{-# LANGUAGE AllowAmbiguousTypes #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE TypeApplications #-}
module Test.Validity.Applicative
( applicativeSpec,
applicativeSpecOnArbitrary,
applicativeSpecOnGens,
)
where
import Data.Data
import Data.GenValidity
import Data.Kind
import GHC.Stack
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 :: forall (f :: * -> *). Typeable f => String
pureTypeStr = [String] -> String
unwords [String
"pure", String
"::", String
"a", String
"->", forall {k} (a :: k). Typeable a => String
nameOf @f, String
"a"]
seqTypeStr ::
forall (f :: Type -> Type).
(Typeable f) =>
String
seqTypeStr :: forall (f :: * -> *). Typeable f => String
seqTypeStr =
[String] -> String
unwords
[ String
"(<*>)",
String
"::",
forall {k} (a :: k). Typeable a => String
nameOf @f,
String
"(a",
String
"->",
String
"b)",
String
"->",
forall {k} (a :: k). Typeable a => String
nameOf @f,
String
"a",
String
"->",
forall {k} (a :: k). Typeable a => String
nameOf @f,
String
"b"
]
seqrTypeStr ::
forall (f :: Type -> Type).
(Typeable f) =>
String
seqrTypeStr :: forall (f :: * -> *). Typeable f => String
seqrTypeStr =
[String] -> String
unwords
[ String
"(*>)",
String
"::",
forall {k} (a :: k). Typeable a => String
nameOf @f,
String
"a",
String
"->",
forall {k} (a :: k). Typeable a => String
nameOf @f,
String
"b",
String
"->",
forall {k} (a :: k). Typeable a => String
nameOf @f,
String
"b"
]
seqlTypeStr ::
forall (f :: Type -> Type).
(Typeable f) =>
String
seqlTypeStr :: forall (f :: * -> *). Typeable f => String
seqlTypeStr =
[String] -> String
unwords
[ String
"(<*)",
String
"::",
forall {k} (a :: k). Typeable a => String
nameOf @f,
String
"a",
String
"->",
forall {k} (a :: k). Typeable a => String
nameOf @f,
String
"b",
String
"->",
forall {k} (a :: k). Typeable a => String
nameOf @f,
String
"a"
]
applicativeSpec ::
forall (f :: Type -> Type).
( HasCallStack,
Eq (f Int),
Show (f Int),
Applicative f,
Typeable f,
GenValid (f Int)
) =>
Spec
applicativeSpec :: forall (f :: * -> *).
(HasCallStack, Eq (f Int), Show (f Int), Applicative f, Typeable f,
GenValid (f Int)) =>
Spec
applicativeSpec = forall a. HasCallStack => (HasCallStack => a) -> a
withFrozenCallStack forall a b. (a -> b) -> a -> b
$ forall (f :: * -> *).
(HasCallStack, Show (f Int), Eq (f Int), Applicative f,
Typeable f) =>
Gen (f Int) -> Spec
applicativeSpecWithInts @f forall a. GenValid a => Gen a
genValid
applicativeSpecOnArbitrary ::
forall (f :: Type -> Type).
( HasCallStack,
Eq (f Int),
Show (f Int),
Applicative f,
Typeable f,
Arbitrary (f Int)
) =>
Spec
applicativeSpecOnArbitrary :: forall (f :: * -> *).
(HasCallStack, Eq (f Int), Show (f Int), Applicative f, Typeable f,
Arbitrary (f Int)) =>
Spec
applicativeSpecOnArbitrary = forall a. HasCallStack => (HasCallStack => a) -> a
withFrozenCallStack forall a b. (a -> b) -> a -> b
$ forall (f :: * -> *).
(HasCallStack, Show (f Int), Eq (f Int), Applicative f,
Typeable f) =>
Gen (f Int) -> Spec
applicativeSpecWithInts @f forall a. Arbitrary a => Gen a
arbitrary
applicativeSpecWithInts ::
forall (f :: Type -> Type).
(HasCallStack, Show (f Int), Eq (f Int), Applicative f, Typeable f) =>
Gen (f Int) ->
Spec
applicativeSpecWithInts :: forall (f :: * -> *).
(HasCallStack, Show (f Int), Eq (f Int), Applicative f,
Typeable f) =>
Gen (f Int) -> Spec
applicativeSpecWithInts Gen (f Int)
gen =
forall a. HasCallStack => (HasCallStack => a) -> a
withFrozenCallStack forall a b. (a -> b) -> a -> b
$
forall (f :: * -> *) a b c.
(HasCallStack, 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
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
<$> forall a. GenValid a => Gen a
genValid)
String
"increments"
(forall (f :: * -> *) a. Applicative f => a -> f a
pure forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (forall a. Num a => a -> a -> a
(+) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> forall a. GenValid a => Gen a
genValid))
([String] -> String
unwords [forall {k} (a :: k). Typeable a => String
nameOf @f, String
"of increments"])
(forall (f :: * -> *) a. Applicative f => a -> f a
pure forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
<$> (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 scalings"])
applicativeSpecOnGens ::
forall (f :: Type -> Type) (a :: Type) (b :: Type) (c :: Type).
