Safe Haskell | None |
---|---|
Language | Haskell2010 |
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 name
. The class also provides functionsRep
Afrom
andto
that convert betweenA
and
and witness the isomorphism.Rep
A - Since all
Rep
types are sums of products, you can define functions over them by performing induction on the structure, of by using predefined combinators that the library provides. Such functions then work for allRep
types. - By combining the conversion functions
from
andto
with the function that works onRep
types, we obtain a function that works on all types that are in theGeneric
class. - 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 theGeneric
class from module GHC.Generics, then an instance of the SOPGeneric
can automatically be derived. There is also Template Haskell code in Generics.SOP.TH that allows to auto-generate an instance ofGeneric
for 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
AB
and
).
For example,Rep
B
>>>
from (D (C True) 3) :: Rep A
SOP (S (Z (I (C True) :* I 3 :* Nil)))>>>
to it :: A
D (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 :: (Generic
a,All2
NFData (Code
a)) => a -> () grnf x = grnfS (from
x) grnfS :: (All2
NFData xss) =>SOP
I
xss -> () grnfS (SOP
(Z
xs)) = grnfP xs grnfS (SOP
(S
xss)) = grnfS (SOP
xss) grnfP :: (All
NFData xs) =>NP
I
xs -> () grnfPNil
= () grnfP (I
x:*
xs) = x `deepseq` (grnfP xs)
The grnf
function performs the conversion between a
and
by applying Rep
afrom
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 :: (Generic
a,All2
NFData (Code
a)) => a -> () grnf =rnf
.hcollapse
.hcliftA
(Proxy
::Proxy
NFData) (\ (I
x) ->K
(rnf x)) .from
The following interaction should provide an idea of the individual transformation steps:
>>>
let x = G 2.5 'A' False :: B Double
>>>
from x
SOP (S (Z (I 2.5 :* I 'A' :* I False :* Nil)))>>>
hcliftA (Proxy :: Proxy NFData) (\ (I x) -> K (rnf x)) it
SOP (S (Z (K () :* K () :* K () :* Nil)))>>>
hcollapse it
[(),(),()]>>>
rnf it
()
The from
call converts into the structural representation.
Via hcliftA
, 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-sop
basic examples,pretty-sop
generic pretty printing,lens-sop
generically computed lenses,json-sop
generic 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.
- class All SListI (Code a) => Generic a where
- type Rep a = SOP I (Code a)
- data NP :: (k -> *) -> [k] -> * where
- data NS :: (k -> *) -> [k] -> * where
- newtype SOP f xss = SOP (NS (NP f) xss)
- unSOP :: SOP f xss -> NS (NP f) xss
- newtype POP f xss = POP (NP (NP f) xss)
- unPOP :: POP f xss -> NP (NP f) xss
- data DatatypeInfo :: [[*]] -> * where
- ADT :: ModuleName -> DatatypeName -> NP ConstructorInfo 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 :: [*] -> * 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 :: * -> * where
- fieldName :: FieldInfo a -> FieldName
- class HasDatatypeInfo a where
- type DatatypeInfoOf a :: DatatypeInfo
- type DatatypeName = String
- type ModuleName = String
- type ConstructorName = String
- type FieldName = String
- data Associativity :: *
- type Fixity = Int
- class HPure h where
- hd :: NP f (x ': xs) -> f x
- tl :: NP f (x ': xs) -> NP f xs
- type Projection f xs = K (NP f xs) -.-> f
- projections :: forall xs f. SListI xs => NP (Projection f xs) xs
- shiftProjection :: Projection f xs a -> Projection f (x ': xs) a
- newtype (f -.-> g) a = Fn {
- apFn :: f a -> g a
- fn :: (f a -> f' a) -> (f -.-> f') a
- fn_2 :: (f a -> f' a -> f'' a) -> (f -.-> (f' -.-> f'')) a
- fn_3 :: (f a -> f' a -> f'' a -> f''' a) -> (f -.-> (f' -.-> (f'' -.-> f'''))) a
- fn_4 :: (f a -> f' a -> f'' a -> f''' a -> f'''' a) -> (f -.-> (f' -.-> (f'' -.-> (f''' -.-> f'''')))) a
- type family Prod (h :: (k -> *) -> l -> *) :: (k -> *) -> l -> *
- class (Prod (Prod h) ~ Prod h, HPure (Prod h)) => HAp h where
- hliftA :: (SListIN (Prod h) xs, HAp h) => (forall a. f a -> f' a) -> h f xs -> h f' xs
