{-# LANGUAGE CPP #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# OPTIONS_GHC -Wall #-}
module Test.QuickCheck.Classes.Semiring
(
#if HAVE_SEMIRINGS
semiringLaws
#endif
) where
#if HAVE_SEMIRINGS
import Data.Semiring hiding (fromInteger)
import Prelude hiding (Num(..))
import Prelude (fromInteger)
#endif
import Data.Proxy (Proxy)
import Test.QuickCheck hiding ((.&.))
import Test.QuickCheck.Property (Property)
import Test.QuickCheck.Classes.Internal (Laws(..), myForAllShrink)
#if HAVE_SEMIRINGS
semiringLaws :: (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Laws
semiringLaws :: Proxy a -> Laws
semiringLaws Proxy a
p = String -> [(String, Property)] -> Laws
Laws String
"Semiring"
[ (String
"Additive Commutativity", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringCommutativePlus Proxy a
p)
, (String
"Additive Left Identity", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringLeftIdentityPlus Proxy a
p)
, (String
"Additive Right Identity", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringRightIdentityPlus Proxy a
p)
, (String
"Multiplicative Associativity", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringAssociativeTimes Proxy a
p)
, (String
"Multiplicative Left Identity", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringLeftIdentityTimes Proxy a
p)
, (String
"Multiplicative Right Identity", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringRightIdentityTimes Proxy a
p)
, (String
"Multiplication Left Distributes Over Addition", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringLeftMultiplicationDistributes Proxy a
p)
, (String
"Multiplication Right Distributes Over Addition", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringRightMultiplicationDistributes Proxy a
p)
, (String
"Multiplicative Left Annihilation", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringLeftAnnihilation Proxy a
p)
, (String
"Multiplicative Right Annihilation", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringRightAnnihilation Proxy a
p)
, (String
"FromNatural Maps Zero", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringFromNaturalMapsZero Proxy a
p)
, (String
"FromNatural Maps One", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringFromNaturalMapsOne Proxy a
p)
, (String
"FromNatural Maps Plus", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringFromNaturalMapsPlus Proxy a
p)
, (String
"FromNatural Maps Times", Proxy a -> Property
forall a.
(Semiring a, Eq a, Arbitrary a, Show a) =>
Proxy a -> Property
semiringFromNaturalMapsTimes Proxy a
p)
]
semiringLeftMultiplicationDistributes :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringLeftMultiplicationDistributes :: Proxy a -> Property
semiringLeftMultiplicationDistributes Proxy a
_ = 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,a
b,a
c) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a, String
"b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
b, String
"c = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
c])
String
"a * (b + c)"
(\(a
a,a
b,a
c) -> a
a a -> a -> a
forall a. Semiring a => a -> a -> a
* (a
b a -> a -> a
forall a. Semiring a => a -> a -> a
+ a
c))
String
"(a * b) + (a * c)"
(\(a
a,a
b,a
c) -> (a
a a -> a -> a
forall a. Semiring a => a -> a -> a
* a
b) a -> a -> a
forall a. Semiring a => a -> a -> a
+ (a
a a -> a -> a
forall a. Semiring a => a -> a -> a
* a
c))
semiringRightMultiplicationDistributes :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringRightMultiplicationDistributes :: Proxy a -> Property
semiringRightMultiplicationDistributes Proxy a
_ = 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,a
b,a
c) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a, String
"b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
b, String
"c = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
c])
String
"(a + b) * c"
(\(a
a,a
b,a
c) -> (a
a a -> a -> a
forall a. Semiring a => a -> a -> a
+ a
b) a -> a -> a
forall a. Semiring a => a -> a -> a
* a
c)
String
"(a * c) + (b * c)"
(\(a
a,a
b,a
c) -> (a
a a -> a -> a
forall a. Semiring a => a -> a -> a
* a
c) a -> a -> a
