module LawfulConversions.Properties
( isSomeProperties,
isManyProperties,
isProperties,
)
where
import LawfulConversions.Classes
import LawfulConversions.Prelude
import Test.QuickCheck
isSomeProperties ::
(IsSome a b, Eq a, Eq b, Show a, Show b, Arbitrary b) =>
Proxy a ->
Proxy b ->
[(String, Property)]
isSomeProperties :: forall a b.
(IsSome a b, Eq a, Eq b, Show a, Show b, Arbitrary b) =>
Proxy a -> Proxy b -> [(String, Property)]
isSomeProperties Proxy a
aProxy Proxy b
bProxy =
[ ( String
"'to' is injective",
(b -> b -> Property) -> Property
forall prop. Testable prop => prop -> Property
property \b
a b
b ->
b
a b -> b -> Bool
forall a. Eq a => a -> a -> Bool
/= b
b Bool -> Property -> Property
forall prop. Testable prop => Bool -> prop -> Property
==>
b -> a
to' b
a a -> a -> Property
forall a. (Eq a, Show a) => a -> a -> Property
=/= b -> a
to' b
b
),
( String
"'maybeFrom' is a partial inverse of 'to'",
(b -> Property) -> Property
forall prop. Testable prop => prop -> Property
property \b
a ->
a -> Maybe b
maybeFrom' (b -> a
to' b
a) Maybe b -> Maybe b -> Property
forall a. (Eq a, Show a) => a -> a -> Property
=== b -> Maybe b
forall a. a -> Maybe a
Just b
a
)
]
where
to' :: b -> a
to' = Proxy a -> a -> a
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy a
aProxy (a -> a) -> (b -> a) -> b -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. b -> a
forall a b. IsSome a b => b -> a
to (b -> a) -> (b -> b) -> b -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Proxy b -> b -> b
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy b
bProxy
maybeFrom' :: a -> Maybe b
maybeFrom' = (b -> b) -> Maybe b -> Maybe b
forall a b. (a -> b) -> Maybe a -> Maybe b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (Proxy b -> b -> b
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy b
bProxy) (Maybe b -> Maybe b) -> (a -> Maybe b) -> a -> Maybe b
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. a -> Maybe b
forall a b. IsSome a b => a -> Maybe b
maybeFrom (a -> Maybe b) -> (a -> a) -> a -> Maybe b
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Proxy a -> a -> a
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy a
aProxy
isManyProperties ::
(IsMany a b, Eq a, Eq b, Show a, Show b, Arbitrary b) =>
Proxy a ->
Proxy b ->
[(String, Property)]
isManyProperties :: forall a b.
(IsMany a b, Eq a, Eq b, Show a, Show b, Arbitrary b) =>
Proxy a -> Proxy b -> [(String, Property)]
isManyProperties Proxy a
aProxy Proxy b
bProxy =
( String
"'from' is an inverse of 'to'",
(b -> Property) -> Property
forall prop. Testable prop => prop -> Property
property \b
b -> b
b b -> b -> Property
forall a. (Eq a, Show a) => a -> a -> Property
=== a -> b
from' (b -> a
to' b
b)
)
(String, Property) -> [(String, Property)] -> [(String, Property)]
forall a. a -> [a] -> [a]
: Proxy a -> Proxy b -> [(String, Property)]
forall a b.
(IsSome a b, Eq a, Eq b, Show a, Show b, Arbitrary b) =>
Proxy a -> Proxy b -> [(String, Property)]
isSomeProperties Proxy a
aProxy Proxy b
bProxy
where
to' :: b -> a
to' = Proxy a -> a -> a
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy a
aProxy (a -> a) -> (b -> a) -> b -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. b -> a
forall a b. IsSome a b => b -> a
to (b -> a) -> (b -> b) -> b -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Proxy b -> b -> b
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy b
bProxy
from' :: a -> b
from' = Proxy b -> b -> b
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy b
bProxy (b -> b) -> (a -> b) -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. a -> b
forall a b. IsMany a b => a -> b
from (a -> b) -> (a -> a) -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Proxy a -> a -> a
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy a
aProxy
isProperties ::
(Is a b, Eq a, Eq b, Show a, Show b, Arbitrary a, Arbitrary b) =>
Proxy a ->
Proxy b ->
[(String, Property)]
isProperties :: forall a b.
(Is a b, Eq a, Eq b, Show a, Show b, Arbitrary a, Arbitrary b) =>
Proxy a -> Proxy b -> [(String, Property)]
isProperties Proxy a
aProxy Proxy b
bProxy =
( String
"'to' is an inverse of 'from'",
(a -> Property) -> Property
forall prop. Testable prop => prop -> Property
property \a
b -> a
b a -> a -> Property
forall a. (Eq a, Show a) => a -> a -> Property
=== b -> a
to' (a -> b
from' a
b)
)
(String, Property) -> [(String, Property)] -> [(String, Property)]
forall a. a -> [a] -> [a]
: Proxy a -> Proxy b -> [(String, Property)]
forall a b.
(IsMany a b, Eq a, Eq b, Show a, Show b, Arbitrary b) =>
Proxy a -> Proxy b -> [(String, Property)]
isManyProperties Proxy a
aProxy Proxy b
bProxy
where
to' :: b -> a
to' = Proxy a -> a -> a
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy a
aProxy (a -> a) -> (b -> a) -> b -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. b -> a
forall a b. IsSome a b => b -> a
to (b -> a) -> (b -> b) -> b -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Proxy b -> b -> b
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy b
bProxy
from' :: a -> b
from' = Proxy b -> b -> b
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy b
bProxy (b -> b) -> (a -> b) -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. a -> b
forall a b. IsMany a b => a -> b
from (a -> b) -> (a -> a) -> a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
forall {k} (cat :: k -> k -> *) (b :: k) (c :: k) (a :: k).
Category cat =>
cat b c -> cat a b -> cat a c
. Proxy a -> a -> a
forall (proxy :: * -> *) c. proxy c -> c -> c
as Proxy a
aProxy