| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Generics.SOP
Description
Main module of
generics-sop
In most cases, you will probably want to import just this module,
and possibly
Generics.SOP.TH
if you want to use Template Haskell
to generate
Generic
instances for you.
Generic programming with sums of products
You need this library if you want to define your own generic functions in the sum-of-products SOP style. Generic programming in the SOP style follows the following idea:
-
A large class of datatypes can be viewed in a uniform, structured
way: the choice between constructors is represented using an n-ary
sum (called
NS), and the arguments of each constructor are represented using an n-ary product (calledNP). -
The library captures the notion of a datatype being representable
in the following way. There is a class
Generic, which for a given datatypeA, associates the isomorphic SOP representation with the original type under the nameRepAfromandtothat convert betweenAandRepA -
Since all
Reptypes are sums of products, you can define functions over them by performing induction on the structure, or by using predefined combinators that the library provides. Such functions then work for allReptypes. -
By combining the conversion functions
fromandtowith the function that works onReptypes, we obtain a function that works on all types that are in theGenericclass. -
Most types can very easily be made an instance of
Generic. For example, if the datatype can be represented using GHC's built-in approach to generic programming and has an instance for theGenericclass from module GHC.Generics , then an instance of the SOPGenericcan automatically be derived. There is also Template Haskell code in Generics.SOP.TH that allows to auto-generate an instance ofGenericfor most types.
Example
Instantiating a datatype for use with SOP generics
Let's assume we have the datatypes:
data A = C Bool | D A Int | E (B ()) data B a = F | G a Char Bool
To create
Generic
instances for
A
and
B
via
GHC.Generics
, we say
{-# LANGUAGE DeriveGeneric #-}
import qualified GHC.Generics as GHC
import Generics.SOP
data A = C Bool | D A Int | E (B ())
deriving (Show, GHC.Generic)
data B a = F | G a Char Bool
deriving (Show, GHC.Generic)
instance Generic A -- empty
instance Generic (B a) -- empty
Now we can convert between
A
and
(and between
Rep
A
B
and
).
For example,
Rep
B
>>>from (D (C True) 3) :: Rep ASOP (S (Z (I (C True) :* I 3 :* Nil)))>>>to it :: AD (C True) 3
Note that the transformation is shallow: In
D (C True) 3
, the
inner value
C True
of type
A
is not affected by the
transformation.
For more details about
, have a look at the
Generics.SOP.Universe
module.
Rep
A
Defining a generic function
As an example of a generic function, let us define a generic
version of
rnf
from the
deepseq
package.
The type of
rnf
is
NFData a => a -> ()
and the idea is that for a term
x
of type
a
in the
NFData
class,
rnf x
forces complete evaluation
of
x
(i.e., evaluation to
normal form
), and returns
()
.
We call the generic version of this function
grnf
. A direct
definition in SOP style, making use of structural recursion on the
sums and products, looks as follows:
grnf :: (Generica,All2NFData (Codea)) => a -> () grnf x = grnfS (fromx) grnfS :: (All2NFData xss) =>SOPIxss -> () grnfS (SOP(Zxs)) = grnfP xs grnfS (SOP(Sxss)) = grnfS (SOPxss) grnfP :: (AllNFData xs) =>NPIxs -> () grnfPNil= () grnfP (Ix:*xs) = x `deepseq` (grnfP xs)
The
grnf
function performs the conversion between
a
and
by applying
Rep
a
from
and then applies
grnfS
. The type of
grnf
indicates that
a
must be in the
Generic
class so that we can
apply
from
, and that all the components of
a
(i.e., all the types
that occur as constructor arguments) must be in the
NFData
class
(
All2
).
The function
grnfS
traverses the outer sum structure of the
sum of products (note that
). It
encodes which constructor was used to construct the original
argument of type
Rep
a =
SOP
I
(
Code
a)
a
. Once we've found the constructor in question
(
Z
), we traverse the arguments of that constructor using
grnfP
.
The function
grnfP
traverses the product structure of the
constructor arguments. Each argument is evaluated using the
deepseq
function from the
NFData
class. This requires that all components of the product must be
in the
NFData
class (
All
) and triggers the corresponding
constraints on the other functions. Once the end of the product
is reached (
Nil
), we return
()
.
Defining a generic function using combinators
In many cases, generic functions can be written in a much more concise way by avoiding the explicit structural recursion and resorting to the powerful combinators provided by this library instead.
For example, the
grnf
function can also be defined as a one-liner
as follows:
grnf :: (Generica,All2NFData (Codea)) => a -> () grnf =rnf.hcollapse.hcmap(Proxy::ProxyNFData) (mapIKrnf) .from
mapIK
and friends (
mapII
,
mapKI
, etc.) are small helpers for working
with
I
and
K
functors, for example
mapIK
is defined as
mapIK
f = \ (
I
x) ->
K
(f x)
The following interaction should provide an idea of the individual transformation steps:
>>>let x = G 2.5 'A' False :: B Double>>>from xSOP (S (Z (I 2.5 :* I 'A' :* I False :* Nil)))>>>hcmap (Proxy :: Proxy NFData) (mapIK rnf) itSOP (S (Z (K () :* K () :* K () :* Nil)))>>>hcollapse it[(),(),()]>>>rnf it()
The
from
call converts into the structural representation.
Via
hcmap
, we apply
rnf
to all the components. The result
is a sum of products of the same shape, but the components are
no longer heterogeneous (
I
), but homogeneous (
). A
homogeneous structure can be collapsed (
K
()
hcollapse
) into a
normal Haskell list. Finally,
rnf
actually forces evaluation
of this list (and thereby actually drives the evaluation of all
the previous steps) and produces the final result.
Using a generic function
We can directly invoke
grnf
on any type that is an instance of
class
Generic
.
>>>grnf (G 2.5 'A' False)()>>>grnf (G 2.5 undefined False)*** Exception: Prelude.undefined ...
Note that the type of
grnf
requires that all components of the
type are in the
NFData
class. For a recursive
datatype such as
B
, this means that we have to make
A
(and in this case, also
B
) an instance of
NFData
in order to be able to use the
grnf
function. But we can use
grnf
to supply the instance definitions:
instance NFData A where rnf = grnf instance NFData a => NFData (B a) where rnf = grnf
More examples
The best way to learn about how to define generic functions in the SOP style is to look at a few simple examples. Examples are provided by the following packages:
-
basic-sopbasic examples, -
pretty-sopgeneric pretty printing, -
lens-sopgenerically computed lenses, -
json-sopgeneric JSON conversions.
The generic functions in these packages use a wide variety of the combinators that are offered by the library.
Paper
A detailed description of the ideas behind this library is provided by the paper:
- Edsko de Vries and Andres Löh. True Sums of Products . Workshop on Generic Programming (WGP) 2014.
Synopsis
- class All SListI ( Code a) => Generic (a :: Type ) where
- type Rep a = SOP I ( Code a)
- type IsProductType (a :: Type ) (xs :: [ Type ]) = ( Generic a, Code a ~ '[xs])
- type ProductCode (a :: Type ) = Head ( Code a)
- productTypeFrom :: IsProductType a xs => a -> NP I xs
- productTypeTo :: IsProductType a xs => NP I xs -> a
- type IsEnumType (a :: Type ) = ( Generic a, All ((~) '[]) ( Code a))
- enumTypeFrom :: IsEnumType a => a -> NS ( K ()) ( Code a)
- enumTypeTo :: IsEnumType a => NS ( K ()) ( Code a) -> a
- type IsWrappedType (a :: Type ) (x :: Type ) = ( Generic a, Code a ~ '['[x]])
- type WrappedCode (a :: Type ) = Head ( Head ( Code a))
- wrappedTypeFrom :: IsWrappedType a x => a -> x
- wrappedTypeTo :: IsWrappedType a x => x -> a
- type IsNewtype (a :: Type ) (x :: Type ) = ( IsWrappedType a x, Coercible a x)
- newtypeFrom :: IsNewtype a x => a -> x
- newtypeTo :: IsNewtype a x => x -> a
- data NP (a :: k -> Type ) (b :: [k]) where
- data NS (a :: k -> Type ) (b :: [k]) where
- newtype SOP (f :: k -> Type ) (xss :: [[k]]) = SOP ( NS ( NP f) xss)
- unSOP :: forall k (f :: k -> Type ) (xss :: [[k]]). SOP f xss -> NS ( NP f) xss
- newtype POP (f :: k -> Type ) (xss :: [[k]]) = POP ( NP ( NP f) xss)
- unPOP :: forall k (f :: k -> Type ) (xss :: [[k]]). POP f xss -> NP ( NP f) xss
-
data
DatatypeInfo
:: [[
Type
]] ->
Type
where
- ADT :: ModuleName -> DatatypeName -> NP ConstructorInfo xss -> POP StrictnessInfo xss -> DatatypeInfo xss
- Newtype :: ModuleName -> DatatypeName -> ConstructorInfo '[x] -> DatatypeInfo '['[x]]
- moduleName :: DatatypeInfo xss -> ModuleName
- datatypeName :: DatatypeInfo xss -> DatatypeName
- constructorInfo :: DatatypeInfo xss -> NP ConstructorInfo xss
-
data
ConstructorInfo
:: [
Type
] ->
Type
where
- Constructor :: SListI xs => ConstructorName -> ConstructorInfo xs
- Infix :: ConstructorName -> Associativity -> Fixity -> ConstructorInfo '[x, y]
- Record :: SListI xs => ConstructorName -> NP FieldInfo xs -> ConstructorInfo xs
- constructorName :: ConstructorInfo xs -> ConstructorName
- data FieldInfo :: Type -> Type where
- fieldName :: FieldInfo a -> FieldName
-
class
Generic
a =>
HasDatatypeInfo
a
where
- type DatatypeInfoOf a :: DatatypeInfo
- datatypeInfo :: proxy a -> DatatypeInfo ( Code a)
- type DatatypeName = String
- type ModuleName = String
- type ConstructorName = String
- type FieldName = String
- data Associativity
- type Fixity = Int
- class HPure (h :: (k -> Type ) -> l -> Type ) where
- hd :: forall k f (x :: k) (xs :: [k]). NP f (x ': xs) -> f x
- tl :: forall k (f :: k -> Type ) (x :: k) (xs :: [k]). NP f (x ': xs) -> NP f xs
- type Projection (f :: k -> Type ) (xs :: [k]) = ( K ( NP f xs) :: k -> Type ) -.-> f
- projections :: forall k (xs :: [k]) (f :: k -> Type ). SListI xs => NP ( Projection f xs) xs
- shiftProjection :: forall a1 (f :: a1 -> Type ) (xs :: [a1]) (a2 :: a1) (x :: a1). Projection f xs a2 -> Projection f (x ': xs) a2
-
newtype
((f :: k ->
Type
)
-.->
(g :: k ->
Type
)) (a :: k) =
Fn
{
- apFn :: f a -> g a
- fn :: forall k f (a :: k) f'. (f a -> f' a) -> (f -.-> f') a
- fn_2 :: forall k f (a :: k) f' f''. (f a -> f' a -> f'' a) -> (f -.-> (f' -.-> f'')) a
- fn_3 :: forall k f (a :: k) f' f'' f'''. (f a -> f' a -> f'' a -> f''' a) -> (f -.-> (f' -.-> (f'' -.-> f'''))) a
- fn_4 :: forall k f (a :: k) f' f'' f''' f''''. (f a -> f' a -> f'' a -> f''' a -> f'''' a) -> (f -.-> (f' -.-> (f'' -.-> (f''' -.-> f'''')))) a
- type family Prod (h :: (k -> Type ) -> l -> Type ) :: (k -> Type ) -> l -> Type
- class ( Prod ( Prod h) ~ Prod h, HPure ( Prod h)) => HAp (h :: (k -> Type ) -> l -> Type ) where
- hliftA :: forall k l h (xs :: l) f f'. ( SListIN ( Prod h) xs, HAp h) => ( forall (a :: k). f a -> f' a) -> h f xs -> h f' xs
- hliftA2 :: forall k l h (xs :: l) f f' f''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hliftA3 :: forall k l h (xs :: l) f f' f'' f'''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
- hcliftA :: forall k l h c (xs :: l) proxy f f'. ( AllN ( Prod h) c xs, HAp h) => proxy c -> ( forall (a :: k). c a => f a -> f' a) -> h f xs -> h f' xs
- hcliftA2 :: forall k l h c (xs :: l) proxy f f' f''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c -> ( forall (a :: k). c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hcliftA3 :: forall k l h c (xs :: l) proxy f f' f'' f'''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c -> ( forall (a :: k). c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
- hmap :: forall k l h (xs :: l) f f'. ( SListIN ( Prod h) xs, HAp h) => ( forall (a :: k). f a -> f' a) -> h f xs -> h f' xs
- hzipWith :: forall k l h (xs :: l) f f' f''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hzipWith3 :: forall k l h (xs :: l) f f' f'' f'''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
- hcmap :: forall k l h c (xs :: l) proxy f f'. ( AllN ( Prod h) c xs, HAp h) => proxy c -> ( forall (a :: k). c a => f a -> f' a) -> h f xs -> h f' xs
- hczipWith :: forall k l h c (xs :: l) proxy f f' f''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c -> ( forall (a :: k). c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hczipWith3 :: forall k l h c (xs :: l) proxy f f' f'' f'''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c -> ( forall (a :: k). c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
- type Injection (f :: k -> Type ) (xs :: [k]) = f -.-> ( K ( NS f xs) :: k -> Type )
- injections :: forall k (xs :: [k]) (f :: k -> Type ). SListI xs => NP ( Injection f xs) xs
- shift :: forall a1 (f :: a1 -> Type ) (xs :: [a1]) (a2 :: a1) (x :: a1). Injection f xs a2 -> Injection f (x ': xs) a2
- shiftInjection :: forall a1 (f :: a1 -> Type ) (xs :: [a1]) (a2 :: a1) (x :: a1). Injection f xs a2 -> Injection f (x ': xs) a2
- type family UnProd (h :: (k -> Type ) -> l -> Type ) :: (k -> Type ) -> l -> Type
- class UnProd ( Prod h) ~ h => HApInjs (h :: (k -> Type ) -> l -> Type ) where
- apInjs_NP :: forall k (xs :: [k]) (f :: k -> Type ). SListI xs => NP f xs -> [ NS f xs]
- apInjs_POP :: forall k (xss :: [[k]]) (f :: k -> Type ). SListI xss => POP f xss -> [ SOP f xss]
- unZ :: forall k f (x :: k). NS f '[x] -> f x
- class HIndex (h :: (k -> Type ) -> l -> Type ) where
- type Ejection (f :: k -> Type ) (xs :: [k]) = ( K ( NS f xs) :: k -> Type ) -.-> ( Maybe :.: f)
- ejections :: forall k (xs :: [k]) (f :: k -> Type ). SListI xs => NP ( Ejection f xs) xs
- shiftEjection :: forall a1 (f :: a1 -> Type ) (x :: a1) (xs :: [a1]) (a2 :: a1). Ejection f xs a2 -> Ejection f (x ': xs) a2
- hcliftA' :: forall k (c :: k -> Constraint ) (xss :: [[k]]) h proxy f f'. ( All2 c xss, Prod h ~ ( NP :: ([k] -> Type ) -> [[k]] -> Type ), HAp h) => proxy c -> ( forall (xs :: [k]). All c xs => f xs -> f' xs) -> h f xss -> h f' xss
- hcliftA2' :: forall k (c :: k -> Constraint ) (xss :: [[k]]) h proxy f f' f''. ( All2 c xss, Prod h ~ ( NP :: ([k] -> Type ) -> [[k]] -> Type ), HAp h) => proxy c -> ( forall (xs :: [k]). All c xs => f xs -> f' xs -> f'' xs) -> Prod h f xss -> h f' xss -> h f'' xss
- hcliftA3' :: forall k (c :: k -> Constraint ) (xss :: [[k]]) h proxy f f' f'' f'''. ( All2 c xss, Prod h ~ ( NP :: ([k] -> Type ) -> [[k]] -> Type ), HAp h) => proxy c -> ( forall (xs :: [k]). 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
- compare_NS :: forall k r f g (xs :: [k]). r -> ( forall (x :: k). f x -> g x -> r) -> r -> NS f xs -> NS g xs -> r
- ccompare_NS :: forall k c proxy r f g (xs :: [k]). All c xs => proxy c -> r -> ( forall (x :: k). c x => f x -> g x -> r) -> r -> NS f xs -> NS g xs -> r
- compare_SOP :: forall k r (f :: k -> Type ) (g :: k -> Type ) (xss :: [[k]]). r -> ( forall (xs :: [k]). NP f xs -> NP g xs -> r) -> r -> SOP f xss -> SOP g xss -> r
- ccompare_SOP :: forall k (c :: k -> Constraint ) proxy r (f :: k -> Type ) (g :: k -> Type ) (xss :: [[k]]). All2 c xss => proxy c -> r -> ( forall (xs :: [k]). All c xs => NP f xs -> NP g xs -> r) -> r -> SOP f xss -> SOP g xss -> r
- type family CollapseTo (h :: (k -> Type ) -> l -> Type ) x
-
class
HCollapse
(h :: (k ->
Type
) -> l ->
Type
)
where
- hcollapse :: forall (xs :: l) a. SListIN h xs => h ( K a :: k -> Type ) xs -> CollapseTo h a
-
class
HTraverse_
(h :: (k ->
Type
) -> l ->
Type
)
where
- hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN h c xs, Applicative g) => proxy c -> ( forall (a :: k). c a => f a -> g ()) -> h f xs -> g ()
- htraverse_ :: forall (xs :: l) g f. ( SListIN h xs, Applicative g) => ( forall (a :: k). f a -> g ()) -> h f xs -> g ()
- hcfoldMap :: forall k l h c (xs :: l) m proxy f. ( HTraverse_ h, AllN h c xs, Monoid m) => proxy c -> ( forall (a :: k). c a => f a -> m) -> h f xs -> m
- hcfor_ :: forall k l h c (xs :: l) g proxy f. ( HTraverse_ h, AllN h c xs, Applicative g) => proxy c -> h f xs -> ( forall (a :: k). c a => f a -> g ()) -> g ()
-
class
HAp
h =>
HSequence
(h :: (k ->
Type
) -> l ->
Type
)
where
- hsequence' :: forall (xs :: l) f (g :: k -> Type ). ( SListIN h xs, Applicative f) => h (f :.: g) xs -> f (h g xs)
- hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN h c xs, Applicative g) => proxy c -> ( forall (a :: k). c a => f a -> g (f' a)) -> h f xs -> g (h f' xs)
- htraverse' :: forall (xs :: l) g f f'. ( SListIN h xs, Applicative g) => ( forall (a :: k). f a -> g (f' a)) -> h f xs -> g (h f' xs)
