{-# LANGUAGE AllowAmbiguousTypes #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}

-- | Applicative properties
--
-- You will need @TypeApplications@ to use these.
module Test.Validity.Applicative
  ( applicativeSpec,
    applicativeSpecOnArbitrary,
    applicativeSpecOnGens,
  )
where

import Data.Data
import Data.GenValidity
import Data.Kind
import Test.Hspec
import Test.QuickCheck
import Test.Validity.Functions
import Test.Validity.Utils

{-# ANN module "HLint: ignore Avoid lambda" #-}

pureTypeStr ::
  forall (f :: Type -> Type).
  (Typeable f) =>
  String
pureTypeStr :: String
pureTypeStr = [String] -> String
unwords [String
"pure", String
"::", String
"a", String
"->", Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f, String
"a"]

seqTypeStr ::
  forall (f :: Type -> Type).
  (Typeable f) =>
  String
seqTypeStr :: String
seqTypeStr =
  [String] -> String
unwords
    [ String
"(<*>)",
      String
"::",
      Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f,
      String
"(a",
      String
"->",
      String
"b)",
      String
"->",
      Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f,
      String
"a",
      String
"->",
      Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f,
      String
"b"
    ]

seqrTypeStr ::
  forall (f :: Type -> Type).
  (Typeable f) =>
  String
seqrTypeStr :: String
seqrTypeStr =
  [String] -> String
unwords
    [ String
"(*>)",
      String
"::",
      Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f,
      String
"a",
      String
"->",
      Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f,
      String
"b",
      String
"->",
      Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f,
      String
"b"
    ]

seqlTypeStr ::
  forall (f :: Type -> Type).
  (Typeable f) =>
  String
seqlTypeStr :: String
seqlTypeStr =
  [String] -> String
unwords
    [ String
"(<*)",
      String
"::",
      Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f,
      String
"a",
      String
"->",
      Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f,
      String
"b",
      String
"->",
      Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f,
      String
"a"
    ]

-- | Standard test spec for properties of Applicative instances for values generated with GenValid instances
--
-- Example usage:
--
-- > applicativeSpecOnArbitrary @[]
applicativeSpec ::
  forall (f :: Type -> Type).
  ( Eq (f Int),
    Show (f Int),
    Applicative f,
    Typeable f,
    GenValid (f Int)
  ) =>
  Spec
applicativeSpec :: Spec
applicativeSpec = Gen (f Int) -> Spec
forall (f :: * -> *).
(Show (f Int), Eq (f Int), Applicative f, Typeable f) =>
Gen (f Int) -> Spec
applicativeSpecWithInts @f Gen (f Int)
forall a. GenValid a => Gen a
genValid

-- | Standard test spec for properties of Applicative instances for values generated with Arbitrary instances
--
-- Example usage:
--
-- > applicativeSpecOnArbitrary @[]
applicativeSpecOnArbitrary ::
  forall (f :: Type -> Type).
  (Eq (f Int), Show (f Int), Applicative f, Typeable f, Arbitrary (f Int)) =>
  Spec
applicativeSpecOnArbitrary :: Spec
applicativeSpecOnArbitrary = Gen (f Int) -> Spec
forall (f :: * -> *).
(Show (f Int), Eq (f Int), Applicative f, Typeable f) =>
Gen (f Int) -> Spec
applicativeSpecWithInts @f Gen (f Int)
forall a. Arbitrary a => Gen a
arbitrary

