Safe Haskell | None |
---|---|
Language | Haskell2010 |
- Tests for GenValidity instances
- Standard tests involving functions
- Properties of relations
- Properties of operations
Synopsis
- 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
- genGeneratesValid :: forall a. (Show a, Validity a) => Gen a -> Property
- genGeneratesInvalid :: forall a. (Show a, Validity a) => Gen a -> Property
- producesValidsOnGen :: forall a b. (Show a, Show b, Validity b) => (a -> b) -> Gen a -> (a -> [a]) -> Property
- producesValidsOnValids :: (Show a, Show b, GenValid a, Validity b) => (a -> b) -> Property
- producesValid :: (Show a, Show b, GenUnchecked a, Validity b) => (a -> b) -> Property
- producesValidsOnArbitrary :: (Show a, Show b, Arbitrary a, Validity b) => (a -> b) -> Property
- 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
- class CanFail f where
- hasFailed :: f a -> Bool
- resultIfSucceeded :: f a -> Maybe a
- succeedsOnGen :: (Show a, Show b, Show (f b), CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property
- succeedsOnValid :: (Show a, Show b, Show (f b), GenValid a, CanFail f) => (a -> f b) -> Property
- succeeds :: (Show a, Show b, Show (f b), GenUnchecked a, CanFail f) => (a -> f b) -> Property
- succeedsOnArbitrary :: (Show a, Show b, Show (f b), Arbitrary a, CanFail f) => (a -> f b) -> Property
- 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
- failsOnInvalid :: (Show a, Show b, Show (f b), GenInvalid a, CanFail f) => (a -> f b) -> Property
- 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), GenUnchecked a, GenUnchecked b, 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
- validIfSucceedsOnValid :: (Show a, Show b, Show (f b), GenValid a, Validity b, CanFail f) => (a -> f b) -> Property
- validIfSucceedsOnArbitrary :: (Show a, Show b, Show (f b), Arbitrary a, Validity b, CanFail f) => (a -> f b) -> Property
- validIfSucceeds :: (Show a, Show b, Show (f b), GenUnchecked a, Validity b, CanFail f) => (a -> f b) -> Property
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- reflexiveOnElem :: (a -> a -> Bool) -> a -> Bool
- reflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
- reflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
- reflexivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property
- reflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
- transitiveOnElems :: (a -> a -> Bool) -> a -> a -> a -> Bool
- transitivityOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property
- transitivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
- transitivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property
- transitivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
- antisymmetricOnElemsWithEquality :: (a -> a -> Bool) -> (a -> a -> Bool) -> a -> a -> Bool
- 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
- antisymmetry :: (Show a, Eq a, GenUnchecked a) => (a -> a -> Bool) -> Property
- antisymmetryOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> Bool) -> Property
- antireflexiveOnElem :: (a -> a -> Bool) -> a -> Bool
- antireflexivityOnGen :: Show a => (a -> a -> Bool) -> Gen a -> (a -> [a]) -> Property
- antireflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
- antireflexivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property
- antireflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
- symmetricOnElems :: (a -> a -> Bool) -> a -> a -> Bool
- symmetryOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property
- symmetryOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property
- symmetry :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property
- symmetryOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property
- leftIdentityOnElemWithEquality :: (b -> a -> a) -> (a -> a -> Bool) -> b -> a -> Bool
- leftIdentityOnGenWithEquality :: Show a => (b -> a -> a) -> (a -> a -> Bool) -> b -> Gen a -> (a -> [a]) -> Property
- leftIdentityOnGen :: (Show a, Eq a) => (b -> a -> a) -> b -> Gen a -> (a -> [a]) -> Property
- leftIdentityOnValid :: (Show a, Eq a, GenValid a) => (b -> a -> a) -> b -> Property
- leftIdentity :: (Show a, Eq a, GenUnchecked a) => (b -> a -> a) -> b -> Property
- leftIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (b -> a -> a) -> b -> Property
- rightIdentityOnElemWithEquality :: (a -> b -> a) -> (a -> a -> Bool) -> b -> a -> Bool
