{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables #-}

-- | Standard tests involving inverse functions
module Test.Validity.Functions.Inverse
  ( inverseFunctionsOnGen,
    inverseFunctions,
    inverseFunctionsOnArbitrary,
    inverseFunctionsIfFirstSucceedsOnGen,
    inverseFunctionsIfFirstSucceeds,
    inverseFunctionsIfFirstSucceedsOnArbitrary,
    inverseFunctionsIfSecondSucceedsOnGen,
    inverseFunctionsIfSecondSucceeds,
    inverseFunctionsIfSecondSucceedsOnArbitrary,
    inverseFunctionsIfSucceedOnGen,
    inverseFunctionsIfSucceed,
    inverseFunctionsIfSucceedOnArbitrary,
  )
where

import Data.GenValidity
import Test.Hspec
import Test.QuickCheck
import Test.Validity.Types

inverseFunctionsOnGen ::
  (Show a, Eq a) => (a -> b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsOnGen :: (a -> b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsOnGen a -> b
f b -> a
g Gen a
gen a -> [a]
s =
  Gen a -> (a -> [a]) -> (a -> Expectation) -> Property
forall a prop.
(Show a, Testable prop) =>
Gen a -> (a -> [a]) -> (a -> prop) -> Property
forAllShrink Gen a
gen a -> [a]
s ((a -> Expectation) -> Property) -> (a -> Expectation) -> Property
forall a b. (a -> b) -> a -> b
$ \a
a -> b -> a
g (a -> b
f a
a) a -> a -> Expectation
forall a. (HasCallStack, Show a, Eq a) => a -> a -> Expectation
`shouldBe` a
a

inverseFunctions ::
  (Show a, Eq a, GenValid a) => (a -> b) -> (b -> a) -> Property
inverseFunctions :: (a -> b) -> (b -> a) -> Property
inverseFunctions a -> b
f b -> a
g = (a -> b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
forall a b.
(Show a, Eq a) =>
(a -> b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsOnGen a -> b
f b -> a
g Gen a
forall a. GenValid a => Gen a
genValid a -> [a]
forall a. GenValid a => a -> [a]
shrinkValid

-- |
-- 'id' is its own inverse function for every type:
-- prop> inverseFunctionsOnArbitrary id (id :: Int -> Int)
inverseFunctionsOnArbitrary ::
  (Show a, Eq a, Arbitrary a) => (a -> b) -> (b -> a) -> Property
inverseFunctionsOnArbitrary :: (a -> b) -> (b -> a) -> Property
inverseFunctionsOnArbitrary a -> b
f b -> a
g = (a -> b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
forall a b.
(Show a, Eq a) =>
(a -> b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsOnGen a -> b
f b -> a
g Gen a
forall a. Arbitrary a => Gen a
arbitrary a -> [a]
forall a. Arbitrary a => a -> [a]
shrink

inverseFunctionsIfFirstSucceedsOnGen ::
  (Show a, Eq a, CanFail f) =>
  (a -> f b) ->
  (b -> a) ->
  Gen a ->
  (a -> [a]) ->
  Property
inverseFunctionsIfFirstSucceedsOnGen :: (a -> f b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfFirstSucceedsOnGen a -> f b
f b -> a
g Gen a
gen a -> [a]
s =
  Gen a -> (a -> [a]) -> (a -> Expectation) -> Property
forall a prop.
(Show a, Testable prop) =>
Gen a -> (a -> [a]) -> (a -> prop) -> Property
forAllShrink Gen a
gen a -> [a]
s ((a -> Expectation) -> Property) -> (a -> Expectation) -> Property
forall a b. (a -> b) -> a -> b
$ \a
a ->
    case f b -> Maybe b
forall (f :: * -> *) a. CanFail f => f a -> Maybe a
resultIfSucceeded (a -> f b
f a
a) of
      Maybe b
Nothing -> () -> Expectation
forall (m :: * -> *) a. Monad m => a -> m a
return () -- fine
      Just b
b -> b -> a
g b
b a -> a -> Expectation
forall a. (HasCallStack, Show a, Eq a) => a -> a -> Expectation
`shouldBe` a
a

