| Copyright | (c) Justin Le 2019 |
|---|---|
| License | BSD3 |
| Maintainer | justin@jle.im |
| Stability | experimental |
| Portability | non-portable |
| Safe Haskell | None |
| Language | Haskell2010 |
Data.Functor.Combinator
Contents
Description
Functor combinators and tools (typeclasses and utiility functions) to manipulate them. This is the main "entrypoint" of the library.
Classes include:
HFunctorandHBifunctor, used to swap out the functors that the combinators modifyInterpret,Associative,Monoidal, used to inject and interpret functor values with respect to their combinators.
We have some helpful utility functions, as well, built on top of these typeclasses.
The second half of this module exports the various useful functor combinators that can modify functors to add extra functionality, or join two functors together and mix them in different ways. Use them to build your final structure by combining simpler ones in composable ways!
See https://blog.jle.im/entry/functor-combinatorpedia.html and the README for a tutorial and a rundown on each different functor combinator.
Synopsis
- type (~>) (f :: k -> Type) (g :: k -> Type) = forall (x :: k). f x -> g x
- type (<~>) f g = forall p a. Profunctor p => p (g a) (g a) -> p (f a) (f a)
- class HFunctor t where
- class HFunctor t => Inject t where
- class Inject t => Interpret t where
- forI :: (Interpret t, C t g) => t f a -> (f ~> g) -> g a
- getI :: (Interpret t, C t (Const b)) => (forall x. f x -> b) -> t f a -> b
- collectI :: (Interpret t, C t (Const [b])) => (forall x. f x -> b) -> t f a -> [b]
- class HBifunctor t where
- class HBifunctor t => Associative t where
- associating :: (Functor f, Functor g, Functor h) => t f (t g h) <~> t (t f g) h
- class (Associative t, Interpret (SF t)) => Semigroupoidal t where
- type CS t = C (SF t)
- biget :: (Semigroupoidal t, CS t (Const b)) => (forall x. f x -> b) -> (forall x. g x -> b) -> t f g a -> b
- bicollect :: (Semigroupoidal t, CS t (Const [b])) => (forall x. f x -> b) -> (forall x. g x -> b) -> t f g a -> [b]
- (!*!) :: (Semigroupoidal t, CS t h) => (f ~> h) -> (g ~> h) -> t f g ~> h
- (!$!) :: (Semigroupoidal t, CS t (Const b)) => (forall x. f x -> b) -> (forall x. g x -> b) -> t f g a -> b
- class Associative t => Tensor t where
- class (Tensor t, Semigroupoidal t, Interpret (MF t)) => Monoidal t where
- type CM t = C (MF t)
- nilMF :: forall t f. Monoidal t => I t ~> MF t f
- consMF :: Monoidal t => t f (MF t f) ~> MF t f
- inL :: forall t f g. (Monoidal t, CM t g) => f ~> t f g
- inR :: forall t f g. (Monoidal t, CM t f) => g ~> t f g
- outL :: (Tensor t, I t ~ Proxy, Functor f) => t f g ~> f
- outR :: (Tensor t, I t ~ Proxy, Functor g) => t f g ~> g
- data Coyoneda (f :: Type -> Type) a where
- newtype ListF f a = ListF {
- runListF :: [f a]
- newtype NonEmptyF f a where
- NonEmptyF {
- runNonEmptyF :: NonEmpty (f a)
- pattern ProdNonEmpty :: (f :*: ListF f) a -> NonEmptyF f a
- NonEmptyF {
- newtype MaybeF f a = MaybeF {}
- newtype MapF k f a = MapF {}
- newtype NEMapF k f a = NEMapF {}
- data Ap (f :: Type -> Type) a
- data Ap1 :: (Type -> Type) -> Type -> Type where
- data Alt (f :: Type -> Type) a
- data Free f a
- data Free1 f a
- data Lift (f :: Type -> Type) a
- data Step f a = Step {}
- newtype Steps f a = Steps {}
- data ProxyF f a = ProxyF
- data ConstF e f a = ConstF {
- getConstF :: e
- data EnvT e (w :: Type -> Type) a = EnvT e (w a)
- newtype ReaderT r (m :: k -> Type) (a :: k) :: forall k. Type -> (k -> Type) -> k -> Type = ReaderT {
- runReaderT :: r -> m a
- data Flagged f a = Flagged {
- flaggedFlag :: Bool
- flaggedVal :: f a
- newtype IdentityT (f :: k -> Type) (a :: k) :: forall k. (k -> Type) -> k -> Type = IdentityT {
- runIdentityT :: f a
- data Void2 a b
- newtype Final c f a = Final {
- runFinal :: forall g. c g => (forall x. f x -> g x) -> g a
- class Interpret t => FreeOf c t | t -> c where
- newtype ComposeT (f :: (Type -> Type) -> Type -> Type) (g :: (Type -> Type) -> Type -> Type) (m :: Type -> Type) a = ComposeT {
- getComposeT :: f (g m) a
- data Day (f :: Type -> Type) (g :: Type -> Type) a where
- data ((f :: k -> Type) :*: (g :: k -> Type)) (p :: k) :: forall k. (k -> Type) -> (k -> Type) -> k -> Type = (f p) :*: (g p)
- prodOutL :: (f :*: g) ~> f
- prodOutR :: (f :*: g) ~> g
- data ((f :: k -> Type) :+: (g :: k -> Type)) (p :: k) :: forall k. (k -> Type) -> (k -> Type) -> k -> Type
- data V1 (p :: k) :: forall k. k -> Type
- data These1 (f :: Type -> Type) (g :: Type -> Type) a
- data Comp f g a where
- newtype LeftF f g a = LeftF {
- runLeftF :: f a
- newtype RightF f g a = RightF {
- runRightF :: g a
- data HLift t f a
- data HFree t f a
- generalize :: Applicative f => Identity ~> f
- absorb :: f ~> Proxy
Classes
A lot of type signatures are stated in terms of ~>. ~>
represents a "natural transformation" between two functors: a value of
type f is a value of type 'f a -> g a~> g that works for any
a@.
type (~>) (f :: k -> Type) (g :: k -> Type) = forall (x :: k). f x -> g x infixr 0 #
A natural transformation from f to g.
type (<~>) f g = forall p a. Profunctor p => p (g a) (g a) -> p (f a) (f a) infixr 0 Source #
The type of an isomorphism between two functors. f means that
<~> gf and g are isomorphic to each other.
We can effectively use an f <~> g with:
viewF:: (f <~> g) -> f a -> g areviewF:: (f <~> g) -> g a -> a a
Use viewF to extract the "f to g" function, and reviewF to
extract the "g to f" function. Reviewing and viewing the same value
(or vice versa) leaves the value unchanged.
