{-# LANGUAGE PolyKinds, StandaloneDeriving, UndecidableInstances #-} -- | n-ary products (and products of products) module Data.SOP.NP ( -- * Datatypes NP(..) , POP(..) , unPOP -- * Constructing products , pure_NP , pure_POP , cpure_NP , cpure_POP -- ** Construction from a list , fromList -- * Application , ap_NP , ap_POP -- * Destructing products , hd , tl , Projection , projections , shiftProjection -- * Lifting / mapping , liftA_NP , liftA_POP , liftA2_NP , liftA2_POP , liftA3_NP , liftA3_POP , map_NP , map_POP , zipWith_NP , zipWith_POP , zipWith3_NP , zipWith3_POP , cliftA_NP , cliftA_POP , cliftA2_NP , cliftA2_POP , cliftA3_NP , cliftA3_POP , cmap_NP , cmap_POP , czipWith_NP , czipWith_POP , czipWith3_NP , czipWith3_POP -- * Dealing with @'All' c@ , hcliftA' , hcliftA2' , hcliftA3' , cliftA2'_NP -- * Collapsing , collapse_NP , collapse_POP -- * Folding and sequencing , ctraverse__NP , ctraverse__POP , traverse__NP , traverse__POP , cfoldMap_NP , cfoldMap_POP , sequence'_NP , sequence'_POP , sequence_NP , sequence_POP , ctraverse'_NP , ctraverse'_POP , traverse'_NP , traverse'_POP , ctraverse_NP , ctraverse_POP -- * Catamorphism and anamorphism , cata_NP , ccata_NP , ana_NP , cana_NP -- * Transformation of index lists and coercions , trans_NP , trans_POP , coerce_NP , coerce_POP , fromI_NP , fromI_POP , toI_NP , toI_POP ) where import Data.Coerce import Data.Kind (Type) import Data.Proxy (Proxy(..)) import Unsafe.Coerce #if !MIN_VERSION_base(4,11,0) import Data.Semigroup (Semigroup (..)) #endif import Control.DeepSeq (NFData(..)) import Data.SOP.BasicFunctors import Data.SOP.Classes import Data.SOP.Constraint import Data.SOP.Sing -- | An n-ary product. -- -- The product is parameterized by a type constructor @f@ and -- indexed by a type-level list @xs@. The length of the list -- determines the number of elements in the product, and if the -- @i@-th element of the list is of type @x@, then the @i@-th -- element of the product is of type @f x@. -- -- The constructor names are chosen to resemble the names of the -- list constructors. -- -- Two common instantiations of @f@ are the identity functor 'I' -- and the constant functor 'K'. For 'I', the product becomes a -- heterogeneous list, where the type-level list describes the -- types of its components. For @'K' a@, the product becomes a -- homogeneous list, where the contents of the type-level list are -- ignored, but its length still specifies the number of elements. -- -- In the context of the SOP approach to generic programming, an -- n-ary product describes the structure of the arguments of a -- single data constructor. -- -- /Examples:/ -- -- > I 'x' :* I True :* Nil :: NP I '[ Char, Bool ] -- > K 0 :* K 1 :* Nil :: NP (K Int) '[ Char, Bool ] -- > Just 'x' :* Nothing :* Nil :: NP Maybe '[ Char, Bool ] -- data NP :: (k -> Type) -> [k] -> Type where Nil :: NP f '[] (:*) :: f x -> NP f xs -> NP f (x ': xs) infixr 5 :* -- This is written manually, -- because built-in deriving doesn't use associativity information! instance All (Show `Compose` f) xs => Show (NP f xs) where showsPrec _ Nil = showString "Nil" showsPrec d (f :* fs) = showParen (d > 5) $ showsPrec (5 + 1) f . showString " :* " . showsPrec 5 fs deriving instance All (Eq `Compose` f) xs => Eq (NP f xs) deriving instance (All (Eq `Compose` f) xs, All (Ord `Compose` f) xs) => Ord (NP f xs) -- | @since 0.4.0.0 instance All (Semigroup `Compose` f) xs => Semigroup (NP f xs) where (<>) = czipWith_NP (Proxy :: Proxy (Semigroup `Compose` f)) (<>) -- | @since 0.4.0.0 instance (All (Monoid `Compose` f) xs #if MIN_VERSION_base(4,11,0) , All (Semigroup `Compose` f) xs -- GHC isn't smart enough to figure this out #endif ) => Monoid (NP f xs) where mempty = cpure_NP (Proxy :: Proxy (Monoid `Compose` f)) mempty mappend = czipWith_NP (Proxy :: Proxy (Monoid `Compose` f)) mappend -- | @since 0.2.5.0 instance All (NFData `Compose` f) xs => NFData (NP f xs) where rnf Nil = () rnf (x :* xs) = rnf x `seq` rnf xs -- | A product of products. -- -- This is a 'newtype' for an 'NP' of an 'NP'. The elements of the -- inner products are applications of the parameter @f@. The type -- 'POP' is indexed by the list of lists that determines the lengths -- of both the outer and all the inner products, as well as the types -- of all the elements of the inner products. -- -- A 'POP' is reminiscent of a two-dimensional table (but the inner -- lists can all be of different length). In the context of the SOP -- approach to generic programming, a 'POP' is useful to represent -- information that is available for all arguments of all constructors -- of a datatype. -- newtype POP (f :: (k -> Type)) (xss :: [[k]]) = POP (NP (NP f) xss) deriving instance (Show (NP (NP f) xss)) => Show (POP f xss) deriving instance (Eq (NP (NP f) xss)) => Eq (POP f xss) deriving instance (Ord (NP (NP f) xss)) => Ord (POP f xss) -- | @since 0.4.0.0 instance (Semigroup (NP (NP f) xss)) => Semigroup (POP f xss) where POP xss <> POP yss = POP (xss <> yss) -- | @since 0.4.0.0 instance (Monoid (NP (NP f) xss)) => Monoid (POP f xss) where mempty = POP mempty mappend (POP xss) (POP yss) = POP (mappend xss yss) -- | @since 0.2.5.0 instance (NFData (NP (NP f) xss)) => NFData (POP f xss) where rnf (POP xss) = rnf xss -- | Unwrap a product of products. unPOP :: POP f xss -> NP (NP f) xss unPOP (POP xss) = xss type instance AllN NP c = All c type instance AllN POP c = All2 c type instance AllZipN NP c = AllZip c type instance AllZipN POP c = AllZip2 c type instance SListIN NP = SListI type instance SListIN POP = SListI2 -- * Constructing products -- | Specialization of 'hpure'. -- -- The call @'pure_NP' x@ generates a product that contains 'x' in every -- element position. -- -- /Example:/ -- -- >>> pure_NP [] :: NP [] '[Char, Bool] -- "" :* [] :* Nil -- >>> pure_NP (K 0) :: NP (K Int) '[Double, Int, String] -- K 0 :* K 0 :* K 0 :* Nil -- pure_NP :: forall f xs. SListI xs => (forall a. f a) -> NP f xs pure_NP f = cpure_NP topP f {-# INLINE pure_NP #-} -- | Specialization of 'hpure'. -- -- The call @'pure_POP' x@ generates a product of products that contains 'x' -- in every element position. -- pure_POP :: All SListI xss => (forall a. f a) -> POP f xss pure_POP f = cpure_POP topP f {-# INLINE pure_POP #-} topP :: Proxy Top topP = Proxy -- | Specialization of 'hcpure'. -- -- The call @'cpure_NP' p x@ generates a product that contains 'x' in every -- element position. -- cpure_NP :: forall c xs proxy f. All c xs => proxy c -> (forall a. c a => f a) -> NP f xs cpure_NP p f = case sList :: SList xs of SNil -> Nil SCons -> f :* cpure_NP p f -- | Specialization of 'hcpure'. -- -- The call @'cpure_NP' p x@ generates a product of products that contains 'x' -- in every element position. -- cpure_POP :: forall c xss proxy f. All2 c xss => proxy c -> (forall a. c a => f a) -> POP f xss cpure_POP p f = POP (cpure_NP (allP p) (cpure_NP p f)) allP :: proxy c -> Proxy (All c) allP _ = Proxy instance HPure NP where hpure = pure_NP hcpure = cpure_NP instance HPure POP where hpure = pure_POP hcpure = cpure_POP -- ** Construction from a list -- | Construct a homogeneous n-ary product from a normal Haskell list. -- -- Returns 'Nothing' if the length of the list does not exactly match the -- expected size of the product. -- fromList :: SListI xs => [a] -> Maybe (NP (K a) xs) fromList = go sList where go :: SList xs -> [a] -> Maybe (NP (K a) xs) go SNil [] = return Nil go SCons (x:xs) = do ys <- go sList xs ; return (K x :* ys) go _ _ = Nothing -- * Application -- | Specialization of 'hap'. -- -- Applies a product of (lifted) functions pointwise to a product of -- suitable arguments. -- ap_NP :: NP (f -.-> g) xs -> NP f xs -> NP g xs ap_NP Nil Nil = Nil ap_NP (Fn f :* fs) (x :* xs) = f x :* ap_NP fs xs -- | Specialization of 'hap'. -- -- Applies a product of (lifted) functions pointwise to a product of -- suitable arguments. -- ap_POP :: POP (f -.-> g) xss -> POP f xss -> POP g xss ap_POP (POP fss') (POP xss') = POP (go fss' xss') where go :: NP (NP (f -.-> g)) xss -> NP (NP f) xss -> NP (NP g) xss go Nil Nil = Nil go (fs :* fss) (xs :* xss) = ap_NP fs xs :* go fss xss -- The definition of 'ap_POP' is a more direct variant of -- '_ap_POP_spec'. The direct definition has the advantage -- that it avoids the 'SListI' constraint. _ap_POP_spec :: SListI xss => POP (f -.-> g) xss -> POP f xss -> POP g xss _ap_POP_spec (POP fs) (POP xs) = POP (liftA2_NP ap_NP fs xs) type instance Same NP = NP type instance Same POP = POP type instance Prod NP = NP type instance Prod POP = POP instance HAp NP where hap = ap_NP instance HAp POP where hap = ap_POP -- * Destructing products -- | Obtain the head of an n-ary product. -- -- @since 0.2.1.0 -- hd :: NP f (x ': xs) -> f x hd (x :* _xs) = x -- | Obtain the tail of an n-ary product. -- -- @since 0.2.1.0 -- tl :: NP f (x ': xs) -> NP f xs tl (_x :* xs) = xs -- | The type of projections from an n-ary product. -- -- A projection is a function from the n-ary product to a single element. -- type Projection (f :: k -> Type) (xs :: [k]) = K (NP f xs) -.-> f -- | Compute all projections from an n-ary product. -- -- Each element of the resulting product contains one of the projections. -- projections :: forall xs f . SListI xs => NP (Projection f xs) xs projections = case sList :: SList xs of SNil -> Nil SCons -> fn (hd . unK) :* liftA_NP shiftProjection projections shiftProjection :: Projection f xs a -> Projection f (x ': xs) a shiftProjection (Fn f) = Fn $ f . K . tl . unK -- * Lifting / mapping -- | Specialization of 'hliftA'. liftA_NP :: SListI xs => (forall a. f a -> g a) -> NP f xs -> NP g xs -- | Specialization of 'hliftA'. liftA_POP :: All SListI xss => (forall a. f a -> g a) -> POP f xss -> POP g xss liftA_NP = hliftA liftA_POP = hliftA -- | Specialization of 'hliftA2'. liftA2_NP :: SListI xs => (forall a. f a -> g a -> h a) -> NP f xs -> NP g xs -> NP h xs -- | Specialization of 'hliftA2'. liftA2_POP :: All SListI xss => (forall a. f a -> g a -> h a) -> POP f xss -> POP g xss -> POP h xss liftA2_NP = hliftA2 liftA2_POP = hliftA2 -- | Specialization of 'hliftA3'. liftA3_NP :: SListI xs => (forall a. f a -> g a -> h a -> i a) -> NP f xs -> NP g xs -> NP h xs -> NP i xs -- | Specialization of 'hliftA3'. liftA3_POP :: All SListI xss => (forall a. f a -> g a -> h a -> i a) -> POP f xss -> POP g xss -> POP h xss -> POP i xss liftA3_NP = hliftA3 liftA3_POP = hliftA3 -- | Specialization of 'hmap', which is equivalent to 'hliftA'. map_NP :: SListI xs => (forall a. f a -> g a) -> NP f xs -> NP g xs -- | Specialization of 'hmap', which is equivalent to 'hliftA'. map_POP :: All SListI xss => (forall a. f a -> g a) -> POP f xss -> POP g xss map_NP = hmap map_POP = hmap -- | Specialization of 'hzipWith', which is equivalent to 'hliftA2'. zipWith_NP :: SListI xs => (forall a. f a -> g a -> h a) -> NP f xs -> NP g xs -> NP h xs -- | Specialization of 'hzipWith', which is equivalent to 'hliftA2'. zipWith_POP :: All SListI xss => (forall a. f a -> g a -> h a) -> POP f xss -> POP g xss -> POP h xss zipWith_NP = hzipWith zipWith_POP = hzipWith -- | Specialization of 'hzipWith3', which is equivalent to 'hliftA3'. zipWith3_NP :: SListI xs => (forall a. f a -> g a -> h a -> i a) -> NP f xs -> NP g xs -> NP h xs -> NP i xs -- | Specialization of 'hzipWith3', which is equivalent to 'hliftA3'. zipWith3_POP :: All SListI xss => (forall a. f a -> g a -> h a -> i a) -> POP f xss -> POP g xss -> POP h xss -> POP i xss zipWith3_NP = hzipWith3 zipWith3_POP = hzipWith3 -- | Specialization of 'hcliftA'. cliftA_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a) -> NP f xs -> NP g xs -- | Specialization of 'hcliftA'. cliftA_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a) -> POP f xss -> POP g xss cliftA_NP = hcliftA cliftA_POP = hcliftA -- | Specialization of 'hcliftA2'. cliftA2_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a -> h a) -> NP f xs -> NP g xs -> NP h xs -- | Specialization of 'hcliftA2'. cliftA2_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a -> h a) -> POP f xss -> POP g xss -> POP h xss cliftA2_NP = hcliftA2 cliftA2_POP = hcliftA2 -- | Specialization of 'hcliftA3'. cliftA3_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a -> h a -> i a) -> NP f xs -> NP g xs -> NP h xs -> NP i xs -- | Specialization of 'hcliftA3'. cliftA3_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a -> h a -> i a) -> POP f xss -> POP g xss -> POP h xss -> POP i xss cliftA3_NP = hcliftA3 cliftA3_POP = hcliftA3 -- | Specialization of 'hcmap', which is equivalent to 'hcliftA'. cmap_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a) -> NP f xs -> NP g xs -- | Specialization of 'hcmap', which is equivalent to 'hcliftA'. cmap_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a) -> POP f xss -> POP g xss cmap_NP = hcmap cmap_POP = hcmap -- | Specialization of 'hczipWith', which is equivalent to 'hcliftA2'. czipWith_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a -> h a) -> NP f xs -> NP g xs -> NP h xs -- | Specialization of 'hczipWith', which is equivalent to 'hcliftA2'. czipWith_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a -> h a) -> POP f xss -> POP g xss -> POP h xss czipWith_NP = hczipWith czipWith_POP = hczipWith -- | Specialization of 'hczipWith3', which is equivalent to 'hcliftA3'. czipWith3_NP :: All c xs => proxy c -> (forall a. c a => f a -> g a -> h a -> i a) -> NP f xs -> NP g xs -> NP h xs -> NP i xs -- | Specialization of 'hczipWith3', which is equivalent to 'hcliftA3'. czipWith3_POP :: All2 c xss => proxy c -> (forall a. c a => f a -> g a -> h a -> i a) -> POP f xss -> POP g xss -> POP h xss -> POP i xss czipWith3_NP = hczipWith3 czipWith3_POP = hczipWith3 -- * Dealing with @'All' c@ -- | Lift a constrained function operating on a list-indexed structure -- to a function on a list-of-list-indexed structure. -- -- This is a variant of 'hcliftA'. -- -- /Specification:/ -- -- @ -- 'hcliftA'' p f xs = 'hpure' ('fn_2' $ \\ 'AllDictC' -> f) \` 'hap' \` 'allDict_NP' p \` 'hap' \` xs -- @ -- -- /Instances:/ -- -- @ -- 'hcliftA'' :: 'All2' c xss => proxy c -> (forall xs. 