{-# LANGUAGE AllowAmbiguousTypes #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
module Test.Validity.Monad
( monadSpec,
monadSpecOnArbitrary,
monadSpecOnGens,
)
where
import Control.Monad (ap)
import Data.Data
import Data.GenValidity
import Data.Kind (Type)
import Test.Hspec
import Test.QuickCheck
import Test.QuickCheck.Gen (unGen)
import Test.QuickCheck.Random (mkQCGen)
import Test.Validity.Functions
import Test.Validity.Utils
{-# ANN module "HLint: ignore Use fmap" #-}
{-# ANN module "HLint: ignore Use <$>" #-}
{-# ANN module "HLint: ignore Use >=>" #-}
{-# ANN module "HLint: ignore Use id" #-}
{-# ANN module "HLint: ignore Monad law, left identity" #-}
{-# ANN module "HLint: ignore Monad law, right identity" #-}
{-# ANN module "HLint: ignore Avoid lambda" #-}
{-# ANN module "HLint: ignore Reduce duplication" #-}
returnTypeStr ::
forall (m :: Type -> Type).
(Typeable m) =>
String
returnTypeStr :: forall (m :: * -> *). Typeable m => String
returnTypeStr = [String] -> String
unwords [String
"return", String
"::", String
"a", String
"->", forall {k} (a :: k). Typeable a => String
nameOf @m, String
"a"]
bindTypeStr ::
forall (m :: Type -> Type).
(Typeable m) =>
String
bindTypeStr :: forall (m :: * -> *). Typeable m => String
bindTypeStr =
[String] -> String
unwords
[ String
"(>>=)",
String
"::",
forall {k} (a :: k). Typeable a => String
nameOf @m,
String
"a",
String
"->",
String
"(b",
String
"->",
forall {k} (a :: k). Typeable a => String
nameOf @m,
String
"a)",
String
"->",
forall {k} (a :: k). Typeable a => String
nameOf @m,
String
"b"
]
monadSpec ::
forall (f :: Type -> Type).
(Eq (f Int), Show (f Int), Monad f, Typeable f, GenValid (f Int)) =>
Spec
monadSpec :: forall (f :: * -> *).
(Eq (f Int), Show (f Int), Monad f, Typeable f,
GenValid (f Int)) =>
Spec
monadSpec = forall (f :: * -> *).
(Eq (f Int), Show (f Int), Monad f, Typeable f) =>
Gen (f Int) -> Spec
monadSpecWithInts @f forall a. GenValid a => Gen a
genValid
monadSpecOnArbitrary ::
forall (f :: Type -> Type).
(Eq (f Int), Show (f Int), Monad f, Typeable f, Arbitrary (f Int)) =>
Spec
monadSpecOnArbitrary :: forall (f :: * -> *).
(Eq (f Int), Show (f Int), Monad f, Typeable f,
Arbitrary (f Int)) =>
Spec
monadSpecOnArbitrary = forall (f :: * -> *).
(Eq (f Int), Show (f Int), Monad f, Typeable f) =>
Gen (f Int) -> Spec
monadSpecWithInts @f forall a. Arbitrary a => Gen a
arbitrary
monadSpecWithInts ::
forall (f :: Type -> Type).
(Eq (f Int), Show (f Int), Monad f, Typeable f) =>
Gen (f Int) ->
Spec
monadSpecWithInts :: forall (f :: * -> *).
(Eq (f Int), Show (f Int), Monad f, Typeable f) =>
Gen (f Int) -> Spec
monadSpecWithInts Gen (f Int)
gen =
forall (f :: * -> *) a b c.