forall a. Semiring a => a -> a -> a
+ (a
b a -> a -> a
forall a. Semiring a => a -> a -> a
* a
c))
semiringLeftIdentityPlus :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringLeftIdentityPlus :: Proxy a -> Property
semiringLeftIdentityPlus Proxy a
_ = 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) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
String
"0 + a"
(\a
a -> a
forall a. Semiring a => a
zero a -> a -> a
forall a. Semiring a => a -> a -> a
+ a
a)
String
"a"
(\a
a -> a
a)
semiringRightIdentityPlus :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringRightIdentityPlus :: Proxy a -> Property
semiringRightIdentityPlus Proxy a
_ = 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) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
String
"a + 0"
(\a
a -> a
a a -> a -> a
forall a. Semiring a => a -> a -> a
+ a
forall a. Semiring a => a
zero)
String
"a"
(\a
a -> a
a)
semiringRightIdentityTimes :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringRightIdentityTimes :: Proxy a -> Property
semiringRightIdentityTimes Proxy a
_ = 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) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
String
"a * 1"
(\a
a -> a
a a -> a -> a
forall a. Semiring a => a -> a -> a
* a
forall a. Semiring a => a
one)
String
"a"
(\a
a -> a
a)
semiringLeftIdentityTimes :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringLeftIdentityTimes :: Proxy a -> Property
semiringLeftIdentityTimes Proxy a
_ = 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) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
String
"1 * a"
(\a
a -> a
forall a. Semiring a => a
one a -> a -> a
forall a. Semiring a => a -> a -> a
* a
a)
String
"a"
(\a
a -> a
a)
semiringLeftAnnihilation :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringLeftAnnihilation :: Proxy a -> Property
semiringLeftAnnihilation Proxy a
_ = 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) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
String
"0 * a"
(\a
a -> a
forall a. Semiring a => a
zero a -> a -> a
forall a. Semiring a => a -> a -> a
* a
a)
String
"0"
(\a
_ -> a
forall a. Semiring a => a
zero)
semiringRightAnnihilation :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringRightAnnihilation :: Proxy a -> Property
semiringRightAnnihilation Proxy a
_ = 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) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a])
String
"a * 0"
(\a
a -> a
a a -> a -> a
forall a. Semiring a => a -> a -> a
* a
forall a. Semiring a => a
zero)
String
"0"
(\a
_ -> a
forall a. Semiring a => a
zero)
semiringCommutativePlus :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringCommutativePlus :: Proxy a -> Property
semiringCommutativePlus Proxy a
_ = 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) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a, String
"b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
b])
String
"a + b"
(\(a
a,a
b) -> a
a a -> a -> a
forall a. Semiring a => a -> a -> a
+ a
b)
String
"b + a"
(\(a
a,a
b) -> a
b a -> a -> a
forall a. Semiring a => a -> a -> a
+ a
a)
semiringAssociativeTimes :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringAssociativeTimes :: Proxy a -> Property
semiringAssociativeTimes Proxy a
_ = 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,a
b,a
c) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
a, String
"b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
b, String
"c = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ a -> String
forall a. Show a => a -> String
show a
c])
String
"a * (b * c)"
(\(a
a,a
b,a
c) -> a
a a -> a -> a
forall a. Semiring a => a -> a -> a
* (a
b a -> a -> a
forall a. Semiring a => a -> a -> a
* a
c))
String
"(a * b) * c"
(\(a
a,a
b,a
c) -> (a
a a -> a -> a
forall a. Semiring a => a -> a -> a
* a
b) a -> a -> a
forall a. Semiring a => a -> a -> a
* a
c)
semiringFromNaturalMapsZero :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringFromNaturalMapsZero :: Proxy a -> Property
semiringFromNaturalMapsZero Proxy a
_ = Bool
-> (() -> Bool)
-> (() -> [String])