One nice thing is that we can compose isomorphisms using . from
Prelude:
(.) :: f <~> g
-> g <~> h
-> f <~> h
Another nice thing about this representation is that we have the
"identity" isomorphism by using id from Prelude.
id:: f<~>g
As a convention, most isomorphisms have form "X-ing", where the forwards function is "ing". For example, we have:
splittingSF::Monoidalt =>SFt a<~>t f (MFt f)splitSF:: Monoidal t => SF t a~>t f (MF t f)
Single Functors
Classes that deal with single-functor combinators, that enhance a single functor.
class HFunctor t where Source #
An HFunctor can be thought of a unary "functor transformer" ---
a basic functor combinator. It takes a functor as input and returns
a functor as output.
It "enhances" a functor with extra structure (sort of like how a monad
transformer enhances a Monad with extra structure).
As a uniform inteface, we can "swap the underlying functor" (also
sometimes called "hoisting"). This is what hmap does: it lets us swap
out the f in a t f for a t g.
For example, the free monad Free takes a Functor and returns a new
Functor. In the process, it provides a monadic structure over f.
hmap lets us turn a Free fFree gf can be turned into a monad built over g.
For the ability to move in and out of the enhanced functor, see
Inject and Interpret.
This class is similar to MFunctor from
Control.Monad.Morph, but instances must work without a Monad constraint.
This class is also found in the hschema library with the same name.
Methods
hmap :: (f ~> g) -> t f ~> t g Source #
If we can turn an f into a g, then we can turn a t f into
a t g.
It must be the case that
hmapid== id
Essentially, t f adds some "extra structure" to f. hmap
must swap out the functor, without affecting the added structure.
For example, ListF f af as. If we
hmap to swap out the f as for g as, then we must ensure that
the "added structure" (here, the number of items in the list, and
the ordering of those items) remains the same. So, hmap must
preserve the number of items in the list, and must maintain the
ordering.
The law hmap id == id
Instances
class HFunctor t => Inject t where Source #
A typeclass for HFunctors where you can "inject" an f a into a t
f a:
inject :: f a -> t f a
If you think of t f a as an "enhanced f", then inject allows you
to use an f as its enhanced form.
With the exception of directly pattern matching on the result, inject
itself is not too useful in the general case without
Interpret to allow us to interpret or retrieve
back the f.
Methods
Lift from f into the enhanced t f structure. Analogous to
lift from MonadTrans.
Note that this lets us "lift" a f a; if you want to lift an a
with a -> t f a, check if t f is an instance of Applicative or
Pointed.
Instances
class Inject t => Interpret t where Source #
An Interpret lets us move in and out of the "enhanced" Functor.
For example, Free ff enhanced with monadic structure. We get:
inject:: f a ->Freef ainterpret::Monadm => (forall x. f x -> m x) ->Freef a -> m a
inject will let us use our f inside the enhanced Free finterpret will let us "extract" the f from a Free ff into some
target Monad.
The type family C tells us the typeclass constraint of the "target"
functor. For Free, it is Monad, but for other Interpret
instances, we might have other constraints.
We enforce that:
interpretid .inject== id -- orretract.inject== id
That is, if we lift a value into our structure, then immediately interpret it out as itself, it should lave the value unchanged.
Associated Types
Methods
retract :: C t f => t f ~> f Source #
Remove the f out of the enhanced t f structure, provided that
f satisfies the necessary constraints. If it doesn't, it needs to
be properly interpreted out.
interpret :: C t g => (f ~> g) -> t f ~> g Source #
Given an "interpeting function" from f to g, interpret the f
out of the t f into a final context g.
Instances
| Interpret Ap Source # | A free |
| Interpret Ap Source # | A free |
| Interpret Ap Source # | A free |
| Interpret Alt Source # | A free |
| Interpret Coyoneda Source # | A free |
| Interpret WrappedApplicative Source # | |
Defined in Data.HFunctor.Interpret Associated Types type C WrappedApplicative :: (Type -> Type) -> Constraint Source # Methods retract :: C WrappedApplicative f => WrappedApplicative f ~> f Source # interpret :: C WrappedApplicative g => (f ~> g) -> WrappedApplicative f ~> g Source # | |
| Interpret MaybeApply Source # | A free |
Defined in Data.HFunctor.Interpret Associated Types type C MaybeApply :: (Type -> Type) -> Constraint Source # Methods retract :: C MaybeApply f => MaybeApply f ~> f Source # interpret :: C MaybeApply g => (f ~> g) -> MaybeApply f ~> g Source # | |
| Interpret Lift Source # | A free |
| Interpret ListF Source # | A free |
| Interpret NonEmptyF Source # | A free |
| Interpret MaybeF Source # | Technically, |
| Interpret Free1 Source # | A free |
| Interpret Free Source # | A free |
| Interpret Ap1 Source # | |
| Monoid e => Interpret (EnvT e) Source # | |
| Interpret (IdentityT :: (Type -> Type) -> Type -> Type) Source # | A free |
| Interpret (These1 f) Source # | Technically, |
| Interpret (Reverse :: (Type -> Type) -> Type -> Type) Source # | |
| Interpret (Backwards :: (Type -> Type) -> Type -> Type) Source # | |
| Monoid k => Interpret (MapF k) Source # | |
| Monoid k => Interpret (NEMapF k) Source # | |
| Interpret (Step :: (Type -> Type) -> Type -> Type) Source # | |
| Interpret (Steps :: (Type -> Type) -> Type -> Type) Source # | |
| Interpret (Flagged :: (Type -> Type) -> Type -> Type) Source # | |
| Interpret (Final c) Source # | |
| Interpret ((:+:) f) Source # | Technically, |
| Plus f => Interpret ((:*:) f) Source # | |
| Plus f => Interpret (Product f) Source # | |
| Interpret (Sum f) Source # | Technically, |
| (Interpret s, Interpret t) => Interpret (ComposeT s t) Source # | |
| Interpret (ReaderT r :: (Type -> Type) -> Type -> Type) Source # | A free |
| Interpret (ProxyF :: (Type -> Type) -> Type -> Type) Source # | The only way for this to obey |
| Interpret t => Interpret (HFree t) Source # | Never uses |
| Interpret t => Interpret (HLift t) Source # | Never uses |
| (HBifunctor t, Semigroupoidal t) => Interpret (Chain1 t) Source # | |
| Interpret (M1 i c :: (Type -> Type) -> Type -> Type) Source # | |
| Monoid e => Interpret (ConstF e :: (Type -> Type) -> Type -> Type) Source # | The only way for this to obey |
| Interpret (RightF f :: (Type -> Type) -> Type -> Type) Source # | |
| (Monoidal t, i ~ I t) => Interpret (Chain t i) Source # | We can collapse and interpret an |
forI :: (Interpret t, C t g) => t f a -> (f ~> g) -> g a Source #
A convenient flipped version of interpret.
getI :: (Interpret t, C t (Const b)) => (forall x. f x -> b) -> t f a -> b Source #
Useful wrapper over interpret to allow you to directly extract
a value b out of the t f a, if you can convert f x into b.