- hliftA2 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hliftA3 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
- hcliftA :: (AllN (Prod h) c xs, HAp h) => proxy c -> (forall a. c a => f a -> f' a) -> h f xs -> h f' xs
- hcliftA2 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hcliftA3 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. 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 :: (SListIN (Prod h) xs, HAp h) => (forall a. f a -> f' a) -> h f xs -> h f' xs
- hzipWith :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hzipWith3 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a -> f''' a) -> Prod h f xs -> Prod h f' xs -> h f'' xs -> h f''' xs
- hcmap :: (AllN (Prod h) c xs, HAp h) => proxy c -> (forall a. c a => f a -> f' a) -> h f xs -> h f' xs
- hczipWith :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs
- hczipWith3 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. 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 xs = f -.-> K (NS f xs)
- injections :: forall xs f. SListI xs => NP (Injection f xs) xs
- shift :: Injection f xs a -> Injection f (x ': xs) a
- shiftInjection :: Injection f xs a -> Injection f (x ': xs) a
- type family UnProd (h :: (k -> *) -> l -> *) :: (k -> *) -> l -> *
- class UnProd (Prod h) ~ h => HApInjs h where
- apInjs_NP :: SListI xs => NP f xs -> [NS f xs]
- apInjs_POP :: SListI xss => POP f xss -> [SOP f xss]
- unZ :: NS f '[x] -> f x
- class HIndex h where
- hcliftA' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs) -> h f xss -> h f' xss
- hcliftA2' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs -> f'' xs) -> Prod h f xss -> h f' xss -> h f'' xss
- hcliftA3' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs -> f'' xs -> f''' xs) -> Prod h f xss -> Prod h f' xss -> h f'' xss -> h f''' xss
- type family CollapseTo (h :: (k -> *) -> l -> *) (x :: *) :: *
- class HCollapse h where
- class HAp h => HSequence h where
- hsequence :: (SListIN h xs, SListIN (Prod h) xs, HSequence h) => Applicative f => h f xs -> f (h I xs)
- hsequenceK :: (SListIN h xs, SListIN (Prod h) xs, Applicative f, HSequence h) => h (K (f a)) xs -> f (h (K a) xs)
- class HExpand h where
- fromList :: SListI xs => [a] -> Maybe (NP (K a) xs)
- newtype K a b = K a
- unK :: K a b -> a
- newtype I a = I a
- unI :: I a -> a
- newtype (f :.: g) p = Comp (f (g p))
- unComp :: (f :.: g) p -> f (g p)
- mapII :: (a -> b) -> I a -> I b
- mapIK :: (a -> b) -> I a -> K b c
- mapKI :: (a -> b) -> K a c -> I b
- mapKK :: (a -> b) -> K a c -> K b d
- mapIII :: (a -> b -> c) -> I a -> I b -> I c
- mapIIK :: (a -> b -> c) -> I a -> I b -> K c d
- mapIKI :: (a -> b -> c) -> I a -> K b d -> I c
- mapIKK :: (a -> b -> c) -> I a -> K b d -> K c e
- mapKII :: (a -> b -> c) -> K a d -> I b -> I c
- mapKIK :: (a -> b -> c) -> K a d -> I b -> K c e
- mapKKI :: (a -> b -> c) -> K a d -> K b e -> I c
- mapKKK :: (a -> b -> c) -> K a d -> K b e -> K c f
- class (AllF f xs, SListI xs) => All f xs
- class (AllF (All f) xss, SListI xss) => All2 f xss
- class f (g x) => Compose f g x
- class (f x, g x) => And f g x
- class Top x
- type family AllN (h :: (k -> *) -> l -> *) (c :: k -> Constraint) :: l -> Constraint
- data SList :: [k] -> * where
- class SListI xs where
- type SListI2 = All SListI
- type Sing = SList
- class SListI xs => SingI xs where
- data Shape :: [k] -> * where
- shape :: forall xs. SListI xs => Shape xs
- lengthSList :: forall xs proxy. SListI xs => proxy xs -> Int
- lengthSing :: SListI xs => proxy xs -> Int
- data Proxy k t :: forall k. k -> * = Proxy
Codes and interpretations
class All SListI (Code a) => Generic a 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 are 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
::Rep
a ->Rep
a
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
, ...) instanceGeneric
T -- empty instanceHasDatatypeInfo
T -- 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 -- derivesHasDatatypeInfo
as 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.