- hsequence :: forall l h (xs :: l) f. ( SListIN h xs, SListIN ( Prod h) xs, HSequence h, Applicative f) => h f xs -> f (h I xs)
- hsequenceK :: forall k l h (xs :: l) f a. ( SListIN h xs, SListIN ( Prod h) xs, Applicative f, HSequence h) => h ( K (f a) :: k -> Type ) xs -> f (h ( K a :: k -> Type ) xs)
- hctraverse :: forall l h c (xs :: l) g proxy f. ( HSequence h, AllN h c xs, Applicative g) => proxy c -> ( forall a. c a => f a -> g a) -> h f xs -> g (h I xs)
- hcfor :: forall l h c (xs :: l) g proxy f. ( HSequence h, AllN h c xs, Applicative g) => proxy c -> h f xs -> ( forall a. c a => f a -> g a) -> g (h I xs)
- class HExpand (h :: (k -> Type ) -> l -> Type ) where
-
class
((
Same
h1 :: (k2 ->
Type
) -> l2 ->
Type
) ~ h2, (
Same
h2 :: (k1 ->
Type
) -> l1 ->
Type
) ~ h1) =>
HTrans
(h1 :: (k1 ->
Type
) -> l1 ->
Type
) (h2 :: (k2 ->
Type
) -> l2 ->
Type
)
where
- htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod h1) c xs ys => proxy c -> ( forall (x :: k1) (y :: k2). c x y => f x -> g y) -> h1 f xs -> h2 g ys
- hcoerce :: forall (f :: k1 -> Type ) (g :: k2 -> Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod h1) ( LiftedCoercible f g) xs ys => h1 f xs -> h2 g ys
- hfromI :: forall l1 k2 l2 h1 (f :: k2 -> Type ) (xs :: l1) (ys :: l2) h2. ( AllZipN ( Prod h1) ( LiftedCoercible I f) xs ys, HTrans h1 h2) => h1 I xs -> h2 f ys
- htoI :: forall k1 l1 l2 h1 (f :: k1 -> Type ) (xs :: l1) (ys :: l2) h2. ( AllZipN ( Prod h1) ( LiftedCoercible f I ) xs ys, HTrans h1 h2) => h1 f xs -> h2 I ys
- fromList :: forall k (xs :: [k]) a. SListI xs => [a] -> Maybe ( NP ( K a :: k -> Type ) xs)
- newtype K a (b :: k) = K a
- unK :: forall k a (b :: k). K a b -> a
- newtype I a = I a
- unI :: I a -> a
- newtype ((f :: l -> Type ) :.: (g :: k -> l)) (p :: k) = Comp (f (g p))
- unComp :: forall l k f (g :: k -> l) (p :: k). (f :.: g) p -> f (g p)
- mapII :: (a -> b) -> I a -> I b
- mapIK :: forall k a b (c :: k). (a -> b) -> I a -> K b c
- mapKI :: forall k a b (c :: k). (a -> b) -> K a c -> I b
- mapKK :: forall k1 k2 a b (c :: k1) (d :: k2). (a -> b) -> K a c -> K b d
- mapIII :: (a -> b -> c) -> I a -> I b -> I c
- mapIIK :: forall k a b c (d :: k). (a -> b -> c) -> I a -> I b -> K c d
- mapIKI :: forall k a b c (d :: k). (a -> b -> c) -> I a -> K b d -> I c
- mapIKK :: forall k1 k2 a b c (d :: k1) (e :: k2). (a -> b -> c) -> I a -> K b d -> K c e
- mapKII :: forall k a b c (d :: k). (a -> b -> c) -> K a d -> I b -> I c
- mapKIK :: forall k1 k2 a b c (d :: k1) (e :: k2). (a -> b -> c) -> K a d -> I b -> K c e
- mapKKI :: forall k1 k2 a b c (d :: k1) (e :: k2). (a -> b -> c) -> K a d -> K b e -> I c
- mapKKK :: forall k1 k2 k3 a b c (d :: k1) (e :: k2) (f :: k3). (a -> b -> c) -> K a d -> K b e -> K c f
- class ( AllF c xs, SListI xs) => All (c :: k -> Constraint ) (xs :: [k])
- type All2 (c :: k -> Constraint ) = All ( All c)
- cpara_SList :: All c xs => proxy c -> r ('[] :: [k]) -> ( forall (y :: k) (ys :: [k]). (c y, All c ys) => r ys -> r (y ': ys)) -> r xs
- ccase_SList :: forall k c (xs :: [k]) proxy r. All c xs => proxy c -> r ('[] :: [k]) -> ( forall (y :: k) (ys :: [k]). (c y, All c ys) => r (y ': ys)) -> r xs
- class ( SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a -> b -> Constraint ) (xs :: [a]) (ys :: [b])
- class ( AllZipF ( AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 (f :: a -> b -> Constraint ) (xss :: [[a]]) (yss :: [[b]])
- type family AllN (h :: (k -> Type ) -> l -> Type ) (c :: k -> Constraint ) :: l -> Constraint
- type family AllZipN (h :: (k -> Type ) -> l -> Type ) (c :: k1 -> k2 -> Constraint ) :: l1 -> l2 -> Constraint
- class f (g x) => Compose (f :: k -> Constraint ) (g :: k1 -> k) (x :: k1)
- class (f x, g x) => And (f :: k -> Constraint ) (g :: k -> Constraint ) (x :: k)
- class Top (x :: k)
- class Coercible (f x) (g y) => LiftedCoercible (f :: k -> k1) (g :: k2 -> k1) (x :: k) (y :: k2)
- type family SameShapeAs (xs :: [a]) (ys :: [b]) where ...
- data SList (a :: [k]) where
- type SListI = All ( Top :: k -> Constraint )
- type SListI2 = All ( SListI :: [k] -> Constraint )
- sList :: forall k (xs :: [k]). SListI xs => SList xs
- para_SList :: forall k (xs :: [k]) r. SListI xs => r ('[] :: [k]) -> ( forall (y :: k) (ys :: [k]). SListI ys => r ys -> r (y ': ys)) -> r xs
- case_SList :: forall k (xs :: [k]) r. SListI xs => r ('[] :: [k]) -> ( forall (y :: k) (ys :: [k]). SListI ys => r (y ': ys)) -> r xs
- data Shape (a :: [k]) where
- shape :: forall k (xs :: [k]). SListI xs => Shape xs
- lengthSList :: forall k (xs :: [k]) proxy. SListI xs => proxy xs -> Int
- data Proxy (t :: k) = Proxy
Codes and interpretations
class All SListI ( Code a) => Generic (a :: Type ) where Source #
The class of representable datatypes.
The SOP approach to generic programming is based on viewing
datatypes as a representation (
Rep
) built from the sum of
products of its components. The components of a datatype
are specified using the
Code
type family.
The isomorphism between the original Haskell datatype and its
representation is witnessed by the methods of this class,
from
and
to
. So for instances of this class, the following
laws should (in general) hold:
to.from===id:: a -> afrom.to===id::Repa ->Repa
You typically don't define instances of this class by hand, but rather derive the class instance automatically.
Option 1:
Derive via the built-in GHC-generics. For this, you
need to use the
DeriveGeneric
extension to first derive an
instance of the
Generic
class from module
GHC.Generics
.
With this, you can then give an empty instance for
Generic
, and
the default definitions will just work. The pattern looks as
follows:
import qualified GHC.Generics as GHC import Generics.SOP ... data T = ... deriving (GHC.Generic, ...) instanceGenericT -- empty instanceHasDatatypeInfoT -- empty, if you want/need metadata
Option 2:
Derive via Template Haskell. For this, you need to
enable the
TemplateHaskell
extension. You can then use
deriveGeneric
from module
Generics.SOP.TH
to have the instance generated for you. The pattern looks as
follows:
import Generics.SOP import Generics.SOP.TH ... data T = ...deriveGeneric''T -- derivesHasDatatypeInfoas well
Tradeoffs: 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.
Non-standard instances:
It is possible to give
Generic
instances manually that deviate
from the standard scheme, as long as at least
to.from===id:: a -> a
still holds.
Minimal complete definition
Nothing
Associated Types
type Code a :: [[ Type ]] Source #
The code of a datatype.
This is a list of lists of its components. The outer list contains one element per constructor. The inner list contains one element per constructor argument (field).
Example: The datatype
data Tree = Leaf Int | Node Tree Tree
is supposed to have the following code:
type instance Code (Tree a) = '[ '[ Int ] , '[ Tree, Tree ] ]
Methods
Converts from a value to its structural representation.
Converts from a structural representation back to the original value.
Instances
| Generic Bool Source # | |
| Generic Ordering Source # | |
| Generic RuntimeRep Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code RuntimeRep :: [[ Type ]] Source # |
|
| Generic VecCount Source # | |
| Generic VecElem Source # | |
| Generic R Source # | |
| Generic D Source # | |
| Generic C Source # | |
| Generic S Source # | |
| Generic CallStack Source # | |
| Generic () Source # | |
| Generic E0 Source # | |
| Generic E1 Source # | |
| Generic E2 Source # | |
| Generic E3 Source # | |
| Generic E6 Source # | |
| Generic E9 Source # | |
| Generic E12 Source # | |
| Generic Void Source # | |
| Generic SpecConstrAnnotation Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code SpecConstrAnnotation :: [[ Type ]] Source # Methods from :: SpecConstrAnnotation -> Rep SpecConstrAnnotation Source # to :: Rep SpecConstrAnnotation -> SpecConstrAnnotation Source # |
|
| Generic DataRep Source # | |
| Generic ConstrRep Source # | |
| Generic Fixity Source # | |
| Generic SrcLoc Source # | |
| Generic Location Source # | |
| Generic GiveGCStats Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code GiveGCStats :: [[ Type ]] Source # Methods from :: GiveGCStats -> Rep GiveGCStats Source # to :: Rep GiveGCStats -> GiveGCStats Source # |
|
| Generic GCFlags Source # | |
| Generic ConcFlags Source # | |
| Generic MiscFlags Source # | |
| Generic DebugFlags Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code DebugFlags :: [[ Type ]] Source # |
|
| Generic DoCostCentres Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code DoCostCentres :: [[ Type ]] Source # Methods from :: DoCostCentres -> Rep DoCostCentres Source # to :: Rep DoCostCentres -> DoCostCentres Source # |
|
| Generic CCFlags Source # | |
| Generic DoHeapProfile Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code DoHeapProfile :: [[ Type ]] Source # Methods from :: DoHeapProfile -> Rep DoHeapProfile Source # to :: Rep DoHeapProfile -> DoHeapProfile Source # |
|
| Generic ProfFlags Source # | |
| Generic DoTrace Source # | |
| Generic TraceFlags Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code TraceFlags :: [[ Type ]] Source # |
|
| Generic TickyFlags Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code TickyFlags :: [[ Type ]] Source # |
|
| Generic ParFlags Source # | |
| Generic RTSFlags Source # | |
| Generic RTSStats Source # | |
| Generic GCDetails Source # | |
| Generic ByteOrder Source # | |
| Generic StaticPtrInfo Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code StaticPtrInfo :: [[ Type ]] Source # Methods from :: StaticPtrInfo -> Rep StaticPtrInfo Source # to :: Rep StaticPtrInfo -> StaticPtrInfo Source # |
|
| Generic FormatAdjustment Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code FormatAdjustment :: [[ Type ]] Source # Methods from :: FormatAdjustment -> Rep FormatAdjustment Source # to :: Rep FormatAdjustment -> FormatAdjustment Source # |
|
| Generic FormatSign Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code FormatSign :: [[ Type ]] Source # |
|
| Generic FieldFormat Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code FieldFormat :: [[ Type ]] Source # Methods from :: FieldFormat -> Rep FieldFormat Source # to :: Rep FieldFormat -> FieldFormat Source # |
|
| Generic FormatParse Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code FormatParse :: [[ Type ]] Source # Methods from :: FormatParse -> Rep FormatParse Source # to :: Rep FormatParse -> FormatParse Source # |
|
| Generic Version Source # | |
| Generic HandlePosn Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code HandlePosn :: [[ Type ]] Source # |
|
| Generic PatternMatchFail Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code PatternMatchFail :: [[ Type ]] Source # Methods from :: PatternMatchFail -> Rep PatternMatchFail Source # to :: Rep PatternMatchFail -> PatternMatchFail Source # |
|
| Generic RecSelError Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code RecSelError :: [[ Type ]] Source # Methods from :: RecSelError -> Rep RecSelError Source # to :: Rep RecSelError -> RecSelError Source # |
|
| Generic RecConError Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code RecConError :: [[ Type ]] Source # Methods from :: RecConError -> Rep RecConError Source # to :: Rep RecConError -> RecConError Source # |
|
| Generic RecUpdError Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code RecUpdError :: [[ Type ]] Source # Methods from :: RecUpdError -> Rep RecUpdError Source # to :: Rep RecUpdError -> RecUpdError Source # |
|
| Generic NoMethodError Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code NoMethodError :: [[ Type ]] Source # Methods from :: NoMethodError -> Rep NoMethodError Source # to :: Rep NoMethodError -> NoMethodError Source # |
|
| Generic TypeError Source # | |
| Generic NonTermination Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code NonTermination :: [[ Type ]] Source # Methods from :: NonTermination -> Rep NonTermination Source # to :: Rep NonTermination -> NonTermination Source # |
|
| Generic NestedAtomically Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code NestedAtomically :: [[ Type ]] Source # Methods from :: NestedAtomically -> Rep NestedAtomically Source # to :: Rep NestedAtomically -> NestedAtomically Source # |
|
| Generic BlockReason Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code BlockReason :: [[ Type ]] Source # Methods from :: BlockReason -> Rep BlockReason Source # to :: Rep BlockReason -> BlockReason Source # |
|
| Generic ThreadStatus Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code ThreadStatus :: [[ Type ]] Source # Methods from :: ThreadStatus -> Rep ThreadStatus Source # to :: Rep ThreadStatus -> ThreadStatus Source # |
|
| Generic Errno Source # | |
| Generic CodingFailureMode Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code CodingFailureMode :: [[ Type ]] Source # Methods |
|
| Generic BlockedIndefinitelyOnMVar Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code BlockedIndefinitelyOnMVar :: [[ Type ]] Source # |
|
| Generic BlockedIndefinitelyOnSTM Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code BlockedIndefinitelyOnSTM :: [[ Type ]] Source # Methods from :: BlockedIndefinitelyOnSTM -> Rep BlockedIndefinitelyOnSTM Source # to :: Rep BlockedIndefinitelyOnSTM -> BlockedIndefinitelyOnSTM Source # |
|
| Generic Deadlock Source # | |
| Generic AllocationLimitExceeded Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code AllocationLimitExceeded :: [[ Type ]] Source # Methods from :: AllocationLimitExceeded -> Rep AllocationLimitExceeded Source # to :: Rep AllocationLimitExceeded -> AllocationLimitExceeded Source # |
|
| Generic AssertionFailed Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code AssertionFailed :: [[ Type ]] Source # Methods from :: AssertionFailed -> Rep AssertionFailed Source # to :: Rep AssertionFailed -> AssertionFailed Source # |
|
| Generic AsyncException Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code AsyncException :: [[ Type ]] Source # Methods from :: AsyncException -> Rep AsyncException Source # to :: Rep AsyncException -> AsyncException Source # |
|
| Generic ArrayException Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code ArrayException :: [[ Type ]] Source # Methods from :: ArrayException -> Rep ArrayException Source # to :: Rep ArrayException -> ArrayException Source # |
|
| Generic FixIOException Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code FixIOException :: [[ Type ]] Source # Methods from :: FixIOException -> Rep FixIOException Source # to :: Rep FixIOException -> FixIOException Source # |
|
| Generic ExitCode Source # | |
| Generic IOErrorType Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code IOErrorType :: [[ Type ]] Source # Methods from :: IOErrorType -> Rep IOErrorType Source # to :: Rep IOErrorType -> IOErrorType Source # |
|
| Generic BufferMode Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code BufferMode :: [[ Type ]] Source # |
|
| Generic Newline Source # | |
| Generic NewlineMode Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code NewlineMode :: [[ Type ]] Source # Methods from :: NewlineMode -> Rep NewlineMode Source # to :: Rep NewlineMode -> NewlineMode Source # |
|
| Generic IODeviceType Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code IODeviceType :: [[ Type ]] Source # Methods from :: IODeviceType -> Rep IODeviceType Source # to :: Rep IODeviceType -> IODeviceType Source # |
|
| Generic SeekMode Source # | |
| Generic CodingProgress Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code CodingProgress :: [[ Type ]] Source # Methods from :: CodingProgress -> Rep CodingProgress Source # to :: Rep CodingProgress -> CodingProgress Source # |
|
| Generic BufferState Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code BufferState :: [[ Type ]] Source # Methods from :: BufferState -> Rep BufferState Source # to :: Rep BufferState -> BufferState Source # |
|
| Generic MaskingState Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code MaskingState :: [[ Type ]] Source # Methods from :: MaskingState -> Rep MaskingState Source # to :: Rep MaskingState -> MaskingState Source # |
|
| Generic IOException Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code IOException :: [[ Type ]] Source # Methods from :: IOException -> Rep IOException Source # to :: Rep IOException -> IOException Source # |
|