Note that depending on the constraints on the interpretation of t, you
may have extra constraints on b.
- If
CtUnconstrained, there are no constraints onb - If
CtApply,bneeds to be an instance ofSemigroup - If
CtApplicative,bneeds to be an instance ofMonoid
For some constraints (like Monad), this will not be usable.
-- get the length of theMap Stringin theStep.collectIlength :: Step (Map String) Bool -> Int
collectI :: (Interpret t, C t (Const [b])) => (forall x. f x -> b) -> t f a -> [b] Source #
Useful wrapper over getI to allow you to collect a b from all
instances of f inside a t f a.
This will work if C tUnconstrained, Apply, or Applicative.
-- get the lengths of allMap Strings in theAp.collectIlength :: Ap (Map String) Bool -> [Int]
Multi-Functors
Classes that deal with two-functor combinators, that "mix" two functors together in some way.
class HBifunctor t where Source #
A HBifunctor is like an HFunctor, but it enhances two different
functors instead of just one.
Usually, it enhaces them "together" in some sort of combining way.
This typeclass provides a uniform instance for "swapping out" or
"hoisting" the enhanced functors. We can hoist the first one with
hleft, the second one with hright, or both at the same time with
hbimap.
For example, the f :*: g type gives us "both f and g":
data (f :*: g) a = f a :*: g a
It combines both f and g into a unified structure --- here, it does
it by providing both f and g.
The single law is:
hbimapidid == id
This ensures that hleft, hright, and hbimap do not affect the
structure that t adds on top of the underlying functors.
Methods
hleft :: (f ~> j) -> t f g ~> t j g Source #
Swap out the first transformed functor.
hright :: (g ~> k) -> t f g ~> t f k Source #
Swap out the second transformed functor.
hbimap :: (f ~> j) -> (g ~> k) -> t f g ~> t j k Source #
Swap out both transformed functors at the same time.
Instances
| HBifunctor (Sum :: (k -> Type) -> (k -> Type) -> k -> Type) Source # | |
| HBifunctor ((:+:) :: (k -> Type) -> (k -> Type) -> k -> Type) Source # | |
| HBifunctor (Product :: (k -> Type) -> (k -> Type) -> k -> Type) Source # | |
| HBifunctor ((:*:) :: (k -> Type) -> (k -> Type) -> k -> Type) Source # | |
| HBifunctor (Joker :: (k2 -> Type) -> (k1 -> Type) -> k2 -> Type) Source # | |
| HBifunctor (LeftF :: (k2 -> Type) -> (k1 -> Type) -> k2 -> Type) Source # | |
| HBifunctor (RightF :: (k1 -> Type) -> (k2 -> Type) -> k2 -> Type) Source # | |
| HBifunctor (Void3 :: (k1 -> Type) -> (k2 -> Type) -> k3 -> Type) Source # | |
| HBifunctor Day Source # | |
| HBifunctor These1 Source # | |
| HBifunctor Comp Source # | |
Associative
class HBifunctor t => Associative t where Source #
An HBifunctor where it doesn't matter which binds first is
Associative. Knowing this gives us a lot of power to rearrange the
internals of our HFunctor at will.
For example, for the functor product:
data (f :*: g) a = f a :*: g a
We know that f :*: (g :*: h) is the same as (f :*: g) :*: h.
Instances
| Associative Day Source # | |
| Associative These1 Source # | |
| Associative Comp Source # | |
| Associative ((:+:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Associative ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Associative (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Associative (Sum :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Associative (Joker :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Associative (LeftF :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Associative (RightF :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Associative (Void3 :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
class (Associative t, Interpret (SF t)) => Semigroupoidal t where Source #
For some ts, you can represent the act of applying a functor f to
t many times, as a single type. That is, there is some type SF
t f
f a-- 1 timet f f a-- 2 timest f (t f f) a-- 3 timest f (t f (t f f)) a-- 4 timest f (t f (t f (t f f))) a-- 5 times- .. etc
This typeclass associates each t with its "induced semigroupoidal
functor combinator" SF t
This is useful because sometimes you might want to describe a type that
can be t f f, t f (t f f), t f (t f (t f f)), etc.; "f applied to
itself", with at least one f. This typeclass lets you use a type like
NonEmptyF in terms of repeated applications of :*:, or Ap1 in
terms of repeated applications of Day, or Free1 in terms of repeated
applications of Comp, etc.
For example, f can be interpreted as "a free selection of two
:*: ffs", allowing you to specify "I have to fs that I can use". If you
want to specify "I want 1, 2, or many different fs that I can use",
you can use NonEmptyF f
At the high level, the main way to use a Semigroupoidal is with
biretract and binterpret:
biretract:: t f f~>fbinterpret:: (f ~> h) -> (g ~> h) -> t f g ~> h
which are like the HBifunctor versions of retract and interpret:
they fully "mix" together the two inputs of t.
Also useful is:
toSF :: t f f a -> SF t f a
Which converts a t into its aggregate type SF.
In reality, most Semigroupoidal instances are also
Monoidal instances, so you can think of the
separation as mostly to help organize functionality. However, there are
two non-monoidal semigroupoidal instances of note: LeftF and RightF,
which are higher order analogues of the First and
Last semigroups, roughly.
Associated Types
type SF t :: (Type -> Type) -> Type -> Type Source #
The "semigroup functor combinator" generated by t.
A value of type SF t f a is equivalent to one of:
f a
t f f a
t f (t f f) a
t f (t f (t f f)) a
t f (t f (t f (t f f))) a
- .. etc
For example, for :*:, we have NonEmptyF. This is because:
x ~NonEmptyF(x:|[]) ~injectx x:*:y ~ NonEmptyF (x :| [y]) ~toSF(x :*: y) x :*: y :*: z ~ NonEmptyF (x :| [y,z]) -- etc.
You can create an "singleton" one with inject, or else one from
a single t f f with toSF.
Methods
appendSF :: t (SF t f) (SF t f) ~> SF t f Source #
If a SF t ft f to
itself, then we can also "append" two SF t fSF t ft fs.
consSF :: t f (SF t f) ~> SF t f Source #
Prepend an application of t f to the front of a SF t f
toSF :: t f f ~> SF t f Source #
Embed a direct application of f to itself into a SF t f
biretract :: CS t f => t f f ~> f Source #
The HBifunctor analogy of retract. It retracts both fs
into a single f, effectively fully mixing them together.
binterpret :: CS t h => (f ~> h) -> (g ~> h) -> t f g ~> h Source #
The HBifunctor analogy of interpret. It takes two
interpreting functions, and mixes them together into a target
functor h.
Instances
Convenient alias for the constraint required for biretract,
binterpret, etc.
It's usually a constraint on the target/result context of interpretation
that allows you to "exit" or "run" a Semigroupoidal t
biget :: (Semigroupoidal t, CS t (Const b)) => (forall x. f x -> b) -> (forall x. g x -> b) -> t f g a -> b Source #
Useful wrapper over binterpret to allow you to directly extract
a value b out of the t f a, if you can convert f x into b.