'All' c xs => f xs -> f' xs) -> 'NP' f xss -> 'NP' f' xss -- 'hcliftA'' :: 'All2' c xss => proxy c -> (forall xs. 'All' c xs => f xs -> f' xs) -> 'Data.SOP.NS.NS' f xss -> 'Data.SOP.NS.NS' f' xss -- @ -- {-# DEPRECATED hcliftA' "Use 'hcliftA' or 'hcmap' instead." #-} hcliftA' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs) -> h f xss -> h f' xss -- | Like 'hcliftA'', but for binary functions. {-# DEPRECATED hcliftA2' "Use 'hcliftA2' or 'hczipWith' instead." #-} hcliftA2' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs -> f'' xs) -> Prod h f xss -> h f' xss -> h f'' xss -- | Like 'hcliftA'', but for ternary functions. {-# DEPRECATED hcliftA3' "Use 'hcliftA3' or 'hczipWith3' instead." #-} hcliftA3' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs -> f'' xs -> f''' xs) -> Prod h f xss -> Prod h f' xss -> h f'' xss -> h f''' xss hcliftA' p = hcliftA (allP p) hcliftA2' p = hcliftA2 (allP p) hcliftA3' p = hcliftA3 (allP p) -- | Specialization of 'hcliftA2''. {-# DEPRECATED cliftA2'_NP "Use 'cliftA2_NP' instead." #-} cliftA2'_NP :: All2 c xss => proxy c -> (forall xs. All c xs => f xs -> g xs -> h xs) -> NP f xss -> NP g xss -> NP h xss cliftA2'_NP = hcliftA2' -- * Collapsing -- | Specialization of 'hcollapse'. -- -- /Example:/ -- -- >>> collapse_NP (K 1 :* K 2 :* K 3 :* Nil) -- [1,2,3] -- collapse_NP :: NP (K a) xs -> [a] -- | Specialization of 'hcollapse'. -- -- /Example:/ -- -- >>> collapse_POP (POP ((K 'a' :* Nil) :* (K 'b' :* K 'c' :* Nil) :* Nil) :: POP (K Char) '[ '[(a :: Type)], '[b, c] ]) -- ["a","bc"] -- -- (The type signature is only necessary in this case to fix the kind of the type variables.) -- collapse_POP :: SListI xss => POP (K a) xss -> [[a]] collapse_NP Nil = [] collapse_NP (K x :* xs) = x : collapse_NP xs collapse_POP = collapse_NP . hliftA (K . collapse_NP) . unPOP type instance CollapseTo NP a = [a] type instance CollapseTo POP a = [[a]] instance HCollapse NP where hcollapse = collapse_NP instance HCollapse POP where hcollapse = collapse_POP -- * Folding -- | Specialization of 'hctraverse_'. -- -- @since 0.3.2.0 -- ctraverse__NP :: forall c proxy xs f g. (All c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> NP f xs -> g () ctraverse__NP _ f = go where go :: All c ys => NP f ys -> g () go Nil = pure () go (x :* xs) = f x *> go xs -- | Specialization of 'htraverse_'. -- -- @since 0.3.2.0 -- traverse__NP :: forall xs f g. (SListI xs, Applicative g) => (forall a. f a -> g ()) -> NP f xs -> g () traverse__NP f = ctraverse__NP topP f {-# INLINE traverse__NP #-} -- | Specialization of 'hctraverse_'. -- -- @since 0.3.2.0 -- ctraverse__POP :: forall c proxy xss f g. (All2 c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g ()) -> POP f xss -> g () ctraverse__POP p f = ctraverse__NP (allP p) (ctraverse__NP p f) . unPOP -- | Specialization of 'htraverse_'. -- -- @since 0.3.2.0 -- traverse__POP :: forall xss f g. (SListI2 xss, Applicative g) => (forall a. f a -> g ()) -> POP f xss -> g () traverse__POP f = ctraverse__POP topP f {-# INLINE traverse__POP #-} instance HTraverse_ NP where hctraverse_ = ctraverse__NP htraverse_ = traverse__NP instance HTraverse_ POP where hctraverse_ = ctraverse__POP htraverse_ = traverse__POP -- | Specialization of 'hcfoldMap'. -- -- @since 0.3.2.0 -- cfoldMap_NP :: (All c xs, Monoid m) => proxy c -> (forall a. c a => f a -> m) -> NP f xs -> m cfoldMap_NP = hcfoldMap -- | Specialization of 'hcfoldMap'. -- -- @since 0.3.2.0 -- cfoldMap_POP :: (All2 c xs, Monoid m) => proxy c -> (forall a. c a => f a -> m) -> POP f xs -> m cfoldMap_POP = hcfoldMap -- * Sequencing -- | Specialization of 'hsequence''. sequence'_NP :: Applicative f => NP (f :.: g) xs -> f (NP g xs) sequence'_NP Nil = pure Nil sequence'_NP (mx :* mxs) = (:*) <$> unComp mx <*> sequence'_NP mxs -- | Specialization of 'hsequence''. sequence'_POP :: (SListI xss, Applicative f) => POP (f :.: g) xss -> f (POP g xss) sequence'_POP = fmap POP . sequence'_NP . hliftA (Comp . sequence'_NP) . unPOP -- | Specialization of 'hctraverse''. -- -- @since 0.3.2.0 -- ctraverse'_NP :: forall c proxy xs f f' g. (All c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> NP f xs -> g (NP f' xs) ctraverse'_NP _ f = go where go :: All c ys => NP f ys -> g (NP f' ys) go Nil = pure Nil go (x :* xs) = (:*) <$> f x <*> go xs -- | Specialization of 'htraverse''. -- -- @since 0.3.2.0 -- traverse'_NP :: forall xs f f' g. (SListI xs, Applicative g) => (forall a. f a -> g (f' a)) -> NP f xs -> g (NP f' xs) traverse'_NP f = ctraverse'_NP topP f {-# INLINE traverse'_NP #-} -- | Specialization of 'hctraverse''. -- -- @since 0.3.2.0 -- ctraverse'_POP :: (All2 c xss, Applicative g) => proxy c -> (forall a. c a => f a -> g (f' a)) -> POP f xss -> g (POP f' xss) ctraverse'_POP p f = fmap POP . ctraverse'_NP (allP p) (ctraverse'_NP p f) . unPOP -- | Specialization of 'hctraverse''. -- -- @since 0.3.2.0 -- traverse'_POP :: (SListI2 xss, Applicative g) => (forall a. f a -> g (f' a)) -> POP f xss -> g (POP f' xss) traverse'_POP f = ctraverse'_POP topP f {-# INLINE traverse'_POP #-} instance HSequence NP where hsequence' = sequence'_NP hctraverse' = ctraverse'_NP htraverse' = traverse'_NP instance HSequence POP where hsequence' = sequence'_POP hctraverse' = ctraverse'_POP htraverse' = traverse'_POP -- | Specialization of 'hsequence'. -- -- /Example:/ -- -- >>> sequence_NP (Just 1 :* Just 2 :* Nil) -- Just (I 1 :* I 2 :* Nil) -- sequence_NP :: (SListI xs, Applicative f) => NP f xs -> f (NP I xs) -- | Specialization of 'hsequence'. -- -- /Example:/ -- -- >>> sequence_POP (POP ((Just 1 :* Nil) :* (Just 2 :* Just 3 :* Nil) :* Nil)) -- Just (POP ((I 1 :* Nil) :* (I 2 :* I 3 :* Nil) :* Nil)) -- sequence_POP :: (All SListI xss, Applicative f) => POP f xss -> f (POP I xss) sequence_NP = hsequence sequence_POP = hsequence -- | Specialization of 'hctraverse'. -- -- @since 0.3.2.0 -- ctraverse_NP :: (All c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g a) -> NP f xs -> g (NP I xs) -- | Specialization of 'hctraverse'. -- -- @since 0.3.2.0 -- ctraverse_POP :: (All2 c xs, Applicative g) => proxy c -> (forall a. c a => f a -> g a) -> POP f xs -> g (POP I xs) ctraverse_NP = hctraverse ctraverse_POP = hctraverse -- * Catamorphism and anamorphism -- | Catamorphism for 'NP'. -- -- This is a suitable generalization of 'foldr'. It takes -- parameters on what to do for 'Nil' and ':*'. Since the -- input list is heterogeneous, the result is also indexed -- by a type-level list. -- -- @since 0.2.3.0 -- cata_NP :: forall r f xs . r '[] -> (forall y ys . f y -> r ys -> r (y ': ys)) -> NP f xs -> r xs cata_NP nil cons = go where go :: forall ys . NP f ys -> r ys go Nil = nil go (x :* xs) = cons x (go xs) -- | Constrained catamorphism for 'NP'. -- -- The difference compared to 'cata_NP' is that the function -- for the cons-case can make use of the fact that the specified -- constraint holds