- rightIdentityOnGenWithEquality :: Show a => (a -> b -> a) -> (a -> a -> Bool) -> b -> Gen a -> (a -> [a]) -> Property
- rightIdentityOnGen :: (Show a, Eq a) => (a -> b -> a) -> b -> Gen a -> (a -> [a]) -> Property
- rightIdentityOnValid :: (Show a, Eq a, GenValid a) => (a -> b -> a) -> b -> Property
- rightIdentity :: (Show a, Eq a, GenUnchecked a) => (a -> b -> a) -> b -> Property
- rightIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> b -> a) -> b -> Property
- identityOnGen :: (Show a, Eq a) => (a -> a -> a) -> a -> Gen a -> (a -> [a]) -> Property
- identityOnValid :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> a -> Property
- identity :: (Show a, Eq a, GenUnchecked a) => (a -> a -> a) -> a -> Property
- identityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> a -> Property
- associativeOnGens :: (Show a, Eq a) => (a -> a -> a) -> Gen (a, a, a) -> ((a, a, a) -> [(a, a, a)]) -> Property
- associativeOnValids :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> Property
- associative :: (Show a, Eq a, GenUnchecked a) => (a -> a -> a) -> Property
- associativeOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> Property
- commutativeOnGens :: (Show a, Eq a) => (a -> a -> a) -> Gen (a, a) -> ((a, a) -> [(a, a)]) -> Property
- commutativeOnValids :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> Property
- commutative :: (Show a, Eq a, GenUnchecked a) => (a -> a -> a) -> Property
- commutativeOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> Property
Documentation
module Data.GenValidity
forAllUnchecked :: (Show a, GenUnchecked a, Testable prop) => (a -> prop) -> Property Source #
forAllInvalid :: (Show a, GenInvalid a, Testable prop) => (a -> prop) -> Property Source #
Tests for GenValidity instances
genGeneratesValid :: forall a. (Show a, Validity a) => Gen a -> Property Source #
The given generator generates only valid data points
genGeneratesInvalid :: forall a. (Show a, Validity a) => Gen a -> Property Source #
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 Source #
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 Source #
The function produces valid output when the input is generated by
genValid
producesValid :: (Show a, Show b, GenUnchecked a, Validity b) => (a -> b) -> Property Source #
The function produces valid output when the input is generated by
genUnchecked
producesValidsOnArbitrary :: (Show a, Show b, Arbitrary a, Validity b) => (a -> b) -> Property Source #
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 Source #
producesValidsOnValids2 :: (Show a, Show b, Show c, GenValid a, GenValid b, Validity c) => (a -> b -> c) -> Property Source #
producesValid2 :: (Show a, Show b, Show c, GenUnchecked a, GenUnchecked b, Validity c) => (a -> b -> c) -> Property Source #
producesValidsOnArbitrary2 :: (Show a, Show b, Show c, Arbitrary a, Arbitrary b, Validity c) => (a -> b -> c) -> Property Source #
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 Source #
producesValidsOnValids3 :: (Show a, Show b, Show c, Show d, GenValid a, GenValid b, GenValid c, Validity d) => (a -> b -> c -> d) -> Property Source #
producesValid3 :: (Show a, Show b, Show c, Show d, GenUnchecked a, GenUnchecked b, GenUnchecked c, Validity d) => (a -> b -> c -> d) -> Property Source #
producesValidsOnArbitrary3 :: (Show a, Show b, Show c, Show d, Arbitrary a, Arbitrary b, Arbitrary c, Validity d) => (a -> b -> c -> d) -> Property Source #
Standard tests involving functions that can fail
class CanFail f where Source #
A class of types that are the result of functions that can fail
succeedsOnGen :: (Show a, Show b, Show (f b), CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property Source #
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 Source #
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 Source #
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 Source #
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 Source #
succeedsOnValids2 :: (Show a, Show b, Show c, Show (f c), GenValid a, GenValid b, CanFail f) => (a -> b -> f c) -> Property Source #
succeeds2 :: (Show a, Show b, Show c, Show (f c), GenUnchecked a, GenUnchecked b, CanFail f) => (a -> b -> f c) -> Property Source #
succeedsOnArbitrary2 :: (Show a, Show b, Show c, Show (f c), Arbitrary a, Arbitrary b, CanFail f) => (a -> b -> f c) -> Property Source #
