Test.Validity.Property

Documentation

module Data.GenValidity

forAllUnchecked :: (Show a, GenUnchecked a, Testable prop) => (a -> prop) -> Property

forAllValid :: (Show a, GenValid a, Testable prop) => (a -> prop) -> Property

forAllInvalid :: (Show a, GenInvalid a, Testable prop) => (a -> prop) -> Property

Tests for GenValidity instances

genGeneratesValid :: forall a. (Show a, Validity a) => Gen a -> (a -> [a]) -> Property

The given generator generates only valid data points

genGeneratesInvalid :: forall a. (Show a, Validity a) => Gen a -> (a -> [a]) -> Property

The given generator generates only invalid data points

Standard tests involving functions

Standard tests involving validity

producesValidsOnGen :: forall a b. (Show a, Show b, Validity b) => (a -> b) -> Gen a -> (a -> [a]) -> Property

The function produces valid output when the input is generated as specified by the given generator.

producesValidsOnValids :: (Show a, Show b, GenValid a, Validity b) => (a -> b) -> Property

The function produces valid output when the input is generated by genValid

producesValid :: (Show a, Show b, GenUnchecked a, Validity b) => (a -> b) -> Property

The function produces valid output when the input is generated by genUnchecked

producesValidsOnArbitrary :: (Show a, Show b, Arbitrary a, Validity b) => (a -> b) -> Property

The function produces valid output when the input is generated by arbitrary

producesValidsOnGens2 :: (Show a, Show b, Show c, Validity c) => (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property

producesValidsOnValids2 :: (Show a, Show b, Show c, GenValid a, GenValid b, Validity c) => (a -> b -> c) -> Property

producesValid2 :: (Show a, Show b, Show c, GenUnchecked a, GenUnchecked b, Validity c) => (a -> b -> c) -> Property

producesValidsOnArbitrary2 :: (Show a, Show b, Show c, Arbitrary a, Arbitrary b, Validity c) => (a -> b -> c) -> Property

producesValidsOnGens3 :: (Show a, Show b, Show c, Show d, Validity d) => (a -> b -> c -> d) -> Gen (a, b, c) -> ((a, b, c) -> [(a, b, c)]) -> Property

producesValidsOnValids3 :: (Show a, Show b, Show c, Show d, GenValid a, GenValid b, GenValid c, Validity d) => (a -> b -> c -> d) -> Property

producesValid3 :: (Show a, Show b, Show c, Show d, GenUnchecked a, GenUnchecked b, GenUnchecked c, Validity d) => (a -> b -> c -> d) -> Property

producesValidsOnArbitrary3 :: (Show a, Show b, Show c, Show d, Arbitrary a, Arbitrary b, Arbitrary c, Validity d) => (a -> b -> c -> d) -> Property

Standard tests involving functions that can fail

class CanFail f where

A class of types that are the result of functions that can fail

Minimal complete definition

hasFailed, resultIfSucceeded

Methods

hasFailed :: f a -> Bool

resultIfSucceeded :: f a -> Maybe a

Instances

CanFail Maybe

Defined in Test.Validity.Types

Methods

hasFailed :: Maybe a -> Bool

resultIfSucceeded :: Maybe a -> Maybe a

CanFail (Either e)

Defined in Test.Validity.Types

Methods

hasFailed :: Either e a -> Bool

resultIfSucceeded :: Either e a -> Maybe a

succeedsOnGen :: (Show a, Show b, Show (f b), CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property

The function succeeds if the input is generated by the given generator

succeedsOnValid :: (Show a, Show b, Show (f b), GenValid a, CanFail f) => (a -> f b) -> Property

The function succeeds if the input is generated by genValid

succeeds :: (Show a, Show b, Show (f b), GenUnchecked a, CanFail f) => (a -> f b) -> Property

The function succeeds if the input is generated by genUnchecked

succeedsOnArbitrary :: (Show a, Show b, Show (f b), Arbitrary a, CanFail f) => (a -> f b) -> Property