| Generic LockMode Source # | |
| Generic ErrorCall Source # | |
| Generic ArithException Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code ArithException :: [[ Type ]] Source # Methods from :: ArithException -> Rep ArithException Source # to :: Rep ArithException -> ArithException Source # |
|
| Generic All Source # | |
| Generic Any Source # | |
| Generic Fixity Source # | |
| Generic Associativity Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code Associativity :: [[ Type ]] Source # Methods from :: Associativity -> Rep Associativity Source # to :: Rep Associativity -> Associativity Source # |
|
| Generic SourceUnpackedness Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code SourceUnpackedness :: [[ Type ]] Source # Methods from :: SourceUnpackedness -> Rep SourceUnpackedness Source # |
|
| Generic SourceStrictness Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code SourceStrictness :: [[ Type ]] Source # Methods from :: SourceStrictness -> Rep SourceStrictness Source # to :: Rep SourceStrictness -> SourceStrictness Source # |
|
| Generic DecidedStrictness Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code DecidedStrictness :: [[ Type ]] Source # Methods |
|
| Generic CChar Source # | |
| Generic CSChar Source # | |
| Generic CUChar Source # | |
| Generic CShort Source # | |
| Generic CUShort Source # | |
| Generic CInt Source # | |
| Generic CUInt Source # | |
| Generic CLong Source # | |
| Generic CULong Source # | |
| Generic CLLong Source # | |
| Generic CULLong Source # | |
| Generic CFloat Source # | |
| Generic CDouble Source # | |
| Generic CPtrdiff Source # | |
| Generic CSize Source # | |
| Generic CWchar Source # | |
| Generic CSigAtomic Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code CSigAtomic :: [[ Type ]] Source # |
|
| Generic CClock Source # | |
| Generic CTime Source # | |
| Generic CUSeconds Source # | |
| Generic CSUSeconds Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code CSUSeconds :: [[ Type ]] Source # |
|
| Generic CIntPtr Source # | |
| Generic CUIntPtr Source # | |
| Generic CIntMax Source # | |
| Generic CUIntMax Source # | |
| Generic IOMode Source # | |
| Generic Fingerprint Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code Fingerprint :: [[ Type ]] Source # Methods from :: Fingerprint -> Rep Fingerprint Source # to :: Rep Fingerprint -> Fingerprint Source # |
|
| Generic Lexeme Source # | |
| Generic Number Source # | |
| Generic FFFormat Source # | |
| Generic GeneralCategory Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code GeneralCategory :: [[ Type ]] Source # Methods from :: GeneralCategory -> Rep GeneralCategory Source # to :: Rep GeneralCategory -> GeneralCategory Source # |
|
| Generic SrcLoc Source # | |
| Generic [a] Source # | |
| Generic ( Maybe a) Source # | |
| Generic ( Par1 p) Source # | |
| Generic ( Complex a) Source # | |
| Generic ( Min a) Source # | |
| Generic ( Max a) Source # | |
| Generic ( First a) Source # | |
| Generic ( Last a) Source # | |
| Generic ( WrappedMonoid m) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code ( WrappedMonoid m) :: [[ Type ]] Source # Methods from :: WrappedMonoid m -> Rep ( WrappedMonoid m) Source # to :: Rep ( WrappedMonoid m) -> WrappedMonoid m Source # |
|
| Generic ( Option a) Source # | |
| Generic ( ArgOrder a) Source # | |
| Generic ( OptDescr a) Source # | |
| Generic ( ArgDescr a) Source # | |
| Generic ( Identity a) Source # | |
| Generic ( Buffer e) Source # | |
| Generic ( First a) Source # | |
| Generic ( Last a) Source # | |
| Generic ( Dual a) Source # | |
| Generic ( Endo a) Source # | |
| Generic ( Sum a) Source # | |
| Generic ( Product a) Source # | |
| Generic ( Down a) Source # | |
| Generic ( NonEmpty a) Source # | |
| Generic ( I a) Source # | |
| Generic ( Either a b) Source # | |
| Generic ( V1 p) Source # | |
| Generic ( U1 p) Source # | |
| Generic (a, b) Source # | |
| Generic ( Fixed a) Source # | |
| Generic ( Arg a b) Source # | |
| Generic ( Proxy t) Source # | |
| Generic (a, b, c) Source # | |
| Generic ( BufferCodec from to state) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code ( BufferCodec from to state) :: [[ Type ]] Source # Methods from :: BufferCodec from to state -> Rep ( BufferCodec from to state) Source # to :: Rep ( BufferCodec from to state) -> BufferCodec from to state Source # |
|
| Generic ( Const a b) Source # | |
| Generic ( Alt f a) Source # | |
| Generic ( K a b) Source # | |
| Generic ( K1 i c p) Source # | |
| Generic ((f :+: g) p) Source # | |
| Generic ((f :*: g) p) Source # | |
| Generic (a, b, c, d) Source # | |
| Generic ( Product f g a) Source # | |
| Generic ( Sum f g a) Source # | |
| Generic ((f -.-> g) a) Source # | |
| Generic ( M1 i c f p) Source # | |
| Generic ((f :.: g) p) Source # | |
| Generic (a, b, c, d, e) Source # | |
| Generic ( Compose f g a) Source # | |
| Generic ((f :.: g) p) Source # | |
| Generic (a, b, c, d, e, f) Source # | |
| Generic (a, b, c, d, e, f, g) Source # | |
| Generic (a, b, c, d, e, f, g, h) Source # | |
| Generic (a, b, c, d, e, f, g, h, i) Source # | |
| Generic (a, b, c, d, e, f, g, h, i, j) Source # | |
| Generic (a, b, c, d, e, f, g, h, i, j, k) Source # | |
|
Defined in Generics.SOP.Instances |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l) Source # | |
|
Defined in Generics.SOP.Instances |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m) Source # | |
|
Defined in Generics.SOP.Instances |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n) Source # | |
|
Defined in Generics.SOP.Instances |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o) Source # | |
|
Defined in Generics.SOP.Instances |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) Source # | |
|
Defined in Generics.SOP.Instances |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q) Source # | |
|
Defined in Generics.SOP.Instances |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r) Source # | |
|
Defined in Generics.SOP.Instances |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s) Source # | |
|
Defined in Generics.SOP.Instances |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t) Source # | |
|
Defined in Generics.SOP.Instances |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u) :: [[ Type ]] Source # Methods from :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u) -> Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u) Source # to :: Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u) Source # |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v) :: [[ Type ]] Source # Methods from :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v) -> Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v) Source # to :: Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v) Source # |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) :: [[ Type ]] Source # Methods from :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) Source # to :: Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w) Source # |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type Code (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x) :: [[ Type ]] Source # Methods from :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x) -> Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x) Source # to :: Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x) Source # |
|
| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y) Source # | |
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Defined in Generics.SOP.Instances Associated Types type Code (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y) :: [[ Type ]] Source # Methods from :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y) -> Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y) Source # to :: Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y) Source # |
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| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z) Source # | |
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Defined in Generics.SOP.Instances Associated Types type Code (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z) :: [[ Type ]] Source # Methods from :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z) -> Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z) Source # to :: Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z) Source # |
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| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26) Source # | |
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Defined in Generics.SOP.Instances Associated Types type Code (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26) :: [[ Type ]] Source # Methods from :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26) -> Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26) Source # to :: Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26) Source # |
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| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27) Source # | |
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Defined in Generics.SOP.Instances Associated Types type Code (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27) :: [[ Type ]] Source # Methods from :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27) -> Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27) Source # to :: Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27) Source # |
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| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28) Source # | |
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Defined in Generics.SOP.Instances Associated Types type Code (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28) :: [[ Type ]] Source # Methods from :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28) -> Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28) Source # to :: Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28) Source # |
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| Generic (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28, t29) Source # | |
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Defined in Generics.SOP.Instances Associated Types type Code (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28, t29) :: [[ Type ]] Source # Methods from :: (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28, t29) -> Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28, t29) Source # to :: Rep (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28, t29) -> (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z, t26, t27, t28, t29) Source # |
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type IsProductType (a :: Type ) (xs :: [ Type ]) = ( Generic a, Code a ~ '[xs]) Source #
Constraint that captures that a datatype is a product type, i.e., a type with a single constructor.
It also gives access to the code for the arguments of that constructor.
Since: 0.3.1.0
type ProductCode (a :: Type ) = Head ( Code a) Source #
Direct access to the part of the code that is relevant for a product type.
Since: 0.4.0.0
productTypeFrom :: IsProductType a xs => a -> NP I xs Source #
Convert from a product type to its product representation.
Since: 0.4.0.0
productTypeTo :: IsProductType a xs => NP I xs -> a Source #
Convert a product representation to the original type.
Since: 0.4.0.0
type IsEnumType (a :: Type ) = ( Generic a, All ((~) '[]) ( Code a)) Source #
Constraint that captures that a datatype is an enumeration type, i.e., none of the constructors have any arguments.
Since: 0.3.1.0
enumTypeFrom :: IsEnumType a => a -> NS ( K ()) ( Code a) Source #
Convert from an enum type to its sum representation.
Since: 0.4.0.0
enumTypeTo :: IsEnumType a => NS ( K ()) ( Code a) -> a Source #
Convert a sum representation to ihe original type.
type IsWrappedType (a :: Type ) (x :: Type ) = ( Generic a, Code a ~ '['[x]]) Source #
Constraint that captures that a datatype is a single-constructor, single-field datatype. This always holds for newtype-defined types, but it can also be true for data-defined types.
The constraint also gives access to the type that is wrapped.
Since: 0.3.1.0
type WrappedCode (a :: Type ) = Head ( Head ( Code a)) Source #
Direct access to the part of the code that is relevant for wrapped types and newtypes.
Since: 0.4.0.0
wrappedTypeFrom :: IsWrappedType a x => a -> x Source #
Convert from a wrapped type to its inner type.
Since: 0.4.0.0
wrappedTypeTo :: IsWrappedType a x => x -> a Source #
Convert a type to a wrapped type.
Since: 0.4.0.0
type IsNewtype (a :: Type ) (x :: Type ) = ( IsWrappedType a x, Coercible a x) Source #
Constraint that captures that a datatype is a newtype. This makes use of the fact that newtypes are always coercible to the type they wrap, whereas datatypes are not.
Since: 0.3.1.0
newtypeFrom :: IsNewtype a x => a -> x Source #
n-ary datatypes
data NP (a :: k -> Type ) (b :: [k]) where Source #
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
, 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.
K
a
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 ]
Constructors
| Nil :: forall k (a :: k -> Type ). NP a ('[] :: [k]) | |
| (:*) :: forall k (a :: k -> Type ) (x :: k) (xs :: [k]). a x -> NP a xs -> NP a (x ': xs) infixr 5 |
Instances
| HTrans ( NP :: (k1 -> Type ) -> [k1] -> Type ) ( NP :: (k2 -> Type ) -> [k2] -> Type ) | |
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Defined in Data.SOP.NP Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod NP ) c xs ys => proxy c -> ( forall (x :: k10) (y :: k20). c x y => f x -> g y) -> NP f xs -> NP g ys Source # hcoerce :: forall (f :: k10 -> Type ) (g :: k20 -> Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod NP ) ( LiftedCoercible f g) xs ys => NP f xs -> NP g ys Source # |
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| HPure ( NP :: (k -> Type ) -> [k] -> Type ) | |
| HAp ( NP :: (k -> Type ) -> [k] -> Type ) | |
| HCollapse ( NP :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NP |
|
| HTraverse_ ( NP :: (k -> Type ) -> [k] -> Type ) | |
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Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN NP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g ()) -> NP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN NP xs, Applicative g) => ( forall (a :: k0). f a -> g ()) -> NP f xs -> g () Source # |
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| HSequence ( NP :: (k -> Type ) -> [k] -> Type ) | |
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Defined in Data.SOP.NP Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type ). ( SListIN NP xs, Applicative f) => NP (f :.: g) xs -> f ( NP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN NP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g (f' a)) -> NP f xs -> g ( NP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN NP xs, Applicative g) => ( forall (a :: k0). f a -> g (f' a)) -> NP f xs -> g ( NP f' xs) Source # |
|
| All ( Compose Eq f) xs => Eq ( NP f xs) | |
| ( All ( Compose Eq f) xs, All ( Compose Ord f) xs) => Ord ( NP f xs) | |
|
Defined in Data.SOP.NP |
|
| All ( Compose Show f) xs => Show ( NP f xs) | |
| All ( Compose Semigroup f) xs => Semigroup ( NP f xs) |
Since: sop-core-0.4.0.0 |
| ( All ( Compose Monoid f) xs, All ( Compose Semigroup f) xs) => Monoid ( NP f xs) |
Since: sop-core-0.4.0.0 |
| All ( Compose NFData f) xs => NFData ( NP f xs) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.NP |
|
| type AllZipN ( NP :: (k -> Type ) -> [k] -> Type ) (c :: a -> b -> Constraint ) | |
|
Defined in Data.SOP.NP |
|
| type Same ( NP :: (k1 -> Type ) -> [k1] -> Type ) | |
| type Prod ( NP :: (k -> Type ) -> [k] -> Type ) | |
| type UnProd ( NP :: (k -> Type ) -> [k] -> Type ) | |
| type SListIN ( NP :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NP |
|
| type CollapseTo ( NP :: (k -> Type ) -> [k] -> Type ) a | |
|
Defined in Data.SOP.NP |
|
| type AllN ( NP :: (k -> Type ) -> [k] -> Type ) (c :: k -> Constraint ) | |
|
Defined in Data.SOP.NP |
|
data NS (a :: k -> Type ) (b :: [k]) where Source #
An n-ary sum.
The sum is parameterized by a type constructor
f
and
indexed by a type-level list
xs
. The length of the list
determines the number of choices in the sum and if the
i
-th element of the list is of type
x
, then the
i
-th
choice of the sum is of type
f x
.