(Show 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
monadSpecOnGens
@f
@Int
forall a. GenValid a => Gen a
genValid
String
"int"
Gen (f Int)
gen
([String] -> String
unwords [forall {k} (a :: k). Typeable a => String
nameOf @f, String
"of ints"])
Gen (f Int)
gen
([String] -> String
unwords [forall {k} (a :: k). Typeable a => String
nameOf @f, String
"of ints"])
(forall a. Num a => a -> a -> a
(+) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall a. GenValid a => Gen a
genValid)
String
"increments"
( do
Int
s <- Gen Int
genListLength
forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$ \Int
b -> forall a. Gen a -> QCGen -> Int -> a
unGen Gen (f Int)
gen (Int -> QCGen
mkQCGen Int
b) Int
s
)
String
"perturbations using the int"
( do
Int
s <- Gen Int
genListLength
forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$ \Int
b -> forall a. Gen a -> QCGen -> Int -> a
unGen Gen (f Int)
gen (Int -> QCGen
mkQCGen forall a b. (a -> b) -> a -> b
$ Int
2 forall a. Num a => a -> a -> a
* Int
b) Int
s
)
String
"perturbations using the double the int"
(forall (f :: * -> *) a. Applicative f => a -> f a
pure forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (forall a. Num a => a -> a -> a
(+) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall a. GenValid a => Gen a
genValid))
([String] -> String
unwords [forall {k} (a :: k). Typeable a => String
nameOf @f, String
"of additions"])
monadSpecOnGens ::
forall (f :: Type -> Type) (a :: Type) (b :: Type) (c :: Type).
( Show 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
monadSpecOnGens :: forall (f :: * -> *) a b c.
(Show 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
monadSpecOnGens Gen a
gena String
genaname Gen (f a)
gen String
genname Gen (f b)
genb String
genbname Gen (a -> b)
geng String
gengname Gen (a -> f b)
genbf String
genbfname Gen (b -> f c)
gencf String
gencfname Gen (f (a -> b))
genfab String
genfabname =
forall a. SpecWith a -> SpecWith a
parallel forall a b. (a -> b) -> a -> b
$
forall a. HasCallStack => String -> SpecWith a -> SpecWith a
describe (String
"Monad " forall a. [a] -> [a] -> [a]
++ forall {k} (a :: k). Typeable a => String
nameOf @f) forall a b. (a -> b) -> a -> b
$ do
forall a. HasCallStack => String -> SpecWith a -> SpecWith a
describe ([String] -> String
unwords [forall (m :: * -> *). Typeable m => String
returnTypeStr @f, String
"and", forall (m :: * -> *). Typeable m => String
bindTypeStr @f]) forall a b. (a -> b) -> a -> b
$ do
forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
( [String] -> String
unwords
[ String
"satisfy the first Monad law: 'return a >>= k = k a' for",
forall {k} (a :: k). Typeable a => String -> String
genDescr @a String
genaname,
String
"and",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(a -> f b) String
genbfname
]
)
forall a b. (a -> b) -> a -> b
$ forall a b c.
(Show a, Show b, Show c, Eq c) =>
(a -> b -> c)
-> (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalentOnGens2
(\a
a (Anon a -> f b
k) -> forall (m :: * -> *) a. Monad m => a -> m a
return a
a forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= a -> f b
k)
(\a
a (Anon a -> f b
k) -> a -> f b
k a
a)
((,) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen a
gena forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (forall a. a -> Anon a
Anon forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (a -> f b)
genbf))
forall a. a -> [a]
shrinkNothing
forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
( [String] -> String
unwords
[ String
"satisfy the second Monad law: 'm >>= return = m' for",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname
]
)
forall a b. (a -> b) -> a -> b
$ forall a b.
(Show a, Show b, Eq b) =>
(a -> b) -> (a -> b) -> Gen a -> (a -> [a]) -> Property
equivalentOnGen (\f a
m -> f a
m forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= forall (m :: * -> *) a. Monad m => a -> m a
return) (\f a
m -> f a
m) Gen (f a)
gen forall a. a -> [a]
shrinkNothing
forall a. HasCallStack => String -> SpecWith a -> SpecWith a
describe (forall (m :: * -> *). Typeable m => String
bindTypeStr @f)
forall a b. (a -> b) -> a -> b
$ forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
( [String] -> String
unwords
[ String
"satisfies the third Monad law: 'm >>= (x -> k x >>= h) = (m >>= k) >>= h' for",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname,
forall {k} (a :: k). Typeable a => String -> String
genDescr @(a -> f b) String
genbfname,
String
"and",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(b -> f c) String
gencfname
]
)
forall a b. (a -> b) -> a -> b
$ forall a b c d.