The function succeeds if the input is generated by arbitrary

succeedsOnGens2 :: (Show a, Show b, Show c, Show (f c), CanFail f) => (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property

succeedsOnValids2 :: (Show a, Show b, Show c, Show (f c), GenValid a, GenValid b, CanFail f) => (a -> b -> f c) -> Property

succeeds2 :: (Show a, Show b, Show c, Show (f c), GenUnchecked a, GenUnchecked b, CanFail f) => (a -> b -> f c) -> Property

succeedsOnArbitrary2 :: (Show a, Show b, Show c, Show (f c), Arbitrary a, Arbitrary b, CanFail f) => (a -> b -> f c) -> Property

failsOnGen :: (Show a, Show b, Show (f b), CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property

The function fails if the input is generated by the given generator

failsOnInvalid :: (Show a, Show b, Show (f b), GenInvalid a, CanFail f) => (a -> f b) -> Property

The function fails if the input is generated by genInvalid

failsOnGens2 :: (Show a, Show b, Show c, Show (f c), CanFail f) => (a -> b -> f c) -> Gen a -> (a -> [a]) -> Gen b -> (b -> [b]) -> Property

failsOnInvalid2 :: (Show a, Show b, Show c, Show (f c), GenInvalid a, GenInvalid b, CanFail f) => (a -> b -> f c) -> Property

validIfSucceedsOnGen :: (Show a, Show b, Show (f b), Validity b, CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property

The function produces output that satisfies isValid if it is given input that is generated by the given generator.

validIfSucceedsOnValid :: (Show a, Show b, Show (f b), GenValid a, Validity b, CanFail f) => (a -> f b) -> Property

The function produces output that satisfies isValid if it is given input that is generated by arbitrary.

validIfSucceedsOnArbitrary :: (Show a, Show b, Show (f b), Arbitrary a, Validity b, CanFail f) => (a -> f b) -> Property

The function produces output that satisfies isValid if it is given input that is generated by arbitrary.

validIfSucceeds :: (Show a, Show b, Show (f b), GenUnchecked a, Validity b, CanFail f) => (a -> f b) -> Property

The function produces output that satisfies isValid if it is given input that is generated by genUnchecked.

validIfSucceedsOnGens2 :: (Show a, Show b, Show c, Show (f c), Validity c, CanFail f) => (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property

validIfSucceedsOnValids2 :: (Show a, Show b, Show c, Show (f c), GenValid a, GenValid b, Validity c, CanFail f) => (a -> b -> f c) -> Property

validIfSucceeds2 :: (Show a, Show b, Show c, Show (f c), GenUnchecked a, GenUnchecked b, Validity c, CanFail f) => (a -> b -> f c) -> Property

validIfSucceedsOnArbitrary2 :: (Show a, Show b, Show c, Show (f c), Arbitrary a, Arbitrary b, Validity c, CanFail f) => (a -> b -> f c) -> Property

validIfSucceedsOnGens3 :: (Show a, Show b, Show c, Show d, Show (f d), Validity d, CanFail f) => (a -> b -> c -> f d) -> Gen (a, b, c) -> ((a, b, c) -> [(a, b, c)]) -> Property

validIfSucceedsOnValids3 :: (Show a, Show b, Show c, Show d, Show (f d), GenValid a, GenValid b, GenValid c, Validity d, CanFail f) => (a -> b -> c -> f d) -> Property

validIfSucceeds3 :: (Show a, Show b, Show c, Show d, Show (f d), GenUnchecked a, GenUnchecked b, GenUnchecked c, Validity d, CanFail f) => (a -> b -> c -> f d) -> Property

validIfSucceedsOnArbitrary3 :: (Show a, Show b, Show c, Show d, Show (f d), Arbitrary a, Arbitrary b, Arbitrary c, Validity d, CanFail f) => (a -> b -> c -> f d) -> Property