The constructor names are chosen to resemble Peano-style
natural numbers, i.e.,
Z
is for "zero", and
S
is for
"successor". Chaining
S
and
Z
chooses the corresponding
component of the sum.
Examples:
Z :: f x -> NS f (x ': xs) S . Z :: f y -> NS f (x ': y ': xs) S . S . Z :: f z -> NS f (x ': y ': z ': xs) ...
Note that empty sums (indexed by an empty list) have no non-bottom elements.
Two common instantiations of
f
are the identity functor
I
and the constant functor
K
. For
I
, the sum becomes a
direct generalization of the
Either
type to arbitrarily many
choices. For
, the result is a homogeneous choice type,
where the contents of the type-level list are ignored, but its
length specifies the number of options.
K
a
In the context of the SOP approach to generic programming, an n-ary sum describes the top-level structure of a datatype, which is a choice between all of its constructors.
Examples:
Z (I 'x') :: NS I '[ Char, Bool ] S (Z (I True)) :: NS I '[ Char, Bool ] S (Z (K 1)) :: NS (K Int) '[ Char, Bool ]
Constructors
| Z :: forall k (a :: k -> Type ) (x :: k) (xs :: [k]). a x -> NS a (x ': xs) | |
| S :: forall k (a :: k -> Type ) (xs :: [k]) (x :: k). NS a xs -> NS a (x ': xs) |
Instances
| HTrans ( NS :: (k1 -> Type ) -> [k1] -> Type ) ( NS :: (k2 -> Type ) -> [k2] -> Type ) | |
|
Defined in Data.SOP.NS Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod NS ) c xs ys => proxy c -> ( forall (x :: k10) (y :: k20). c x y => f x -> g y) -> NS f xs -> NS g ys Source # hcoerce :: forall (f :: k10 -> Type ) (g :: k20 -> Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod NS ) ( LiftedCoercible f g) xs ys => NS f xs -> NS g ys Source # |
|
| HAp ( NS :: (k -> Type ) -> [k] -> Type ) | |
| HCollapse ( NS :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NS |
|
| HTraverse_ ( NS :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN NS c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g ()) -> NS f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN NS xs, Applicative g) => ( forall (a :: k0). f a -> g ()) -> NS f xs -> g () Source # |
|
| HSequence ( NS :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NS Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type ). ( SListIN NS xs, Applicative f) => NS (f :.: g) xs -> f ( NS g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN NS c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g (f' a)) -> NS f xs -> g ( NS f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN NS xs, Applicative g) => ( forall (a :: k0). f a -> g (f' a)) -> NS f xs -> g ( NS f' xs) Source # |
|
| HIndex ( NS :: (k -> Type ) -> [k] -> Type ) | |
| HApInjs ( NS :: (k -> Type ) -> [k] -> Type ) | |
| HExpand ( NS :: (k -> Type ) -> [k] -> Type ) | |
| All ( Compose Eq f) xs => Eq ( NS f xs) | |
| ( All ( Compose Eq f) xs, All ( Compose Ord f) xs) => Ord ( NS f xs) | |
|
Defined in Data.SOP.NS |
|
| All ( Compose Show f) xs => Show ( NS f xs) | |
| All ( Compose NFData f) xs => NFData ( NS f xs) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.NS |
|
| type Same ( NS :: (k1 -> Type ) -> [k1] -> Type ) | |
| type Prod ( NS :: (k -> Type ) -> [k] -> Type ) | |
| type SListIN ( NS :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NS |
|
| type CollapseTo ( NS :: (k -> Type ) -> [k] -> Type ) a | |
|
Defined in Data.SOP.NS |
|
| type AllN ( NS :: (k -> Type ) -> [k] -> Type ) (c :: k -> Constraint ) | |
|
Defined in Data.SOP.NS |
|
newtype SOP (f :: k -> Type ) (xss :: [[k]]) Source #
A sum of products.
This is a 'newtype' for an
NS
of an
NP
. The elements of the
(inner) products are applications of the parameter
f
. The type
SOP
is indexed by the list of lists that determines the sizes
of both the (outer) sum and all the (inner) products, as well as
the types of all the elements of the inner products.
A
reflects the structure of a normal Haskell datatype.
The sum structure represents the choice between the different
constructors, the product structure represents the arguments of
each constructor.
SOP
I
Instances
| HTrans ( SOP :: (k1 -> Type ) -> [[k1]] -> Type ) ( SOP :: (k2 -> Type ) -> [[k2]] -> Type ) | |
|
Defined in Data.SOP.NS Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod SOP ) c xs ys => proxy c -> ( forall (x :: k10) (y :: k20). c x y => f x -> g y) -> SOP f xs -> SOP g ys Source # hcoerce :: forall (f :: k10 -> Type ) (g :: k20 -> Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod SOP ) ( LiftedCoercible f g) xs ys => SOP f xs -> SOP g ys Source # |
|
| HAp ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
| HCollapse ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NS |
|
| HTraverse_ ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN SOP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g ()) -> SOP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN SOP xs, Applicative g) => ( forall (a :: k0). f a -> g ()) -> SOP f xs -> g () Source # |
|
| HSequence ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NS Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type ). ( SListIN SOP xs, Applicative f) => SOP (f :.: g) xs -> f ( SOP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN SOP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g (f' a)) -> SOP f xs -> g ( SOP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN SOP xs, Applicative g) => ( forall (a :: k0). f a -> g (f' a)) -> SOP f xs -> g ( SOP f' xs) Source # |
|
| HIndex ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
| HApInjs ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
| HExpand ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
| Eq ( NS ( NP f) xss) => Eq ( SOP f xss) | |
| Ord ( NS ( NP f) xss) => Ord ( SOP f xss) | |
|
Defined in Data.SOP.NS Methods compare :: SOP f xss -> SOP f xss -> Ordering Source # (<) :: SOP f xss -> SOP f xss -> Bool Source # (<=) :: SOP f xss -> SOP f xss -> Bool Source # (>) :: SOP f xss -> SOP f xss -> Bool Source # (>=) :: SOP f xss -> SOP f xss -> Bool Source # |
|
| Show ( NS ( NP f) xss) => Show ( SOP f xss) | |
| NFData ( NS ( NP f) xss) => NFData ( SOP f xss) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.NS |
|
| type Same ( SOP :: (k1 -> Type ) -> [[k1]] -> Type ) | |
| type Prod ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
| type SListIN ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NS |
|
| type CollapseTo ( SOP :: (k -> Type ) -> [[k]] -> Type ) a | |
|
Defined in Data.SOP.NS |
|
| type AllN ( SOP :: (k -> Type ) -> [[k]] -> Type ) (c :: k -> Constraint ) | |
|
Defined in Data.SOP.NS |
|
unSOP :: forall k (f :: k -> Type ) (xss :: [[k]]). SOP f xss -> NS ( NP f) xss Source #
Unwrap a sum of products.
newtype POP (f :: k -> Type ) (xss :: [[k]]) Source #
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.
Instances
| HTrans ( POP :: (k1 -> Type ) -> [[k1]] -> Type ) ( POP :: (k2 -> Type ) -> [[k2]] -> Type ) | |
|
Defined in Data.SOP.NP Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod POP ) c xs ys => proxy c -> ( forall (x :: k10) (y :: k20). c x y => f x -> g y) -> POP f xs -> POP g ys Source # hcoerce :: forall (f :: k10 -> Type ) (g :: k20 -> Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod POP ) ( LiftedCoercible f g) xs ys => POP f xs -> POP g ys Source # |
|
| HPure ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
| HAp ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
| HCollapse ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NP |
|
| HTraverse_ ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN POP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g ()) -> POP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN POP xs, Applicative g) => ( forall (a :: k0). f a -> g ()) -> POP f xs -> g () Source # |
|
| HSequence ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NP Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type ). ( SListIN POP xs, Applicative f) => POP (f :.: g) xs -> f ( POP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN POP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g (f' a)) -> POP f xs -> g ( POP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN POP xs, Applicative g) => ( forall (a :: k0). f a -> g (f' a)) -> POP f xs -> g ( POP f' xs) Source # |
|
| Eq ( NP ( NP f) xss) => Eq ( POP f xss) | |
| Ord ( NP ( NP f) xss) => Ord ( POP f xss) | |
|
Defined in Data.SOP.NP Methods compare :: POP f xss -> POP f xss -> Ordering Source # (<) :: POP f xss -> POP f xss -> Bool Source # (<=) :: POP f xss -> POP f xss -> Bool Source # (>) :: POP f xss -> POP f xss -> Bool Source # (>=) :: POP f xss -> POP f xss -> Bool Source # |
|
| Show ( NP ( NP f) xss) => Show ( POP f xss) | |
| Semigroup ( NP ( NP f) xss) => Semigroup ( POP f xss) |
Since: sop-core-0.4.0.0 |
| Monoid ( NP ( NP f) xss) => Monoid ( POP f xss) |
Since: sop-core-0.4.0.0 |
| NFData ( NP ( NP f) xss) => NFData ( POP f xss) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.NP |
|
| type AllZipN ( POP :: (k -> Type ) -> [[k]] -> Type ) (c :: a -> b -> Constraint ) | |
|
Defined in Data.SOP.NP |
|
| type Same ( POP :: (k1 -> Type ) -> [[k1]] -> Type ) | |
| type Prod ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
| type UnProd ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
| type SListIN ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NP |
|
| type CollapseTo ( POP :: (k -> Type ) -> [[k]] -> Type ) a | |
|
Defined in Data.SOP.NP |
|
| type AllN ( POP :: (k -> Type ) -> [[k]] -> Type ) (c :: k -> Constraint ) | |
|
Defined in Data.SOP.NP |
|
unPOP :: forall k (f :: k -> Type ) (xss :: [[k]]). POP f xss -> NP ( NP f) xss Source #
Unwrap a product of products.
Metadata
data DatatypeInfo :: [[ Type ]] -> Type where Source #
Metadata for a datatype.
A value of type
contains the information about a datatype
that is not contained in
DatatypeInfo
c
. This information consists
primarily of the names of the datatype, its constructors, and possibly its
record selectors.
Code
c
The constructor indicates whether the datatype has been declared using
newtype
or not.
Constructors
| ADT :: ModuleName -> DatatypeName -> NP ConstructorInfo xss -> POP StrictnessInfo xss -> DatatypeInfo xss | |
| Newtype :: ModuleName -> DatatypeName -> ConstructorInfo '[x] -> DatatypeInfo '['[x]] |
Instances
moduleName :: DatatypeInfo xss -> ModuleName Source #
The module name where a datatype is defined.
Since: 0.2.3.0
datatypeName :: DatatypeInfo xss -> DatatypeName Source #
The name of a datatype (or newtype).
Since: 0.2.3.0
constructorInfo :: DatatypeInfo xss -> NP ConstructorInfo xss Source #
The constructor info for a datatype (or newtype).
Since: 0.2.3.0
data ConstructorInfo :: [ Type ] -> Type where Source #
Metadata for a single constructor.
This is indexed by the product structure of the constructor components.
Constructors
| Constructor :: SListI xs => ConstructorName -> ConstructorInfo xs | |
| Infix :: ConstructorName -> Associativity -> Fixity -> ConstructorInfo '[x, y] | |
| Record :: SListI xs => ConstructorName -> NP FieldInfo xs -> ConstructorInfo xs |
Instances
| All ( Compose Eq FieldInfo ) xs => Eq ( ConstructorInfo xs) Source # | |
|
Defined in Generics.SOP.Metadata Methods (==) :: ConstructorInfo xs -> ConstructorInfo xs -> Bool Source # (/=) :: ConstructorInfo xs -> ConstructorInfo xs -> Bool Source # |
|
| ( All ( Compose Eq FieldInfo ) xs, All ( Compose Ord FieldInfo ) xs) => Ord ( ConstructorInfo xs) Source # | |
|
Defined in Generics.SOP.Metadata Methods compare :: ConstructorInfo xs -> ConstructorInfo xs -> Ordering Source # (<) :: ConstructorInfo xs -> ConstructorInfo xs -> Bool Source # (<=) :: ConstructorInfo xs -> ConstructorInfo xs -> Bool Source # (>) :: ConstructorInfo xs -> ConstructorInfo xs -> Bool Source # (>=) :: ConstructorInfo xs -> ConstructorInfo xs -> Bool Source # max :: ConstructorInfo xs -> ConstructorInfo xs -> ConstructorInfo xs Source # min :: ConstructorInfo xs -> ConstructorInfo xs -> ConstructorInfo xs Source # |
|
| All ( Compose Show FieldInfo ) xs => Show ( ConstructorInfo xs) Source # | |
|
Defined in Generics.SOP.Metadata |
|
constructorName :: ConstructorInfo xs -> ConstructorName Source #
The name of a constructor.
Since: 0.2.3.0
data FieldInfo :: Type -> Type where Source #
For records, this functor maps the component to its selector name.
Instances
| Functor FieldInfo Source # | |
| Eq ( FieldInfo a) Source # | |
| Ord ( FieldInfo a) Source # | |
|
Defined in Generics.SOP.Metadata Methods compare :: FieldInfo a -> FieldInfo a -> Ordering Source # (<) :: FieldInfo a -> FieldInfo a -> Bool Source # (<=) :: FieldInfo a -> FieldInfo a -> Bool Source # (>) :: FieldInfo a -> FieldInfo a -> Bool Source # (>=) :: FieldInfo a -> FieldInfo a -> Bool Source # |
|
| Show ( FieldInfo a) Source # | |
class Generic a => HasDatatypeInfo a where Source #
A class of datatypes that have associated metadata.
It is possible to use the sum-of-products approach to generic programming without metadata. If you need metadata in a function, an additional constraint on this class is in order.
You typically don't define instances of this class by hand, but
rather derive the class instance automatically. See the documentation
of
Generic
for the options.
Minimal complete definition
Nothing
Associated Types
type DatatypeInfoOf a :: DatatypeInfo Source #
Type-level datatype info
type DatatypeInfoOf a = GDatatypeInfoOf a
Methods
datatypeInfo :: proxy a -> DatatypeInfo ( Code a) Source #
Term-level datatype info; by default, the term-level datatype info is produced from the type-level info.
default datatypeInfo :: ( GDatatypeInfo a, GCode a ~ Code a) => proxy a -> DatatypeInfo ( Code a) Source #
Instances
type DatatypeName = String Source #
The name of a datatype.
type ModuleName = String Source #
The name of a module.
type ConstructorName = String Source #
The name of a data constructor.
data Associativity Source #
Datatype to represent the associativity of a constructor
Constructors
| LeftAssociative | |
| RightAssociative | |
| NotAssociative |
Instances
Combinators
Constructing products
class HPure (h :: (k -> Type ) -> l -> Type ) where Source #
Methods
hpure :: forall (xs :: l) f. SListIN h xs => ( forall (a :: k). f a) -> h f xs Source #
Corresponds to
pure
directly.
Instances:
hpure,pure_NP::SListIxs => (forall a. f a) ->NPf xshpure,pure_POP::SListI2xss => (forall a. f a) ->POPf xss
hcpure :: forall c (xs :: l) proxy f. AllN h c xs => proxy c -> ( forall (a :: k). c a => f a) -> h f xs Source #
A variant of
hpure
that allows passing in a constrained
argument.
Calling
where
hcpure
f s
s :: h f xs
causes
f
to be
applied at all the types that are contained in
xs
. Therefore,
the constraint
c
has to be satisfied for all elements of
xs
,
which is what
states.
AllN
h c xs
Instances:
hcpure,cpure_NP:: (Allc xs ) => proxy c -> (forall a. c a => f a) ->NPf xshcpure,cpure_POP:: (All2c xss) => proxy c -> (forall a. c a => f a) ->POPf xss
Destructing products
hd :: forall k f (x :: k) (xs :: [k]). NP f (x ': xs) -> f x Source #
Obtain the head of an n-ary product.
Since: sop-core-0.2.1.0
tl :: forall k (f :: k -> Type ) (x :: k) (xs :: [k]). NP f (x ': xs) -> NP f xs Source #
Obtain the tail of an n-ary product.
Since: sop-core-0.2.1.0
type Projection (f :: k -> Type ) (xs :: [k]) = ( K ( NP f xs) :: k -> Type ) -.-> f Source #
The type of projections from an n-ary product.
A projection is a function from the n-ary product to a single element.
projections :: forall k (xs :: [k]) (f :: k -> Type ). SListI xs => NP ( Projection f xs) xs Source #
Compute all projections from an n-ary product.
Each element of the resulting product contains one of the projections.
shiftProjection :: forall a1 (f :: a1 -> Type ) (xs :: [a1]) (a2 :: a1) (x :: a1). Projection f xs a2 -> Projection f (x ': xs) a2 Source #
Application
newtype ((f :: k -> Type ) -.-> (g :: k -> Type )) (a :: k) infixr 1 Source #
Lifted functions.