applicativeSpecWithInts ::
  forall (f :: Type -> Type).
  (Show (f Int), Eq (f Int), Applicative f, Typeable f) =>
  Gen (f Int) ->
  Spec
applicativeSpecWithInts :: Gen (f Int) -> Spec
applicativeSpecWithInts Gen (f Int)
gen =
  Gen Int
-> String
-> Gen (f Int)
-> String
-> Gen (f Int)
-> String
-> Gen (Int -> Int)
-> String
-> Gen (f (Int -> Int))
-> String
-> Gen (f (Int -> Int))
-> String
-> Spec
forall (f :: * -> *) a b c.
(Show 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
applicativeSpecOnGens
    @f
    @Int
    Gen Int
forall a. GenValid a => Gen a
genValid
    String
"int"
    Gen (f Int)
gen
    ([String] -> String
unwords [Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f, String
"of ints"])
    Gen (f Int)
gen
    ([String] -> String
unwords [Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f, String
"of ints"])
    (Int -> Int -> Int
forall a. Num a => a -> a -> a
(+) (Int -> Int -> Int) -> Gen Int -> Gen (Int -> Int)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen Int
forall a. GenValid a => Gen a
genValid)
    String
"increments"
    ((Int -> Int) -> f (Int -> Int)
forall (f :: * -> *) a. Applicative f => a -> f a
pure ((Int -> Int) -> f (Int -> Int))
-> Gen (Int -> Int) -> Gen (f (Int -> Int))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (Int -> Int -> Int
forall a. Num a => a -> a -> a
(+) (Int -> Int -> Int) -> Gen Int -> Gen (Int -> Int)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen Int
forall a. GenValid a => Gen a
genValid))
    ([String] -> String
unwords [Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f, String
"of increments"])
    ((Int -> Int) -> f (Int -> Int)
forall (f :: * -> *) a. Applicative f => a -> f a
pure ((Int -> Int) -> f (Int -> Int))
-> Gen (Int -> Int) -> Gen (f (Int -> Int))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (Int -> Int -> Int
forall a. Num a => a -> a -> a
(*) (Int -> Int -> Int) -> Gen Int -> Gen (Int -> Int)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen Int
forall a. GenValid a => Gen a
genValid))
    ([String] -> String
unwords [Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f, String
"of scalings"])

