Test.Validity

To use the Spec functions in this module, you will need TypeApplications.

Documentation

module Data.GenValidity

Tests for Arbitrary instances involving Validity

arbitrarySpec :: forall a. (Typeable a, Show a, Validity a, Arbitrary a) => Spec

A Spec that specifies that arbitrary only generates data that satisfy isValid

Example usage:

arbitrarySpec @Int

arbitraryGeneratesOnlyValid :: forall a. (Show a, Validity a, Arbitrary a) => Property

arbitrary only generates valid data

arbitraryGeneratesOnlyValid @Int

Tests for GenValidity instances

genValiditySpec :: forall a. (Typeable a, Show a, GenValid a, GenInvalid a) => Spec

A spec for properties of GenValid and GenInvalid instances.

In general it is a good idea to add this spec to your test suite if you write a custom implementation of genValid or genInvalid.

Example usage:

genValiditySpec @Int

genValidSpec :: forall a. (Typeable a, Show a, GenValid a) => Spec

A Spec that specifies that genValid only generates valid data.

Example usage:

genValidSpec @Int

genInvalidSpec :: forall a. (Typeable a, Show a, GenInvalid a) => Spec

A Spec that specifies that genInvalid only generates invalid data.

Example usage:

genInvalidSpec @Double

genValidGeneratesValid :: forall a. (Show a, GenValid a) => Property

genValid only generates valid data

genValidGeneratesValid @()

genValidGeneratesValid @Bool

genValidGeneratesValid @Ordering

genValidGeneratesValid @Char

genValidGeneratesValid @Int

genValidGeneratesValid @Float

genValidGeneratesValid @Double

genValidGeneratesValid @Integer

genValidGeneratesValid @(Maybe Int)

genValidGeneratesValid @[Int]

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

The given generator generates only valid data points

genInvalidGeneratesInvalid :: forall a. (Show a, GenInvalid a) => Property

genValid only generates invalid data

genInvalidGeneratesInvalid @Float

genInvalidGeneratesInvalid @Double

genInvalidGeneratesInvalid @(Maybe Double)

genInvalidGeneratesInvalid @[Double]

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

The given generator generates only invalid data points

Tests for RelativeValidity instances

relativeValiditySpec :: forall a b. (Typeable a, Typeable b, Show a, Show b, Validity a, Validity b, GenUnchecked a, GenUnchecked b, RelativeValidity a b) => Spec

A Spec that specifies that isValidFor implies isValid

In general it is a good idea to add this spec to your test suite if the a and b in RelativeValidity a b also have a Validity instance.

Example usage:

relativeValiditySpec @MyDataFor @MyOtherData

relativeValidityImpliesValidA :: forall a b. (Show a, Show b, Validity a, GenUnchecked a, GenUnchecked b, RelativeValidity a b) => Property

isValidFor a b implies isValid a for all b

relativeValidityImpliesValidB :: forall a b. (Show a, Show b, Validity b, GenUnchecked a, GenUnchecked b, RelativeValidity a b) => Property

isValidFor a b implies isValid b for all a

Tests for GenRelativeValidity instances

genRelativeValiditySpec :: forall a b. (Typeable a, Typeable b, Show a, Show b, GenValid a, GenValid b, RelativeValidity a b, GenRelativeValid a b, GenRelativeInvalid a b) => Spec

A Spec that specifies that genValidFor and genInvalidFor work as intended.

In general it is a good idea to add this spec to your test suite if you write a custom implementation of genValidFor or genInvalidFor.

Example usage:

relativeGenValiditySpec @MyDataFor @MyOtherData

genRelativeValidGeneratesValid :: forall a b. (Show a, Show b, GenValid b, RelativeValidity a b, GenRelativeValid a b) => Property

genValidFor b only generates values that satisfy isValidFor b

genRelativeInvalidGeneratesInvalid :: forall a b. (Show a, Show b, GenUnchecked b, RelativeValidity a b, GenRelativeInvalid a b) => Property

genInvalidFor b only generates values that do not satisfy isValidFor b

Standard tests involving functions

Standard tests involving validity

producesValidsOnGen :: (Show a, Show b, Validity b) => (a -> b) -> Gen 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) -> 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) -> 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

Methods

hasFailed :: Maybe a -> Bool

resultIfSucceeded :: Maybe a -> Maybe a

CanFail (Either e)

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 -> 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) -> 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 -> 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 -> Gen b -> Property

failsOnInvalid2 :: (Show a, Show b, Show c, Show (f c), GenInvalid a, GenUnchecked a, GenInvalid b, GenUnchecked 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 -> 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) -> 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

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 -> 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) -> Property

