: Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Bool
- distributesOver :: Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Bool
- inflating :: ([a] -> [b]) -> [a] -> Bool
- deflating :: ([a] -> [b]) -> [a] -> Bool
- cyclesWithin :: Eq a => (a -> a) -> Int -> a -> Bool
- invariatesOver :: Eq b => (a -> b) -> (a -> a) -> a -> Bool
Documentation
(<=>) :: Eq b => (a -> b) -> (a -> b) -> a -> Bool infix 1 Source
Defines extensional equality. This allows concise, point-free, definitions of laws. For example idempotence:
f <=> f . f
(&>) :: Testable b => (a -> Bool) -> (a -> b) -> a -> Property infix 1 Source
Pointfree version of QuickChecks ==>. This notation reduces a lot of lambdas, for example:
>>>quickCheck $ (/=0) &> not . idempotent (*(2::Int))+++ OK, passed 100 tests.
idempotent :: Eq a => (a -> a) -> a -> Bool Source
Checks whether a function is idempotent.
f(f(x)) == f(x)
>>>quickCheck $ idempotent (abs :: Int -> Int)+++ OK, passed 100 tests.
pointSymmetric :: (Num a, Num b, Eq b) => (a -> b) -> a -> Bool Source
Checks whether a function is pointSymmetric.
f(-x) == -f(x)
>>>quickCheck $ pointSymmetric (^3)+++ OK, passed 100 tests.
reflectionSymmetric :: (Num a, Eq b) => (a -> b) -> a -> Bool Source
Checks whether a function is reflectionSymmetric.
f(x) == f(-x)
>>>quickCheck $ pointSymmetric (^2)+++ OK, passed 100 tests.
monotonicIncreasing :: (Ord a, Ord b) => (a -> b) -> a -> a -> Bool Source
Checks whether a function is monotonicIncreasing.
x >= y, f(x) >= f(y)
>>>quickCheck $ monotonicIncreasing ceiling+++ OK, passed 100 tests.
monotonicIncreasing' :: (Ord a, Ord b) => (a -> b) -> a -> a -> Bool Source
Checks whether a function is strictly monotonicIncreasing'.
x > y, f(x) > f(y)
>>>quickCheck $ monotonicIncreasing' (+1)+++ OK, passed 100 tests.
monotonicDecreasing :: (Ord a, Ord b) => (a -> b) -> a -> a -> Bool Source
Checks whether a function is monotonicDecreasing.
x >= y, f(x) <= f(y)
>>>quickCheck $ monotonicDecreasing (\x -> floor $ negate x)+++ OK, passed 100 tests.
monotonicDecreasing' :: (Ord a, Ord b) => (a -> b) -> a -> a -> Bool Source
Checks whether a function is strictly monotonicDecreasing'.
x > y, f(x) < f(y)
>>>quickCheck $ monotonicDecreasing' (-1)+++ OK, passed 100 tests.
involutory :: Eq a => (a -> a) -> a -> Bool Source
Checks whether a function is involutory.
f(f(x)) = x
>>>quickCheck $ involutory negate+++ OK, passed 100 tests.
inverts :: Eq a => (b -> a) -> (a -> b) -> a -> Bool Source
Checks whether a function is the inverse of another function.
f(g(x)) = x
>>>quickCheck $ (`div` 2) `inverts` (*2)+++ OK, passed 100 tests.
commutative :: Eq b => (a -> a -> b) -> a -> a -> Bool Source
Checks whether an binary operator is commutative.
a * b = b * a
>>>quickCheck $ commutative (+)+++ OK, passed 100 tests.
associative :: Eq a => (a -> a -> a) -> a -> a -> a -> Bool Source
Checks whether an binary operator is associative.
a + (b + c) = (a + b) + c
>>>quickCheck $ associative (+)+++ OK, passed 100 tests.
distributesLeftOver :: Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Bool Source
Checks whether an operator is left-distributive over an other operator.
a * (b + c) = (a * b) + (a * c)
>>>quickCheck $ (*) `distributesLeftOver` (+)+++ OK, passed 100 tests.
distributesRightOver :: Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Bool Source
Checks whether an operator is right-distributive over an other operator.
(b + c) / a = (b / a) + (c / a)
>>>quickCheck $ (/) `distributesRightOver` (+)+++ OK, passed 100 tests.
distributesOver :: Eq a => (a -> a -> a) -> (a -> a -> a) -> a -> a -> a -> Bool Source
Checks whether an operator is distributive over an other operator.
a * (b + c) = (a * b) + (a * c) = (b + c) * a
>>>quickCheck $ (*) `distributesOver` (+)+++ OK, passed 100 tests.
inflating :: ([a] -> [b]) -> [a] -> Bool Source
Checks whether a function increases the size of a foldable.
>>>quickCheck $ inflating (1:)+++ OK, passed 100 tests.
deflating :: ([a] -> [b]) -> [a] -> Bool Source
Checks whether a function decreases the size of a foldable.
>>>quickCheck $ deflating tail+++ OK, passed 100 tests.
cyclesWithin :: Eq a => (a -> a) -> Int -> a -> Bool Source
Checks whether a function is cyclic by applying its result to itself within n applications.
>>>quickCheck $ (`div` 10) `cyclesWithin` 100+++ OK, passed 100 tests.
invariatesOver :: Eq b => (a -> b) -> (a -> a) -> a -> Bool Source
Checks whether a function is invariant over an other function.
>>>quickCheck $ length `invariatesOver` reverse+++ OK, passed 100 tests.