-> String
-> (() -> a)
-> String
-> (() -> 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 -> () -> Bool
forall a b. a -> b -> a
const Bool
True)
(\()
_ -> [String
""])
String
"fromNatural 0"
(\() -> Natural -> a
forall a. Semiring a => Natural -> a
fromNatural Natural
0 :: a)
String
"zero"
(\() -> a
forall a. Semiring a => a
zero)
semiringFromNaturalMapsOne :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringFromNaturalMapsOne :: Proxy a -> Property
semiringFromNaturalMapsOne Proxy a
_ = Bool
-> (() -> Bool)
-> (() -> [String])
-> String
-> (() -> a)
-> String
-> (() -> 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 -> () -> Bool
forall a b. a -> b -> a
const Bool
True)
(\()
_ -> [String
""])
String
"fromNatural 1"
(\() -> Natural -> a
forall a. Semiring a => Natural -> a
fromNatural Natural
1 :: a)
String
"one"
(\() -> a
forall a. Semiring a => a
one)
semiringFromNaturalMapsPlus :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringFromNaturalMapsPlus :: Proxy a -> Property
semiringFromNaturalMapsPlus Proxy a
_ = Bool
-> ((NonNegative Integer, NonNegative Integer) -> Bool)
-> ((NonNegative Integer, NonNegative Integer) -> [String])
-> String
-> ((NonNegative Integer, NonNegative Integer) -> a)
-> String
-> ((NonNegative Integer, NonNegative Integer) -> 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 -> (NonNegative Integer, NonNegative Integer) -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(NonNegative Integer
a, NonNegative Integer
b) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ Integer -> String
forall a. Show a => a -> String
show Integer
a, String
"b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ Integer -> String
forall a. Show a => a -> String
show Integer
b])
String
"fromNatural (a + b)"
(\(NonNegative Integer
a, NonNegative Integer
b) -> Natural -> a
forall a. Semiring a => Natural -> a
fromNatural (Integer -> Natural
forall a. Num a => Integer -> a
fromInteger (Integer
a Integer -> Integer -> Integer
forall a. Semiring a => a -> a -> a
+ Integer
b)) :: a)
String
"fromNatural a + fromNatural b"
(\(NonNegative Integer
a, NonNegative Integer
b) -> Natural -> a
forall a. Semiring a => Natural -> a
fromNatural (Integer -> Natural
forall a. Num a => Integer -> a
fromInteger Integer
a) a -> a -> a
forall a. Semiring a => a -> a -> a
+ Natural -> a
forall a. Semiring a => Natural -> a
fromNatural (Integer -> Natural
forall a. Num a => Integer -> a
fromInteger Integer
b))
semiringFromNaturalMapsTimes :: forall a. (Semiring a, Eq a, Arbitrary a, Show a) => Proxy a -> Property
semiringFromNaturalMapsTimes :: Proxy a -> Property
semiringFromNaturalMapsTimes Proxy a
_ = Bool
-> ((NonNegative Integer, NonNegative Integer) -> Bool)
-> ((NonNegative Integer, NonNegative Integer) -> [String])
-> String
-> ((NonNegative Integer, NonNegative Integer) -> a)
-> String
-> ((NonNegative Integer, NonNegative Integer) -> 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 -> (NonNegative Integer, NonNegative Integer) -> Bool
forall a b. a -> b -> a
const Bool
True)
(\(NonNegative Integer
a, NonNegative Integer
b) -> [String
"a = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ Integer -> String
forall a. Show a => a -> String
show Integer
a, String
"b = " String -> String -> String
forall a. [a] -> [a] -> [a]
++ Integer -> String
forall a. Show a => a -> String
show Integer
b])
String
"fromNatural (a * b)"
(\(NonNegative Integer
a, NonNegative Integer
b) -> Natural -> a
forall a. Semiring a => Natural -> a
fromNatural (Integer -> Natural
forall a. Num a => Integer -> a
fromInteger (Integer
a Integer -> Integer -> Integer
forall a. Semiring a => a -> a -> a
* Integer
b)) :: a)
String
"fromNatural a * fromNatural b"
(\(NonNegative Integer
a, NonNegative Integer
b) -> Natural -> a
forall a. Semiring a => Natural -> a
fromNatural (Integer -> Natural
forall a. Num a => Integer -> a
fromInteger Integer
a) a -> a -> a
forall a. Semiring a => a -> a -> a
* Natural -> a
forall a. Semiring a => Natural -> a
fromNatural (Integer -> Natural
forall a. Num a => Integer -> a
fromInteger Integer
b))
#endif