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

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

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

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

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

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

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

reflexivityOnValid ((<=) @Double)

reflexivityOnValid ((==) @Double)

reflexivityOnValid ((>=) @Double)

reflexivityOnValid (Data.List.isPrefixOf @Double)

reflexivityOnValid (Data.List.isSuffixOf @Double)

reflexivityOnValid (Data.List.isInfixOf @Double)

reflexivityOnValid (Data.List.isSubsequenceOf @Double)

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

reflexivity ((<=) @Int)

reflexivity ((==) @Int)

reflexivity ((>=) @Int)

reflexivity (Data.List.isPrefixOf @Int)

reflexivity (Data.List.isSuffixOf @Int)

reflexivity (Data.List.isInfixOf @Int)

reflexivity (Data.List.isSubsequenceOf @Int)

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

reflexivityOnArbitrary ((<=) @Int)

reflexivityOnArbitrary ((==) @Int)

reflexivityOnArbitrary ((>=) @Int)

reflexivityOnArbitrary (Data.List.isPrefixOf @Int)

reflexivityOnArbitrary (Data.List.isSuffixOf @Int)

reflexivityOnArbitrary (Data.List.isInfixOf @Int)

reflexivityOnArbitrary (Data.List.isSubsequenceOf @Int)

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) -> Property

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

transitivityOnValid ((>) @Double)

transitivityOnValid ((>=) @Double)

transitivityOnValid ((==) @Double)

transitivityOnValid ((<=) @Double)

transitivityOnValid ((<) @Double)

transitivityOnValid (Data.List.isPrefixOf @Double)

transitivityOnValid (Data.List.isSuffixOf @Double)

transitivityOnValid (Data.List.isInfixOf @Double)

transitivityOnValid (Data.List.isSubsequenceOf @Double)

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

transitivity ((>) @Int)

transitivity ((>=) @Int)

transitivity ((==) @Int)

transitivity ((<=) @Int)

transitivity ((<) @Int)

transitivity (Data.List.isPrefixOf @Int)

transitivity (Data.List.isSuffixOf @Int)

transitivity (Data.List.isInfixOf @Int)

transitivity (Data.List.isSubsequenceOf @Int)

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

transitivityOnArbitrary ((>) @Int)

transitivityOnArbitrary ((>=) @Int)

transitivityOnArbitrary ((==) @Int)

transitivityOnArbitrary ((<=) @Int)

transitivityOnArbitrary ((<) @Int)

transitivityOnArbitrary (Data.List.isPrefixOf @Int)

transitivityOnArbitrary (Data.List.isSuffixOf @Int)

transitivityOnArbitrary (Data.List.isInfixOf @Int)

transitivityOnArbitrary (Data.List.isSubsequenceOf @Int)

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) -> Property

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

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

antisymmetryOnValid ((>) @Double)

antisymmetryOnValid ((>=) @Double)

antisymmetryOnValid ((<=) @Double)

antisymmetryOnValid ((<) @Double)

antisymmetryOnValid (Data.List.isPrefixOf @Double)

antisymmetryOnValid (Data.List.isSuffixOf @Double)

antisymmetryOnValid (Data.List.isInfixOf @Double)

antisymmetryOnValid (Data.List.isSubsequenceOf @Double)

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

antisymmetry ((>) @Int)

antisymmetry ((>=) @Int)

antisymmetry ((<=) @Int)

antisymmetry ((<) @Int)

antisymmetry (Data.List.isPrefixOf @Int)

antisymmetry (Data.List.isSuffixOf @Int)

antisymmetry (Data.List.isInfixOf @Int)

antisymmetry (Data.List.isSubsequenceOf @Int)

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

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

antisymmetryOnArbitrary ((>) @Int)

antisymmetryOnArbitrary ((>=) @Int)

antisymmetryOnArbitrary ((<=) @Int)

antisymmetryOnArbitrary ((<) @Int)

antisymmetryOnArbitrary (Data.List.isPrefixOf @Int)

antisymmetryOnArbitrary (Data.List.isSuffixOf @Int)

antisymmetryOnArbitrary (Data.List.isInfixOf @Int)

antisymmetryOnArbitrary (Data.List.isSubsequenceOf @Int)

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 -> Property

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

antireflexivityOnValid ((<) @Double)

antireflexivityOnValid ((/=) @Double)

antireflexivityOnValid ((>) @Double)

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

antireflexivity ((<) @Int)

antireflexivity ((/=) @Int)

antireflexivity ((>) @Int)

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

antireflexivityOnArbitrary ((<) @Int)

antireflexivityOnArbitrary ((/=) @Int)

antireflexivityOnArbitrary ((>) @Int)

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) -> Property

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

symmetryOnValid ((==) @Double)

symmetryOnValid ((/=) @Double)

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

symmetry ((==) @Int)

symmetry ((/=) @Int)

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

symmetryOnArbitrary ((==) @Int)

symmetryOnArbitrary ((/=) @Int)

