-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | A product-of-sums generics library
--   
--   A generics library that represents a non-recursive Haskell 98 datatype
--   as a product-of-sums. Each type is represented with a single tag, and
--   a product of sums of fields. The tag represents all constructor
--   choices in the type, the fields contain all the values in the type.
--   This representation maps easily to a struct of unions, which is a
--   memory-efficient way to store sum datatypes.
@package posable
@version 1.0.0.0


-- | This module exports the <a>Product</a> and <a>Sum</a> type, and type-
--   and valuelevel functions on these types.
module Generics.POSable.Representation

-- | Concatenation of typelevel lists
type family (++) (xs :: [k]) (ys :: [k]) :: [k]
infixr 5 ++

-- | Type witness for <a>Product</a>
data ProductType :: [[Type]] -> Type
[PTNil] :: ProductType '[]
[PTCons] :: SumType x -> ProductType xs -> ProductType (x : xs)

-- | Concatenates <a>ProductType</a> values
concatPT :: ProductType x -> ProductType y -> ProductType (x ++ y)

-- | Typelevel product of <a>Sum</a>s with values
data Product :: [[Type]] -> Type
[Nil] :: Product '[]
[Cons] :: Sum x -> Product xs -> Product (x : xs)

-- | Concatenates <a>Product</a> values
concatP :: Product x -> Product y -> Product (x ++ y)

-- | Type witness for <a>Sum</a>
data SumType :: [Type] -> Type
[STSucc] :: Ground x => x -> SumType xs -> SumType (x : xs)
[STZero] :: SumType '[]

-- | Typelevel sum, contains one value from the typelevel list of types, or
--   undefined.
data Sum :: [Type] -> Type
[Pick] :: Ground x => x -> Sum (x : xs)
[Skip] :: Ground x => Sum xs -> Sum (x : xs)

-- | Zip two lists of lists with ++` as operator, while keeping the length
--   of the longest outer list
--   
--   Example:
--   
--   <pre>
--   &gt;&gt;&gt; :kind! Merge '[ '[A, B, C], '[D, E]] '[ '[F, G]]
--   Merge '[ '[A, B, C], '[D, E]] '[ '[F, G]] :: [[Type]]
--   = '[ '[A, B, C, F, G], '[D, E]]
--   </pre>
type family Merge (xs :: [[Type]]) (ys :: [[Type]]) :: [[Type]]

-- | Fold <a>Merge</a> over a list (of lists, of lists)
--   
--   Example:
--   
--   <pre>
--   &gt;&gt;&gt; :kind! FoldMerge '[ '[ '[A, B, C], '[D, E]], '[ '[F, G]], '[ '[H]]]
--   FoldMerge '[ '[ '[A, B, C], '[D, E]], '[ '[F, G]], '[ '[H]]] :: [[Type]]
--   = '[ '[A, B, C, F, G, H], '[D, E]]
--   </pre>
type family FoldMerge (xss :: [[[Type]]]) :: [[Type]]

-- | Map <a>Concat</a> over a list (of lists, of lists), typelevel
--   equivalent of
--   
--   <pre>
--   map . concat :: [[[a]]] -&gt; [[a]]
--   </pre>
--   
--   Example:
--   
--   <pre>
--   &gt;&gt;&gt; :kind! MapConcat '[ '[ '[A, B], '[C, D]], '[[E, F], '[G, H]]]
--   MapConcat '[ '[ '[A, B], '[C, D]], '[[E, F], '[G, H]]] :: [[Type]]
--   = '[ '[A, B, C, D], '[E, F, G, H]]
--   </pre>
type family MapConcat (xsss :: [[[x]]]) :: [[x]]

-- | Concatenate a list of lists, typelevel equivalent of
--   
--   <pre>
--   concat :: [[a]] -&gt; [a]`
--   </pre>
--   
--   Example:
--   
--   <pre>
--   &gt;&gt;&gt; :kind! Concat '[ '[A, B], '[C, D]]
--   Concat '[ '[A, B], '[C, D]] :: [Type]
--   = '[A, B, C, D]
--   </pre>
type family Concat (xss :: [[x]]) :: [x]

-- | The set of types that can exist in the sums. This set can be extended
--   by the user by providing an instance of Ground for their types. The
--   mkGround function gives a default value for the type. Ground depends
--   on Typeable, as this makes it possible for library users to inspect
--   the types of the contents of the sums.
class (Typeable a) => Ground a
mkGround :: Ground a => a

-- | Merge two <a>ProductType</a>s
mergeT :: ProductType l -> ProductType r -> ProductType (Merge l r)