inverseFunctionsIfFirstSucceeds ::
  (Show a, Eq a, GenValid a, CanFail f) =>
  (a -> f b) ->
  (b -> a) ->
  Property
inverseFunctionsIfFirstSucceeds :: (a -> f b) -> (b -> a) -> Property
inverseFunctionsIfFirstSucceeds a -> f b
f b -> a
g =
  (a -> f b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
forall a (f :: * -> *) b.
(Show a, Eq a, CanFail f) =>
(a -> f b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfFirstSucceedsOnGen a -> f b
f b -> a
g Gen a
forall a. GenValid a => Gen a
genValid a -> [a]
forall a. GenValid a => a -> [a]
shrinkValid

inverseFunctionsIfFirstSucceedsOnArbitrary ::
  (Show a, Eq a, Arbitrary a, CanFail f) =>
  (a -> f b) ->
  (b -> a) ->
  Property
inverseFunctionsIfFirstSucceedsOnArbitrary :: (a -> f b) -> (b -> a) -> Property
inverseFunctionsIfFirstSucceedsOnArbitrary a -> f b
f b -> a
g =
  (a -> f b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
forall a (f :: * -> *) b.
(Show a, Eq a, CanFail f) =>
(a -> f b) -> (b -> a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfFirstSucceedsOnGen a -> f b
f b -> a
g Gen a
forall a. Arbitrary a => Gen a
arbitrary a -> [a]
forall a. Arbitrary a => a -> [a]
shrink

inverseFunctionsIfSecondSucceedsOnGen ::
  (Show a, Eq a, CanFail f) =>
  (a -> b) ->
  (b -> f a) ->
  Gen a ->
  (a -> [a]) ->
  Property
inverseFunctionsIfSecondSucceedsOnGen :: (a -> b) -> (b -> f a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfSecondSucceedsOnGen a -> b
f b -> f a
g Gen a
gen a -> [a]
s =
  Gen a -> (a -> [a]) -> (a -> Expectation) -> Property
forall a prop.
(Show a, Testable prop) =>
Gen a -> (a -> [a]) -> (a -> prop) -> Property
forAllShrink Gen a
gen a -> [a]
s ((a -> Expectation) -> Property) -> (a -> Expectation) -> Property
forall a b. (a -> b) -> a -> b
$ \a
a ->
    case f a -> Maybe a
forall (f :: * -> *) a. CanFail f => f a -> Maybe a
resultIfSucceeded (b -> f a
g (a -> b
f a
a)) of
      Maybe a
Nothing -> () -> Expectation
forall (m :: * -> *) a. Monad m => a -> m a
return () -- fine
      Just a
r -> a
r a -> a -> Expectation
forall a. (HasCallStack, Show a, Eq a) => a -> a -> Expectation
`shouldBe` a
a

inverseFunctionsIfSecondSucceeds ::
  (Show a, Eq a, GenValid a, CanFail f) =>
  (a -> b) ->
  (b -> f a) ->
  Property
inverseFunctionsIfSecondSucceeds :: (a -> b) -> (b -> f a) -> Property
inverseFunctionsIfSecondSucceeds a -> b
f b -> f a
g =
  (a -> b) -> (b -> f a) -> Gen a -> (a -> [a]) -> Property
forall a (f :: * -> *) b.
(Show a, Eq a, CanFail f) =>
(a -> b) -> (b -> f a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfSecondSucceedsOnGen a -> b
f b -> f a
g Gen a
forall a. GenValid a => Gen a
genValid a -> [a]
forall a. GenValid a => a -> [a]
shrinkValid