failsOnGen :: (Show a, Show b, Show (f b), CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property Source #
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 Source #
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 Source #
failsOnInvalid2 :: (Show a, Show b, Show c, Show (f c), GenUnchecked a, GenUnchecked b, GenInvalid a, GenInvalid b, CanFail f) => (a -> b -> f c) -> Property Source #
validIfSucceedsOnGen :: (Show a, Show b, Show (f b), Validity b, CanFail f) => (a -> f b) -> Gen a -> (a -> [a]) -> Property Source #
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 Source #
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 Source #
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 Source #
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 Source #
validIfSucceedsOnValids2 :: (Show a, Show b, Show c, Show (f c), GenValid a, GenValid b, Validity c, CanFail f) => (a -> b -> f c) -> Property Source #
validIfSucceeds2 :: (Show a, Show b, Show c, Show (f c), GenUnchecked a, GenUnchecked b, Validity c, CanFail f) => (a -> b -> f c) -> Property Source #
validIfSucceedsOnArbitrary2 :: (Show a, Show b, Show c, Show (f c), Arbitrary a, Arbitrary b, Validity c, CanFail f) => (a -> b -> f c) -> Property Source #
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 Source #
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 Source #
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 Source #
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 Source #
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 Source #
equivalentOnValid :: (Show a, Eq a, GenValid a, Show b, Eq b) => (a -> b) -> (a -> b) -> Property Source #
equivalent :: (Show a, Eq a, GenUnchecked a, Show b, Eq b) => (a -> b) -> (a -> b) -> Property Source #
equivalentOnArbitrary :: (Show a, Eq a, Arbitrary a, Show b, Eq b) => (a -> b) -> (a -> b) -> Property Source #
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 Source #
equivalentOnValids2 :: (Show a, GenValid a, Show b, GenValid b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Property Source #
equivalent2 :: (Show a, GenUnchecked a, Show b, GenUnchecked b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Property Source #
equivalentOnArbitrary2 :: (Show a, Arbitrary a, Show b, Arbitrary b, Show c, Eq c) => (a -> b -> c) -> (a -> b -> c) -> Property Source #
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 Source #
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 Source #
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 Source #
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 Source #
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 Source #
equivalentWhenFirstSucceedsOnValid :: (Show a, Eq a, GenValid a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Property Source #
equivalentWhenFirstSucceeds :: (Show a, Eq a, GenUnchecked a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Property Source #
equivalentWhenFirstSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> b) -> Property Source #
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 Source #
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 Source #
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 Source #
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 Source #
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 Source #
equivalentWhenSecondSucceedsOnValid :: (Show a, Eq a, GenValid a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Property Source #
equivalentWhenSecondSucceeds :: (Show a, Eq a, GenUnchecked a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Property Source #
equivalentWhenSecondSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> b) -> (a -> f b) -> Property Source #
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 Source #
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 Source #
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 Source #
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 Source #
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 Source #
equivalentWhenSucceedOnValid :: (Show a, Eq a, GenValid a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Property Source #
equivalentWhenSucceed :: (Show a, Eq a, GenUnchecked a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Property Source #
equivalentWhenSucceedOnArbitrary :: (Show a, Eq a, Arbitrary a, Show b, Eq b, CanFail f) => (a -> f b) -> (a -> f b) -> Property Source #