-- | Merge a <a>ProductType</a> and a <a>Product</a>
merge :: Either (Product l, ProductType r) (ProductType l, Product r) -> Product (Merge l r)

-- | UnMerge a <a>Product</a>, using two <a>ProductType</a>s as witnesses
--   for the left and right argument of <a>Merge</a>. Produces a value of
--   type Product left
splitLeft :: Product (Merge l r) -> ProductType l -> ProductType r -> Product l

-- | UnMerge a <a>Product</a>, using two <a>ProductType</a>s as witnesses
--   for the left and right argument of <a>Merge</a>. Produces a value of
--   type Product right
splitRight :: Product (Merge l r) -> ProductType l -> ProductType r -> Product r

-- | UnConcat a <a>Product</a>, using a <a>ProductType</a> as the witness
--   for the first argument of <a>++</a>. Produces a tuple with the first
--   and second argument of <a>++</a>
unConcatP :: Product (x ++ y) -> ProductType x -> (Product x, Product y)
data Undef
Undef :: Undef
instance Generics.SOP.Universe.Generic Generics.POSable.Representation.Undef
instance GHC.Generics.Generic Generics.POSable.Representation.Undef
instance GHC.Show.Show Generics.POSable.Representation.Undef
instance GHC.Classes.Eq Generics.POSable.Representation.Undef
instance Data.SOP.Constraint.All2 GHC.Classes.Eq xs => GHC.Classes.Eq (Generics.POSable.Representation.Product xs)
instance Data.SOP.Constraint.All GHC.Classes.Eq xs => GHC.Classes.Eq (Generics.POSable.Representation.Sum xs)
instance Data.SOP.Constraint.All2 GHC.Show.Show (Generics.POSable.Representation.Map2TypeRep xs) => GHC.Show.Show (Generics.POSable.Representation.ProductType xs)
instance Data.SOP.Constraint.All GHC.Show.Show (Generics.POSable.Representation.MapTypeRep xs) => GHC.Show.Show (Generics.POSable.Representation.SumType xs)
instance Generics.POSable.Representation.Ground Generics.POSable.Representation.Undef
instance Data.SOP.Constraint.All2 GHC.Show.Show xs => GHC.Show.Show (Generics.POSable.Representation.Product xs)
instance Data.SOP.Constraint.All GHC.Show.Show x => GHC.Show.Show (Generics.POSable.Representation.Sum x)


-- | Exports the <a>POSable</a> class, which has a generic implementation
--   <a>GPOSable</a>. Also re-exports Generic.SOP, which is needed to
--   derive POSable.
module Generics.POSable.POSable

-- | POSable, the base of this library. Provide a compact memory
--   representation for a type and a function to get back to the original
--   type. This memory representation consist of <a>choices</a>, that
--   represent all constructor choices in the type in a single Finite
--   integer, and <a>fields</a> which represents all values in the type as
--   a Product of Sums, which can be mapped to a struct-of-arrays
--   representation for use in array-based languages like Accelerate.
class (KnownNat (Choices x)) => POSable x where {
    type family Choices x :: Nat;
    type family Fields x :: [[Type]];
    type Choices x = GChoices (SOP I (Code x));
    type Fields x = GFields (SOP I (Code x));
}
choices :: POSable x => x -> Finite (Choices x)
choices :: (POSable x, Generic x, GPOSable (SOP I (Code x)), GChoices (SOP I (Code x)) ~ Choices x) => x -> Finite (Choices x)

-- | The <a>tags</a> function returns the range of each constructor. A few
--   examples: &gt;&gt;&gt; tags <tt>Bool [1,1] &gt;&gt;&gt; tags
--   </tt>(Either Float Float) [1,1] &gt;&gt;&gt; tags <tt>(Bool, Bool) [4]
--   &gt;&gt;&gt; tags </tt>(Either Bool Bool) [2,2]
tags :: POSable x => [Integer]