inverseFunctionsIfSecondSucceedsOnArbitrary ::
  (Show a, Eq a, Arbitrary a, CanFail f) =>
  (a -> b) ->
  (b -> f a) ->
  Property
inverseFunctionsIfSecondSucceedsOnArbitrary :: (a -> b) -> (b -> f a) -> Property
inverseFunctionsIfSecondSucceedsOnArbitrary a -> b
f b -> f a
g =
  (a -> b) -> (b -> f a) -> Gen a -> (a -> [a]) -> Property
forall a (f :: * -> *) b.
(Show a, Eq a, CanFail f) =>
(a -> b) -> (b -> f a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfSecondSucceedsOnGen a -> b
f b -> f a
g Gen a
forall a. Arbitrary a => Gen a
arbitrary a -> [a]
forall a. Arbitrary a => a -> [a]
shrink

inverseFunctionsIfSucceedOnGen ::
  (Show a, Eq a, CanFail f, CanFail g) =>
  (a -> f b) ->
  (b -> g a) ->
  Gen a ->
  (a -> [a]) ->
  Property
inverseFunctionsIfSucceedOnGen :: (a -> f b) -> (b -> g a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfSucceedOnGen a -> f b
f b -> g a
g Gen a
gen a -> [a]
s =
  Gen a -> (a -> [a]) -> (a -> Expectation) -> Property
forall a prop.
(Show a, Testable prop) =>
Gen a -> (a -> [a]) -> (a -> prop) -> Property
forAllShrink Gen a
gen a -> [a]
s ((a -> Expectation) -> Property) -> (a -> Expectation) -> Property
forall a b. (a -> b) -> a -> b
$ \a
a ->
    case do
      b
fa <- f b -> Maybe b
forall (f :: * -> *) a. CanFail f => f a -> Maybe a
resultIfSucceeded (f b -> Maybe b) -> f b -> Maybe b
forall a b. (a -> b) -> a -> b
$ a -> f b
f a
a
      g a -> Maybe a
forall (f :: * -> *) a. CanFail f => f a -> Maybe a
resultIfSucceeded (g a -> Maybe a) -> g a -> Maybe a
forall a b. (a -> b) -> a -> b
$ b -> g a
g b
fa of
      Maybe a
Nothing -> () -> Expectation
forall (m :: * -> *) a. Monad m => a -> m a
return () -- fine
      Just a
r -> a
r a -> a -> Expectation
forall a. (HasCallStack, Show a, Eq a) => a -> a -> Expectation
`shouldBe` a
a

inverseFunctionsIfSucceed ::
  (Show a, Eq a, GenValid a, CanFail f, CanFail g) =>
  (a -> f b) ->
  (b -> g a) ->
  Property
inverseFunctionsIfSucceed :: (a -> f b) -> (b -> g a) -> Property
inverseFunctionsIfSucceed a -> f b
f b -> g a
g =
  (a -> f b) -> (b -> g a) -> Gen a -> (a -> [a]) -> Property
forall a (f :: * -> *) (g :: * -> *) b.
(Show a, Eq a, CanFail f, CanFail g) =>
(a -> f b) -> (b -> g a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfSucceedOnGen a -> f b
f b -> g a
g Gen a
forall a. GenValid a => Gen a
genValid a -> [a]
forall a. GenValid a => a -> [a]
shrinkValid

inverseFunctionsIfSucceedOnArbitrary ::
  (Show a, Eq a, Arbitrary a, CanFail f, CanFail g) =>
  (a -> f b) ->
  (b -> g a) ->
  Property
inverseFunctionsIfSucceedOnArbitrary :: (a -> f b) -> (b -> g a) -> Property
inverseFunctionsIfSucceedOnArbitrary a -> f b
f b -> g a
g =
  (a -> f b) -> (b -> g a) -> Gen a -> (a -> [a]) -> Property
forall a (f :: * -> *) (g :: * -> *) b.
(Show a, Eq a, CanFail f, CanFail g) =>
(a -> f b) -> (b -> g a) -> Gen a -> (a -> [a]) -> Property
inverseFunctionsIfSucceedOnGen a -> f b
f b -> g a
g Gen a
forall a. Arbitrary a => Gen a
arbitrary a -> [a]
forall a. Arbitrary a => a -> [a]
shrink