{-# LANGUAGE ScopedTypeVariables #-}
{-# OPTIONS_GHC -Wall #-}
module Test.QuickCheck.Classes.Num
( numLaws
) where
import Data.Proxy (Proxy)
import Test.QuickCheck hiding ((.&.))
import Test.QuickCheck.Property (Property)
import Test.QuickCheck.Classes.Internal (Laws(..), myForAllShrink)
numLaws :: (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws
numLaws :: Proxy a -> Laws
numLaws p :: Proxy a
p = String -> [(String, Property)] -> Laws
Laws "Num"
[ ("Additive Commutativity", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numCommutativePlus Proxy a
p)
, ("Additive Left Identity", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numLeftIdentityPlus Proxy a
p)
, ("Additive Right Identity", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numRightIdentityPlus Proxy a
p)
, ("Multiplicative Associativity", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numAssociativeTimes Proxy a
p)
, ("Multiplicative Left Identity", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numLeftIdentityTimes Proxy a
p)
, ("Multiplicative Right Identity", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numRightIdentityTimes Proxy a
p)
, ("Multiplication Left Distributes Over Addition", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numLeftMultiplicationDistributes Proxy a
p)
, ("Multiplication Right Distributes Over Addition", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numRightMultiplicationDistributes Proxy a
p)
, ("Multiplicative Left Annihilation", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numLeftAnnihilation Proxy a
p)
, ("Multiplicative Right Annihilation", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numRightAnnihilation Proxy a
p)
, ("Additive Inverse", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numAdditiveInverse Proxy a
p)
, ("Subtraction", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numSubtraction Proxy a
p)
, ("Abs Is Idempotent", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
absIdempotence Proxy a
p)
, ("Signum Is Idempotent", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
signumIdempotence Proxy a
p)
, ("Product Of Abs And Signum Is Id", Proxy a -> Property
forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
absSignumId Proxy a
p)
]
numLeftMultiplicationDistributes :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numLeftMultiplicationDistributes :: Proxy a -> Property
numLeftMultiplicationDistributes _ = Bool
-> ((a, a, a) -> Bool)
-> ((a, a, a) -> [String])
-> String
-> ((a, a, a) -> a)
-> String
-> ((a, a, a) -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
True (Bool -> (a, a, a) -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a,b :: a
b,c :: a
c) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a, "b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
b, "c = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
c])
"a * (b + c)"
(\(a :: a
a,b :: a
b,c :: a
c) -> a
a a -> a -> a
forall a. Num a => a -> a -> a
* (a
b a -> a -> a
forall a. Num a => a -> a -> a
+ a
c))
"(a * b) + (a * c)"
(\(a :: a
a,b :: a
b,c :: a
c) -> (a
a a -> a -> a
forall a. Num a => a -> a -> a
* a
b) a -> a -> a
forall a. Num a => a -> a -> a
+ (a
a a -> a -> a
forall a. Num a => a -> a -> a
* a
c))
numRightMultiplicationDistributes :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numRightMultiplicationDistributes :: Proxy a -> Property
numRightMultiplicationDistributes _ = Bool
-> ((a, a, a) -> Bool)
-> ((a, a, a) -> [String])
-> String
-> ((a, a, a) -> a)
-> String
-> ((a, a, a) -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
True (Bool -> (a, a, a) -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a,b :: a
b,c :: a
c) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a, "b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
b, "c = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
c])
"(a + b) * c"
(\(a :: a
a,b :: a
b,c :: a
c) -> (a
a a -> a -> a
forall a. Num a => a -> a -> a
+ a
b) a -> a -> a
forall a. Num a => a -> a -> a
* a
c)
"(a * c) + (b * c)"
(\(a :: a
a,b :: a
b,c :: a
c) -> (a
a a -> a -> a
forall a. Num a => a -> a -> a
* a
c) a -> a -> a
forall a. Num a => a -> a -> a
+ (a
b a -> a -> a
forall a. Num a => a -> a -> a
* a
c))
numLeftIdentityPlus :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numLeftIdentityPlus :: Proxy a -> Property
numLeftIdentityPlus _ = Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> a)
-> String
-> (a -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
False (Bool -> a -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
"0 + a"
(\a :: a
a -> 0 a -> a -> a
forall a. Num a => a -> a -> a
+ a
a)
"a"
(\a :: a
a -> a
a)
numRightIdentityPlus :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numRightIdentityPlus :: Proxy a -> Property
numRightIdentityPlus _ = Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> a)
-> String
-> (a -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
False (Bool -> a -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
"a + 0"
(\a :: a
a -> a
a a -> a -> a
forall a. Num a => a -> a -> a
+ 0)
"a"
(\a :: a
a -> a
a)
numRightIdentityTimes :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numRightIdentityTimes :: Proxy a -> Property
numRightIdentityTimes _ = Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> a)
-> String
-> (a -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
False (Bool -> a -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
"a * 1"
(\a :: a
a -> a
a a -> a -> a
forall a. Num a => a -> a -> a
* 1)
"a"
(\a :: a
a -> a
a)
numLeftIdentityTimes :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numLeftIdentityTimes :: Proxy a -> Property