-- | 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"
applicativeSpecOnGens ::
  forall (f :: Type -> Type) (a :: Type) (b :: Type) (c :: Type).
  ( Show 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
applicativeSpecOnGens :: 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
applicativeSpecOnGens Gen a
gena String
genaname Gen (f a)
gen String
genname Gen (f b)
genb String
genbname Gen (a -> b)
genfa String
genfaname Gen (f (a -> b))
genffa String
genffaname Gen (f (b -> c))
genffb String
genffbname =
  Spec -> Spec
forall a. SpecWith a -> SpecWith a
parallel (Spec -> Spec) -> Spec -> Spec
forall a b. (a -> b) -> a -> b
$
    String -> Spec -> Spec
forall a. HasCallStack => String -> SpecWith a -> SpecWith a
describe (String
"Applicative " String -> String -> String
forall a. [a] -> [a] -> [a]
++ Typeable f => String
forall k (a :: k). Typeable a => String
nameOf @f) (Spec -> Spec) -> Spec -> Spec
forall a b. (a -> b) -> a -> b
$ do
      String -> Spec -> Spec
forall a. HasCallStack => String -> SpecWith a -> SpecWith a
describe ([String] -> String
unwords [Typeable f => String
forall (f :: * -> *). Typeable f => String
pureTypeStr @f, String
"and", Typeable f => String
forall (f :: * -> *). Typeable f => String
seqTypeStr @f]) (Spec -> Spec) -> Spec -> Spec
forall a b. (a -> b) -> a -> b
$ do
        String -> Property -> SpecWith (Arg Property)
forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
          ( [String] -> String
unwords
              [ String
"satisfy the identity law: 'pure id <*> v = v' for",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname
              ]
          )
          (Property -> SpecWith (Arg Property))
-> Property -> SpecWith (Arg Property)
forall a b. (a -> b) -> a -> b
$ (f a -> f a)
-> (f a -> f a) -> Gen (f a) -> (f a -> [f a]) -> Property
forall a b.
(Show a, Show b, Eq b) =>
(a -> b) -> (a -> b) -> Gen a -> (a -> [a]) -> Property
equivalentOnGen ((a -> a) -> f (a -> a)
forall (f :: * -> *) a. Applicative f => a -> f a
pure a -> a
forall a. a -> a
id f (a -> a) -> f a -> f a
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*>) f a -> f a
forall a. a -> a
id Gen (f a)
gen f a -> [f a]
forall a. a -> [a]
shrinkNothing
        String -> Property -> SpecWith (Arg Property)
forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
          ( [String] -> String
unwords
              [ String
"satisfy the composition law: 'pure (.) <*> u <*> v <*> w = u <*> (v <*> w)' for",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @(f (b -> c)) String
genffbname,
                String
"composed with",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @(f (a -> b)) String
genffaname,
                String
"and applied to",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname
              ]
          )
          (Property -> SpecWith (Arg Property))
-> Property -> SpecWith (Arg Property)
forall a b. (a -> b) -> a -> b
$ (Anon (f (b -> c)) -> Anon (f (a -> b)) -> f a -> f c)
-> (Anon (f (b -> c)) -> Anon (f (a -> b)) -> f a -> f c)
-> Gen (Anon (f (b -> c)), Anon (f (a -> b)), f a)
-> ((Anon (f (b -> c)), Anon (f (a -> b)), f a)
    -> [(Anon (f (b -> c)), Anon (f (a -> b)), f a)])
-> Property
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
            ( \(Anon f (b -> c)
u) (Anon f (a -> b)
v) f a
w ->
                ((b -> c) -> (a -> b) -> a -> c)
-> f ((b -> c) -> (a -> b) -> a -> c)
forall (f :: * -> *) a. Applicative f => a -> f a
pure (b -> c) -> (a -> b) -> a -> c
forall b c a. (b -> c) -> (a -> b) -> a -> c
(.) f ((b -> c) -> (a -> b) -> a -> c)
-> f (b -> c) -> f ((a -> b) -> a -> c)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (f (b -> c)
u :: f (b -> c)) f ((a -> b) -> a -> c) -> f (a -> b) -> f (a -> c)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (f (a -> b)
v :: f (a -> b))
                  f (a -> c) -> f a -> f c
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (f a
w :: f a) ::
                  f c
            )
            (\(Anon f (b -> c)
u) (Anon f (a -> b)
v) f a
w -> f (b -> c)
u f (b -> c) -> f b -> f c
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (f (a -> b)
v f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
w) :: f c)
            ((,,) (Anon (f (b -> c))
 -> Anon (f (a -> b))
 -> f a
 -> (Anon (f (b -> c)), Anon (f (a -> b)), f a))
-> Gen (Anon (f (b -> c)))
-> Gen
     (Anon (f (a -> b))
      -> f a -> (Anon (f (b -> c)), Anon (f (a -> b)), f a))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (f (b -> c) -> Anon (f (b -> c))
forall a. a -> Anon a
Anon (f (b -> c) -> Anon (f (b -> c)))
-> Gen (f (b -> c)) -> Gen (Anon (f (b -> c)))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (f (b -> c))
genffb) Gen
  (Anon (f (a -> b))
   -> f a -> (Anon (f (b -> c)), Anon (f (a -> b)), f a))