(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
equivalentOnGens3
(\f a
m (Anon a -> f b
k) (Anon b -> f c
h) -> f a
m forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= (\a
x -> a -> f b
k a
x forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= b -> f c
h))
(\f a
m (Anon a -> f b
k) (Anon b -> f c
h) -> (f a
m forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= a -> f b
k) forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= b -> f c
h)
((,,) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (f a)
gen forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (forall a. a -> Anon a
Anon forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (a -> f b)
genbf) forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (forall a. a -> Anon a
Anon forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (b -> f c)
gencf))
forall a. a -> [a]
shrinkNothing
forall a. HasCallStack => String -> SpecWith a -> SpecWith a
describe ([String] -> String
unwords [String
"relation with Applicative", forall {k} (a :: k). Typeable a => String
nameOf @f]) forall a b. (a -> b) -> a -> b
$ do
forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
( [String] -> String
unwords
[String
"satisfies 'pure = return' for", forall {k} (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname]
)
forall a b. (a -> b) -> a -> b
$ forall a b.
(Show a, Show b, Eq b) =>
(a -> b) -> (a -> b) -> Gen a -> (a -> [a]) -> Property
equivalentOnGen (forall (f :: * -> *) a. Applicative f => a -> f a
pure @f) (forall (m :: * -> *) a. Monad m => a -> m a
return @f) Gen a
gena forall a. a -> [a]
shrinkNothing
forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
( [String] -> String
unwords
[ String
"satisfies '(<*>) = ap' for",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f (a -> b)) String
genfabname,
String
"and",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname
]
)
forall a b. (a -> b) -> a -> b
$ forall a b c.
(Show a, Show b, Show c, Eq c) =>
(a -> b -> c)
-> (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalentOnGens2
(\(Anon f (a -> b)
a) f a
b -> f (a -> b)
a forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
b)
(\(Anon f (a -> b)
a) f a
b -> forall (m :: * -> *) a b. Monad m => m (a -> b) -> m a -> m b
ap f (a -> b)
a f a
b)
((,) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (forall a. a -> Anon a
Anon forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (f (a -> b))
genfab) forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Gen (f a)
gen)
forall a. a -> [a]
shrinkNothing
forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
( [String] -> String
unwords
[ String
"satisfies '(>>) = (*>)' for",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname,
String
"and",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f b) String
genbname
]
)
forall a b. (a -> b) -> a -> b
$ forall a b c.
(Show a, Show b, Show c, Eq c) =>
(a -> b -> c)
-> (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalentOnGens2 forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
(>>) forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
(*>) ((,) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (f a)
gen forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Gen (f b)
genb) forall a. a -> [a]
shrinkNothing
forall a. HasCallStack => String -> SpecWith a -> SpecWith a
describe ([String] -> String
unwords [String
"relation with Functor", forall {k} (a :: k). Typeable a => String
nameOf @f])
forall a b. (a -> b) -> a -> b
$ forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
( [String] -> String
unwords
[ String
"satisfies 'fmap f xs = xs >>= return . f' for",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(a -> b) String
gengname,
String
"and",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname
]
)
forall a b. (a -> b) -> a -> b
$ forall a b c.
(Show a, Show b, Show c, Eq c) =>
(a -> b -> c)
-> (a -> b -> c) -> Gen (a, b) -> ((a, b) -> [(a, b)]) -> Property
equivalentOnGens2
(\(Anon a -> b
f) f a
xs -> forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f f a
xs)
(\(Anon a -> b
f) f a
xs -> f a
xs forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= (forall (m :: * -> *) a. Monad m => a -> m a
return forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> b
f))
((,) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (forall a. a -> Anon a
Anon forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (a -> b)
geng) forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Gen (f a)
gen)
forall a. a -> [a]
shrinkNothing