Note that depending on the constraints on the interpretation of t, you
may have extra constraints on b.
- If
C(SFt)Unconstrained, there are no constraints onb - If
C(SFt)Apply,bneeds to be an instance ofSemigroup - If
C(SFt)Applicative,bneeds to be an instance ofMonoid
For some constraints (like Monad), this will not be usable.
-- Return the length of either the list, or the Map, depending on which -- one s in the+bigetlengthlength :: ([] :+:MapInt)Char-> Int -- Return the length of both the list and the map, added togetherbiget(Sum. length) (Sum . length) ::Day[] (Map Int) Char -> Sum Int
bicollect :: (Semigroupoidal t, CS t (Const [b])) => (forall x. f x -> b) -> (forall x. g x -> b) -> t f g a -> [b] Source #
Useful wrapper over biget to allow you to collect a b from all
instances of f and g inside a t f g a.
This will work if C tUnconstrained,
Apply, or Applicative.
(!*!) :: (Semigroupoidal t, CS t h) => (f ~> h) -> (g ~> h) -> t f g ~> h infixr 5 Source #
Infix alias for binterpret
(!$!) :: (Semigroupoidal t, CS t (Const b)) => (forall x. f x -> b) -> (forall x. g x -> b) -> t f g a -> b infixr 5 Source #
Tensor
class Associative t => Tensor t where Source #
An Associative HBifunctor can be a Tensor if there is some
identity i where t i f is equivalent to just f.
That is, "enhancing" f with t i does nothing.
The methods in this class provide us useful ways of navigating
a Tensor t
The Tensor is essentially the HBifunctor equivalent of Inject,
with intro1 and intro2 taking the place of inject.
Associated Types
type I t :: Type -> Type Source #
The identity of Tensor tf with the
identity, it leaves f unchanged.
For example, the identity of :*: is Proxy. This is because
(Proxy :*: f) a
is equivalent to just
f a
:*:-ing f with Proxy gives you no additional structure.
Another example:
(V1:+:f) a
is equivalent to just
f a
because the L1 case is unconstructable.
Methods
intro1 :: f ~> t f (I t) Source #
Because t f (I t) is equivalent to f, we can always "insert"
f into t f (I t).
This is analogous to inject from Inject, but for HBifunctors.
intro2 :: g ~> t (I t) g Source #
Because t (I t) g is equivalent to f, we can always "insert"
g into t (I t) g.
This is analogous to inject from Inject, but for HBifunctors.
Instances
| Tensor Day Source # | |
| Tensor These1 Source # | |
| Tensor Comp Source # | |
| Tensor ((:+:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Tensor ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Tensor (Product :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HBifunctor.Tensor | |
| Tensor (Sum :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
class (Tensor t, Semigroupoidal t, Interpret (MF t)) => Monoidal t where Source #
A Monoidal tSemigroupoidal, in that it provides some type
MF t f
I a-- 0 timesf a-- 1 timet f f a-- 2 timest f (t f f) a-- 3 timest f (t f (t f f)) a-- 4 timest f (t f (t f (t f f))) a-- 5 times- .. etc
The difference is that unlike SF tMF t
This typeclass lets you use a type like ListF in terms of repeated
applications of :*:, or Ap in terms of repeated applications of
Day, or Free in terms of repeated applications of Comp, etc.
For example, f can be interpreted as "a free selection of two
:*: ffs", allowing you to specify "I have to fs that I can use". If you
want to specify "I want 0, 1, or many different fs that I can use",
you can use ListF f
At the high level, the thing that Monoidal adds to Semigroupoidal
is inL, inR, and nilMF:
inL:: f a -> t f g ainR:: g a -> t f g anilMF:: I a -> MF t f a
which are like the HBifunctor versions of inject: it lets you inject
an f into t f g, so you can start doing useful mixing operations
with it. nilMF lets you construct an "empty" MF t
Also useful is:
toMF :: t f f a -> MF t f a
Which converts a t into its aggregate type MF
Minimal complete definition
Associated Types
type MF t :: (Type -> Type) -> Type -> Type Source #
The "monoidal functor combinator" induced by t.
A value of type MF t f a is equivalent to one of:
I a-- zero fsf a-- one ft f f a-- two fst f (t f f) a-- three fst f (t f (t f f)) a
t f (t f (t f (t f f))) a
- .. etc
For example, for :*:, we have ListF. This is because:
Proxy~ListF[] ~nilMF@(:*:) x ~ ListF [x] ~injectx x :*: y ~ ListF [x,y] ~toMF(x :*: y) x :*: y :*: z ~ ListF [x,y,z] -- etc.
You can create an "empty" one with nilMF, a "singleton" one with
inject, or else one from a single t f f with toMF.
Methods
appendMF :: t (MF t f) (MF t f) ~> MF t f Source #
If a MF t ft f to
itself, then we can also "append" two MF t fMF t ft fs.
splitSF :: SF t f ~> t f (MF t f) Source #
Lets you convert an SF t ff to
MF t f
Analogous to a function NonEmpty a -> (a,
[a])
Note that this is not reversible in general unless we have
Matchable t
toMF :: t f f ~> MF t f Source #
Embed a direct application of f to itself into a MF t f
fromSF :: SF t f ~> MF t f Source #
SF t ffs", and 'MF t f is "zero or more
fs". This function lets us convert from one to the other.
This is analogous to a function NonEmpty a ->
[a]
Note that because t is not inferrable from the input or output
type, you should call this using -XTypeApplications:
fromSF@(:*:) ::NonEmptyFf a ->ListFf a fromSF @Comp::Free1f a ->Freef a
pureT :: CM t f => I t ~> f Source #
If we have an I tf based on how it
interacts with t.
Specialized (and simplified), this type is:
pureT@Day::Applicativef =>Identitya -> f a --purepureT @Comp::Monadf => Identity a -> f a --returnpureT @(:*:) ::Plusf =>Proxya -> f a --zero
Note that because t appears nowhere in the input or output types,
you must always use this with explicit type application syntax (like
pureT @Day)
upgradeC :: CM t f => proxy f -> (CS t f => r) -> r Source #
If we have a constraint on the Monoidal satisfied, it should
also imply the constraint on the Semigroupoidal.
This is basically saying that C (SF t)C (MF t)
For example, for :*:, this type signature says that Alt is
a superclass of Plus, so whenever you have Plus, you should
always also have Alt.
For Day, this type signature says that Apply is a superclass of
Applicative, so whenever you have Applicative, you should always
also have Apply.
This is necessary because in the current class hierarchy, Apply
isn't a true superclass of Applicative. upgradeC basically
"imbues" f with an Apply instance based on its Applicative
instance, so things can be easier to use.
For example, let's say I have a type Parser that is an
Applicative instance, but the source library does not define an
Apply instance. I cannot use biretract or binterpret with it,
even though I should be able to, because they require Apply.