for all the types in the signature of the -- product. -- -- @since 0.2.3.0 -- ccata_NP :: forall c proxy r f xs . (All c xs) => proxy c -> r '[] -> (forall y ys . c y => f y -> r ys -> r (y ': ys)) -> NP f xs -> r xs ccata_NP _ nil cons = go where go :: forall ys . (All c ys) => NP f ys -> r ys go Nil = nil go (x :* xs) = cons x (go xs) -- | Anamorphism for 'NP'. -- -- In contrast to the anamorphism for normal lists, the -- generating function does not return an 'Either', but -- simply an element and a new seed value. -- -- This is because the decision on whether to generate a -- 'Nil' or a ':*' is determined by the types. -- -- @since 0.2.3.0 -- ana_NP :: forall s f xs . SListI xs => (forall y ys . s (y ': ys) -> (f y, s ys)) -> s xs -> NP f xs ana_NP uncons = cana_NP topP uncons {-# INLINE ana_NP #-} -- | Constrained anamorphism for 'NP'. -- -- Compared to 'ana_NP', the generating function can -- make use of the specified constraint here for the -- elements that it generates. -- -- @since 0.2.3.0 -- cana_NP :: forall c proxy s f xs . (All c xs) => proxy c -> (forall y ys . c y => s (y ': ys) -> (f y, s ys)) -> s xs -> NP f xs cana_NP _ uncons = go sList where go :: forall ys . (All c ys) => SList ys -> s ys -> NP f ys go SNil _ = Nil go SCons s = case uncons s of (x, s') -> x :* go sList s' -- | Specialization of 'htrans'. -- -- @since 0.3.1.0 -- trans_NP :: AllZip c xs ys => proxy c -> (forall x y . c x y => f x -> g y) -> NP f xs -> NP g ys trans_NP _ _t Nil = Nil trans_NP p t (x :* xs) = t x :* trans_NP p t xs -- | Specialization of 'htrans'. -- -- @since 0.3.1.0 -- trans_POP :: AllZip2 c xss yss => proxy c -> (forall x y . c x y => f x -> g y) -> POP f xss -> POP g yss trans_POP p t = POP . trans_NP (allZipP p) (trans_NP p t) . unPOP allZipP :: proxy c -> Proxy (AllZip c) allZipP _ = Proxy -- | Specialization of 'hcoerce'. -- -- @since 0.3.1.0 -- coerce_NP :: forall f g xs ys . AllZip (LiftedCoercible f g) xs ys => NP f xs -> NP g ys coerce_NP = unsafeCoerce -- | Safe version of 'coerce_NP'. -- -- For documentation purposes only; not exported. -- _safe_coerce_NP :: forall f g xs ys . AllZip (LiftedCoercible f g) xs ys => NP f xs -> NP g ys _safe_coerce_NP = trans_NP (Proxy :: Proxy (LiftedCoercible f g)) coerce -- | Specialization of 'hcoerce'. -- -- @since 0.3.1.0 -- coerce_POP :: forall f g xss yss . AllZip2 (LiftedCoercible f g) xss yss => POP f xss -> POP g yss coerce_POP = unsafeCoerce -- | Safe version of 'coerce_POP'. -- -- For documentation purposes only; not exported. -- _safe_coerce_POP :: forall f g xss yss . AllZip2 (LiftedCoercible f g) xss yss => POP f xss -> POP g yss _safe_coerce_POP = trans_POP (Proxy :: Proxy (LiftedCoercible f g)) coerce -- | Specialization of 'hfromI'. -- -- @since 0.3.1.0 -- fromI_NP :: forall f xs ys . AllZip (LiftedCoercible I f) xs ys => NP I xs -> NP f ys fromI_NP = hfromI -- | Specialization of 'htoI'. -- -- @since 0.3.1.0 -- toI_NP :: forall f xs ys . AllZip (LiftedCoercible f I) xs ys => NP f xs -> NP I ys toI_NP = htoI -- | Specialization of 'hfromI'. -- -- @since 0.3.1.0 -- fromI_POP :: forall f xss yss . AllZip2 (LiftedCoercible I f) xss yss => POP I xss -> POP f yss fromI_POP = hfromI -- | Specialization of 'htoI'. -- -- @since 0.3.1.0 -- toI_POP :: forall f xss yss . AllZip2 (LiftedCoercible f I) xss yss => POP f xss -> POP I yss toI_POP = htoI instance HTrans NP NP where htrans = trans_NP hcoerce = coerce_NP instance HTrans POP POP where htrans = trans_POP hcoerce = coerce_POP