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 ] ]
Converts from a value to its structural representation.
from :: (GFrom a, Generic a, Rep a ~ SOP I (GCode a)) => a -> Rep a Source #
Converts from a value to its structural representation.
Converts from a structural representation back to the original value.
to :: (GTo a, Generic a, Rep a ~ SOP I (GCode a)) => Rep a -> a Source #
Converts from a structural representation back to the original value.
n-ary datatypes
data NP :: (k -> *) -> [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 ]
HSequence [k] k (NP k) Source # | |
HCollapse [k] k (NP k) Source # | |
HAp [k] k (NP k) Source # | |
HPure [k] k (NP k) Source # | |
All k (Compose k * Eq f) xs => Eq (NP k f xs) Source # | |
(All k (Compose k * Eq f) xs, All k (Compose k * Ord f) xs) => Ord (NP k f xs) Source # | |
All k (Compose k * Show f) xs => Show (NP k f xs) Source # | |
All k (Compose k * NFData f) xs => NFData (NP k f xs) Source # | Since: 0.2.5.0 |
type SListIN [k] k (NP k) Source # | |
type UnProd [k] k (NP k) Source # | |
type Prod [k] k (NP k) Source # | |
type AllN [k] k (NP k) c Source # | |
type CollapseTo [k] k (NP k) a Source # | |
data NS :: (k -> *) -> [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 ]
HExpand [k] k (NS k) Source # | |
HApInjs [k] k (NS k) Source # | |
HIndex [k] k (NS k) Source # | |
HSequence [k] k (NS k) Source # | |
HCollapse [k] k (NS k) Source # | |
HAp [k] k (NS k) Source # | |
All k (Compose k * Eq f) xs => Eq (NS k f xs) Source # | |
(All k (Compose k * Eq f) xs, All k (Compose k * Ord f) xs) => Ord (NS k f xs) Source # | |
All k (Compose k * Show f) xs => Show (NS k f xs) Source # | |
All k (Compose k * NFData f) xs => NFData (NS k f xs) Source # | Since: 0.2.5.0 |
type SListIN [k] k (NS k) Source # | |
type Prod [k] k (NS k) Source # | |
type CollapseTo [k] k (NS k) a 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.
An
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
HExpand [[k]] k (SOP k) Source # | |
HApInjs [[k]] k (SOP k) Source # | |
HIndex [[k]] k (SOP k) Source # | |
HSequence [[k]] k (SOP k) Source # | |
HCollapse [[k]] k (SOP k) Source # | |
HAp [[k]] k (SOP k) Source # | |
Eq (NS [k] (NP k f) xss) => Eq (SOP k f xss) Source # | |
Ord (NS [k] (NP k f) xss) => Ord (SOP k f xss) Source # | |
Show (NS [k] (NP k f) xss) => Show (SOP k f xss) Source # | |
NFData (NS [k] (NP k f) xss) => NFData (SOP k f xss) Source # | Since: 0.2.5.0 |
type SListIN [[k]] k (SOP k) Source # | |
type Prod [[k]] k (SOP k) Source # | |
type CollapseTo [[k]] k (SOP k) a 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.