That is:
biretract::DayParser Parser a -> Parser a
is a type error, because it requires Apply Parser
But, if we know that Parser has an Applicative instance, we can
use:
upgradeC@Day(Proxy@Parser)biretract:: Day Parser Parser a -> a
and this will now typecheck properly.
Ideally, Parser would also have an Apply instance. But we
cannot control this if an external library defines Parser.
(Alternatively you can just use biretractT.)
Note that you should only use this if f doesn't already have the
SF constraint. If it does, this could lead to conflicting
instances. Only use this with specific, concrete fs. Otherwise
this is unsafe and can possibly break coherence guarantees.
The proxy argument can be provided using something like Proxy
@ff you want to upgrade.
Instances
nilMF :: forall t f. Monoidal t => I t ~> MF t f Source #
Create the "empty MF@.
If MF t ft f with
itself, then nilMF gives us "zero applications of f".
Note that t cannot be inferred from the input or output type of
nilMF, so this function must always be called with -XTypeApplications:
nilMF@Day::Identity~>Apf nilMF @Comp:: Identity ~>Freef nilMF @(:*:) ::Proxy~>ListFf
consMF :: Monoidal t => t f (MF t f) ~> MF t f Source #
Lets us "cons" an application of f to the front of an MF t f
inL :: forall t f g. (Monoidal t, CM t g) => f ~> t f g Source #
Convenient wrapper over intro1 that lets us introduce an arbitrary
functor g to the right of an f.
You can think of this as an HBifunctor analogue of inject.
inR :: forall t f g. (Monoidal t, CM t f) => g ~> t f g Source #
Convenient wrapper over intro2 that lets us introduce an arbitrary
functor f to the right of a g.
You can think of this as an HBifunctor analogue of inject.
Combinators
Functor combinators ** Single
data Coyoneda (f :: Type -> Type) a where #
A covariant Functor suitable for Yoneda reduction
Instances
A list of f as. Can be used to describe a product of many different
values of type f a.
This is the Free Plus.
Instances
| Interpret ListF Source # | A free |
| FreeOf Plus ListF Source # | |
| Functor f => Functor (ListF f) Source # | |
| Applicative f => Applicative (ListF f) Source # | |
| Foldable f => Foldable (ListF f) Source # | |
Defined in Control.Applicative.ListF Methods fold :: Monoid m => ListF f m -> m # foldMap :: Monoid m => (a -> m) -> ListF f a -> m # foldr :: (a -> b -> b) -> b -> ListF f a -> b # foldr' :: (a -> b -> b) -> b -> ListF f a -> b # foldl :: (b -> a -> b) -> b -> ListF f a -> b # foldl' :: (b -> a -> b) -> b -> ListF f a -> b # foldr1 :: (a -> a -> a) -> ListF f a -> a # foldl1 :: (a -> a -> a) -> ListF f a -> a # elem :: Eq a => a -> ListF f a -> Bool # maximum :: Ord a => ListF f a -> a # minimum :: Ord a => ListF f a -> a # | |
| Traversable f => Traversable (ListF f) Source # | |
| Applicative f => Alternative (ListF f) Source # | |
| Eq1 f => Eq1 (ListF f) Source # | |
| Ord1 f => Ord1 (ListF f) Source # | |
Defined in Control.Applicative.ListF | |
| Read1 f => Read1 (ListF f) Source # | |
Defined in Control.Applicative.ListF | |
| Show1 f => Show1 (ListF f) Source # | |
| Apply f => Apply (ListF f) Source # | |
| Pointed f => Pointed (ListF f) Source # | |
Defined in Control.Applicative.ListF | |
| Functor f => Plus (ListF f) Source # | |
Defined in Control.Applicative.ListF | |
| Functor f => Alt (ListF f) Source # | |
| HBind ListF Source # | |
| Inject ListF Source # | |
| HFunctor ListF Source # | |
| Eq (f a) => Eq (ListF f a) Source # | |
| (Typeable f, Typeable a, Data (f a)) => Data (ListF f a) Source # | |
Defined in Control.Applicative.ListF Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ListF f a -> c (ListF f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (ListF f a) # toConstr :: ListF f a -> Constr # dataTypeOf :: ListF f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (ListF f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (ListF f a)) # gmapT :: (forall b. Data b => b -> b) -> ListF f a -> ListF f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ListF f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ListF f a -> r # gmapQ :: (forall d. Data d => d -> u) -> ListF f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> ListF f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ListF f a -> m (ListF f a) # | |
| Ord (f a) => Ord (ListF f a) Source # | |
| Read (f a) => Read (ListF f a) Source # | |
| Show (f a) => Show (ListF f a) Source # | |
| Generic (ListF f a) Source # | |
| Semigroup (ListF f a) Source # | |
| Monoid (ListF f a) Source # | |
| type C ListF Source # | |
Defined in Data.HFunctor.Interpret | |
| type Rep (ListF f a) Source # | |
Defined in Control.Applicative.ListF | |
newtype NonEmptyF f a Source #
A non-empty list of f as. Can be used to describe a product between
many different possible values of type f a.
Essentially:
NonEmptyFf ~ f -- one f:+:(f:*:f) -- two f's :+: (f :*: f :*: f) -- three f's :+: (f :*: f :*: f :*: f) -- four f's :+: ... -- etc.
This is the Free Plus.
Constructors
| NonEmptyF | |
Fields
| |
Bundled Patterns
| pattern ProdNonEmpty :: (f :*: ListF f) a -> NonEmptyF f a | Treat a
|
Instances
A maybe f a.
Can be useful for describing a "an f a that may or may not be there".
This is the free structure for a "fail"-like typeclass that would only
have zero :: f a.
