content: {-# LANGUAGE Rank2Types #-}
  {-# LANGUAGE LiberalTypeSynonyms #-}
  {-# LANGUAGE ScopedTypeVariables #-}
  -- | A collection of properties that can be tested with QuickCheck, to guarantee
  -- that you are working with valid 'Lens'es, 'Setter's, 'Traversal's, 'Iso's and
  -- 'Prism's.
  module Control.Lens.Properties
      ( isLens
      , isTraversal
      , isSetter
      , isIso
      , isPrism
      ) where
  
  import Control.Lens
  import Data.Functor.Compose
  import Test.QuickCheck
  
  --------------------------------------------------------------------------------
  -- | A 'Setter' is only legal if the following 3 laws hold:
  --
  -- 1. @set l y (set l x a) ≡ set l y a@
  --
  -- 2. @over l id ≡ id@
  --
  -- 3. @over l f . over l g ≡ over l (f . g)@
  isSetter :: (Arbitrary s, Arbitrary a, CoArbitrary a, Show s, Show a, Eq s, Function a)
           => Setter' s a -> Property
  isSetter l = setter_id l .&. setter_composition l .&. setter_set_set l
  
  
  --------------------------------------------------------------------------------
  -- | A 'Traversal' is only legal if it is a valid 'Setter' (see 'isSetter' for
  -- what makes a 'Setter' valid), and the following laws hold:
  --
  -- 1. @t pure ≡ pure@
  --
  -- 2. @fmap (t f) . t g ≡ getCompose . t (Compose . fmap f . g)@
  isTraversal :: (Arbitrary s, Arbitrary a, CoArbitrary a, Show s, Show a, Eq s, Function a)
           => Traversal' s a -> Property
  isTraversal l = isSetter l .&. traverse_pureMaybe l .&. traverse_pureList l
                    .&. do as <- arbitrary
                           bs <- arbitrary
                           t <- arbitrary
                           return $ traverse_compose l (\x -> as++[x]++bs)
                                                       (\x -> if t then Just x else Nothing)
  
  
  --------------------------------------------------------------------------------
  -- | A 'Lens' is only legal if it is a valid 'Traversal' (see 'isTraversal' for
  -- what this means), and if the following laws hold:
  --
  -- 1. @view l (set l b a)  ≡ b@
  --
  -- 2. @set l (view l a) a  ≡ a@
  --
  -- 3. @set l c (set l b a) ≡ set l c a@
  isLens :: (Arbitrary s, Arbitrary a, CoArbitrary a, Show s, Show a, Eq s, Eq a, Function a)
         => Lens' s a -> Property
  isLens l = lens_set_view l .&. lens_view_set l .&. isTraversal l
  
  
  --------------------------------------------------------------------------------
  isIso :: (Arbitrary s, Arbitrary a, CoArbitrary s, CoArbitrary a, Show s, Show a, Eq s, Eq a, Function s, Function a)
        => Iso' s a -> Property
  isIso l = iso_hither l .&. iso_yon l .&. isLens l .&. isLens (from l)
  
  
  --------------------------------------------------------------------------------
  isPrism :: (Arbitrary s, Arbitrary a, CoArbitrary a, Show s, Show a, Eq s, Eq a, Function a)
        => Prism' s a -> Property
  isPrism l = isTraversal l .&. prism_yin l .&. prism_yang l
  
  
  --------------------------------------------------------------------------------
  -- The first setter law:
  setter_id :: Eq s => Setter' s a -> s -> Bool
  setter_id l s = over l id s == s
  
  --  The second setter law:
  setter_composition :: Eq s => Setter' s a -> s -> Fun a a -> Fun a a -> Bool
  setter_composition l s (Fun _ f) (Fun _ g) = over l f (over l g s) == over l (f . g) s
  
  lens_set_view :: Eq s => Lens' s a -> s -> Bool
  lens_set_view l s = set l (view l s) s == s
  
  lens_view_set :: Eq a => Lens' s a -> s -> a -> Bool
  lens_view_set l s a = view l (set l a s) == a
  
  setter_set_set :: Eq s => Setter' s a -> s -> a -> a -> Bool
  setter_set_set l s a b = set l b (set l a s) == set l b s
  
  iso_hither :: Eq s => AnIso' s a -> s -> Bool
  iso_hither l s = s ^.cloneIso l.from l == s
  
  iso_yon :: Eq a => AnIso' s a -> a -> Bool
  iso_yon l a = a^.from l.cloneIso l == a
  
  prism_yin :: Eq a => Prism' s a -> a -> Bool
  prism_yin l a = preview l (review l a) == Just a
  
  prism_yang :: Eq s => Prism' s a -> s -> Bool
  prism_yang l s = maybe s (review l) (preview l s) == s
  
  traverse_pure :: forall f s a. (Applicative f, Eq (f s)) => LensLike' f s a -> s -> Bool
  traverse_pure l s = l pure s == (pure s :: f s)
  
  traverse_pureMaybe :: Eq s => LensLike' Maybe s a -> s -> Bool
  traverse_pureMaybe = traverse_pure
  
  traverse_pureList :: Eq s => LensLike' [] s a -> s -> Bool
  traverse_pureList = traverse_pure
  
  traverse_compose :: (Applicative f, Applicative g, Eq (f (g s)))
                      => Traversal' s a -> (a -> g a) -> (a -> f a) -> s -> Bool
  traverse_compose t f g s = (fmap (t f) . t g) s == (getCompose . t (Compose . fmap f . g)) s
  