{-# LANGUAGE PolyKinds, StandaloneDeriving, UndecidableInstances #-} -- | n-ary products (and products of products) module Generics.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 -- * Sequencing , sequence'_NP , sequence'_POP , sequence_NP , sequence_POP ) where #if !(MIN_VERSION_base(4,8,0)) import Control.Applicative #endif import Data.Proxy (Proxy(..)) import Generics.SOP.BasicFunctors import Generics.SOP.Classes import Generics.SOP.Constraint import Generics.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 -> *) -> [k] -> * where Nil :: NP f '[] (:*) :: f x -> NP f xs -> NP f (x ': xs) infixr 5 :* deriving instance All (Show `Compose` f) xs => Show (NP f xs) 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) -- | 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 -> *)) (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) -- | 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 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 = case sList :: SList xs of SNil -> Nil SCons -> f :* pure_NP f -- | 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 = POP (cpure_NP sListP (pure_NP f)) sListP :: Proxy SListI sListP = 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 #if __GLASGOW_HASKELL__ < 800 ap_NP _ _ = error "inaccessible" #endif -- | 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 #if __GLASGOW_HASKELL__ < 800 go _ _ = error "inaccessible" #endif -- 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 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. -- type Projection (f :: k -> *) (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) -> 'Generics.SOP.NS.NS' f xss -> 'Generics.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 ternay 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 :: *)], '[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 -- * Sequencing -- | Specialization of 'hsequence''. sequence'_NP :: Applicative f => NP (f :.: g) xs -> f (NP g xs) -- | Specialization of 'hsequence''. sequence'_POP :: (SListI xss, Applicative f) => POP (f :.: g) xss -> f (POP g xss) sequence'_NP Nil = pure Nil sequence'_NP (mx :* mxs) = (:*) <$> unComp mx <*> sequence'_NP mxs sequence'_POP = fmap POP . sequence'_NP . hliftA (Comp . sequence'_NP) . unPOP instance HSequence NP where hsequence' = sequence'_NP instance HSequence POP where hsequence' = sequence'_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