-> Gen (Anon (f (a -> b)))
-> Gen (f a -> (Anon (f (b -> c)), Anon (f (a -> b)), f a))
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (f (a -> b) -> Anon (f (a -> b))
forall a. a -> Anon a
Anon (f (a -> b) -> Anon (f (a -> b)))
-> Gen (f (a -> b)) -> Gen (Anon (f (a -> b)))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (f (a -> b))
genffa) Gen (f a -> (Anon (f (b -> c)), Anon (f (a -> b)), f a))
-> Gen (f a) -> Gen (Anon (f (b -> c)), Anon (f (a -> b)), f a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Gen (f a)
gen)
            (Anon (f (b -> c)), Anon (f (a -> b)), f a)
-> [(Anon (f (b -> c)), Anon (f (a -> b)), f a)]
forall a. a -> [a]
shrinkNothing
        String -> Property -> SpecWith (Arg Property)
forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
          ( [String] -> String
unwords
              [ String
"satisfy the homomorphism law: 'pure f <*> pure x = pure (f x)' for",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @(a -> b) String
genfaname,
                String
"sequenced with",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @a String
genaname
              ]
          )
          (Property -> SpecWith (Arg Property))
-> Property -> SpecWith (Arg Property)
forall a b. (a -> b) -> a -> b
$ (Anon (a -> b) -> a -> f b)
-> (Anon (a -> b) -> a -> f b)
-> Gen (Anon (a -> b), a)
-> ((Anon (a -> b), a) -> [(Anon (a -> b), a)])
-> Property
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) a
x -> (a -> b) -> f (a -> b)
forall (f :: * -> *) a. Applicative f => a -> f a
pure a -> b
f f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
x :: f b)
            (\(Anon a -> b
f) a
x -> b -> f b
forall (f :: * -> *) a. Applicative f => a -> f a
pure (b -> f b) -> b -> f b
forall a b. (a -> b) -> a -> b
$ a -> b
f a
x :: f b)
            ((,) (Anon (a -> b) -> a -> (Anon (a -> b), a))
-> Gen (Anon (a -> b)) -> Gen (a -> (Anon (a -> b), a))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> ((a -> b) -> Anon (a -> b)
forall a. a -> Anon a
Anon ((a -> b) -> Anon (a -> b)) -> Gen (a -> b) -> Gen (Anon (a -> b))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (a -> b)
genfa) Gen (a -> (Anon (a -> b), a)) -> Gen a -> Gen (Anon (a -> b), a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Gen a
gena)
            (Anon (a -> b), a) -> [(Anon (a -> b), a)]
forall a. a -> [a]
shrinkNothing
        String -> Property -> SpecWith (Arg Property)
forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
          ( [String] -> String
unwords
              [ String
"satisfy the interchange law: 'u <*> pure y = pure ($ y) <*> u' for",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @(f (a -> b)) String
genffaname,
                String
"sequenced with",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @a String
genaname
              ]
          )
          (Property -> SpecWith (Arg Property))
-> Property -> SpecWith (Arg Property)
forall a b. (a -> b) -> a -> b
$ (Anon (f (a -> b)) -> a -> f b)
-> (Anon (f (a -> b)) -> a -> f b)
-> Gen (Anon (f (a -> b)), a)
-> ((Anon (f (a -> b)), a) -> [(Anon (f (a -> b)), a)])
-> Property
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)
u) a
y -> f (a -> b)
u f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> a -> f a
forall (f :: * -> *) a. Applicative f => a -> f a
pure a
y :: f b)
            (\(Anon f (a -> b)
u) a
y -> ((a -> b) -> b) -> f ((a -> b) -> b)
forall (f :: * -> *) a. Applicative f => a -> f a
pure ((a -> b) -> a -> b
forall a b. (a -> b) -> a -> b
$ a
y) f ((a -> b) -> b) -> f (a -> b) -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f (a -> b)
u :: f b)
            ((,) (Anon (f (a -> b)) -> a -> (Anon (f (a -> b)), a))
-> Gen (Anon (f (a -> b))) -> Gen (a -> (Anon (f (a -> b)), a))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (f (a -> b) -> Anon (f (a -> b))
forall a. a -> Anon a
Anon (f (a -> b) -> Anon (f (a -> b)))
-> Gen (f (a -> b)) -> Gen (Anon (f (a -> b)))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (f (a -> b))
genffa) Gen (a -> (Anon (f (a -> b)), a))
-> Gen a -> Gen (Anon (f (a -> b)), a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Gen a
gena)
            (Anon (f (a -> b)), a) -> [(Anon (f (a -> b)), a)]
forall a. a -> [a]
shrinkNothing
        String -> Property -> SpecWith (Arg Property)
forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
          ( [String] -> String
unwords
              [ String
"satisfy the law about the functor instance: fmap f x = pure f <*> x for",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @(a -> b) String
genfaname,
                String
"mapped over",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname
              ]
          )
          (Property -> SpecWith (Arg Property))
-> Property -> SpecWith (Arg Property)