numLeftIdentityTimes _ = Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> a)
-> String
-> (a -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
False (Bool -> a -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
"1 * a"
(\a :: a
a -> 1 a -> a -> a
forall a. Num a => a -> a -> a
* a
a)
"a"
(\a :: a
a -> a
a)
numLeftAnnihilation :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numLeftAnnihilation :: Proxy a -> Property
numLeftAnnihilation _ = Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> a)
-> String
-> (a -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
False (Bool -> a -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
"0 * a"
(\a :: a
a -> 0 a -> a -> a
forall a. Num a => a -> a -> a
* a
a)
"0"
(\_ -> 0)
numRightAnnihilation :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numRightAnnihilation :: Proxy a -> Property
numRightAnnihilation _ = Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> a)
-> String
-> (a -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
False (Bool -> a -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
"a * 0"
(\a :: a
a -> a
a a -> a -> a
forall a. Num a => a -> a -> a
* 0)
"0"
(\_ -> 0)
numCommutativePlus :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numCommutativePlus :: Proxy a -> Property
numCommutativePlus _ = Bool
-> ((a, a) -> Bool)
-> ((a, a) -> [String])
-> String
-> ((a, a) -> a)
-> String
-> ((a, a) -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
True (Bool -> (a, a) -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a,b :: a
b) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a, "b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
b])
"a + b"
(\(a :: a
a,b :: a
b) -> a
a a -> a -> a
forall a. Num a => a -> a -> a
+ a
b)
"b + a"
(\(a :: a
a,b :: a
b) -> a
b a -> a -> a
forall a. Num a => a -> a -> a
+ a
a)
numAssociativeTimes :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numAssociativeTimes :: Proxy a -> Property
numAssociativeTimes _ = Bool
-> ((a, a, a) -> Bool)
-> ((a, a, a) -> [String])
-> String
-> ((a, a, a) -> a)
-> String
-> ((a, a, a) -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
True (Bool -> (a, a, a) -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a,b :: a
b,c :: a
c) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a, "b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
b, "c = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
c])
"a * (b * c)"
(\(a :: a
a,b :: a
b,c :: a
c) -> a
a a -> a -> a
forall a. Num a => a -> a -> a
* (a
b a -> a -> a
forall a. Num a => a -> a -> a
* a
c))
"(a * b) * c"
(\(a :: a
a,b :: a
b,c :: a
c) -> (a
a a -> a -> a
forall a. Num a => a -> a -> a
* a
b) a -> a -> a
forall a. Num a => a -> a -> a
* a
c)
numAdditiveInverse :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numAdditiveInverse :: Proxy a -> Property
numAdditiveInverse _ = Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> a)
-> String
-> (a -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
True (Bool -> a -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
"negate a + a"
(\a :: a
a -> (-a
a) a -> a -> a
forall a. Num a => a -> a -> a
+ a
a)
"0"
(a -> a -> a
forall a b. a -> b -> a
const 0)
numSubtraction :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
numSubtraction :: Proxy a -> Property
numSubtraction _ = Bool
-> ((a, a) -> Bool)
-> ((a, a) -> [String])
-> String
-> ((a, a) -> a)
-> String
-> ((a, a) -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
True (Bool -> (a, a) -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a, a
b :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a, "b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
b])
"a + negate b"
(\(a :: a
a,b :: a
b) -> a
a a -> a -> a
forall a. Num a => a -> a -> a
+ a -> a
forall a. Num a => a -> a
negate a
b)
"a - b"
(\(a :: a
a,b :: a
b) -> a
a a -> a -> a
forall a. Num a => a -> a -> a
- a
b)
absIdempotence :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
absIdempotence :: Proxy a -> Property
absIdempotence _ = Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> a)
-> String
-> (a -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
True (Bool -> a -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
"abs (abs a)"
(a -> a
forall a. Num a => a -> a
abs (a -> a) -> (a -> a) -> a -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> a
forall a. Num a => a -> a
abs)
"abs a"
a -> a
forall a. Num a => a -> a
abs
signumIdempotence :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
signumIdempotence :: Proxy a -> Property
signumIdempotence _ = Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> a)
-> String
-> (a -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
True (Bool -> a -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
"signum (signum a)"
(a -> a
forall a. Num a => a -> a
signum (a -> a) -> (a -> a) -> a -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> a
forall a. Num a => a -> a
signum)
"signum a"
a -> a
forall a. Num a => a -> a
signum
absSignumId :: forall a. (Num a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
absSignumId :: Proxy a -> Property
absSignumId _ = Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> a)
-> String
-> (a -> a)
-> Property
forall a b.
(Arbitrary a, Show b, Eq b) =>
Bool
-> (a -> Bool)
-> (a -> [String])
-> String
-> (a -> b)
-> String
-> (a -> b)
-> Property
myForAllShrink Bool
True (Bool -> a -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(a
a :: a) -> ["a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
"abs a * signum a"
(\a :: a
a -> a -> a
forall a. Num a => a -> a
abs a
a a -> a -> a
forall a. Num a => a -> a -> a
* a -> a
forall a. Num a => a -> a
signum a
a)
"a"
a -> a
forall a. a -> a
id