HSequence [[k]] k (POP k) Source # | |
HCollapse [[k]] k (POP k) Source # | |
HAp [[k]] k (POP k) Source # | |
HPure [[k]] k (POP k) Source # | |
Eq (NP [k] (NP k f) xss) => Eq (POP k f xss) Source # | |
Ord (NP [k] (NP k f) xss) => Ord (POP k f xss) Source # | |
Show (NP [k] (NP k f) xss) => Show (POP k f xss) Source # | |
NFData (NP [k] (NP k f) xss) => NFData (POP k f xss) Source # | Since: 0.2.5.0 |
type SListIN [[k]] k (POP k) Source # | |
type UnProd [[k]] k (POP k) Source # | |
type Prod [[k]] k (POP k) Source # | |
type AllN [[k]] k (POP k) c Source # | |
type CollapseTo [[k]] k (POP k) a Source # | |
Metadata
data DatatypeInfo :: [[*]] -> * 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.
ADT :: ModuleName -> DatatypeName -> NP ConstructorInfo xss -> DatatypeInfo xss | |
Newtype :: ModuleName -> DatatypeName -> ConstructorInfo '[x] -> DatatypeInfo '['[x]] |
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 :: [*] -> * where Source #
Metadata for a single constructors.
This is indexed by the product structure of the constructor components.
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 Source #
The name of a constructor.
Since: 0.2.3.0
data FieldInfo :: * -> * where Source #
For records, this functor maps the component to its selector name.
class 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.
type DatatypeInfoOf a :: DatatypeInfo Source #
Type-level datatype info
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.
datatypeInfo :: (GDatatypeInfo a, GCode a ~ Code a) => proxy a -> DatatypeInfo (Code a) Source #
Term-level datatype info; by default, the term-level datatype info is produced from the type-level info.
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 :: * #
Datatype to represent the associativity of a constructor
Bounded Associativity | |
Enum Associativity | |
Eq Associativity | |
Data Associativity | |
Ord Associativity | |
Read Associativity | |
Show Associativity | |
Ix Associativity | |
Generic Associativity | |
SingI Associativity LeftAssociative | |
SingI Associativity RightAssociative | |
SingI Associativity NotAssociative | |
SingKind Associativity (KProxy Associativity) | |
type Rep Associativity | |
data Sing Associativity | |
type DemoteRep Associativity (KProxy Associativity) | |
Combinators
Constructing products
hpure :: SListIN h xs => (forall a. f a) -> h f xs Source #
Corresponds to pure
directly.
Instances:
hpure
,pure_NP
::SListI
xs => (forall a. f a) ->NP
f xshpure
,pure_POP
::SListI2
xss => (forall a. f a) ->POP
f xss
hcpure :: AllN h c xs => proxy c -> (forall a. c a => f a) -> h f xs Source #
A variant of hpure
that allows passing in a constrained
argument.
Calling
where hcpure
f ss :: 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.AllMap
h c xs
Morally, hpure
is a special case of hcpure
where the
constraint is empty. However, it is in the nature of how AllMap
is defined as well as current GHC limitations that it is tricky
to prove to GHC in general that
is
always satisfied. Therefore, we typically define AllMap
h c NoConstraint xshpure
separately and directly, and make it a member of the class.
Instances:
hcpure
,cpure_NP
:: (All
c xs ) => proxy c -> (forall a. c a => f a) ->NP
f xshcpure
,cpure_POP
:: (All2
c xss) => proxy c -> (forall a. c a => f a) ->POP
f xss
Destructing products
projections :: forall xs f. 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 :: Projection f xs a -> Projection f (x ': xs) a Source #
Application
fn :: (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 :: (f a -> f' a -> f'' a) -> (f -.-> (f' -.-> f'')) a Source #
Construct a binary lifted function.
fn_3 :: (f a -> f' a -> f'' a -> f''' a) -> (f -.-> (f' -.-> (f'' -.-> f'''))) a Source #
Construct a ternary lifted function.
fn_4 :: (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 -> *) -> l -> *) :: (k -> *) -> l -> * Source #
Maps a structure containing sums to the corresponding product structure.