Standard tests involving equivalence of functions

Simple functions

One argument

equivalentOnGen :: (Show a, Eq a, Show b, Eq b) => (a -> b) -> (a -> b) -> Gen a -> (a -> [a]) -> Property

equivalentOnValid :: (Show a, Eq a, GenValid a, Show b, Eq b) => (a -> b) -> (a -> b) -> Property

equivalent :: (Show a, Eq a, GenUnchecked a, Show b, Eq b) => (a -> b) -> (a -> b) -> Property

equivalentOnArbitrary :: (Show a, Eq a, Arbitrary a, Show b, Eq b) => (a -> b) -> (a -> b) -> Property

equivalentOnArbitrary ((* 2) . (+ 1)) ((+ 2) . (* 2) :: Int -> Int)

Two arguments

equivalentOnGens2 :: (Show a, Show b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property

equivalentOnValids2 :: (Show a, GenValid a, Show b, GenValid b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Property

equivalent2 :: (Show a, GenUnchecked a, Show b, GenUnchecked b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Property

equivalentOnArbitrary2 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Property

equivalentOnArbitrary2 (+) ((+) :: Int -> Int -> Int)

Three arguments

equivalentOnGens3 :: (Show a, Show b, Show c, Show d, Eq d) => (a -> b -> c -> d) -> (a -> b -> c -> d) -> Gen (a, b, c) -> ((a, b, c) -> [(a, b, c)]) -> Property

equivalentOnValids3 :: (Show a, GenValid a, Show b, GenValid b, Show c, GenValid c, Show d, Eq d) => (a -> b -> c -> d) -> (a -> b -> c -> d) -> Property

equivalent3 :: (Show a, GenUnchecked a, Show b, GenUnchecked b, Show c, GenUnchecked c, Show d, Eq d) => (a -> b -> c -> d) -> (a -> b -> c -> d) -> Property

equivalentOnArbitrary3 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Arbitrary c, Show d, Eq d) => (a -> b -> c -> d) -> (a -> b -> c -> d) -> Property

First function can fail

One argument

equivalentWhenFirstSucceedsOnGen :: (Show a, Eq a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Gen a -> (a -> [a]) -> Property

equivalentWhenFirstSucceedsOnValid :: (Show a, Eq a, GenValid a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Property

equivalentWhenFirstSucceeds :: (Show a, Eq a, GenUnchecked a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Property

equivalentWhenFirstSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Property

Two arguments

equivalentWhenFirstSucceedsOnGens2 :: (Show a, Eq a, Show b, Eq b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property

equivalentWhenFirstSucceedsOnValids2 :: (Show a, Eq a, GenValid a, Show b, Eq b, GenValid b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> c) -> Property

equivalentWhenFirstSucceeds2 :: (Show a, Eq a, GenUnchecked a, Show b, Eq b, GenUnchecked b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> c) -> Property

equivalentWhenFirstSucceedsOnArbitrary2 :: (Show a, Eq a, Arbitrary a, Show b, Eq b, Arbitrary b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> c) -> Property

Second function can fail

One argument

equivalentWhenSecondSucceedsOnGen :: (Show a, Eq a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Gen a -> (a -> [a]) -> Property

equivalentWhenSecondSucceedsOnValid :: (Show a, Eq a, GenValid a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Property

equivalentWhenSecondSucceeds :: (Show a, Eq a, GenUnchecked a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Property

equivalentWhenSecondSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Property

Two arguments

equivalentWhenSecondSucceedsOnGens2 :: (Show a, Eq a, Show b, Eq b, Show c, Eq c, CanFail f) => (a -> b -> c) -> (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property

equivalentWhenSecondSucceedsOnValids2 :: (Show a, Eq a, GenValid a, Show b, Eq b, GenValid b, Show c, Eq c, CanFail f) => (a -> b -> c) -> (a -> b -> f c) -> Property

equivalentWhenSecondSucceeds2 :: (Show a, Eq a, GenUnchecked a, Show b, Eq b, GenUnchecked b, Show c, Eq c, CanFail f) => (a -> b -> c) -> (a -> b -> f c) -> Property

equivalentWhenSecondSucceedsOnArbitrary2 :: (Show a, Eq a, Arbitrary a, Show b, Eq b, Arbitrary b, Show c, Eq c, CanFail f) => (a -> b -> c) -> (a -> b -> f c) -> Property