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 Source #
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 Source #
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 Source #
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 Source #
Standard tests involving inverse functions
inverseFunctionsOnGen :: (Show a, Eq a) => (a -> b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property Source #
inverseFunctions :: (Show a, Eq a, GenUnchecked a) => (a -> b) -> (b -> a) -> Property Source #
inverseFunctionsOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> b) -> (b -> a) -> Property Source #
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 Source #
inverseFunctionsIfFirstSucceedsOnValid :: (Show a, Eq a, GenValid a, CanFail f) => (a -> f b) -> (b -> a) -> Property Source #
inverseFunctionsIfFirstSucceeds :: (Show a, Eq a, GenUnchecked a, CanFail f) => (a -> f b) -> (b -> a) -> Property Source #
inverseFunctionsIfFirstSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f) => (a -> f b) -> (b -> a) -> Property Source #
inverseFunctionsIfSecondSucceedsOnGen :: (Show a, Eq a, CanFail f) => (a -> b) -> (b -> f a) -> Gen a -> (a -> [a]) -> Property Source #
inverseFunctionsIfSecondSucceedsOnValid :: (Show a, Eq a, GenValid a, CanFail f) => (a -> b) -> (b -> f a) -> Property Source #
inverseFunctionsIfSecondSucceeds :: (Show a, Eq a, GenUnchecked a, CanFail f) => (a -> b) -> (b -> f a) -> Property Source #
inverseFunctionsIfSecondSucceedsOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f) => (a -> b) -> (b -> f a) -> Property Source #
inverseFunctionsIfSucceedOnGen :: (Show a, Eq a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Gen a -> (a -> [a]) -> Property Source #
inverseFunctionsIfSucceedOnValid :: (Show a, Eq a, GenValid a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Property Source #
inverseFunctionsIfSucceed :: (Show a, Eq a, GenUnchecked a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Property Source #
inverseFunctionsIfSucceedOnArbitrary :: (Show a, Eq a, Arbitrary a, CanFail f, CanFail g) => (a -> f b) -> (b -> g a) -> Property Source #
Properties involving idempotence
idempotent :: (Show a, Eq a, GenUnchecked a) => (a -> a) -> Property Source #
Properties of relations
Reflexivity
\[ Reflexive(\prec) \quad\equiv\quad \forall a: (a \prec a) \]
reflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property Source #
reflexivityOnValid ((<=) :: Rational -> Rational -> Bool)
reflexivityOnValid ((==) :: Rational -> Rational -> Bool)
reflexivityOnValid ((>=) :: Rational -> Rational -> Bool)
reflexivityOnValid (Data.List.isPrefixOf :: [Rational] -> [Rational] -> Bool)
reflexivityOnValid (Data.List.isSuffixOf :: [Rational] -> [Rational] -> Bool)
reflexivityOnValid (Data.List.isInfixOf :: [Rational] -> [Rational] -> Bool)
reflexivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property Source #
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 Source #
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
\[ Transitive(\prec) \quad\equiv\quad \forall a, b, c: ((a \prec b) \wedge (b \prec c)) \Rightarrow (a \prec c) \]
transitivityOnGens :: Show a => (a -> a -> Bool) -> Gen (a, a, a) -> (a -> [a]) -> Property Source #
transitivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property Source #
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 Source #
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 Source #
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 Source #
\[ Antisymmetric(\prec, \doteq) \quad\equiv\quad \forall a, b: ((a \prec b) \wedge (b \prec a)) \Rightarrow (a \doteq b) \]
antisymmetryOnGensWithEquality :: Show a => (a -> a -> Bool) -> Gen (a, a) -> (a -> a -> Bool) -> (a -> [a]) -> Property Source #
antisymmetryOnGens :: (Show a, Eq a) => (a -> a -> Bool) -> Gen (a, a) -> (a -> [a]) -> Property Source #
antisymmetryOnValid :: (Show a, Eq a, GenValid a) => (a -> a -> Bool) -> Property Source #
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 Source #
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 Source #
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
\[ Antireflexive(\prec) \quad\equiv\quad \forall a: \neg (a \prec a) \]
antireflexivityOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property Source #
antireflexivityOnValid ((<) :: Rational -> Rational -> Bool)