Instances
| HasDatatypeInfo ((f -.-> g) a) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type DatatypeInfoOf ((f -.-> g) a) :: DatatypeInfo Source # Methods datatypeInfo :: proxy ((f -.-> g) a) -> DatatypeInfo ( Code ((f -.-> g) a)) Source # |
|
| Generic ((f -.-> g) a) Source # | |
| type DatatypeInfoOf ((f -.-> g) a) Source # | |
|
Defined in Generics.SOP.Instances
type
DatatypeInfoOf
((f
-.->
g) a) = '
Newtype
"Data.SOP.Classes" "-.->" ('
Record
"Fn" '['
FieldInfo
"apFn"])
|
|
| type Code ((f -.-> g) a) Source # | |
|
Defined in Generics.SOP.Instances |
|
fn :: forall k f (a :: k) f'. (f a -> f' a) -> (f -.-> f') a Source #
Construct a lifted function.
Same as
Fn
. Only available for uniformity with the
higher-arity versions.
fn_2 :: forall k f (a :: k) f' f''. (f a -> f' a -> f'' a) -> (f -.-> (f' -.-> f'')) a Source #
Construct a binary lifted function.
fn_3 :: forall k f (a :: k) f' f'' f'''. (f a -> f' a -> f'' a -> f''' a) -> (f -.-> (f' -.-> (f'' -.-> f'''))) a Source #
Construct a ternary lifted function.
fn_4 :: forall k f (a :: k) f' f'' f''' f''''. (f a -> f' a -> f'' a -> f''' a -> f'''' a) -> (f -.-> (f' -.-> (f'' -.-> (f''' -.-> f'''')))) a Source #
Construct a quarternary lifted function.
type family Prod (h :: (k -> Type ) -> l -> Type ) :: (k -> Type ) -> l -> Type Source #
Maps a structure containing sums to the corresponding product structure.
class ( Prod ( Prod h) ~ Prod h, HPure ( Prod h)) => HAp (h :: (k -> Type ) -> l -> Type ) where Source #
A generalization of
<*>
.
Methods
hap :: forall (f :: k -> Type ) (g :: k -> Type ) (xs :: l). Prod h (f -.-> g) xs -> h f xs -> h g xs Source #
Corresponds to
<*>
.
For products (
NP
) as well as products of products
(
POP
), the correspondence is rather direct. We combine
a structure containing (lifted) functions and a compatible structure
containing corresponding arguments into a compatible structure
containing results.
The same combinator can also be used to combine a product structure of functions with a sum structure of arguments, which then results in another sum structure of results. The sum structure determines which part of the product structure will be used.
Instances:
hap,ap_NP::NP(f -.-> g) xs ->NPf xs ->NPg xshap,ap_NS::NP(f -.-> g) xs ->NSf xs ->NSg xshap,ap_POP::POP(f -.-> g) xss ->POPf xss ->POPg xsshap,ap_SOP::POP(f -.-> g) xss ->SOPf xss ->SOPg xss
Lifting / mapping
hliftA :: forall k l h (xs :: l) f f'. ( SListIN ( Prod h) xs, HAp h) => ( forall (a :: k). f a -> f' a) -> h f xs -> h f' xs Source #
A generalized form of
liftA
,
which in turn is a generalized
map
.
Takes a lifted function and applies it to every element of a structure while preserving its shape.
Specification:
hliftAf xs =hpure(fnf) `hap` xs
Instances:
hliftA,liftA_NP::SListIxs => (forall a. f a -> f' a) ->NPf xs ->NPf' xshliftA,liftA_NS::SListIxs => (forall a. f a -> f' a) ->NSf xs ->NSf' xshliftA,liftA_POP::SListI2xss => (forall a. f a -> f' a) ->POPf xss ->POPf' xsshliftA,liftA_SOP::SListI2xss => (forall a. f a -> f' a) ->SOPf xss ->SOPf' xss
hliftA2 :: forall k l h (xs :: l) f f' f''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #
A generalized form of
liftA2
,
which in turn is a generalized
zipWith
.
Takes a lifted binary function and uses it to combine two structures of equal shape into a single structure.
It either takes two product structures to a product structure, or one product and one sum structure to a sum structure.
Specification:
hliftA2f xs ys =hpure(fn_2f) `hap` xs `hap` ys
Instances:
hliftA2,liftA2_NP::SListIxs => (forall a. f a -> f' a -> f'' a) ->NPf xs ->NPf' xs ->NPf'' xshliftA2,liftA2_NS::SListIxs => (forall a. f a -> f' a -> f'' a) ->NPf xs ->NSf' xs ->NSf'' xshliftA2,liftA2_POP::SListI2xss => (forall a. f a -> f' a -> f'' a) ->POPf xss ->POPf' xss ->POPf'' xsshliftA2,liftA2_SOP::SListI2xss => (forall a. f a -> f' a -> f'' a) ->POPf xss ->SOPf' xss ->SOPf'' xss
hliftA3 :: forall k l h (xs :: l) f f' f'' f'''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs Source #
A generalized form of
liftA3
,
which in turn is a generalized
zipWith3
.
Takes a lifted ternary function and uses it to combine three structures of equal shape into a single structure.
It either takes three product structures to a product structure, or two product structures and one sum structure to a sum structure.
Specification:
hliftA3f xs ys zs =hpure(fn_3f) `hap` xs `hap` ys `hap` zs
Instances:
hliftA3,liftA3_NP::SListIxs => (forall a. f a -> f' a -> f'' a -> f''' a) ->NPf xs ->NPf' xs ->NPf'' xs ->NPf''' xshliftA3,liftA3_NS::SListIxs => (forall a. f a -> f' a -> f'' a -> f''' a) ->NPf xs ->NPf' xs ->NSf'' xs ->NSf''' xshliftA3,liftA3_POP::SListI2xss => (forall a. f a -> f' a -> f'' a -> f''' a) ->POPf xss ->POPf' xss ->POPf'' xss ->POPf''' xshliftA3,liftA3_SOP::SListI2xss => (forall a. f a -> f' a -> f'' a -> f''' a) ->POPf xss ->POPf' xss ->SOPf'' xss ->SOPf''' xs
hcliftA :: forall k l h c (xs :: l) proxy f f'. ( AllN ( Prod h) c xs, HAp h) => proxy c -> ( forall (a :: k). c a => f a -> f' a) -> h f xs -> h f' xs Source #
hcliftA2 :: forall k l h c (xs :: l) proxy f f' f''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c -> ( forall (a :: k). c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #
hcliftA3 :: forall k l h c (xs :: l) proxy f f' f'' f'''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c -> ( forall (a :: k). c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs Source #
hmap :: forall k l h (xs :: l) f f'. ( SListIN ( Prod h) xs, HAp h) => ( forall (a :: k). f a -> f' a) -> h f xs -> h f' xs Source #
Another name for
hliftA
.
Since: sop-core-0.2
hzipWith :: forall k l h (xs :: l) f f' f''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #
Another name for
hliftA2
.
Since: sop-core-0.2
hzipWith3 :: forall k l h (xs :: l) f f' f'' f'''. ( SListIN ( Prod h) xs, HAp h, HAp ( Prod h)) => ( forall (a :: k). f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs Source #
Another name for
hliftA3
.
Since: sop-core-0.2
hcmap :: forall k l h c (xs :: l) proxy f f'. ( AllN ( Prod h) c xs, HAp h) => proxy c -> ( forall (a :: k). c a => f a -> f' a) -> h f xs -> h f' xs Source #
Another name for
hcliftA
.
Since: sop-core-0.2
hczipWith :: forall k l h c (xs :: l) proxy f f' f''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c -> ( forall (a :: k). c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #
Another name for
hcliftA2
.
Since: sop-core-0.2
hczipWith3 :: forall k l h c (xs :: l) proxy f f' f'' f'''. ( AllN ( Prod h) c xs, HAp h, HAp ( Prod h)) => proxy c -> ( forall (a :: k). c a => f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs Source #
Another name for
hcliftA3
.
Since: sop-core-0.2
Constructing sums
type Injection (f :: k -> Type ) (xs :: [k]) = f -.-> ( K ( NS f xs) :: k -> Type ) Source #
The type of injections into an n-ary sum.
If you expand the type synonyms and newtypes involved, you get
Injection f xs a = (f -.-> K (NS f xs)) a ~= f a -> K (NS f xs) a ~= f a -> NS f xs
If we pick
a
to be an element of
xs
, this indeed corresponds to an
injection into the sum.
injections :: forall k (xs :: [k]) (f :: k -> Type ). SListI xs => NP ( Injection f xs) xs Source #
Compute all injections into an n-ary sum.
Each element of the resulting product contains one of the injections.
shift :: forall a1 (f :: a1 -> Type ) (xs :: [a1]) (a2 :: a1) (x :: a1). Injection f xs a2 -> Injection f (x ': xs) a2 Source #
Shift an injection.
Given an injection, return an injection into a sum that is one component larger.
shiftInjection :: forall a1 (f :: a1 -> Type ) (xs :: [a1]) (a2 :: a1) (x :: a1). Injection f xs a2 -> Injection f (x ': xs) a2 Source #
Shift an injection.
Given an injection, return an injection into a sum that is one component larger.
type family UnProd (h :: (k -> Type ) -> l -> Type ) :: (k -> Type ) -> l -> Type Source #
Maps a structure containing products to the corresponding sum structure.
Since: sop-core-0.2.4.0
class UnProd ( Prod h) ~ h => HApInjs (h :: (k -> Type ) -> l -> Type ) where Source #
A class for applying all injections corresponding to a sum-like structure to a table containing suitable arguments.
Methods
hapInjs :: forall (xs :: l) (f :: k -> Type ). SListIN h xs => Prod h f xs -> [h f xs] Source #
For a given table (product-like structure), produce a list where each element corresponds to the application of an injection function into the corresponding sum-like structure.
Instances:
hapInjs,apInjs_NP::SListIxs =>NPf xs -> [NSf xs ]hapInjs,apInjs_SOP::SListI2xss =>POPf xs -> [SOPf xss]
Examples:
>>>hapInjs (I 'x' :* I True :* I 2 :* Nil) :: [NS I '[Char, Bool, Int]][Z (I 'x'),S (Z (I True)),S (S (Z (I 2)))]
>>>hapInjs (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil)) :: [SOP I '[ '[Char], '[Bool, Int]]][SOP (Z (I 'x' :* Nil)),SOP (S (Z (I True :* I 2 :* Nil)))]
Unfortunately the type-signatures are required in GHC-7.10 and older.
Since: sop-core-0.2.4.0
apInjs_NP :: forall k (xs :: [k]) (f :: k -> Type ). SListI xs => NP f xs -> [ NS f xs] Source #
Apply injections to a product.
Given a product containing all possible choices, produce a list of sums by applying each injection to the appropriate element.
Example:
>>>apInjs_NP (I 'x' :* I True :* I 2 :* Nil)[Z (I 'x'),S (Z (I True)),S (S (Z (I 2)))]
apInjs_POP :: forall k (xss :: [[k]]) (f :: k -> Type ). SListI xss => POP f xss -> [ SOP f xss] Source #
Apply injections to a product of product.
This operates on the outer product only. Given a product containing all possible choices (that are products), produce a list of sums (of products) by applying each injection to the appropriate element.
Example:
>>>apInjs_POP (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil))[SOP (Z (I 'x' :* Nil)),SOP (S (Z (I True :* I 2 :* Nil)))]
Destructing sums
unZ :: forall k f (x :: k). NS f '[x] -> f x Source #
Extract the payload from a unary sum.
For larger sums, this function would be partial, so it is only provided with a rather restrictive type.
Example:
>>>unZ (Z (I 'x'))I 'x'
Since: sop-core-0.2.2.0
class HIndex (h :: (k -> Type ) -> l -> Type ) where Source #
A class for determining which choice in a sum-like structure a value represents.
Methods
hindex :: forall (f :: k -> Type ) (xs :: l). h f xs -> Int Source #
If
h
is a sum-like structure representing a choice
between
n
different options, and
x
is a value of
type
h f xs
, then
returns a number between
hindex
x
0
and
n - 1
representing the index of the choice
made by
x
.
Instances:
hindex,index_NS::NSf xs -> Inthindex,index_SOP::SOPf xs -> Int
Examples:
>>>hindex (S (S (Z (I False))))2>>>hindex (Z (K ()))0>>>hindex (SOP (S (Z (I True :* I 'x' :* Nil))))1
Since: sop-core-0.2.4.0
Instances
type Ejection (f :: k -> Type ) (xs :: [k]) = ( K ( NS f xs) :: k -> Type ) -.-> ( Maybe :.: f) Source #
The type of ejections from an n-ary sum.
An ejection is the pattern matching function for one part of the n-ary sum.
It is the opposite of an
Injection
.
Since: sop-core-0.5.0.0
ejections :: forall k (xs :: [k]) (f :: k -> Type ). SListI xs => NP ( Ejection f xs) xs Source #
Compute all ejections from an n-ary sum.
Each element of the resulting product contains one of the ejections.
Since: sop-core-0.5.0.0
shiftEjection :: forall a1 (f :: a1 -> Type ) (x :: a1) (xs :: [a1]) (a2 :: a1). Ejection f xs a2 -> Ejection f (x ': xs) a2 Source #
Since: sop-core-0.5.0.0
Dealing with
All
c
All
c
hcliftA' :: forall k (c :: k -> Constraint ) (xss :: [[k]]) h proxy f f'. ( All2 c xss, Prod h ~ ( NP :: ([k] -> Type ) -> [[k]] -> Type ), HAp h) => proxy c -> ( forall (xs :: [k]). All c xs => f xs -> f' xs) -> h f xss -> h f' xss Source #
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_NPp `hap` xs
Instances:
hcliftA'::All2c xss => proxy c -> (forall xs.Allc xs => f xs -> f' xs) ->NPf xss ->NPf' xsshcliftA'::All2c xss => proxy c -> (forall xs.Allc xs => f xs -> f' xs) ->NSf xss ->NSf' xss
hcliftA2' :: forall k (c :: k -> Constraint ) (xss :: [[k]]) h proxy f f' f''. ( All2 c xss, Prod h ~ ( NP :: ([k] -> Type ) -> [[k]] -> Type ), HAp h) => proxy c -> ( forall (xs :: [k]). All c xs => f xs -> f' xs -> f'' xs) -> Prod h f xss -> h f' xss -> h f'' xss Source #
Like
hcliftA'
, but for binary functions.
hcliftA3' :: forall k (c :: k -> Constraint ) (xss :: [[k]]) h proxy f f' f'' f'''. ( All2 c xss, Prod h ~ ( NP :: ([k] -> Type ) -> [[k]] -> Type ), HAp h) => proxy c -> ( forall (xs :: [k]). 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 Source #
Like
hcliftA'
, but for ternary functions.
Comparison
Arguments
| :: forall k r f g (xs :: [k]). r |
what to do if first is smaller |
| -> ( forall (x :: k). f x -> g x -> r) |
what to do if both are equal |
| -> r |
what to do if first is larger |
| -> NS f xs | |
| -> NS g xs | |
| -> r |
Compare two sums with respect to the choice they are making.
A value that chooses the first option is considered smaller than one that chooses the second option.
If the choices are different, then either the first (if the first is smaller than the second) or the third (if the first is larger than the second) argument are called. If both choices are equal, then the second argument is called, which has access to the elements contained in the sums.
Since: sop-core-0.3.2.0
Arguments
| :: forall k c proxy r f g (xs :: [k]). All c xs | |
| => proxy c | |
| -> r |
what to do if first is smaller |
| -> ( forall (x :: k). c x => f x -> g x -> r) |
what to do if both are equal |
| -> r |
what to do if first is larger |
| -> NS f xs | |
| -> NS g xs | |
| -> r |
Constrained version of
compare_NS
.
Since: sop-core-0.3.2.0
Arguments
| :: forall k r (f :: k -> Type ) (g :: k -> Type ) (xss :: [[k]]). r |
what to do if first is smaller |
| -> ( forall (xs :: [k]). NP f xs -> NP g xs -> r) |
what to do if both are equal |
| -> r |
what to do if first is larger |
| -> SOP f xss | |
| -> SOP g xss | |
| -> r |
Compare two sums of products with respect to the choice in the sum they are making.
Only the sum structure is used for comparison.
This is a small wrapper around
ccompare_NS
for
a common special case.