forall a b. (a -> b) -> a -> b
$ (Anon (a -> b) -> f a -> f b)
-> (Anon (a -> b) -> f a -> f b)
-> Gen (Anon (a -> b), f a)
-> ((Anon (a -> b), f a) -> [(Anon (a -> b), f a)])
-> Property
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
x -> (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> b
f f a
x)
            (\(Anon a -> b
f) f a
x -> (a -> b) -> f (a -> b)
forall (f :: * -> *) a. Applicative f => a -> f a
pure a -> b
f f (a -> b) -> f a -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
x)
            ((,) (Anon (a -> b) -> f a -> (Anon (a -> b), f a))
-> Gen (Anon (a -> b)) -> Gen (f a -> (Anon (a -> b), f a))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> ((a -> b) -> Anon (a -> b)
forall a. a -> Anon a
Anon ((a -> b) -> Anon (a -> b)) -> Gen (a -> b) -> Gen (Anon (a -> b))
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (a -> b)
genfa) Gen (f a -> (Anon (a -> b), f a))
-> Gen (f a) -> Gen (Anon (a -> b), f a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Gen (f a)
gen)
            (Anon (a -> b), f a) -> [(Anon (a -> b), f a)]
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      String -> Spec -> Spec
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describe (Typeable f => String
forall (f :: * -> *). Typeable f => String
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$
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forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
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unwords
              [ String
"is equivalent to its default implementation 'u Type> v = pure (const id) <*> u <*> v' for",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname,
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"in front of",
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forall k (a :: k). Typeable a => String -> String
genDescr @b String
genbname
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(a -> b -> c)
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equivalentOnGens2
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u f b
v -> f a
u f a -> f b -> f b
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> f b
v)
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u f b
v -> (a -> b -> b) -> f (a -> b -> b)
forall (f :: * -> *) a. Applicative f => a -> f a
pure ((b -> b) -> a -> b -> b
forall a b. a -> b -> a
const b -> b
forall a. a -> a
id) f (a -> b -> b) -> f a -> f (b -> b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
u f (b -> b) -> f b -> f b
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f b
v)
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forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (f a)
gen Gen (f b -> (f a, f b)) -> Gen (f b) -> Gen (f a, f b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
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genb)
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forall a. a -> [a]
shrinkNothing
      String -> Spec -> Spec
forall a. HasCallStack => String -> SpecWith a -> SpecWith a
describe (Typeable f => String
forall (f :: * -> *). Typeable f => String
seqlTypeStr @f) (Spec -> Spec) -> Spec -> Spec
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$
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(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
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unwords
              [ String
"is equivalent to its default implementation 'u <* v = pure const <*> u <*> v' for",
                String -> String
forall k (a :: k). Typeable a => String -> String
genDescr @b String
genbname,
                String
"behind",
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forall k (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname
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(a -> b -> c)
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equivalentOnGens2
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u f b
v -> f a
u f a -> f b -> f a
forall (f :: * -> *) a b. Applicative f => f a -> f b -> f a
<* f b
v)
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u f b
v -> (a -> b -> a) -> f (a -> b -> a)
forall (f :: * -> *) a. Applicative f => a -> f a
pure a -> b -> a
forall a b. a -> b -> a
const f (a -> b -> a) -> f a -> f (b -> a)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
u f (b -> a) -> f b -> f a
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f b
v)
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forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> Gen (f a)
gen Gen (f b -> (f a, f b)) -> Gen (f b) -> Gen (f a, f b)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
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genb)
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forall a. a -> [a]
shrinkNothing