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

-> Property

leftIdentityOnGen

Arguments

:: (Show a, Eq a)

=> (b -> a -> a)

A binary operation

-> b

A candidate left-identity

-> Gen a

-> Property

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

leftIdentityOnValid (flip ((^) @Double @Int)) 1

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

leftIdentity (flip ((^) @Int @Int)) 1

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

leftIdentityOnArbitrary (flip ((^) @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

-> Property

rightIdentityOnGen

Arguments

:: (Show a, Eq a)

=> (a -> b -> a)

A binary operation

-> b

A candidate right-identity

-> Gen a

-> Property

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

rightIdentityOnValid ((^) @Double) 1

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

rightIdentity ((^) @Int) 1

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

rightIdentityOnArbitrary ((^) @Int) 1

Identity

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

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

identityOnValid ((*) @Double) 1

identityOnValid ((+) @Double) 0

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

identity ((*) @Int) 1

identity ((+) @Int) 0

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

identityOnArbitrary ((*) @Int) 1

identityOnArbitrary ((+) @Int) 0

Associativity

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

associative ((*) @Int)

associative ((+) @Int)

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

associativeOnArbitrary ((*) @Int)

associativeOnArbitrary ((+) @Int)

Commutativity

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

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

commutative ((+) @Double)

commutative ((*) @Double)

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

commutative ((+) @Int)

commutative ((*) @Int)

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

commutativeOnArbitrary ((+) @Int)

commutativeOnArbitrary ((*) @Int)

Eq properties

eqSpecOnValid :: forall a. (Show a, Eq a, Typeable a, GenValid a) => Spec

Standard test spec for properties of Eq instances for valid values

Example usage:

eqSpecOnValid @Double

eqSpec :: forall a. (Show a, Eq a, Typeable a, GenUnchecked a) => Spec

Standard test spec for properties of Eq instances for unchecked values

Example usage:

eqSpec @Int

eqSpecOnArbitrary :: forall a. (Show a, Eq a, Typeable a, Arbitrary a) => Spec

Standard test spec for properties of Eq instances for arbitrary values

Example usage:

eqSpecOnArbitrary @Int

eqSpecOnGen :: forall a. (Show a, Eq a, Typeable a) => Gen a -> String -> Spec

Standard test spec for properties of Eq instances for values generated by a given generator (and name for that generator).

Example usage:

eqSpecOnGen ((* 2) <$> genValid @Int) "even"

Ord properties

ordSpecOnGen :: forall a. (Show a, Eq a, Ord a, Typeable a) => Gen a -> String -> Spec

Standard test spec for properties of Ord instances for values generated by a given generator (and name for that generator).

Example usage:

ordSpecOnGen ((* 2) <$> genValid @Int) "even"

ordSpecOnValid :: forall a. (Show a, Ord a, Typeable a, Arbitrary a) => Spec

Standard test spec for properties of Ord instances for valid values

Example usage:

ordSpecOnValid @Double

ordSpec :: forall a. (Show a, Ord a, Typeable a, GenUnchecked a) => Spec

Standard test spec for properties of Ord instances for unchecked values

Example usage:

ordSpec @Int

ordSpecOnArbitrary :: forall a. (Show a, Ord a, Typeable a, Arbitrary a) => Spec

Standard test spec for properties of Ord instances for arbitrary values

Example usage:

ordSpecOnArbitrary @Int

Monoid properties

monoidSpecOnValid :: forall a. (Show a, Eq a, Monoid a, Typeable a, GenValid a) => Spec

Standard test spec for properties of Monoid instances for valid values

Example usage:

monoidSpecOnValid @[Double]

monoidSpec :: forall a. (Show a, Eq a, Monoid a, Typeable a, GenUnchecked a) => Spec

Standard test spec for properties of Monoid instances for unchecked values

Example usage:

monoidSpec @[Int]

monoidSpecOnArbitrary :: forall a. (Show a, Eq a, Monoid a, Typeable a, Arbitrary a) => Spec

Standard test spec for properties of Monoid instances for arbitrary values

Example usage:

monoidSpecOnArbitrary @[Int]

monoidSpecOnGen :: forall a. (Show a, Eq a, Monoid a, Typeable a) => Gen a -> String -> Spec

Standard test spec for properties of Monoid instances for values generated by a given generator (and name for that generator).