Since: sop-core-0.3.2.0
Arguments
| :: forall k (c :: k -> Constraint ) proxy r (f :: k -> Type ) (g :: k -> Type ) (xss :: [[k]]). All2 c xss | |
| => proxy c | |
| -> r |
what to do if first is smaller |
| -> ( forall (xs :: [k]). All c xs => NP f xs -> NP g xs -> r) |
what to do if both are equal |
| -> r |
what to do if first is larger |
| -> SOP f xss | |
| -> SOP g xss | |
| -> r |
Constrained version of
compare_SOP
.
Since: sop-core-0.3.2.0
Collapsing
type family CollapseTo (h :: (k -> Type ) -> l -> Type ) x Source #
Maps products to lists, and sums to identities.
Instances
| type CollapseTo ( NS :: (k -> Type ) -> [k] -> Type ) a | |
|
Defined in Data.SOP.NS |
|
| type CollapseTo ( SOP :: (k -> Type ) -> [[k]] -> Type ) a | |
|
Defined in Data.SOP.NS |
|
| type CollapseTo ( NP :: (k -> Type ) -> [k] -> Type ) a | |
|
Defined in Data.SOP.NP |
|
| type CollapseTo ( POP :: (k -> Type ) -> [[k]] -> Type ) a | |
|
Defined in Data.SOP.NP |
|
class HCollapse (h :: (k -> Type ) -> l -> Type ) where Source #
A class for collapsing a heterogeneous structure into a homogeneous one.
Methods
hcollapse :: forall (xs :: l) a. SListIN h xs => h ( K a :: k -> Type ) xs -> CollapseTo h a Source #
Collapse a heterogeneous structure with homogeneous elements into a homogeneous structure.
If a heterogeneous structure is instantiated to the constant
functor
K
, then it is in fact homogeneous. This function
maps such a value to a simpler Haskell datatype reflecting that.
An
contains a single
NS
(
K
a)
a
, and an
contains
a list of
NP
(
K
a)
a
s.
Instances:
hcollapse,collapse_NP::NP(Ka) xs -> [a]hcollapse,collapse_NS::NS(Ka) xs -> ahcollapse,collapse_POP::POP(Ka) xss -> [[a]]hcollapse,collapse_SOP::SOP(Ka) xss -> [a]
Instances
| HCollapse ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NS |
|
| HCollapse ( NS :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NS |
|
| HCollapse ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NP |
|
| HCollapse ( NP :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NP |
|
Folding and sequencing
class HTraverse_ (h :: (k -> Type ) -> l -> Type ) where Source #
Methods
hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN h c xs, Applicative g) => proxy c -> ( forall (a :: k). c a => f a -> g ()) -> h f xs -> g () Source #
Corresponds to
traverse_
.
Instances:
hctraverse_,ctraverse__NP:: (Allc xs ,Applicativeg) => proxy c -> (forall a. c a => f a -> g ()) ->NPf xs -> g ()hctraverse_,ctraverse__NS:: (All2c xs ,Applicativeg) => proxy c -> (forall a. c a => f a -> g ()) ->NSf xs -> g ()hctraverse_,ctraverse__POP:: (Allc xss,Applicativeg) => proxy c -> (forall a. c a => f a -> g ()) ->POPf xss -> g ()hctraverse_,ctraverse__SOP:: (All2c xss,Applicativeg) => proxy c -> (forall a. c a => f a -> g ()) ->SOPf xss -> g ()
Since: sop-core-0.3.2.0
htraverse_ :: forall (xs :: l) g f. ( SListIN h xs, Applicative g) => ( forall (a :: k). f a -> g ()) -> h f xs -> g () Source #
Unconstrained version of
hctraverse_
.
Instances:
traverse_,traverse__NP:: (SListIxs ,Applicativeg) => (forall a. f a -> g ()) ->NPf xs -> g ()traverse_,traverse__NS:: (SListIxs ,Applicativeg) => (forall a. f a -> g ()) ->NSf xs -> g ()traverse_,traverse__POP:: (SListI2xss,Applicativeg) => (forall a. f a -> g ()) ->POPf xss -> g ()traverse_,traverse__SOP:: (SListI2xss,Applicativeg) => (forall a. f a -> g ()) ->SOPf xss -> g ()
Since: sop-core-0.3.2.0
Instances
| HTraverse_ ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN SOP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g ()) -> SOP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN SOP xs, Applicative g) => ( forall (a :: k0). f a -> g ()) -> SOP f xs -> g () Source # |
|
| HTraverse_ ( NS :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NS Methods hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN NS c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g ()) -> NS f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN NS xs, Applicative g) => ( forall (a :: k0). f a -> g ()) -> NS f xs -> g () Source # |
|
| HTraverse_ ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN POP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g ()) -> POP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN POP xs, Applicative g) => ( forall (a :: k0). f a -> g ()) -> POP f xs -> g () Source # |
|
| HTraverse_ ( NP :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NP Methods hctraverse_ :: forall c (xs :: l) g proxy f. ( AllN NP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g ()) -> NP f xs -> g () Source # htraverse_ :: forall (xs :: l) g f. ( SListIN NP xs, Applicative g) => ( forall (a :: k0). f a -> g ()) -> NP f xs -> g () Source # |
|
hcfoldMap :: forall k l h c (xs :: l) m proxy f. ( HTraverse_ h, AllN h c xs, Monoid m) => proxy c -> ( forall (a :: k). c a => f a -> m) -> h f xs -> m Source #
Special case of
hctraverse_
.
Since: sop-core-0.3.2.0
hcfor_ :: forall k l h c (xs :: l) g proxy f. ( HTraverse_ h, AllN h c xs, Applicative g) => proxy c -> h f xs -> ( forall (a :: k). c a => f a -> g ()) -> g () Source #
Flipped version of
hctraverse_
.
Since: sop-core-0.3.2.0
class HAp h => HSequence (h :: (k -> Type ) -> l -> Type ) where Source #
A generalization of
sequenceA
.
Methods
hsequence' :: forall (xs :: l) f (g :: k -> Type ). ( SListIN h xs, Applicative f) => h (f :.: g) xs -> f (h g xs) Source #
Corresponds to
sequenceA
.
Lifts an applicative functor out of a structure.
Instances:
hsequence',sequence'_NP:: (SListIxs ,Applicativef) =>NP(f:.:g) xs -> f (NPg xs )hsequence',sequence'_NS:: (SListIxs ,Applicativef) =>NS(f:.:g) xs -> f (NSg xs )hsequence',sequence'_POP:: (SListI2xss,Applicativef) =>POP(f:.:g) xss -> f (POPg xss)hsequence',sequence'_SOP:: (SListI2xss,Applicativef) =>SOP(f:.:g) xss -> f (SOPg xss)
hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN h c xs, Applicative g) => proxy c -> ( forall (a :: k). c a => f a -> g (f' a)) -> h f xs -> g (h f' xs) Source #
Corresponds to
traverse
.
Instances:
hctraverse',ctraverse'_NP:: (Allc xs ,Applicativeg) => proxy c -> (forall a. c a => f a -> g (f' a)) ->NPf xs -> g (NPf' xs )hctraverse',ctraverse'_NS:: (All2c xs ,Applicativeg) => proxy c -> (forall a. c a => f a -> g (f' a)) ->NSf xs -> g (NSf' xs )hctraverse',ctraverse'_POP:: (Allc xss,Applicativeg) => proxy c -> (forall a. c a => f a -> g (f' a)) ->POPf xss -> g (POPf' xss)hctraverse',ctraverse'_SOP:: (All2c xss,Applicativeg) => proxy c -> (forall a. c a => f a -> g (f' a)) ->SOPf xss -> g (SOPf' xss)
Since: sop-core-0.3.2.0
htraverse' :: forall (xs :: l) g f f'. ( SListIN h xs, Applicative g) => ( forall (a :: k). f a -> g (f' a)) -> h f xs -> g (h f' xs) Source #
Unconstrained variant of
hctraverse
`.
Instances:
htraverse',traverse'_NP:: (SListIxs ,Applicativeg) => (forall a. c a => f a -> g (f' a)) ->NPf xs -> g (NPf' xs )htraverse',traverse'_NS:: (SListI2xs ,Applicativeg) => (forall a. c a => f a -> g (f' a)) ->NSf xs -> g (NSf' xs )htraverse',traverse'_POP:: (SListIxss,Applicativeg) => (forall a. c a => f a -> g (f' a)) ->POPf xss -> g (POPf' xss)htraverse',traverse'_SOP:: (SListI2xss,Applicativeg) => (forall a. c a => f a -> g (f' a)) ->SOPf xss -> g (SOPf' xss)
Since: sop-core-0.3.2.0
Instances
| HSequence ( SOP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NS Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type ). ( SListIN SOP xs, Applicative f) => SOP (f :.: g) xs -> f ( SOP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN SOP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g (f' a)) -> SOP f xs -> g ( SOP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN SOP xs, Applicative g) => ( forall (a :: k0). f a -> g (f' a)) -> SOP f xs -> g ( SOP f' xs) Source # |
|
| HSequence ( NS :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NS Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type ). ( SListIN NS xs, Applicative f) => NS (f :.: g) xs -> f ( NS g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN NS c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g (f' a)) -> NS f xs -> g ( NS f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN NS xs, Applicative g) => ( forall (a :: k0). f a -> g (f' a)) -> NS f xs -> g ( NS f' xs) Source # |
|
| HSequence ( POP :: (k -> Type ) -> [[k]] -> Type ) | |
|
Defined in Data.SOP.NP Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type ). ( SListIN POP xs, Applicative f) => POP (f :.: g) xs -> f ( POP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN POP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g (f' a)) -> POP f xs -> g ( POP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN POP xs, Applicative g) => ( forall (a :: k0). f a -> g (f' a)) -> POP f xs -> g ( POP f' xs) Source # |
|
| HSequence ( NP :: (k -> Type ) -> [k] -> Type ) | |
|
Defined in Data.SOP.NP Methods hsequence' :: forall (xs :: l) f (g :: k0 -> Type ). ( SListIN NP xs, Applicative f) => NP (f :.: g) xs -> f ( NP g xs) Source # hctraverse' :: forall c (xs :: l) g proxy f f'. ( AllN NP c xs, Applicative g) => proxy c -> ( forall (a :: k0). c a => f a -> g (f' a)) -> NP f xs -> g ( NP f' xs) Source # htraverse' :: forall (xs :: l) g f f'. ( SListIN NP xs, Applicative g) => ( forall (a :: k0). f a -> g (f' a)) -> NP f xs -> g ( NP f' xs) Source # |
|
hsequence :: forall l h (xs :: l) f. ( SListIN h xs, SListIN ( Prod h) xs, HSequence h, Applicative f) => h f xs -> f (h I xs) Source #
Special case of
hsequence'
where
g =
.
I
hsequenceK :: forall k l h (xs :: l) f a. ( SListIN h xs, SListIN ( Prod h) xs, Applicative f, HSequence h) => h ( K (f a) :: k -> Type ) xs -> f (h ( K a :: k -> Type ) xs) Source #
Special case of
hsequence'
where
g =
.
K
a
hctraverse :: forall l h c (xs :: l) g proxy f. ( HSequence h, AllN h c xs, Applicative g) => proxy c -> ( forall a. c a => f a -> g a) -> h f xs -> g (h I xs) Source #
Special case of
hctraverse'
where
f' =
.
I
Since: sop-core-0.3.2.0
hcfor :: forall l h c (xs :: l) g proxy f. ( HSequence h, AllN h c xs, Applicative g) => proxy c -> h f xs -> ( forall a. c a => f a -> g a) -> g (h I xs) Source #
Flipped version of
hctraverse
.
Since: sop-core-0.3.2.0
Expanding sums to products
class HExpand (h :: (k -> Type ) -> l -> Type ) where Source #
A class for expanding sum structures into corresponding product structures, filling in the slots not targeted by the sum with default values.
Since: sop-core-0.2.5.0
Methods
hexpand :: forall (xs :: l) f. SListIN ( Prod h) xs => ( forall (x :: k). f x) -> h f xs -> Prod h f xs Source #
Expand a given sum structure into a corresponding product structure by placing the value contained in the sum into the corresponding position in the product, and using the given default value for all other positions.
Instances:
hexpand,expand_NS::SListIxs => (forall x . f x) ->NSf xs ->NPf xshexpand,expand_SOP::SListI2xss => (forall x . f x) ->SOPf xss ->POPf xss
Examples:
>>>hexpand Nothing (S (Z (Just 3))) :: NP Maybe '[Char, Int, Bool]Nothing :* Just 3 :* Nothing :* Nil>>>hexpand [] (SOP (S (Z ([1,2] :* "xyz" :* Nil)))) :: POP [] '[ '[Bool], '[Int, Char] ]POP (([] :* Nil) :* ([1,2] :* "xyz" :* Nil) :* Nil)
Since: sop-core-0.2.5.0
hcexpand :: forall c (xs :: l) proxy f. AllN ( Prod h) c xs => proxy c -> ( forall (x :: k). c x => f x) -> h f xs -> Prod h f xs Source #
Variant of
hexpand
that allows passing a constrained default.
Instances:
hcexpand,cexpand_NS::Allc xs => proxy c -> (forall x . c x => f x) ->NSf xs ->NPf xshcexpand,cexpand_SOP::All2c xss => proxy c -> (forall x . c x => f x) ->SOPf xss ->POPf xss
Examples:
>>>hcexpand (Proxy :: Proxy Bounded) (I minBound) (S (Z (I 20))) :: NP I '[Bool, Int, Ordering]I False :* I 20 :* I LT :* Nil>>>hcexpand (Proxy :: Proxy Num) (I 0) (SOP (S (Z (I 1 :* I 2 :* Nil)))) :: POP I '[ '[Double], '[Int, Int] ]POP ((I 0.0 :* Nil) :* (I 1 :* I 2 :* Nil) :* Nil)
Since: sop-core-0.2.5.0
Transformation of index lists and coercions
class (( Same h1 :: (k2 -> Type ) -> l2 -> Type ) ~ h2, ( Same h2 :: (k1 -> Type ) -> l1 -> Type ) ~ h1) => HTrans (h1 :: (k1 -> Type ) -> l1 -> Type ) (h2 :: (k2 -> Type ) -> l2 -> Type ) where Source #
A class for transforming structures into related structures with a different index list, as long as the index lists have the same shape and the elements and interpretation functions are suitably related.
Since: sop-core-0.3.1.0
Methods
htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod h1) c xs ys => proxy c -> ( forall (x :: k1) (y :: k2). c x y => f x -> g y) -> h1 f xs -> h2 g ys Source #
Transform a structure into a related structure given a conversion function for the elements.
Since: sop-core-0.3.1.0
hcoerce :: forall (f :: k1 -> Type ) (g :: k2 -> Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod h1) ( LiftedCoercible f g) xs ys => h1 f xs -> h2 g ys Source #
Safely coerce a structure into a representationally equal structure.
This is a special case of
htrans
, but can be implemented more efficiently;
for example in terms of
unsafeCoerce
.
Examples:
>>>hcoerce (I (Just LT) :* I (Just 'x') :* I (Just True) :* Nil) :: NP Maybe '[Ordering, Char, Bool]Just LT :* Just 'x' :* Just True :* Nil>>>hcoerce (SOP (Z (K True :* K False :* Nil))) :: SOP I '[ '[Bool, Bool], '[Bool] ]SOP (Z (I True :* I False :* Nil))
Since: sop-core-0.3.1.0
Instances
| HTrans ( SOP :: (k1 -> Type ) -> [[k1]] -> Type ) ( SOP :: (k2 -> Type ) -> [[k2]] -> Type ) | |
|
Defined in Data.SOP.NS Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod SOP ) c xs ys => proxy c -> ( forall (x :: k10) (y :: k20). c x y => f x -> g y) -> SOP f xs -> SOP g ys Source # hcoerce :: forall (f :: k10 -> Type ) (g :: k20 -> Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod SOP ) ( LiftedCoercible f g) xs ys => SOP f xs -> SOP g ys Source # |
|
| HTrans ( NS :: (k1 -> Type ) -> [k1] -> Type ) ( NS :: (k2 -> Type ) -> [k2] -> Type ) | |
|
Defined in Data.SOP.NS Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod NS ) c xs ys => proxy c -> ( forall (x :: k10) (y :: k20). c x y => f x -> g y) -> NS f xs -> NS g ys Source # hcoerce :: forall (f :: k10 -> Type ) (g :: k20 -> Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod NS ) ( LiftedCoercible f g) xs ys => NS f xs -> NS g ys Source # |
|
| HTrans ( POP :: (k1 -> Type ) -> [[k1]] -> Type ) ( POP :: (k2 -> Type ) -> [[k2]] -> Type ) | |
|
Defined in Data.SOP.NP Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod POP ) c xs ys => proxy c -> ( forall (x :: k10) (y :: k20). c x y => f x -> g y) -> POP f xs -> POP g ys Source # hcoerce :: forall (f :: k10 -> Type ) (g :: k20 -> Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod POP ) ( LiftedCoercible f g) xs ys => POP f xs -> POP g ys Source # |
|
| HTrans ( NP :: (k1 -> Type ) -> [k1] -> Type ) ( NP :: (k2 -> Type ) -> [k2] -> Type ) | |
|
Defined in Data.SOP.NP Methods htrans :: forall c (xs :: l1) (ys :: l2) proxy f g. AllZipN ( Prod NP ) c xs ys => proxy c -> ( forall (x :: k10) (y :: k20). c x y => f x -> g y) -> NP f xs -> NP g ys Source # hcoerce :: forall (f :: k10 -> Type ) (g :: k20 -> Type ) (xs :: l1) (ys :: l2). AllZipN ( Prod NP ) ( LiftedCoercible f g) xs ys => NP f xs -> NP g ys Source # |
|
hfromI :: forall l1 k2 l2 h1 (f :: k2 -> Type ) (xs :: l1) (ys :: l2) h2. ( AllZipN ( Prod h1) ( LiftedCoercible I f) xs ys, HTrans h1 h2) => h1 I xs -> h2 f ys Source #
Specialization of
hcoerce
.