-- | The <a>tags</a> function returns the range of each constructor. A few
--   examples: &gt;&gt;&gt; tags <tt>Bool [1,1] &gt;&gt;&gt; tags
--   </tt>(Either Float Float) [1,1] &gt;&gt;&gt; tags <tt>(Bool, Bool) [4]
--   &gt;&gt;&gt; tags </tt>(Either Bool Bool) [2,2]
tags :: (POSable x, GPOSable (SOP I (Code x))) => [Integer]
fromPOSable :: POSable x => Finite (Choices x) -> Product (Fields x) -> x
fromPOSable :: (POSable x, Generic x, GPOSable (SOP I (Code x)), Fields x ~ GFields (SOP I (Code x)), Choices x ~ GChoices (SOP I (Code x))) => Finite (Choices x) -> Product (Fields x) -> x
fields :: POSable x => x -> Product (Fields x)
fields :: (POSable x, Generic x, Fields x ~ GFields (SOP I (Code x)), GPOSable (SOP I (Code x))) => x -> Product (Fields x)
emptyFields :: POSable x => ProductType (Fields x)
emptyFields :: (POSable x, GPOSable (SOP I (Code x)), Fields x ~ GFields (SOP I (Code x))) => ProductType (Fields x)

-- | The class of representable datatypes.
--   
--   The SOP approach to generic programming is based on viewing datatypes
--   as a representation (<a>Rep</a>) built from the sum of products of its
--   components. The components of a datatype are specified using the
--   <a>Code</a> type family.
--   
--   The isomorphism between the original Haskell datatype and its
--   representation is witnessed by the methods of this class, <a>from</a>
--   and <a>to</a>. So for instances of this class, the following laws
--   should (in general) hold:
--   
--   <pre>
--   <a>to</a> <a>.</a> <a>from</a> === <a>id</a> :: a -&gt; a
--   <a>from</a> <a>.</a> <a>to</a> === <a>id</a> :: <a>Rep</a> a -&gt; <a>Rep</a> a
--   </pre>
--   
--   You typically don't define instances of this class by hand, but rather
--   derive the class instance automatically.
--   
--   <i>Option 1:</i> Derive via the built-in GHC-generics. For this, you
--   need to use the <tt>DeriveGeneric</tt> extension to first derive an
--   instance of the <a>Generic</a> class from module <a>GHC.Generics</a>.
--   With this, you can then give an empty instance for <a>Generic</a>, and
--   the default definitions will just work. The pattern looks as follows:
--   
--   <pre>
--   import qualified <a>GHC.Generics</a> as GHC
--   import <a>Generics.SOP</a>
--   
--   ...
--   
--   data T = ... deriving (GHC.<a>Generic</a>, ...)
--   
--   instance <a>Generic</a> T -- empty
--   instance <a>HasDatatypeInfo</a> T -- empty, if you want/need metadata
--   </pre>
--   
--   <i>Option 2:</i> Derive via Template Haskell. For this, you need to
--   enable the <tt>TemplateHaskell</tt> extension. You can then use
--   <a>deriveGeneric</a> from module <a>Generics.SOP.TH</a> to have the
--   instance generated for you. The pattern looks as follows:
--   
--   <pre>
--   import <a>Generics.SOP</a>
--   import <a>Generics.SOP.TH</a>
--   
--   ...
--   
--   data T = ...
--   
--   <a>deriveGeneric</a> ''T -- derives <a>HasDatatypeInfo</a> as well
--   </pre>
--   
--   <i>Tradeoffs:</i> Whether to use Option 1 or 2 is mainly a matter of
--   personal taste. The version based on Template Haskell probably has
--   less run-time overhead.
--   
--   <i>Non-standard instances:</i> It is possible to give <a>Generic</a>
--   instances manually that deviate from the standard scheme, as long as
--   at least
--   
--   <pre>
--   <a>to</a> <a>.</a> <a>from</a> === <a>id</a> :: a -&gt; a
--   </pre>
--   
--   still holds.
class All SListI :: [Type] -> Constraint Code a => Generic a

-- | Finite number type. <tt><a>Finite</a> n</tt> is inhabited by exactly
--   <tt>n</tt> values. Invariants:
--   
--   <pre>
--   getFinite x &lt; natVal x
--   </pre>
--   
--   <pre>
--   getFinite x &gt;= 0
--   </pre>
data Finite (n :: Nat)
instance (Data.SOP.Constraint.All2 Generics.POSable.POSable.POSable xss, GHC.TypeNats.KnownNat (Generics.POSable.POSable.Sums (Generics.POSable.POSable.MapProducts (Generics.POSable.POSable.Map2Choices xss))), Data.SOP.Constraint.All2 GHC.TypeNats.KnownNat (Generics.POSable.POSable.Map2Choices xss), Data.SOP.Constraint.All GHC.TypeNats.KnownNat (Generics.POSable.POSable.MapProducts (Generics.POSable.POSable.Map2Choices xss)), GHC.TypeNats.KnownNat (Generics.POSable.POSable.Length xss)) => Generics.POSable.POSable.GPOSable (Data.SOP.NS.SOP Data.SOP.BasicFunctors.I xss)