class (Prod (Prod h) ~ Prod h, HPure (Prod h)) => HAp h where Source #
A generalization of <*>
.
hap :: 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 ->NP
f xs ->NP
g xshap
,ap_NS
::NP
(f -.-> g) xs ->NS
f xs ->NS
g xshap
,ap_POP
::POP
(f -.-> g) xss ->POP
f xss ->POP
g xsshap
,ap_SOP
::POP
(f -.-> g) xss ->SOP
f xss ->SOP
g xss
Lifting / mapping
hliftA :: (SListIN (Prod h) xs, HAp h) => (forall a. 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:
hliftA
f xs =hpure
(fn
f) `hap
` xs
Instances:
hliftA
,liftA_NP
::SListI
xs => (forall a. f a -> f' a) ->NP
f xs ->NP
f' xshliftA
,liftA_NS
::SListI
xs => (forall a. f a -> f' a) ->NS
f xs ->NS
f' xshliftA
,liftA_POP
::SListI2
xss => (forall a. f a -> f' a) ->POP
f xss ->POP
f' xsshliftA
,liftA_SOP
::SListI2
xss => (forall a. f a -> f' a) ->SOP
f xss ->SOP
f' xss
hliftA2 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. 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:
hliftA2
f xs ys =hpure
(fn_2
f) `hap
` xs `hap
` ys
Instances:
hliftA2
,liftA2_NP
::SListI
xs => (forall a. f a -> f' a -> f'' a) ->NP
f xs ->NP
f' xs ->NP
f'' xshliftA2
,liftA2_NS
::SListI
xs => (forall a. f a -> f' a -> f'' a) ->NP
f xs ->NS
f' xs ->NS
f'' xshliftA2
,liftA2_POP
::SListI2
xss => (forall a. f a -> f' a -> f'' a) ->POP
f xss ->POP
f' xss ->POP
f'' xsshliftA2
,liftA2_SOP
::SListI2
xss => (forall a. f a -> f' a -> f'' a) ->POP
f xss ->SOP
f' xss ->SOP
f'' xss
hliftA3 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. 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:
hliftA3
f xs ys zs =hpure
(fn_3
f) `hap
` xs `hap
` ys `hap
` zs
Instances:
hliftA3
,liftA3_NP
::SListI
xs => (forall a. f a -> f' a -> f'' a -> f''' a) ->NP
f xs ->NP
f' xs ->NP
f'' xs ->NP
f''' xshliftA3
,liftA3_NS
::SListI
xs => (forall a. f a -> f' a -> f'' a -> f''' a) ->NP
f xs ->NP
f' xs ->NS
f'' xs ->NS
f''' xshliftA3
,liftA3_POP
::SListI2
xss => (forall a. f a -> f' a -> f'' a -> f''' a) ->POP
f xss ->POP
f' xss ->POP
f'' xss ->POP
f''' xshliftA3
,liftA3_SOP
::SListI2
xss => (forall a. f a -> f' a -> f'' a -> f''' a) ->POP
f xss ->POP
f' xss ->SOP
f'' xss ->SOP
f''' xs
hcliftA :: (AllN (Prod h) c xs, HAp h) => proxy c -> (forall a. c a => f a -> f' a) -> h f xs -> h f' xs Source #
hcliftA2 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #
hcliftA3 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. 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 :: (SListIN (Prod h) xs, HAp h) => (forall a. f a -> f' a) -> h f xs -> h f' xs Source #
Another name for hliftA
.
Since: 0.2
hzipWith :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall a. f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #
Another name for hliftA2
.
Since: 0.2
hzipWith3 :: (SListIN (Prod h) xs, HAp h, HAp (Prod h)) => (forall 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 hliftA3
.
Since: 0.2
hcmap :: (AllN (Prod h) c xs, HAp h) => proxy c -> (forall a. c a => f a -> f' a) -> h f xs -> h f' xs Source #
Another name for hcliftA
.