Since: sop-core-0.3.1.0
htoI :: forall k1 l1 l2 h1 (f :: k1 -> Type ) (xs :: l1) (ys :: l2) h2. ( AllZipN ( Prod h1) ( LiftedCoercible f I ) xs ys, HTrans h1 h2) => h1 f xs -> h2 I ys Source #
Specialization of
hcoerce
.
Since: sop-core-0.3.1.0
Partial operations
fromList :: forall k (xs :: [k]) a. SListI xs => [a] -> Maybe ( NP ( K a :: k -> Type ) xs) Source #
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.
Utilities
Basic functors
The constant type functor.
Like
Constant
, but kind-polymorphic
in its second argument and with a shorter name.
Constructors
| K a |
Instances
| Eq2 ( K :: Type -> Type -> Type ) |
Since: sop-core-0.2.4.0 |
| Ord2 ( K :: Type -> Type -> Type ) |
Since: sop-core-0.2.4.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| Read2 ( K :: Type -> Type -> Type ) |
Since: sop-core-0.2.4.0 |
|
Defined in Data.SOP.BasicFunctors Methods liftReadsPrec2 :: ( Int -> ReadS a) -> ReadS [a] -> ( Int -> ReadS b) -> ReadS [b] -> Int -> ReadS ( K a b) Source # liftReadList2 :: ( Int -> ReadS a) -> ReadS [a] -> ( Int -> ReadS b) -> ReadS [b] -> ReadS [ K a b] Source # liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec ( K a b) Source # liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [ K a b] Source # |
|
| Show2 ( K :: Type -> Type -> Type ) |
Since: sop-core-0.2.4.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| NFData2 ( K :: Type -> Type -> Type ) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| Functor ( K a :: Type -> Type ) | |
| Monoid a => Applicative ( K a :: Type -> Type ) | |
| Foldable ( K a :: Type -> Type ) | |
|
Defined in Data.SOP.BasicFunctors Methods fold :: Monoid m => K a m -> m Source # foldMap :: Monoid m => (a0 -> m) -> K a a0 -> m Source # foldMap' :: Monoid m => (a0 -> m) -> K a a0 -> m Source # foldr :: (a0 -> b -> b) -> b -> K a a0 -> b Source # foldr' :: (a0 -> b -> b) -> b -> K a a0 -> b Source # foldl :: (b -> a0 -> b) -> b -> K a a0 -> b Source # foldl' :: (b -> a0 -> b) -> b -> K a a0 -> b Source # foldr1 :: (a0 -> a0 -> a0) -> K a a0 -> a0 Source # foldl1 :: (a0 -> a0 -> a0) -> K a a0 -> a0 Source # toList :: K a a0 -> [a0] Source # null :: K a a0 -> Bool Source # length :: K a a0 -> Int Source # elem :: Eq a0 => a0 -> K a a0 -> Bool Source # maximum :: Ord a0 => K a a0 -> a0 Source # minimum :: Ord a0 => K a a0 -> a0 Source # |
|
| Traversable ( K a :: Type -> Type ) | |
|
Defined in Data.SOP.BasicFunctors |
|
| Eq a => Eq1 ( K a :: Type -> Type ) |
Since: sop-core-0.2.4.0 |
| Ord a => Ord1 ( K a :: Type -> Type ) |
Since: sop-core-0.2.4.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| Read a => Read1 ( K a :: Type -> Type ) |
Since: sop-core-0.2.4.0 |
|
Defined in Data.SOP.BasicFunctors Methods liftReadsPrec :: ( Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS ( K a a0) Source # liftReadList :: ( Int -> ReadS a0) -> ReadS [a0] -> ReadS [ K a a0] Source # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec ( K a a0) Source # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [ K a a0] Source # |
|
| Show a => Show1 ( K a :: Type -> Type ) |
Since: sop-core-0.2.4.0 |
| NFData a => NFData1 ( K a :: Type -> Type ) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| Eq a => Eq ( K a b) | |
| Ord a => Ord ( K a b) | |
|
Defined in Data.SOP.BasicFunctors |
|
| Read a => Read ( K a b) | |
| Show a => Show ( K a b) | |
| Generic ( K a b) | |
| Semigroup a => Semigroup ( K a b) |
Since: sop-core-0.4.0.0 |
| Monoid a => Monoid ( K a b) |
Since: sop-core-0.4.0.0 |
| NFData a => NFData ( K a b) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| HasDatatypeInfo ( K a b) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type DatatypeInfoOf ( K a b) :: DatatypeInfo Source # Methods datatypeInfo :: proxy ( K a b) -> DatatypeInfo ( Code ( K a b)) Source # |
|
| Generic ( K a b) Source # | |
| type Rep ( K a b) | |
|
Defined in Data.SOP.BasicFunctors |
|
| type DatatypeInfoOf ( K a b) Source # | |
|
Defined in Generics.SOP.Instances |
|
| type Code ( K a b) Source # | |
|
Defined in Generics.SOP.Instances |
|
The identity type functor.
Like
Identity
, but with a shorter name.
Constructors
| I a |
Instances
| Monad I | |
| Functor I | |
| Applicative I | |
| Foldable I | |
|
Defined in Data.SOP.BasicFunctors Methods fold :: Monoid m => I m -> m Source # foldMap :: Monoid m => (a -> m) -> I a -> m Source # foldMap' :: Monoid m => (a -> m) -> I a -> m Source # foldr :: (a -> b -> b) -> b -> I a -> b Source # foldr' :: (a -> b -> b) -> b -> I a -> b Source # foldl :: (b -> a -> b) -> b -> I a -> b Source # foldl' :: (b -> a -> b) -> b -> I a -> b Source # foldr1 :: (a -> a -> a) -> I a -> a Source # foldl1 :: (a -> a -> a) -> I a -> a Source # elem :: Eq a => a -> I a -> Bool Source # maximum :: Ord a => I a -> a Source # minimum :: Ord a => I a -> a Source # |
|
| Traversable I | |
| Eq1 I |
Since: sop-core-0.2.4.0 |
| Ord1 I |
Since: sop-core-0.2.4.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| Read1 I |
Since: sop-core-0.2.4.0 |
|
Defined in Data.SOP.BasicFunctors Methods liftReadsPrec :: ( Int -> ReadS a) -> ReadS [a] -> Int -> ReadS ( I a) Source # liftReadList :: ( Int -> ReadS a) -> ReadS [a] -> ReadS [ I a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec ( I a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [ I a] Source # |
|
| Show1 I |
Since: sop-core-0.2.4.0 |
| NFData1 I |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| Eq a => Eq ( I a) | |
| Ord a => Ord ( I a) | |
| Read a => Read ( I a) | |
| Show a => Show ( I a) | |
| Generic ( I a) | |
| Semigroup a => Semigroup ( I a) |
Since: sop-core-0.4.0.0 |
| Monoid a => Monoid ( I a) |
Since: sop-core-0.4.0.0 |
| NFData a => NFData ( I a) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| HasDatatypeInfo ( I a) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type DatatypeInfoOf ( I a) :: DatatypeInfo Source # Methods datatypeInfo :: proxy ( I a) -> DatatypeInfo ( Code ( I a)) Source # |
|
| Generic ( I a) Source # | |
| type Rep ( I a) | |
|
Defined in Data.SOP.BasicFunctors |
|
| type DatatypeInfoOf ( I a) Source # | |
|
Defined in Generics.SOP.Instances |
|
| type Code ( I a) Source # | |
|
Defined in Generics.SOP.Instances |
|
newtype ((f :: l -> Type ) :.: (g :: k -> l)) (p :: k) infixr 7 Source #
Composition of functors.
Like
Compose
, but kind-polymorphic
and with a shorter name.
Constructors
| Comp (f (g p)) |
Instances
| ( Functor f, Functor g) => Functor (f :.: g) | |
| ( Applicative f, Applicative g) => Applicative (f :.: g) |
Since: sop-core-0.2.5.0 |
| ( Foldable f, Foldable g) => Foldable (f :.: g) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.BasicFunctors Methods fold :: Monoid m => (f :.: g) m -> m Source # foldMap :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldMap' :: Monoid m => (a -> m) -> (f :.: g) a -> m Source # foldr :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldr' :: (a -> b -> b) -> b -> (f :.: g) a -> b Source # foldl :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldl' :: (b -> a -> b) -> b -> (f :.: g) a -> b Source # foldr1 :: (a -> a -> a) -> (f :.: g) a -> a Source # foldl1 :: (a -> a -> a) -> (f :.: g) a -> a Source # toList :: (f :.: g) a -> [a] Source # null :: (f :.: g) a -> Bool Source # length :: (f :.: g) a -> Int Source # elem :: Eq a => a -> (f :.: g) a -> Bool Source # maximum :: Ord a => (f :.: g) a -> a Source # minimum :: Ord a => (f :.: g) a -> a Source # |
|
| ( Traversable f, Traversable g) => Traversable (f :.: g) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.BasicFunctors Methods traverse :: Applicative f0 => (a -> f0 b) -> (f :.: g) a -> f0 ((f :.: g) b) Source # sequenceA :: Applicative f0 => (f :.: g) (f0 a) -> f0 ((f :.: g) a) Source # mapM :: Monad m => (a -> m b) -> (f :.: g) a -> m ((f :.: g) b) Source # sequence :: Monad m => (f :.: g) (m a) -> m ((f :.: g) a) Source # |
|
| ( Eq1 f, Eq1 g) => Eq1 (f :.: g) |
Since: sop-core-0.2.4.0 |
| ( Ord1 f, Ord1 g) => Ord1 (f :.: g) |
Since: sop-core-0.2.4.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| ( Read1 f, Read1 g) => Read1 (f :.: g) |
Since: sop-core-0.2.4.0 |
|
Defined in Data.SOP.BasicFunctors Methods liftReadsPrec :: ( Int -> ReadS a) -> ReadS [a] -> Int -> ReadS ((f :.: g) a) Source # liftReadList :: ( Int -> ReadS a) -> ReadS [a] -> ReadS [(f :.: g) a] Source # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec ((f :.: g) a) Source # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [(f :.: g) a] Source # |
|
| ( Show1 f, Show1 g) => Show1 (f :.: g) |
Since: sop-core-0.2.4.0 |
| ( NFData1 f, NFData1 g) => NFData1 (f :.: g) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| ( Eq1 f, Eq1 g, Eq a) => Eq ((f :.: g) a) | |
| ( Ord1 f, Ord1 g, Ord a) => Ord ((f :.: g) a) | |
|
Defined in Data.SOP.BasicFunctors Methods compare :: (f :.: g) a -> (f :.: g) a -> Ordering Source # (<) :: (f :.: g) a -> (f :.: g) a -> Bool Source # (<=) :: (f :.: g) a -> (f :.: g) a -> Bool Source # (>) :: (f :.: g) a -> (f :.: g) a -> Bool Source # (>=) :: (f :.: g) a -> (f :.: g) a -> Bool Source # |
|
| ( Read1 f, Read1 g, Read a) => Read ((f :.: g) a) | |
| ( Show1 f, Show1 g, Show a) => Show ((f :.: g) a) | |
| Generic ((f :.: g) p) | |
| Semigroup (f (g x)) => Semigroup ((f :.: g) x) |
Since: sop-core-0.4.0.0 |
| Monoid (f (g x)) => Monoid ((f :.: g) x) |
Since: sop-core-0.4.0.0 |
| NFData (f (g a)) => NFData ((f :.: g) a) |
Since: sop-core-0.2.5.0 |
|
Defined in Data.SOP.BasicFunctors |
|
| HasDatatypeInfo ((f :.: g) p) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type DatatypeInfoOf ((f :.: g) p) :: DatatypeInfo Source # Methods datatypeInfo :: proxy ((f :.: g) p) -> DatatypeInfo ( Code ((f :.: g) p)) Source # |
|
| Generic ((f :.: g) p) Source # | |
| type Rep ((f :.: g) p) | |
|
Defined in Data.SOP.BasicFunctors |
|
| type DatatypeInfoOf ((f :.: g) p) Source # | |
|
Defined in Generics.SOP.Instances |
|
| type Code ((f :.: g) p) Source # | |
|
Defined in Generics.SOP.Instances |
|
unComp :: forall l k f (g :: k -> l) (p :: k). (f :.: g) p -> f (g p) Source #
Extract the contents of a
Comp
value.
Mapping functions
mapIK :: forall k a b (c :: k). (a -> b) -> I a -> K b c Source #
Lift the given function.
Since: sop-core-0.2.5.0
mapKI :: forall k a b (c :: k). (a -> b) -> K a c -> I b Source #
Lift the given function.
Since: sop-core-0.2.5.0
mapKK :: forall k1 k2 a b (c :: k1) (d :: k2). (a -> b) -> K a c -> K b d Source #
Lift the given function.
Since: sop-core-0.2.5.0
mapIII :: (a -> b -> c) -> I a -> I b -> I c Source #
Lift the given function.
Since: sop-core-0.2.5.0
mapIIK :: forall k a b c (d :: k). (a -> b -> c) -> I a -> I b -> K c d Source #
Lift the given function.
Since: sop-core-0.2.5.0
mapIKI :: forall k a b c (d :: k). (a -> b -> c) -> I a -> K b d -> I c Source #
Lift the given function.
Since: sop-core-0.2.5.0
mapIKK :: forall k1 k2 a b c (d :: k1) (e :: k2). (a -> b -> c) -> I a -> K b d -> K c e Source #
Lift the given function.
Since: sop-core-0.2.5.0
mapKII :: forall k a b c (d :: k). (a -> b -> c) -> K a d -> I b -> I c Source #
Lift the given function.
Since: sop-core-0.2.5.0
mapKIK :: forall k1 k2 a b c (d :: k1) (e :: k2). (a -> b -> c) -> K a d -> I b -> K c e Source #
Lift the given function.
Since: sop-core-0.2.5.0
mapKKI :: forall k1 k2 a b c (d :: k1) (e :: k2). (a -> b -> c) -> K a d -> K b e -> I c Source #
Lift the given function.
Since: sop-core-0.2.5.0
mapKKK :: forall k1 k2 k3 a b c (d :: k1) (e :: k2) (f :: k3). (a -> b -> c) -> K a d -> K b e -> K c f Source #
Lift the given function.
Since: sop-core-0.2.5.0
Mapping constraints
class ( AllF c xs, SListI xs) => All (c :: k -> Constraint ) (xs :: [k]) Source #
Require a constraint for every element of a list.
If you have a datatype that is indexed over a type-level
list, then you can use
All
to indicate that all elements
of that type-level list must satisfy a given constraint.
Example: The constraint
All Eq '[ Int, Bool, Char ]
is equivalent to the constraint
(Eq Int, Eq Bool, Eq Char)
Example: A type signature such as
f :: All Eq xs => NP I xs -> ...
means that
f
can assume that all elements of the n-ary
product satisfy
Eq
.
Note on superclasses: ghc cannot deduce superclasses from
All
constraints.
You might expect the following to compile
class (Eq a) => MyClass a foo :: (All Eq xs) => NP f xs -> z foo = [..] bar :: (All MyClass xs) => NP f xs -> x bar = foo
but it will fail with an error saying that it was unable to
deduce the class constraint
(or similar) in the
definition of
AllF
Eq
xs
bar
.