Example usage:

monoidSpecOnGen (pure "a") "singleton list of 'a'"

Functor properties

functorSpecOnValid :: forall f. (Eq (f Int), Show (f Int), Functor f, Typeable f, GenValid (f Int)) => Spec

Standard test spec for properties of Functor instances for values generated with GenValid instances

Example usage:

functorSpecOnArbitrary @[]

functorSpec :: forall f. (Eq (f Int), Show (f Int), Functor f, Typeable f, GenUnchecked (f Int)) => Spec

Standard test spec for properties of Functor instances for values generated with GenUnchecked instances

Example usage:

functorSpecOnArbitrary @[]

functorSpecOnArbitrary :: forall f. (Eq (f Int), Show (f Int), Functor f, Typeable f, Arbitrary (f Int)) => Spec

Standard test spec for properties of Functor instances for values generated with Arbitrary instances

Example usage:

functorSpecOnArbitrary @[]

functorSpecOnGens :: forall f a b c. (Show a, Show (f a), Show (f c), Eq (f a), Eq (f c), Functor f, Typeable f, Typeable a, Typeable b, Typeable c) => Gen a -> String -> Gen (f a) -> String -> Gen (b -> c) -> String -> Gen (a -> b) -> String -> Spec

Standard test spec for properties of Functor instances for values generated by given generators (and names for those generator).

Example usage:

functorSpecOnGens
    @[]
    @Int
    (pure 4) "four"
    (genListOf $ pure 5) "list of fives"
    ((+) <$> genValid) "additions"
    ((*) <$> genValid) "multiplications"

Applicative properties

applicativeSpecOnValid :: forall f. (Eq (f Int), Show (f Int), Applicative f, Typeable f, GenValid (f Int)) => Spec

Standard test spec for properties of Applicative instances for values generated with GenValid instances

Example usage:

applicativeSpecOnArbitrary @[]

applicativeSpec :: forall f. (Eq (f Int), Show (f Int), Applicative f, Typeable f, GenUnchecked (f Int)) => Spec

Standard test spec for properties of Applicative instances for values generated with GenUnchecked instances

Example usage:

applicativeSpecOnArbitrary @[]

applicativeSpecOnArbitrary :: forall f. (Eq (f Int), Show (f Int), Applicative f, Typeable f, Arbitrary (f Int)) => Spec

Standard test spec for properties of Applicative instances for values generated with Arbitrary instances

Example usage:

applicativeSpecOnArbitrary @[]

applicativeSpecOnGens :: forall f a b c. (Show a, Eq a, Show (f a), Eq (f a), Show (f b), Eq (f b), Show (f c), Eq (f c), Applicative f, Typeable f, Typeable a, Typeable b, Typeable c) => Gen a -> String -> Gen (f a) -> String -> Gen (f b) -> String -> Gen (a -> b) -> String -> Gen (f (a -> b)) -> String -> Gen (f (b -> c)) -> String -> Spec

Standard test spec for properties of Applicative instances for values generated by given generators (and names for those generator).

Unless you are building a specific regression test, you probably want to use the other applicativeSpec functions.

Example usage:

applicativeSpecOnGens
    @Maybe
    @String
    (pure "ABC")
    "ABC"
    (Just <$> pure "ABC")
    "Just an ABC"
    (pure Nothing)
    "purely Nothing"
    ((++) <$> genValid)
    "prepends"
    (pure <$> ((++) <$> genValid))
    "prepends in a Just"
    (pure <$> (flip (++) <$> genValid))
    "appends in a Just"

Monad properties

monadSpecOnValid :: forall f. (Eq (f Int), Show (f Int), Monad f, Typeable f, GenValid (f Int)) => Spec

Standard test spec for properties of Monad instances for values generated with GenValid instances

Example usage:

monadSpecOnArbitrary @[]

monadSpec :: forall f. (Eq (f Int), Show (f Int), Monad f, Typeable f, GenUnchecked (f Int)) => Spec

Standard test spec for properties of Monad instances for values generated with GenUnchecked instances

Example usage:

monadSpecOnArbitrary @[]

monadSpecOnArbitrary :: forall f. (Eq (f Int), Show (f Int), Monad f, Typeable f, Arbitrary (f Int)) => Spec

Standard test spec for properties of Monad instances for values generated with Arbitrary instances

Example usage:

monadSpecOnArbitrary @[]

monadSpecOnGens :: forall f a b c. (Show a, Eq a, Show (f a), Show (f b), Show (f c), Eq (f a), Eq (f b), Eq (f c), Monad f, Typeable f, Typeable a, Typeable b, Typeable c) => Gen a -> String -> Gen (f a) -> String -> Gen (f b) -> String -> Gen (a -> b) -> String -> Gen (a -> f b) -> String -> Gen (b -> f c) -> String -> Gen (f (a -> b)) -> String -> Spec

Standard test spec for properties of Monad instances for values generated by given generators (and names for those generator).

Example usage:

monadSpecOnGens
    @[]
    @Int
    (pure 4)
    "four"
    (genListOf $ pure 5)
    "list of fives"
    (genListOf $ pure 6)
    "list of sixes"
    ((*) <$> genValid)
    "factorisations"
    (pure $ \a -> [a])
    "singletonisation"
    (pure $ \a -> [a])
    "singletonisation"
    (pure $ pure (+ 1))
    "increment in list"