Both functions can fail

One argument

equivalentWhenSucceedOnGen :: (Show a, Eq a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Gen a -> (a -> [a]) -> Property

equivalentWhenSucceedOnValid :: (Show a, Eq a, GenValid a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Property

equivalentWhenSucceed :: (Show a, Eq a, GenUnchecked a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Property

equivalentWhenSucceedOnArbitrary :: (Show a, Eq a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Property

Two arguments

equivalentWhenSucceedOnGens2 :: (Show a, Eq a, Show b, Eq b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> f c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property

equivalentWhenSucceedOnValids2 :: (Show a, Eq a, GenValid a, Show b, Eq b, GenValid b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> f c) -> Property

equivalentWhenSucceed2 :: (Show a, Eq a, GenUnchecked a, Show b, Eq b, GenUnchecked b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> f c) -> Property

equivalentWhenSucceedOnArbitrary2 :: (Show a, Eq a, Arbitrary a, Show b, Eq b, Arbitrary b, Show c, Eq c, CanFail f) => (a -> b -> f c) -> (a -> b -> f c) -> Property

Standard tests involving inverse functions

inverseFunctionsOnGen :: (Show a, Eq a) => (a -> b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property

inverseFunctionsOnValid :: (Show a, Eq a, GenValid a) => (a -> b) -> (b -> a) -> Property

inverseFunctions :: (Show a, Eq a, GenUnchecked a) => (a -> b) -> (b -> a) -> Property

inverseFunctionsOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> b) -> (b -> a) -> Property

id is its own inverse function for every type: prop> inverseFunctionsOnArbitrary id (id :: Int -> Int)

inverseFunctionsIfFirstSucceedsOnGen :: (Show a, Eq a, CanFail f) => (a -> f b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property

inverseFunctionsIfFirstSucceedsOnValid :: (Show a, Eq a, GenValid a, CanFail f) => (a -> f b) -> (b -> a) -> Property

inverseFunctionsIfFirstSucceeds :: (Show a, Eq a, GenUnchecked a, CanFail f) => (a -> f b) -> (b -> a) -> Property

inverseFunctionsIfFirstSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f) => (a -> f b) -> (b -> a) -> Property

inverseFunctionsIfSecondSucceedsOnGen :: (Show a, Eq a, CanFail f) => (a -> b) -> (b -> f a) -> Gen a -> (a -> [a]) -> Property

inverseFunctionsIfSecondSucceedsOnValid :: (Show a, Eq a, GenValid a, CanFail f) => (a -> b) -> (b -> f a) -> Property

inverseFunctionsIfSecondSucceeds :: (Show a, Eq a, GenUnchecked a, CanFail f) => (a -> b) -> (b -> f a) -> Property

inverseFunctionsIfSecondSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f) => (a -> b) -> (b -> f a) -> Property

inverseFunctionsIfSucceedOnGen :: (Show a, Eq a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Gen a -> (a -> [a]) -> Property

inverseFunctionsIfSucceedOnValid :: (Show a, Eq a, GenValid a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Property

inverseFunctionsIfSucceed :: (Show a, Eq a, GenUnchecked a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Property

inverseFunctionsIfSucceedOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Property

Properties involving idempotence

idempotentOnGen :: (Show a, Eq a) => (a -> a) -> Gen a -> (a -> [a]) -> Property

idempotentOnValid :: (Show a, Eq a, GenValid a) => (a -> a) -> Property

idempotent :: (Show a, Eq a, GenUnchecked a) => (a -> a) -> Property

idempotentOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a) -> Property

id is idempotent for any type:

idempotentOnArbitrary (id :: Int -> Int)

const, given any input, is idempotent for any type as well:

\int -> idempotentOnArbitrary (const int :: Int -> Int)

Properties of relations

Reflexivity

reflexiveOnElem

Arguments

:: (a -> a -> Bool)

A relation

-> a

An element

-> Bool

\[ Reflexive(\prec) \quad\equiv\quad \forall a: (a \prec a) \]

reflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property

reflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

reflexivityOnValid ((<=) :: Double -> Double -> Bool)

reflexivityOnValid ((==) :: Double -> Double -> Bool)

reflexivityOnValid ((>=) :: Double -> Double -> Bool)

reflexivityOnValid (Data.List.isPrefixOf :: [Double] -> [Double] -> Bool)

reflexivityOnValid (Data.List.isSuffixOf :: [Double] -> [Double] -> Bool)

reflexivityOnValid (Data.List.isInfixOf :: [Double] -> [Double] -> Bool)

reflexivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property

reflexivity ((<=) :: Int -> Int -> Bool)

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

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

reflexivity (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)

reflexivity (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)

reflexivity (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)

reflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

reflexivityOnArbitrary ((<=) :: Int -> Int -> Bool)

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

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

reflexivityOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)

reflexivityOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)

reflexivityOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)

Transitivity

transitiveOnElems

Arguments

:: (a -> a -> Bool)

A relation

-> a

-> a

-> a

Three elements

-> Bool

\[ Transitive(\prec) \quad\equiv\quad \forall a, b, c: ((a \prec b) \wedge (b \prec c)) \Rightarrow (a \prec c) \]

transitivityOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property

transitivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

transitivityOnValid ((>) :: Double -> Double -> Bool)

transitivityOnValid ((>=) :: Double -> Double -> Bool)

transitivityOnValid ((==) :: Double -> Double -> Bool)

transitivityOnValid ((<=) :: Double -> Double -> Bool)

transitivityOnValid ((<) :: Double -> Double -> Bool)

transitivityOnValid (Data.List.isPrefixOf :: [Double] -> [Double] -> Bool)

transitivityOnValid (Data.List.isSuffixOf :: [Double] -> [Double] -> Bool)

transitivityOnValid (Data.List.isInfixOf :: [Double] -> [Double] -> Bool)

transitivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property

transitivity ((>) :: Int -> Int -> Bool)

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

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

transitivity ((<=) :: Int -> Int -> Bool)

transitivity ((<) :: Int -> Int -> Bool)

transitivity (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)

transitivity (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)

transitivity (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)

transitivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

transitivityOnArbitrary ((>) :: Int -> Int -> Bool)

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

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

transitivityOnArbitrary ((<=) :: Int -> Int -> Bool)

transitivityOnArbitrary ((<) :: Int -> Int -> Bool)

transitivityOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)

transitivityOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)

transitivityOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)

Antisymmetry

antisymmetricOnElemsWithEquality

Arguments

:: (a -> a -> Bool)

A relation

-> (a -> a -> Bool)

An equivalence relation

-> a

-> a

Two elements

-> Bool

\[ Antisymmetric(\prec, \doteq) \quad\equiv\quad \forall a, b: ((a \prec b) \wedge (b \prec a)) \Rightarrow (a \doteq b) \]

antisymmetryOnGensWithEquality :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> a -> Bool) -> (a -> [a]) -> Property

antisymmetryOnGens :: (Show a, Eq a) => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property

antisymmetryOnValid :: (Show a, Eq a, GenValid a) => (a -> a -> Bool) -> Property

antisymmetryOnValid ((>) :: Double -> Double -> Bool)

antisymmetryOnValid ((>=) :: Double -> Double -> Bool)

antisymmetryOnValid ((<=) :: Double -> Double -> Bool)

antisymmetryOnValid ((<) :: Double -> Double -> Bool)

antisymmetryOnValid (Data.List.isPrefixOf :: [Double] -> [Double] -> Bool)

antisymmetryOnValid (Data.List.isSuffixOf :: [Double] -> [Double] -> Bool)

antisymmetryOnValid (Data.List.isInfixOf :: [Double] -> [Double] -> Bool)

antisymmetry :: (Show a, Eq a, GenUnchecked a) => (a -> a -> Bool) -> Property

antisymmetry ((>) :: Int -> Int -> Bool)