In cases like this you can use
Dict
from
Data.SOP.Dict
to prove conversions between constraints.
See
this answer on SO for more details
.
Minimal complete definition
Instances
| All (c :: k -> Constraint ) ('[] :: [k]) | |
|
Defined in Data.SOP.Constraint Methods cpara_SList :: proxy c -> r '[] -> ( forall (y :: k0) (ys :: [k0]). (c y, All c ys) => r ys -> r (y ': ys)) -> r '[] Source # |
|
| (c x, All c xs) => All (c :: a -> Constraint ) (x ': xs :: [a]) | |
|
Defined in Data.SOP.Constraint Methods cpara_SList :: proxy c -> r '[] -> ( forall (y :: k) (ys :: [k]). (c y, All c ys) => r ys -> r (y ': ys)) -> r (x ': xs) Source # |
|
type All2 (c :: k -> Constraint ) = All ( All c) Source #
Require a constraint for every element of a list of lists.
If you have a datatype that is indexed over a type-level
list of lists, then you can use
All2
to indicate that all
elements of the inner lists must satisfy a given constraint.
Example: The constraint
All2 Eq '[ '[ Int ], '[ Bool, Char ] ]
is equivalent to the constraint
(Eq Int, Eq Bool, Eq Char)
Example: A type signature such as
f :: All2 Eq xss => SOP I xs -> ...
means that
f
can assume that all elements of the sum
of product satisfy
Eq
.
Since 0.4.0.0, this is merely a synonym for 'All (All c)'.
Since: sop-core-0.4.0.0
cpara_SList :: All c xs => proxy c -> r ('[] :: [k]) -> ( forall (y :: k) (ys :: [k]). (c y, All c ys) => r ys -> r (y ': ys)) -> r xs Source #
Constrained paramorphism for a type-level list.
The advantage of writing functions in terms of
cpara_SList
is that
they are then typically not recursive, and can be unfolded statically if
the type-level list is statically known.
Since: sop-core-0.4.0.0
ccase_SList :: forall k c (xs :: [k]) proxy r. All c xs => proxy c -> r ('[] :: [k]) -> ( forall (y :: k) (ys :: [k]). (c y, All c ys) => r (y ': ys)) -> r xs Source #
Constrained case distinction on a type-level list.
Since: sop-core-0.4.0.0
class ( SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a -> b -> Constraint ) (xs :: [a]) (ys :: [b]) Source #
Require a constraint pointwise for every pair of elements from two lists.
Example: The constraint
AllZip (~) '[ Int, Bool, Char ] '[ a, b, c ]
is equivalent to the constraint
(Int ~ a, Bool ~ b, Char ~ c)
Since: sop-core-0.3.1.0
Instances
| ( SListI xs, SListI ys, SameShapeAs xs ys, SameShapeAs ys xs, AllZipF c xs ys) => AllZip (c :: a -> b -> Constraint ) (xs :: [a]) (ys :: [b]) | |
|
Defined in Data.SOP.Constraint |
|
class ( AllZipF ( AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 (f :: a -> b -> Constraint ) (xss :: [[a]]) (yss :: [[b]]) Source #
Require a constraint pointwise for every pair of elements from two lists of lists.
Instances
| ( AllZipF ( AllZip f) xss yss, SListI xss, SListI yss, SameShapeAs xss yss, SameShapeAs yss xss) => AllZip2 (f :: a -> b -> Constraint ) (xss :: [[a]]) (yss :: [[b]]) | |
|
Defined in Data.SOP.Constraint |
|
type family AllN (h :: (k -> Type ) -> l -> Type ) (c :: k -> Constraint ) :: l -> Constraint Source #
A generalization of
All
and
All2
.
The family
AllN
expands to
All
or
All2
depending on whether
the argument is indexed by a list or a list of lists.
Instances
| type AllN ( NS :: (k -> Type ) -> [k] -> Type ) (c :: k -> Constraint ) | |
|
Defined in Data.SOP.NS |
|
| type AllN ( SOP :: (k -> Type ) -> [[k]] -> Type ) (c :: k -> Constraint ) | |
|
Defined in Data.SOP.NS |
|
| type AllN ( NP :: (k -> Type ) -> [k] -> Type ) (c :: k -> Constraint ) | |
|
Defined in Data.SOP.NP |
|
| type AllN ( POP :: (k -> Type ) -> [[k]] -> Type ) (c :: k -> Constraint ) | |
|
Defined in Data.SOP.NP |
|
type family AllZipN (h :: (k -> Type ) -> l -> Type ) (c :: k1 -> k2 -> Constraint ) :: l1 -> l2 -> Constraint Source #
A generalization of
AllZip
and
AllZip2
.
The family
AllZipN
expands to
AllZip
or
AllZip2
depending on
whther the argument is indexed by a list or a list of lists.
Instances
| type AllZipN ( NP :: (k -> Type ) -> [k] -> Type ) (c :: a -> b -> Constraint ) | |
|
Defined in Data.SOP.NP |
|
| type AllZipN ( POP :: (k -> Type ) -> [[k]] -> Type ) (c :: a -> b -> Constraint ) | |
|
Defined in Data.SOP.NP |
|
Other constraints
class f (g x) => Compose (f :: k -> Constraint ) (g :: k1 -> k) (x :: k1) infixr 9 Source #
Composition of constraints.
Note that the result of the composition must be a constraint,
and therefore, in
, the kind of
Compose
f g
f
is
k ->
.
The kind of
Constraint
g
, however, is
l -> k
and can thus be a normal
type constructor.
A typical use case is in connection with
All
on an
NP
or an
NS
. For example, in order to denote that all elements on an
satisfy
NP
f xs
Show
, we can say
.
All
(
Compose
Show
f) xs
Since: sop-core-0.2
Instances
| f (g x) => Compose (f :: k1 -> Constraint ) (g :: k2 -> k1) (x :: k2) | |
|
Defined in Data.SOP.Constraint |
|
class (f x, g x) => And (f :: k -> Constraint ) (g :: k -> Constraint ) (x :: k) infixl 7 Source #
Pairing of constraints.
Since: sop-core-0.2
Instances
| (f x, g x) => And (f :: k -> Constraint ) (g :: k -> Constraint ) (x :: k) | |
|
Defined in Data.SOP.Constraint |
|
A constraint that can always be satisfied.
Since: sop-core-0.2
Instances
| Top (x :: k) | |
|
Defined in Data.SOP.Constraint |
|
class Coercible (f x) (g y) => LiftedCoercible (f :: k -> k1) (g :: k2 -> k1) (x :: k) (y :: k2) Source #
The constraint
is equivalent
to
LiftedCoercible
f g x y
.
Coercible
(f x) (g y)
Since: sop-core-0.3.1.0
Instances
| Coercible (f x) (g y) => LiftedCoercible (f :: k1 -> k2) (g :: k3 -> k2) (x :: k1) (y :: k3) | |
|
Defined in Data.SOP.Constraint |
|
type family SameShapeAs (xs :: [a]) (ys :: [b]) where ... Source #
Type family that forces a type-level list to be of the same shape as the given type-level list.
Since 0.5.0.0, this only tests the top-level structure of
the list, and is intended to be used in conjunction with
a separate construct (such as the
AllZip
,
AllZipF
combination to tie the recursive knot). The reason is that
making
SameShapeAs
directly recursive leads to quadratic
compile times.
The main use of this constraint is to help type inference to learn something about otherwise unknown type-level lists.
Since: sop-core-0.5.0.0
Equations
| SameShapeAs ('[] :: [a]) (ys :: [b]) = ys ~ ('[] :: [b]) | |
| SameShapeAs (x ': xs :: [a1]) (ys :: [a2]) = ys ~ ( Head ys ': Tail ys) |
Singletons
data SList (a :: [k]) where Source #
Explicit singleton list.
A singleton list can be used to reveal the structure of
a type-level list argument that the function is quantified
over. For every type-level list
xs
, there is one non-bottom
value of type
.
SList
xs
Note that these singleton lists are polymorphic in the list elements; we do not require a singleton representation for them.
Since: sop-core-0.2
Constructors
| SNil :: forall k. SList ('[] :: [k]) | |
| SCons :: forall k (xs :: [k]) (x :: k). SListI xs => SList (x ': xs) |
Instances
| Eq ( SList xs) | |
| Ord ( SList xs) | |
|
Defined in Data.SOP.Sing |
|
| Show ( SList xs) | |
type SListI = All ( Top :: k -> Constraint ) Source #
Implicit singleton list.
A singleton list can be used to reveal the structure of a type-level list argument that the function is quantified over.
Since 0.4.0.0, this is now defined in terms of
All
.
A singleton list provides a witness for a type-level list
where the elements need not satisfy any additional
constraints.
Since: sop-core-0.4.0.0
type SListI2 = All ( SListI :: [k] -> Constraint ) Source #
Require a singleton for every inner list in a list of lists.
sList :: forall k (xs :: [k]). SListI xs => SList xs Source #
Get hold of an explicit singleton (that one can then pattern match on) for a type-level list
para_SList :: forall k (xs :: [k]) r. SListI xs => r ('[] :: [k]) -> ( forall (y :: k) (ys :: [k]). SListI ys => r ys -> r (y ': ys)) -> r xs Source #
Paramorphism for a type-level list.
Since: sop-core-0.4.0.0
case_SList :: forall k (xs :: [k]) r. SListI xs => r ('[] :: [k]) -> ( forall (y :: k) (ys :: [k]). SListI ys => r (y ': ys)) -> r xs Source #
Case distinction on a type-level list.
Since: sop-core-0.4.0.0
Shape of type-level lists
data Shape (a :: [k]) where Source #
Occasionally it is useful to have an explicit, term-level, representation of type-level lists (esp because of https://ghc.haskell.org/trac/ghc/ticket/9108 )
Constructors
| ShapeNil :: forall k. Shape ('[] :: [k]) | |
| ShapeCons :: forall k (xs :: [k]) (x :: k). SListI xs => Shape xs -> Shape (x ': xs) |
Instances
| Eq ( Shape xs) | |
| Ord ( Shape xs) | |
|
Defined in Data.SOP.Sing |
|
| Show ( Shape xs) | |
lengthSList :: forall k (xs :: [k]) proxy. SListI xs => proxy xs -> Int Source #
The length of a type-level list.
Since: sop-core-0.2
Re-exports
Proxy
is a type that holds no data, but has a phantom parameter of
arbitrary type (or even kind). Its use is to provide type information, even
though there is no value available of that type (or it may be too costly to
create one).
Historically,
is a safer alternative to the
Proxy
::
Proxy
a
idiom.
undefined
:: a
>>>Proxy :: Proxy (Void, Int -> Int)Proxy
Proxy can even hold types of higher kinds,
>>>Proxy :: Proxy EitherProxy
>>>Proxy :: Proxy FunctorProxy
>>>Proxy :: Proxy complicatedStructureProxy
Constructors
| Proxy |
Instances
| Generic1 ( Proxy :: k -> Type ) |
Since: base-4.6.0.0 |
| Monad ( Proxy :: Type -> Type ) |
Since: base-4.7.0.0 |
| Functor ( Proxy :: Type -> Type ) |
Since: base-4.7.0.0 |
| Applicative ( Proxy :: Type -> Type ) |
Since: base-4.7.0.0 |
| Foldable ( Proxy :: Type -> Type ) |
Since: base-4.7.0.0 |
|
Defined in Data.Foldable Methods fold :: Monoid m => Proxy m -> m Source # foldMap :: Monoid m => (a -> m) -> Proxy a -> m Source # foldMap' :: Monoid m => (a -> m) -> Proxy a -> m Source # foldr :: (a -> b -> b) -> b -> Proxy a -> b Source # foldr' :: (a -> b -> b) -> b -> Proxy a -> b Source # foldl :: (b -> a -> b) -> b -> Proxy a -> b Source # foldl' :: (b -> a -> b) -> b -> Proxy a -> b Source # foldr1 :: (a -> a -> a) -> Proxy a -> a Source # foldl1 :: (a -> a -> a) -> Proxy a -> a Source # toList :: Proxy a -> [a] Source # null :: Proxy a -> Bool Source # length :: Proxy a -> Int Source # elem :: Eq a => a -> Proxy a -> Bool Source # maximum :: Ord a => Proxy a -> a Source # minimum :: Ord a => Proxy a -> a Source # |
|
| Traversable ( Proxy :: Type -> Type ) |
Since: base-4.7.0.0 |
|
Defined in Data.Traversable |
|
| Alternative ( Proxy :: Type -> Type ) |
Since: base-4.9.0.0 |
| MonadPlus ( Proxy :: Type -> Type ) |
Since: base-4.9.0.0 |
| Bounded ( Proxy t) |
Since: base-4.7.0.0 |
| Enum ( Proxy s) |
Since: base-4.7.0.0 |
|
Defined in Data.Proxy Methods succ :: Proxy s -> Proxy s Source # pred :: Proxy s -> Proxy s Source # toEnum :: Int -> Proxy s Source # fromEnum :: Proxy s -> Int Source # enumFrom :: Proxy s -> [ Proxy s] Source # enumFromThen :: Proxy s -> Proxy s -> [ Proxy s] Source # enumFromTo :: Proxy s -> Proxy s -> [ Proxy s] Source # enumFromThenTo :: Proxy s -> Proxy s -> Proxy s -> [ Proxy s] Source # |
|
| Eq ( Proxy s) |
Since: base-4.7.0.0 |
| Data t => Data ( Proxy t) |
Since: base-4.7.0.0 |
|
Defined in Data.Data Methods gfoldl :: ( forall d b. Data d => c (d -> b) -> d -> c b) -> ( forall g. g -> c g) -> Proxy t -> c ( Proxy t) Source # gunfold :: ( forall b r. Data b => c (b -> r) -> c r) -> ( forall r. r -> c r) -> Constr -> c ( Proxy t) Source # toConstr :: Proxy t -> Constr Source # dataTypeOf :: Proxy t -> DataType Source # dataCast1 :: Typeable t0 => ( forall d. Data d => c (t0 d)) -> Maybe (c ( Proxy t)) Source # dataCast2 :: Typeable t0 => ( forall d e. ( Data d, Data e) => c (t0 d e)) -> Maybe (c ( Proxy t)) Source # gmapT :: ( forall b. Data b => b -> b) -> Proxy t -> Proxy t Source # gmapQl :: (r -> r' -> r) -> r -> ( forall d. Data d => d -> r') -> Proxy t -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> ( forall d. Data d => d -> r') -> Proxy t -> r Source # gmapQ :: ( forall d. Data d => d -> u) -> Proxy t -> [u] Source # gmapQi :: Int -> ( forall d. Data d => d -> u) -> Proxy t -> u Source # gmapM :: Monad m => ( forall d. Data d => d -> m d) -> Proxy t -> m ( Proxy t) Source # gmapMp :: MonadPlus m => ( forall d. Data d => d -> m d) -> Proxy t -> m ( Proxy t) Source # gmapMo :: MonadPlus m => ( forall d. Data d => d -> m d) -> Proxy t -> m ( Proxy t) Source # |
|
| Ord ( Proxy s) |
Since: base-4.7.0.0 |
|
Defined in Data.Proxy |
|
| Read ( Proxy t) |
Since: base-4.7.0.0 |
| Show ( Proxy s) |
Since: base-4.7.0.0 |
| Ix ( Proxy s) |
Since: base-4.7.0.0 |
|
Defined in Data.Proxy |
|
| Generic ( Proxy t) |
Since: base-4.6.0.0 |
| Semigroup ( Proxy s) |
Since: base-4.9.0.0 |
| Monoid ( Proxy s) |
Since: base-4.7.0.0 |
| HasDatatypeInfo ( Proxy t) Source # | |
|
Defined in Generics.SOP.Instances Associated Types type DatatypeInfoOf ( Proxy t) :: DatatypeInfo Source # Methods datatypeInfo :: proxy ( Proxy t) -> DatatypeInfo ( Code ( Proxy t)) Source # |
|
| Generic ( Proxy t) Source # | |
| type Rep1 ( Proxy :: k -> Type ) | |
| type Rep ( Proxy t) | |
| type DatatypeInfoOf ( Proxy t) Source # | |
|
Defined in Generics.SOP.Instances
type
DatatypeInfoOf
(
Proxy
t) = '
ADT
"Data.Proxy" "Proxy" '['
Constructor
"Proxy"] '['[] :: [
StrictnessInfo
]]
|
|
| type Code ( Proxy t) Source # | |
|
Defined in Generics.SOP.Instances |
|