( HasCallStack,
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 :: forall (f :: * -> *) a b c.
(HasCallStack, 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
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 =
forall a. HasCallStack => (HasCallStack => a) -> a
withFrozenCallStack forall a b. (a -> b) -> a -> b
$
forall a. SpecWith a -> SpecWith a
parallel forall a b. (a -> b) -> a -> b
$
forall a. HasCallStack => String -> SpecWith a -> SpecWith a
describe (String
"Applicative " 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 (f :: * -> *). Typeable f => String
pureTypeStr @f, String
"and", forall (f :: * -> *). Typeable f => String
seqTypeStr @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 identity law: 'pure id <*> v = v' 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 forall a. a -> a
id forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*>) forall a. a -> a
id Gen (f a)
gen forall a. a -> [a]
shrinkNothing
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",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f (b -> c)) String
genffbname,
String
"composed with",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f (a -> b)) String
genffaname,
String
"and applied to",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname
]
)
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
( \(Anon f (b -> c)
u) (Anon f (a -> b)
v) f a
w ->
forall (f :: * -> *) a. Applicative f => a -> f a
pure forall b c a. (b -> c) -> (a -> b) -> a -> c
(.)
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (f (b -> c)
u :: f (b -> c))
forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (f (a -> b)
v :: f (a -> b))
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 forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> (f (a -> b)
v forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
w) :: f c)
((,,) 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 (b -> c))
genffb) 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 (f (a -> b))
genffa) 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
"satisfy the homomorphism law: 'pure f <*> pure x = pure (f x)' for",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(a -> b) String
genfaname,
String
"sequenced with",
forall {k} (a :: k). Typeable a => String -> String
genDescr @a String
genaname
]
)
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) a
x -> forall (f :: * -> *) a. Applicative f => a -> f a
pure a -> b
f forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> forall (f :: * -> *) a. Applicative f => a -> f a
pure a
x :: f b)
(\(Anon a -> b
f) a
x -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. (a -> b) -> a -> b
$ a -> b
f a
x :: f 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 (a -> b)
genfa) forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Gen a
gena)
forall a. a -> [a]
shrinkNothing
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",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f (a -> b)) String
genffaname,
String
"sequenced with",
forall {k} (a :: k). Typeable a => String -> String
genDescr @a String
genaname
]
)
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)
u) a
y -> f (a -> b)
u forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> forall (f :: * -> *) a. Applicative f => a -> f a
pure a
y :: f b)
(\(Anon f (a -> b)
u) a
y -> forall (f :: * -> *) a. Applicative f => a -> f a
pure (forall a b. (a -> b) -> a -> b
$ a
y) forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f (a -> b)
u :: f 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))
genffa) forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> Gen a
gena)
forall a. a -> [a]
shrinkNothing
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",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(a -> b) String
genfaname,
String
"mapped over",
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
x -> 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 -> forall (f :: * -> *) a. Applicative f => a -> f a
pure a -> b
f forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
x)
((,) 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)
genfa) 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 => String -> SpecWith a -> SpecWith a
describe (forall (f :: * -> *). Typeable f => String
seqrTypeStr @f)
forall a b. (a -> b) -> a -> b
$ forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
( [String] -> String
unwords
[ String
"is equivalent to its default implementation 'u Type> v = pure (const id) <*> u <*> v' for",
forall {k} (a :: k). Typeable a => String -> String
genDescr @(f a) String
genname,
String
"in front of",
forall {k} (a :: k). Typeable a => String -> String
genDescr @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
(\f a
u f b
v -> f a
u forall (f :: * -> *) a b. Applicative f => f a -> f b -> f b
*> f b
v)
(\f a
u f b
v -> forall (f :: * -> *) a. Applicative f => a -> f a
pure (forall a b. a -> b -> a
const forall a. a -> a
id) forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
u forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f b
v)
((,) 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 (forall (f :: * -> *). Typeable f => String
seqlTypeStr @f)
forall a b. (a -> b) -> a -> b
$ forall a.
(HasCallStack, Example a) =>
String -> a -> SpecWith (Arg a)
it
( [String] -> String
unwords
[ String
"is equivalent to its default implementation 'u <* v = pure const <*> u <*> v' for",
forall {k} (a :: k). Typeable a => String -> String
genDescr @b String
genbname,
String
"behind",
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
(\f a
u f b
v -> f a
u forall (f :: * -> *) a b. Applicative f => f a -> f b -> f a
<* f b
v)
(\f a
u f b
v -> forall (f :: * -> *) a. Applicative f => a -> f a
pure forall a b. a -> b -> a
const forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f a
u forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
<*> f b
v)
((,) 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