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

antisymmetry ((<=) :: Int -> Int -> Bool)

antisymmetry ((<) :: Int -> Int -> Bool)

antisymmetry (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)

antisymmetry (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)

antisymmetry (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)

antisymmetry ((\x y -> even x && odd y) :: Int -> Int -> Bool)

antisymmetryOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> Bool) -> Property

antisymmetryOnArbitrary ((>) :: Int -> Int -> Bool)

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

antisymmetryOnArbitrary ((<=) :: Int -> Int -> Bool)

antisymmetryOnArbitrary ((<) :: Int -> Int -> Bool)

antisymmetryOnArbitrary (Data.List.isPrefixOf :: [Int] -> [Int] -> Bool)

antisymmetryOnArbitrary (Data.List.isSuffixOf :: [Int] -> [Int] -> Bool)

antisymmetryOnArbitrary (Data.List.isInfixOf :: [Int] -> [Int] -> Bool)

antisymmetryOnArbitrary ((\x y -> even x && odd y) :: Int -> Int -> Bool)

Antireflexivity

antireflexiveOnElem

Arguments

:: (a -> a -> Bool)

A relation

-> a

An element

-> Bool

\[ Antireflexive(\prec) \quad\equiv\quad \forall a: \neg (a \prec a) \]

antireflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property

antireflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

antireflexivityOnValid ((<) :: Double -> Double -> Bool)

antireflexivityOnValid ((/=) :: Double -> Double -> Bool)

antireflexivityOnValid ((>) :: Double -> Double -> Bool)

antireflexivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property

antireflexivity ((<) :: Int -> Int -> Bool)

antireflexivity ((/=) :: Int -> Int -> Bool)

antireflexivity ((>) :: Int -> Int -> Bool)

antireflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

antireflexivityOnArbitrary ((<) :: Int -> Int -> Bool)

antireflexivityOnArbitrary ((/=) :: Int -> Int -> Bool)

antireflexivityOnArbitrary ((>) :: Int -> Int -> Bool)

Symmetry

symmetricOnElems

Arguments

:: (a -> a -> Bool)

A relation

-> a

-> a

Two elements

-> Bool

\[ Symmetric(\prec) \quad\equiv\quad \forall a, b: (a \prec b) \Leftrightarrow (b \prec a) \]

symmetryOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property

symmetryOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property

symmetryOnValid ((==) :: Double -> Double -> Bool)

symmetryOnValid ((/=) :: Double -> Double -> Bool)

symmetry :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property

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

symmetry ((/=) :: Int -> Int -> Bool)

symmetryOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property

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

symmetryOnArbitrary ((/=) :: Int -> Int -> Bool)

Properties of operations

Identity element

Left Identity

leftIdentityOnElemWithEquality

Arguments

:: (b -> a -> a)

A binary operation

-> (a -> a -> Bool)

An equality

-> b

A candidate left-identity

-> a

An element

-> Bool

\[ LeftIdentity(\star, \doteq, b) \quad\equiv\quad \forall a: (b \star a) \doteq a \]

leftIdentityOnGenWithEquality

Arguments

:: Show a

=> (b -> a -> a)

A binary operation

-> (a -> a -> Bool)

An equality

-> b

A candidate left-identity

-> Gen a

-> (a -> [a])

-> Property

leftIdentityOnGen

Arguments

:: (Show a, Eq a)

=> (b -> a -> a)

A binary operation

-> b

A candidate left-identity

-> Gen a

-> (a -> [a])