Since: 0.2
hczipWith :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. c a => f a -> f' a -> f'' a) -> Prod h f xs -> h f' xs -> h f'' xs Source #
Another name for hcliftA2
.
Since: 0.2
hczipWith3 :: (AllN (Prod h) c xs, HAp h, HAp (Prod h)) => proxy c -> (forall a. 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: 0.2
Constructing sums
type Injection f xs = f -.-> K (NS f xs) 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 xs f. 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 :: Injection f xs a -> Injection f (x ': xs) a Source #
Deprecated: Use shiftInjection
instead.
Shift an injection.
Given an injection, return an injection into a sum that is one component larger.
shiftInjection :: Injection f xs a -> Injection f (x ': xs) a Source #
Shift an injection.
Given an injection, return an injection into a sum that is one component larger.
type family UnProd (h :: (k -> *) -> l -> *) :: (k -> *) -> l -> * Source #
Maps a structure containing products to the corresponding sum structure.
Since: 0.2.4.0
class UnProd (Prod h) ~ h => HApInjs h where Source #
A class for applying all injections corresponding to a sum-like structure to a table containing suitable arguments.
hapInjs :: 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
::SListI
xs =>NP
f xs -> [NS
f xs ]hapInjs
,apInjs_SOP
::SListI2
xss =>POP
f xs -> [SOP
f xss]
Examples:
>>>
hapInjs (I 'x' :* I True :* I 2 :* Nil)
[Z (I 'x'), S (Z (I True)), S (S (Z (I 2)))]
>>>
hapInjs (POP ((I 'x' :* Nil) :* (I True :* I 2 :* Nil) :* Nil)
[SOP (Z (I 'x' :* Nil)), SOP (S (Z (I True :* (I 2 :* Nil))))]
Since: 0.2.4.0
apInjs_NP :: 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 :: 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 :: 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: 0.2.2.0
A class for determining which choice in a sum-like structure a value represents.
hindex :: 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
x0
and n - 1
representing the index of the choice
made by x
.
Instances:
hindex
,index_NS
::NS
f xs -> Inthindex
,index_SOP
::SOP
f 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: 0.2.4.0
Dealing with All
c
All
chcliftA' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs) -> h f xss -> h f' xss 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_NP
p `hap
` xs
Instances:
hcliftA'
::All2
c xss => proxy c -> (forall xs.All
c xs => f xs -> f' xs) ->NP
f xss ->NP
f' xsshcliftA'
::All2
c xss => proxy c -> (forall xs.All
c xs => f xs -> f' xs) ->NS
f xss ->NS
f' xss
hcliftA2' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs -> f'' xs) -> Prod h f xss -> h f' xss -> h f'' xss Source #
hcliftA3' :: (All2 c xss, Prod h ~ NP, HAp h) => proxy c -> (forall xs. All c xs => f xs -> f' xs -> f'' xs -> f''' xs) -> Prod h f xss -> Prod h f' xss -> h f'' xss -> h f''' xss Source #
Deprecated: Use hcliftA3
or hczipWith3
instead.
Like hcliftA'
, but for ternay functions.
Collapsing
type family CollapseTo (h :: (k -> *) -> l -> *) (x :: *) :: * Source #
Maps products to lists, and sums to identities.
type CollapseTo [[k]] k (POP k) a Source # | |
type CollapseTo [[k]] k (SOP k) a Source # | |
type CollapseTo [k] k (NP k) a Source # | |
type CollapseTo [k] k (NS k) a Source # | |
class HCollapse h where Source #
A class for collapsing a heterogeneous structure into a homogeneous one.
hcollapse :: SListIN h xs => h (K a) 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
(K
a) xs -> [a]hcollapse
,collapse_NS
::NS
(K
a) xs -> ahcollapse
,collapse_POP
::POP
(K
a) xss -> [[a]]hcollapse
,collapse_SOP
::SOP
(K
a) xss -> [a]
Sequencing
class HAp h => HSequence h where Source #
A generalization of sequenceA
.