-- | This module contains instances of <a>POSable</a> for all Haskell
--   prelude data types as well as fixed size integers from Data.Int
--   (<tt>Int8</tt>, <tt>Int16</tt>, <tt>Int32</tt> and <tt>Int64</tt>)
module Generics.POSable.Instances

-- | POSable, the base of this library. Provide a compact memory
--   representation for a type and a function to get back to the original
--   type. This memory representation consist of <a>choices</a>, that
--   represent all constructor choices in the type in a single Finite
--   integer, and <a>fields</a> which represents all values in the type as
--   a Product of Sums, which can be mapped to a struct-of-arrays
--   representation for use in array-based languages like Accelerate.
class (KnownNat (Choices x)) => POSable x
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1) => Generics.POSable.POSable.POSable (x0, x1)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2) => Generics.POSable.POSable.POSable (x0, x1, x2)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3) => Generics.POSable.POSable.POSable (x0, x1, x2, x3)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5, Generics.POSable.POSable.POSable x6) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5, x6)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5, Generics.POSable.POSable.POSable x6, Generics.POSable.POSable.POSable x7) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5, x6, x7)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5, Generics.POSable.POSable.POSable x6, Generics.POSable.POSable.POSable x7, Generics.POSable.POSable.POSable x8) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5, Generics.POSable.POSable.POSable x6, Generics.POSable.POSable.POSable x7, Generics.POSable.POSable.POSable x8, Generics.POSable.POSable.POSable x9) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5, Generics.POSable.POSable.POSable x6, Generics.POSable.POSable.POSable x7, Generics.POSable.POSable.POSable x8, Generics.POSable.POSable.POSable x9, Generics.POSable.POSable.POSable x10) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5, Generics.POSable.POSable.POSable x6, Generics.POSable.POSable.POSable x7, Generics.POSable.POSable.POSable x8, Generics.POSable.POSable.POSable x9, Generics.POSable.POSable.POSable x10, Generics.POSable.POSable.POSable x11) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5, Generics.POSable.POSable.POSable x6, Generics.POSable.POSable.POSable x7, Generics.POSable.POSable.POSable x8, Generics.POSable.POSable.POSable x9, Generics.POSable.POSable.POSable x10, Generics.POSable.POSable.POSable x11, Generics.POSable.POSable.POSable x12) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5, Generics.POSable.POSable.POSable x6, Generics.POSable.POSable.POSable x7, Generics.POSable.POSable.POSable x8, Generics.POSable.POSable.POSable x9, Generics.POSable.POSable.POSable x10, Generics.POSable.POSable.POSable x11, Generics.POSable.POSable.POSable x12, Generics.POSable.POSable.POSable x13) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5, Generics.POSable.POSable.POSable x6, Generics.POSable.POSable.POSable x7, Generics.POSable.POSable.POSable x8, Generics.POSable.POSable.POSable x9, Generics.POSable.POSable.POSable x10, Generics.POSable.POSable.POSable x11, Generics.POSable.POSable.POSable x12, Generics.POSable.POSable.POSable x13, Generics.POSable.POSable.POSable x14) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14)
instance (Generics.POSable.POSable.POSable x0, Generics.POSable.POSable.POSable x1, Generics.POSable.POSable.POSable x2, Generics.POSable.POSable.POSable x3, Generics.POSable.POSable.POSable x4, Generics.POSable.POSable.POSable x5, Generics.POSable.POSable.POSable x6, Generics.POSable.POSable.POSable x7, Generics.POSable.POSable.POSable x8, Generics.POSable.POSable.POSable x9, Generics.POSable.POSable.POSable x10, Generics.POSable.POSable.POSable x11, Generics.POSable.POSable.POSable x12, Generics.POSable.POSable.POSable x13, Generics.POSable.POSable.POSable x14, Generics.POSable.POSable.POSable x15) => Generics.POSable.POSable.POSable (x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15)
instance Generics.POSable.POSable.POSable GHC.Types.Bool
instance Generics.POSable.POSable.POSable x => Generics.POSable.POSable.POSable (GHC.Maybe.Maybe x)
instance (Generics.POSable.POSable.POSable l, Generics.POSable.POSable.POSable r) => Generics.POSable.POSable.POSable (Data.Either.Either l r)
instance Generics.POSable.POSable.POSable GHC.Types.Ordering
instance Generics.POSable.POSable.POSable ()
instance Generics.POSable.POSable.POSable Generics.POSable.Representation.Undef

module Generics.POSable.TH
mkPOSableGround :: Name -> DecsQ