-> Property

leftIdentityOnValid :: (Show a, Eq a, GenValid a) => (b -> a -> a) -> b -> Property

leftIdentityOnValid (flip ((^) :: Double -> Int -> Double)) 1

leftIdentity :: (Show a, Eq a, GenUnchecked a) => (b -> a -> a) -> b -> Property

leftIdentity (flip ((^) :: Int -> Int -> Int)) 1

leftIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (b -> a -> a) -> b -> Property

leftIdentityOnArbitrary (flip ((^) :: Int -> Int -> Int)) 1

Right Identity

rightIdentityOnElemWithEquality

Arguments

:: (a -> b -> a)

A binary operation

-> (a -> a -> Bool)

An equality

-> b

A candidate right-identity

-> a

An element

-> Bool

\[ RightIdentity(\star, \doteq, b) \quad\equiv\quad \forall a: (a \star b) \doteq a \]

rightIdentityOnGenWithEquality

Arguments

:: Show a

=> (a -> b -> a)

A binary operation

-> (a -> a -> Bool)

An equality

-> b

A candidate right-identity

-> Gen a

-> (a -> [a])

-> Property

rightIdentityOnGen

Arguments

:: (Show a, Eq a)

=> (a -> b -> a)

A binary operation

-> b

A candidate right-identity

-> Gen a

-> (a -> [a])

-> Property

rightIdentityOnValid :: (Show a, Eq a, GenValid a) => (a -> b -> a) -> b -> Property

rightIdentityOnValid ((^) :: Double -> Int -> Double) 1

rightIdentity :: (Show a, Eq a, GenUnchecked a) => (a -> b -> a) -> b -> Property

rightIdentity ((^) :: Int -> Int -> Int) 1

rightIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> b -> a) -> b -> Property

rightIdentityOnArbitrary ((^) :: Int -> Int -> Int) 1

Identity

identityOnGen :: (Show a, Eq a) => (a -> a -> a) -> a -> Gen a -> (a -> [a]) -> Property

\[ Identity(\star, \doteq, b) \quad\equiv\quad LeftIdentity(\star, \doteq, b) \wedge RightIdentity(\star, \doteq, b) \]

identityOnValid :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> a -> Property

identityOnValid ((*) :: Double -> Double -> Double) 1

identityOnValid ((+) :: Double -> Double -> Double) 0

identity :: (Show a, Eq a, GenUnchecked a) => (a -> a -> a) -> a -> Property

identity ((*) :: Int -> Int -> Int) 1

identity ((+) :: Int -> Int -> Int) 0

identityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> a -> Property

identityOnArbitrary ((*) :: Int -> Int -> Int) 1

identityOnArbitrary ((+) :: Int -> Int -> Int) 0

Associativity

associativeOnGens :: (Show a, Eq a) => (a -> a -> a) -> Gen (a, a, a) -> ((a, a, a) -> [(a, a, a)]) -> Property

\[ Associative(\star) \quad\equiv\quad \forall a, b, c: (a \star b) \star c = a \star (b \star c) \]

associativeOnValids :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> Property

associative :: (Show a, Eq a, GenUnchecked a) => (a -> a -> a) -> Property

associative ((*) :: Int -> Int -> Int)

associative ((+) :: Int -> Int -> Int)

associativeOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> Property

associativeOnArbitrary ((*) :: Int -> Int -> Int)

associativeOnArbitrary ((+) :: Int -> Int -> Int)

Commutativity

commutativeOnGens :: (Show a, Eq a) => (a -> a -> a) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property

\[ Commutative(\star) \quad\equiv\quad \forall a, b: a \star b = b \star a \]

commutativeOnValids :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> Property

commutative ((+) :: Double -> Double -> Double)

commutative ((*) :: Double -> Double -> Double)

commutative :: (Show a, Eq a, GenUnchecked a) => (a -> a -> a) -> Property

commutative ((+) :: Int -> Int -> Int)

commutative ((*) :: Int -> Int -> Int)

commutativeOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> Property

commutativeOnArbitrary ((+) :: Int -> Int -> Int)

commutativeOnArbitrary ((*) :: Int -> Int -> Int)