hsequence' :: (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
:: (SListI
xs ,Applicative
f) =>NP
(f:.:
g) xs -> f (NP
g xs )hsequence'
,sequence'_NS
:: (SListI
xs ,Applicative
f) =>NS
(f:.:
g) xs -> f (NS
g xs )hsequence'
,sequence'_POP
:: (SListI2
xss,Applicative
f) =>POP
(f:.:
g) xss -> f (POP
g xss)hsequence'
,sequence'_SOP
:: (SListI2
xss,Applicative
f) =>SOP
(f:.:
g) xss -> f (SOP
g xss)
hsequence :: (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 :: (SListIN h xs, SListIN (Prod h) xs, Applicative f, HSequence h) => h (K (f a)) xs -> f (h (K a) xs) Source #
Special case of hsequence'
where g =
.K
a
Expanding sums to products
class HExpand h 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: 0.2.5.0
hexpand :: SListIN (Prod h) xs => (forall x. 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
::SListI
xs => (forall x . f x) ->NS
f xs ->NP
f xshexpand
,expand_SOP
::SListI2
xss => (forall x . f x) ->SOP
f xss ->POP
f 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: 0.2.5.0
hcexpand :: AllN (Prod h) c xs => proxy c -> (forall x. 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
::All
c xs => proxy c -> (forall x . c x => f x) ->NS
f xs ->NP
f xshcexpand
,cexpand_SOP
::All2
c xss => proxy c -> (forall x . c x => f x) ->SOP
f xss ->POP
f 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: 0.2.5.0
Partial operations
fromList :: SListI xs => [a] -> Maybe (NP (K a) 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.
K a |
Eq2 (K *) Source # | Since: 0.2.4.0 |
Ord2 (K *) Source # | Since: 0.2.4.0 |
Read2 (K *) Source # | Since: 0.2.4.0 |
Show2 (K *) Source # | Since: 0.2.4.0 |
Functor (K * a) Source # | |
Monoid a => Applicative (K * a) Source # | |
Foldable (K * a) Source # | |
Traversable (K * a) Source # | |
Eq a => Eq1 (K * a) Source # | Since: 0.2.4.0 |
Ord a => Ord1 (K * a) Source # | Since: 0.2.4.0 |
Read a => Read1 (K * a) Source # | Since: 0.2.4.0 |
Show a => Show1 (K * a) Source # | Since: 0.2.4.0 |
Eq a => Eq (K k a b) Source # | |
Ord a => Ord (K k a b) Source # | |
Read a => Read (K k a b) Source # | |
Show a => Show (K k a b) Source # | |
Generic (K k a b) Source # | |
NFData a => NFData (K k a b) Source # | Since: 0.2.5.0 |
type Rep (K k a b) Source # | |
type DatatypeInfoOf (K * a0 b0) Source # | |
type Code (K * a0 b0) Source # | |
The identity type functor.
Like Identity
, but with a shorter name.
I a |
Monad I Source # | |
Functor I Source # | |
Applicative I Source # | |
Foldable I Source # | |
Traversable I Source # | |
Eq1 I Source # | Since: 0.2.4.0 |
Ord1 I Source # | Since: 0.2.4.0 |
Read1 I Source # | Since: 0.2.4.0 |
Show1 I Source # | Since: 0.2.4.0 |
Eq a => Eq (I a) Source # | |
Ord a => Ord (I a) Source # | |
Read a => Read (I a) Source # | |
Show a => Show (I a) Source # | |
Generic (I a) Source # | |
NFData a => NFData (I a) Source # | Since: 0.2.5.0 |
type Rep (I a) Source # | |
type DatatypeInfoOf (I a0) Source # | |
type Code (I a0) Source # | |
newtype (f :.: g) p infixr 7 Source #
Composition of functors.
Like Compose
, but kind-polymorphic
and with a shorter name.