Instances
| Interpret MaybeF Source # | Technically, |
| Functor f => Functor (MaybeF f) Source # | |
| Applicative f => Applicative (MaybeF f) Source # | |
| Foldable f => Foldable (MaybeF f) Source # | |
Defined in Control.Applicative.ListF Methods fold :: Monoid m => MaybeF f m -> m # foldMap :: Monoid m => (a -> m) -> MaybeF f a -> m # foldr :: (a -> b -> b) -> b -> MaybeF f a -> b # foldr' :: (a -> b -> b) -> b -> MaybeF f a -> b # foldl :: (b -> a -> b) -> b -> MaybeF f a -> b # foldl' :: (b -> a -> b) -> b -> MaybeF f a -> b # foldr1 :: (a -> a -> a) -> MaybeF f a -> a # foldl1 :: (a -> a -> a) -> MaybeF f a -> a # elem :: Eq a => a -> MaybeF f a -> Bool # maximum :: Ord a => MaybeF f a -> a # minimum :: Ord a => MaybeF f a -> a # | |
| Traversable f => Traversable (MaybeF f) Source # | |
Defined in Control.Applicative.ListF | |
| Applicative f => Alternative (MaybeF f) Source # | |
| Eq1 f => Eq1 (MaybeF f) Source # | |
| Ord1 f => Ord1 (MaybeF f) Source # | |
Defined in Control.Applicative.ListF | |
| Read1 f => Read1 (MaybeF f) Source # | |
Defined in Control.Applicative.ListF | |
| Show1 f => Show1 (MaybeF f) Source # | |
| Pointed f => Pointed (MaybeF f) Source # | |
Defined in Control.Applicative.ListF | |
| Functor f => Plus (MaybeF f) Source # | |
Defined in Control.Applicative.ListF | |
| Functor f => Alt (MaybeF f) Source # | |
| HBind MaybeF Source # | |
| Inject MaybeF Source # | |
| HFunctor MaybeF Source # | |
| Eq (f a) => Eq (MaybeF f a) Source # | |
| (Typeable f, Typeable a, Data (f a)) => Data (MaybeF f a) Source # | |
Defined in Control.Applicative.ListF Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MaybeF f a -> c (MaybeF f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (MaybeF f a) # toConstr :: MaybeF f a -> Constr # dataTypeOf :: MaybeF f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (MaybeF f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (MaybeF f a)) # gmapT :: (forall b. Data b => b -> b) -> MaybeF f a -> MaybeF f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MaybeF f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MaybeF f a -> r # gmapQ :: (forall d. Data d => d -> u) -> MaybeF f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> MaybeF f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> MaybeF f a -> m (MaybeF f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> MaybeF f a -> m (MaybeF f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> MaybeF f a -> m (MaybeF f a) # | |
| Ord (f a) => Ord (MaybeF f a) Source # | |
Defined in Control.Applicative.ListF | |
| Read (f a) => Read (MaybeF f a) Source # | |
| Show (f a) => Show (MaybeF f a) Source # | |
| Generic (MaybeF f a) Source # | |
| Semigroup (MaybeF f a) Source # | Picks the first |
| Monoid (MaybeF f a) Source # | |
| type C MaybeF Source # | |
Defined in Data.HFunctor.Interpret | |
| type Rep (MaybeF f a) Source # | |
Defined in Control.Applicative.ListF | |
A map of f as, indexed by keys of type k. It can be useful for
represeting a product of many different values of type f a, each "at"
a different k location.
Can be considered a combination of EnvT and
ListF, in a way --- a MapF k f aListF
(EnvT k f) a
One use case might be to extend a schema with many "options", indexed by some string.
For example, if you had a command line argument parser for a single command
data Command a
Then you can represent a command line argument parser for multiple named commands with
type Commands =MapFStringCommand
See NEMapF for a non-empty variant, if you want to enforce that your
bag has at least one f a.
Instances
| Monoid k => Interpret (MapF k) Source # | |
| Monoid k => Inject (MapF k :: (Type -> Type) -> Type -> Type) Source # | Injects into a singleton map at |
| HFunctor (MapF k :: (Type -> Type) -> Type -> Type) Source # | |
| Functor f => Functor (MapF k f) Source # | |
| Foldable f => Foldable (MapF k f) Source # | |
Defined in Control.Applicative.ListF Methods fold :: Monoid m => MapF k f m -> m # foldMap :: Monoid m => (a -> m) -> MapF k f a -> m # foldr :: (a -> b -> b) -> b -> MapF k f a -> b # foldr' :: (a -> b -> b) -> b -> MapF k f a -> b # foldl :: (b -> a -> b) -> b -> MapF k f a -> b # foldl' :: (b -> a -> b) -> b -> MapF k f a -> b # foldr1 :: (a -> a -> a) -> MapF k f a -> a # foldl1 :: (a -> a -> a) -> MapF k f a -> a # elem :: Eq a => a -> MapF k f a -> Bool # maximum :: Ord a => MapF k f a -> a # minimum :: Ord a => MapF k f a -> a # | |
| Traversable f => Traversable (MapF k f) Source # | |
Defined in Control.Applicative.ListF | |
| (Eq k, Eq1 f) => Eq1 (MapF k f) Source # | |
| (Ord k, Ord1 f) => Ord1 (MapF k f) Source # | |
Defined in Control.Applicative.ListF | |
| (Ord k, Read k, Read1 f) => Read1 (MapF k f) Source # | |
Defined in Control.Applicative.ListF | |
| (Show k, Show1 f) => Show1 (MapF k f) Source # | |
| (Monoid k, Pointed f) => Pointed (MapF k f) Source # | |
Defined in Control.Applicative.ListF | |
| (Functor f, Ord k) => Plus (MapF k f) Source # | |
Defined in Control.Applicative.ListF | |
| (Functor f, Ord k) => Alt (MapF k f) Source # | Left-biased union |
| (Eq k, Eq (f a)) => Eq (MapF k f a) Source # | |
| (Typeable f, Typeable a, Data k, Data (f a), Ord k) => Data (MapF k f a) Source # | |
Defined in Control.Applicative.ListF Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> MapF k f a -> c (MapF k f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (MapF k f a) # toConstr :: MapF k f a -> Constr # dataTypeOf :: MapF k f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (MapF k f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (MapF k f a)) # gmapT :: (forall b. Data b => b -> b) -> MapF k f a -> MapF k f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> MapF k f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> MapF k f a -> r # gmapQ :: (forall d. Data d => d -> u) -> MapF k f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> MapF k f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> MapF k f a -> m (MapF k f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> MapF k f a -> m (MapF k f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> MapF k f a -> m (MapF k f a) # | |
| (Ord k, Ord (f a)) => Ord (MapF k f a) Source # | |
Defined in Control.Applicative.ListF | |
| (Ord k, Read k, Read (f a)) => Read (MapF k f a) Source # | |
| (Show k, Show (f a)) => Show (MapF k f a) Source # | |
| Generic (MapF k f a) Source # | |
| (Ord k, Alt f) => Semigroup (MapF k f a) Source # | A union, combining matching keys with |
| (Ord k, Alt f) => Monoid (MapF k f a) Source # | |
| type C (MapF k) Source # | |
Defined in Data.HFunctor.Interpret | |
| type Rep (MapF k f a) Source # | |
Defined in Control.Applicative.ListF | |
A non-empty map of f as, indexed by keys of type k. It can be
useful for represeting a product of many different values of type f a,
each "at" a different k location, where you need to have at least one
f a at all times.
Can be considered a combination of EnvT and
NonEmptyF, in a way --- an NEMapF k f aNonEmptyF
(EnvT k f) a
See MapF for some use cases.