antireflexivityOnValid ((/=) :: Rational -> Rational -> Bool)
antireflexivityOnValid ((>) :: Rational -> Rational -> Bool)
antireflexivity :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property Source #
antireflexivity ((<) :: Int -> Int -> Bool)
antireflexivity ((/=) :: Int -> Int -> Bool)
antireflexivity ((>) :: Int -> Int -> Bool)
antireflexivityOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property Source #
antireflexivityOnArbitrary ((<) :: Int -> Int -> Bool)
antireflexivityOnArbitrary ((/=) :: Int -> Int -> Bool)
antireflexivityOnArbitrary ((>) :: Int -> Int -> Bool)
Symmetry
\[ Symmetric(\prec) \quad\equiv\quad \forall a, b: (a \prec b) \Leftrightarrow (b \prec a) \]
symmetryOnValid :: (Show a, GenValid a) => (a -> a -> Bool) -> Property Source #
symmetryOnValid ((==) :: Double -> Double -> Bool)
symmetryOnValid ((/=) :: Double -> Double -> Bool)
symmetry :: (Show a, GenUnchecked a) => (a -> a -> Bool) -> Property Source #
symmetry ((==) :: Int -> Int -> Bool)
symmetry ((/=) :: Int -> Int -> Bool)
symmetryOnArbitrary :: (Show a, Arbitrary a) => (a -> a -> Bool) -> Property Source #
symmetryOnArbitrary ((==) :: Int -> Int -> Bool)
symmetryOnArbitrary ((/=) :: Int -> Int -> Bool)
Properties of operations
Identity element
Left Identity
leftIdentityOnElemWithEquality Source #
:: (b -> a -> a) | A binary operation |
-> (a -> a -> Bool) | An equality |
-> b | A candidate left-identity |
-> a | An element |
-> Bool |
\[ LeftIdentity(\star, \doteq, b) \quad\equiv\quad \forall a: (b \star a) \doteq a \]
leftIdentityOnValid :: (Show a, Eq a, GenValid a) => (b -> a -> a) -> b -> Property Source #
leftIdentityOnValid (flip ((^) :: Rational -> Int -> Rational)) 1
leftIdentity :: (Show a, Eq a, GenUnchecked a) => (b -> a -> a) -> b -> Property Source #
leftIdentity (flip ((^) :: Int -> Int -> Int)) 1
leftIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (b -> a -> a) -> b -> Property Source #
leftIdentityOnArbitrary (flip ((^) :: Int -> Int -> Int)) 1
Right Identity
rightIdentityOnElemWithEquality Source #
:: (a -> b -> a) | A binary operation |
-> (a -> a -> Bool) | An equality |
-> b | A candidate right-identity |
-> a | An element |
-> Bool |
\[ RightIdentity(\star, \doteq, b) \quad\equiv\quad \forall a: (a \star b) \doteq a \]
rightIdentityOnValid :: (Show a, Eq a, GenValid a) => (a -> b -> a) -> b -> Property Source #
rightIdentityOnValid ((^) :: Rational -> Int -> Rational) 1
rightIdentity :: (Show a, Eq a, GenUnchecked a) => (a -> b -> a) -> b -> Property Source #
rightIdentity ((^) :: Int -> Int -> Int) 1
rightIdentityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> b -> a) -> b -> Property Source #
rightIdentityOnArbitrary ((^) :: Int -> Int -> Int) 1
Identity
identityOnGen :: (Show a, Eq a) => (a -> a -> a) -> a -> Gen a -> (a -> [a]) -> Property Source #
\[ Identity(\star, \doteq, b) \quad\equiv\quad LeftIdentity(\star, \doteq, b) \wedge RightIdentity(\star, \doteq, b) \]
identityOnValid :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> a -> Property Source #
identityOnValid ((*) :: Rational -> Rational -> Rational) 1
identityOnValid ((+) :: Rational -> Rational -> Rational) 0
identity :: (Show a, Eq a, GenUnchecked a) => (a -> a -> a) -> a -> Property Source #
identity ((*) :: Int -> Int -> Int) 1
identity ((+) :: Int -> Int -> Int) 0
identityOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> a -> Property Source #
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 Source #
\[ Associative(\star) \quad\equiv\quad \forall a, b, c: (a \star b) \star c = a \star (b \star c) \]
associative :: (Show a, Eq a, GenUnchecked a) => (a -> a -> a) -> Property Source #
associative ((*) :: Int -> Int -> Int)
associative ((+) :: Int -> Int -> Int)
associativeOnArbitrary :: (Show a, Eq a, Arbitrary a) => (a -> a -> a) -> Property Source #
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 Source #
\[ Commutative(\star) \quad\equiv\quad \forall a, b: a \star b = b \star a \]
commutativeOnValids :: (Show a, Eq a, GenValid a) => (a -> a -> a) -> Property Source #
commutativeOnValids ((+) :: Rational -> Rational -> Rational)
commutativeOnValids ((*) :: Rational -> Rational -> Rational)
commutative :: (Show a, Eq a, GenUnchecked a) => (a -> a -> a) -> Property Source #
commutative ((+) :: Int -> Int -> Int)
commutative ((*) :: Int -> Int -> Int)