Comp (f (g p)) |
(Functor f, Functor g) => Functor ((:.:) * * f g) Source # | |
(Applicative f, Applicative g) => Applicative ((:.:) * * f g) Source # | Since: 0.2.5.0 |
(Foldable f, Foldable g) => Foldable ((:.:) * * f g) Source # | Since: 0.2.5.0 |
(Traversable f, Traversable g) => Traversable ((:.:) * * f g) Source # | Since: 0.2.5.0 |
(Eq1 f, Eq1 g) => Eq1 ((:.:) * * f g) Source # | Since: 0.2.4.0 |
(Ord1 f, Ord1 g) => Ord1 ((:.:) * * f g) Source # | Since: 0.2.4.0 |
(Read1 f, Read1 g) => Read1 ((:.:) * * f g) Source # | Since: 0.2.4.0 |
(Show1 f, Show1 g) => Show1 ((:.:) * * f g) Source # | Since: 0.2.4.0 |
(Eq1 f, Eq1 g, Eq a) => Eq ((:.:) * * f g a) Source # | |
(Ord1 f, Ord1 g, Ord a) => Ord ((:.:) * * f g a) Source # | |
(Read1 f, Read1 g, Read a) => Read ((:.:) * * f g a) Source # | |
(Show1 f, Show1 g, Show a) => Show ((:.:) * * f g a) Source # | |
Generic ((:.:) k l f g p) Source # | |
NFData (f (g a)) => NFData ((:.:) k l f g a) Source # | Since: 0.2.5.0 |
type Rep ((:.:) k l f g p) Source # | |
type DatatypeInfoOf ((:.:) * * f0 g0 p0) Source # | |
type Code ((:.:) * * f0 g0 p0) Source # | |
Mapping functions
Mapping constraints
class (AllF f xs, SListI xs) => All f xs 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
.
class (AllF (All f) xss, SListI xss) => All2 f xss 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 innert 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
.
class f (g x) => Compose f g x infixr 9 Source #
Composition of constraints.
Note that the result of the composition must be a constraint,
and therefore, in f
, the kind of :.
gf
is k ->
.
The kind of Constraint
g
, however, is l -> k
and can thus be an 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 xsShow
, we can say
.All
(Show
:. f) xs
Since: 0.2
type family AllN (h :: (k -> *) -> l -> *) (c :: k -> Constraint) :: l -> Constraint Source #
Singletons
data SList :: [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: 0.2
Deprecated: Use SList
instead.
Explicit singleton type.
Just provided for limited backward compatibility.
class SListI xs => SingI xs where Source #
Deprecated: Use SListI
instead.
General class for implicit singletons.
Just provided for limited backward compatibility.
Shape of type-level lists
data Shape :: [k] -> * where Source #
Occassionally 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)
lengthSList :: forall xs proxy. SListI xs => proxy xs -> Int Source #
The length of a type-level list.
Since: 0.2
lengthSing :: SListI xs => proxy xs -> Int Source #
Deprecated: Use lengthSList
instead.
Old name for lengthSList
.
Re-exports
data Proxy k t :: forall k. k -> * #
A concrete, poly-kinded proxy type
Monad (Proxy *) | |
Functor (Proxy *) | |
Applicative (Proxy *) | |
Foldable (Proxy *) | |
Traversable (Proxy *) | |
Generic1 (Proxy *) | |
Eq1 (Proxy *) | Since: 4.9.0.0 |
Ord1 (Proxy *) | Since: 4.9.0.0 |
Read1 (Proxy *) | Since: 4.9.0.0 |
Show1 (Proxy *) | Since: 4.9.0.0 |
Alternative (Proxy *) | |
MonadPlus (Proxy *) | |
Bounded (Proxy k s) | |
Enum (Proxy k s) | |
Eq (Proxy k s) | |
Data t => Data (Proxy * t) | |
Ord (Proxy k s) | |
Read (Proxy k s) | |
Show (Proxy k s) | |
Ix (Proxy k s) | |
Generic (Proxy k t) | |
Semigroup (Proxy k s) | |
Monoid (Proxy k s) | |
NFData (Proxy k a) | Since: 1.4.0.0 |
type Rep1 (Proxy *) | |
type Rep (Proxy k t) | |
type DatatypeInfoOf (Proxy * t0) Source # | |
type Code (Proxy * t0) Source # | |