Instances
| Monoid k => Interpret (NEMapF k) Source # | |
| Monoid k => Inject (NEMapF k :: (Type -> Type) -> Type -> Type) Source # | Injects into a singleton map at |
| HFunctor (NEMapF k :: (Type -> Type) -> Type -> Type) Source # | |
| Functor f => Functor (NEMapF k f) Source # | |
| Foldable f => Foldable (NEMapF k f) Source # | |
Defined in Control.Applicative.ListF Methods fold :: Monoid m => NEMapF k f m -> m # foldMap :: Monoid m => (a -> m) -> NEMapF k f a -> m # foldr :: (a -> b -> b) -> b -> NEMapF k f a -> b # foldr' :: (a -> b -> b) -> b -> NEMapF k f a -> b # foldl :: (b -> a -> b) -> b -> NEMapF k f a -> b # foldl' :: (b -> a -> b) -> b -> NEMapF k f a -> b # foldr1 :: (a -> a -> a) -> NEMapF k f a -> a # foldl1 :: (a -> a -> a) -> NEMapF k f a -> a # toList :: NEMapF k f a -> [a] # null :: NEMapF k f a -> Bool # length :: NEMapF k f a -> Int # elem :: Eq a => a -> NEMapF k f a -> Bool # maximum :: Ord a => NEMapF k f a -> a # minimum :: Ord a => NEMapF k f a -> a # | |
| Traversable f => Traversable (NEMapF k f) Source # | |
Defined in Control.Applicative.ListF | |
| (Eq k, Eq1 f) => Eq1 (NEMapF k f) Source # | |
| (Ord k, Ord1 f) => Ord1 (NEMapF k f) Source # | |
Defined in Control.Applicative.ListF | |
| (Ord k, Read k, Read1 f) => Read1 (NEMapF k f) Source # | |
Defined in Control.Applicative.ListF Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (NEMapF k f a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [NEMapF k f a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (NEMapF k f a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [NEMapF k f a] # | |
| (Show k, Show1 f) => Show1 (NEMapF k f) Source # | |
| Foldable1 f => Foldable1 (NEMapF k f) Source # | |
| (Monoid k, Pointed f) => Pointed (NEMapF k f) Source # | |
Defined in Control.Applicative.ListF | |
| Traversable1 f => Traversable1 (NEMapF k f) Source # | |
| (Functor f, Ord k) => Alt (NEMapF k f) Source # | Left-biased union |
| (Eq k, Eq (f a)) => Eq (NEMapF k f a) Source # | |
| (Typeable f, Typeable a, Data k, Data (f a), Ord k) => Data (NEMapF k f a) Source # | |
Defined in Control.Applicative.ListF Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> NEMapF k f a -> c (NEMapF k f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (NEMapF k f a) # toConstr :: NEMapF k f a -> Constr # dataTypeOf :: NEMapF k f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (NEMapF k f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (NEMapF k f a)) # gmapT :: (forall b. Data b => b -> b) -> NEMapF k f a -> NEMapF k f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> NEMapF k f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> NEMapF k f a -> r # gmapQ :: (forall d. Data d => d -> u) -> NEMapF k f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> NEMapF k f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> NEMapF k f a -> m (NEMapF k f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> NEMapF k f a -> m (NEMapF k f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> NEMapF k f a -> m (NEMapF k f a) # | |
| (Ord k, Ord (f a)) => Ord (NEMapF k f a) Source # | |
Defined in Control.Applicative.ListF | |
| (Ord k, Read k, Read (f a)) => Read (NEMapF k f a) Source # | |
| (Show k, Show (f a)) => Show (NEMapF k f a) Source # | |
| Generic (NEMapF k f a) Source # | |
| (Ord k, Alt f) => Semigroup (NEMapF k f a) Source # | A union, combining matching keys with |
| type C (NEMapF k) Source # | |
Defined in Data.HFunctor.Interpret | |
| type Rep (NEMapF k f a) Source # | |
Defined in Control.Applicative.ListF | |
data Ap (f :: Type -> Type) a #
The free Applicative for a Functor f.
data Ap1 :: (Type -> Type) -> Type -> Type where Source #
One or more fs convolved with itself.
Essentially:
Ap1f ~ f -- one f:+:(f `Day'f) -- two f's :+: (f `Day` f `Day` f) -- three f's :+: (f `Day` f `Day` f `Day` f) -- four f's :+: ... -- etc.
Useful if you want to promote an f to a situation with "at least one
f sequenced with itself".
Mostly useful for its HFunctor and Interpret instance, along with
its relationship with Ap and Day.
This is the free Apply --- Basically a "non-empty" Ap.
The construction here is based on Ap, similar to now
NonEmpty is built on list.
Bundled Patterns
| pattern DayAp1 :: Day f (Ap f) a -> Ap1 f a | An |
data Alt (f :: Type -> Type) a #
Instances
| Interpret Alt Source # | A free |
| FreeOf Alternative Alt Source # | |
| Functor (Alt f) | |
| Applicative (Alt f) | |
| Alternative (Alt f) | |
| Apply (Alt f) | |
| Alt (Alt f) | |
| HBind Alt Source # | |
| Inject Alt Source # | |
| HFunctor Alt Source # | |
| Semigroup (Alt f a) | |
| Monoid (Alt f a) | |
| type C Alt Source # | |
Defined in Data.HFunctor.Interpret | |
A Free ff enhanced with "sequential binding" capabilities.
It allows you to sequence multiple fs one after the other, and also to
determine "what f to sequence" based on the result of the computation
so far.
Essentially, you can think of this as "giving f a Monad instance",
with all that that entails (return, >>=, etc.).
Lift f into it with inject :: f a -> Free
f a
interpret::Monadg => (forall x. f x -> g x) ->Freef a -> g a
Structurally, this is equivalent to many "nested" f's. A value of type
Free f a
a
f a
f (f a)
f (f (f a))
- .. etc.
Under the hood, this is the Church-encoded Freer monad. It's
Free, or F, but in
a way that is compatible with HFunctor and
Interpret.
Instances
The Free Bind. Imbues any functor f with a Bind instance.
Conceptually, this is "Free without pure". That is, while normally
Free f aa, a f a, a f (f a), etc., a Free1 f af a, f (f a), f (f (f a)), etc. It's a Free with "at least
one layer of f", excluding the a case.
It can be useful as the semigroup formed by :.: (functor composition):
Sometimes we want an f :.: f, or an f :.: f :.: f, or an f :.:
f :.: f :.: f...just as long as we have at least one f.
Instances
data Lift (f :: Type -> Type) a #
Applicative functor formed by adding pure computations to a given applicative functor.
Instances
| Interpret Lift Source # | A free |
| FreeOf Pointed Lift Source # | |
| Functor f => Functor (Lift f) | |
| Applicative f => Applicative (Lift f) | A combination is |
| Foldable f => Foldable (Lift f) | |
Defined in Control.Applicative.Lift Methods fold :: Monoid m => Lift f m -> m # foldMap :: Monoid m => (a -> m) -> Lift f a -> m # foldr :: (a -> b -> b) -> b -> Lift f a -> b # foldr' :: (a -> b -> b) -> b -> Lift f a -> b # foldl :: (b -> a -> b) -> b -> Lift f a -> b # foldl' :: (b -> a -> b) -> b -> Lift f a -> b # foldr1 :: (a -> a -> a) -> Lift f a -> a # foldl1 :: (a -> a -> a) -> Lift f a -> a # elem :: Eq a => a -> Lift f a -> Bool # maximum :: Ord a => Lift f a -> a # minimum :: Ord a => Lift f a -> a # | |
| Traversable f => Traversable (Lift f) | |
| Alternative f => Alternative (Lift f) | A combination is |
| Eq1 f => Eq1 (Lift f) | |
| Ord1 f => Ord1 (Lift f) | |
Defined in Control.Applicative.Lift | |
| Read1 f => Read1 (Lift f) | |
Defined in Control.Applicative.Lift | |
| Show1 f => Show1 (Lift f) | |
| Foldable1 f => Foldable1 (Lift f) | |
| Apply f => Apply (Lift f) | |
| Pointed (Lift f) | |
Defined in Data.Pointed | |
| Traversable1 f => Traversable1 (Lift f) | |
| Plus f => Plus (Lift f) | |
Defined in Data.Functor.Plus | |
| Alt f => Alt (Lift f) | |
| HBind Lift Source # | |
| Inject Lift Source # | |
| HFunctor Lift Source # | |
| (Eq1 f, Eq a) => Eq (Lift f a) | |
| (Ord1 f, Ord a) => Ord (Lift f a) | |
Defined in Control.Applicative.Lift | |
| (Read1 f, Read a) => Read (Lift f a) | |
| (Show1 f, Show a) => Show (Lift f a) | |
| type C Lift Source # | |
Defined in Data.HFunctor.Interpret | |
An f a, along with a Natural index.
Stepf a ~ (Natural, f a) Step f ~ ((,) Natural):.:f -- functor composition
It is the fixed point of infinite applications of :+: (functor sums).
Intuitively, in an infinite f :+: f :+: f :+: f ..., you have
exactly one f somewhere. A Step f af, with
a Natural giving you "where" the f is in the long chain.
Can be useful for using with the Monoidal
instance of :+:.
interpreting it requires no constraint on the
target context.
Note that this type and its instances equivalent to
EnvT (Sum Natural)
Instances
| HFunctor (Step :: (k -> Type) -> k -> Type) Source # | |
| HBind (Step :: (k -> Type) -> k -> Type) Source # | |
| Inject (Step :: (k -> Type) -> k -> Type) Source # | Injects with 0. |
| Interpret (Step :: (Type -> Type) -> Type -> Type) Source # | |
| Functor f => Functor (Step f) Source # | |
| Applicative f => Applicative (Step f) Source # | |
| Foldable f => Foldable (Step f) Source # | |
Defined in Control.Applicative.Step Methods fold :: Monoid m => Step f m -> m # foldMap :: Monoid m => (a -> m) -> Step f a -> m # foldr :: (a -> b -> b) -> b -> Step f a -> b # foldr' :: (a -> b -> b) -> b -> Step f a -> b # foldl :: (b -> a -> b) -> b -> Step f a -> b # foldl' :: (b -> a -> b) -> b -> Step f a -> b # foldr1 :: (a -> a -> a) -> Step f a -> a # foldl1 :: (a -> a -> a) -> Step f a -> a # elem :: Eq a => a -> Step f a -> Bool # maximum :: Ord a => Step f a -> a # minimum :: Ord a => Step f a -> a # | |
| Traversable f => Traversable (Step f) Source # | |
| Eq1 f => Eq1 (Step f) Source # | |
| Ord1 f => Ord1 (Step f) Source # | |
Defined in Control.Applicative.Step | |
| Read1 f => Read1 (Step f) Source # | |
Defined in Control.Applicative.Step | |
| Show1 f => Show1 (Step f) Source # | |
| Foldable1 f => Foldable1 (Step f) Source # | |
| Pointed f => Pointed (Step f) Source # | |
Defined in Control.Applicative.Step | |
| Traversable1 f => Traversable1 (Step f) Source # | |
| Eq (f a) => Eq (Step f a) Source # | |
| (Typeable a, Typeable f, Typeable k, Data (f a)) => Data (Step f a) Source # | |
Defined in Control.Applicative.Step Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Step f a -> c (Step f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Step f a) # toConstr :: Step f a -> Constr # dataTypeOf :: Step f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Step f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Step f a)) # gmapT :: (forall b. Data b => b -> b) -> Step f a -> Step f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Step f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Step f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Step f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Step f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Step f a -> m (Step f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Step f a -> m (Step f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Step f a -> m (Step f a) # | |
| Ord (f a) => Ord (Step f a) Source # | |
Defined in Control.Applicative.Step | |
| Read (f a) => Read (Step f a) Source # | |
| Show (f a) => Show (Step f a) Source # | |
| Generic (Step f a) Source # | |
| type C (Step :: (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HFunctor.Interpret | |
| type Rep (Step f a) Source # | |
Defined in Control.Applicative.Step type Rep (Step f a) = D1 (MetaData "Step" "Control.Applicative.Step" "functor-combinators-0.1.1.1-B2oyFu2GVTM8ySAuzVPoNk" False) (C1 (MetaCons "Step" PrefixI True) (S1 (MetaSel (Just "stepPos") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Natural) :*: S1 (MetaSel (Just "stepVal") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a)))) | |
A non-empty map of Natural to f a. Basically, contains multiple
f as, each at a given Natural index.
Steps f a ~MapNatural(f a) Steps f ~MapNatural:.:f -- functor composition
It is the fixed point of applications of TheseT.
You can think of this as an infinite sparse array of f as.
Intuitively, in an infinite f `TheseT` f `TheseT` f `TheseT` f ...,
each of those infinite positions may have an f in them. However,
because of the at-least-one nature of TheseT, we know we have at least
one f at one position somewhere.
A Steps f afs, each stored at a different
Natural position, with the guaruntee that at least one f exists.
Can be useful for using with the Monoidal instance
of TheseT.
interpreting it requires at least an Alt
instance in the target context, since we have to handle potentially more
than one f.
This type is essentailly the same as NEMapF
(Sum Natural)Semigroup instance).
Instances
| HFunctor (Steps :: (k -> Type) -> k -> Type) Source # | |
| Inject (Steps :: (k -> Type) -> k -> Type) Source # | Injects into a singleton map at 0; same behavior as |
| Interpret (Steps :: (Type -> Type) -> Type -> Type) Source # | |
| Functor f => Functor (Steps f) Source # | |
| Foldable f => Foldable (Steps f) Source # | |
Defined in Control.Applicative.Step Methods fold :: Monoid m => Steps f m -> m # foldMap :: Monoid m => (a -> m) -> Steps f a -> m # foldr :: (a -> b -> b) -> b -> Steps f a -> b # foldr' :: (a -> b -> b) -> b -> Steps f a -> b # foldl :: (b -> a -> b) -> b -> Steps f a -> b # foldl' :: (b -> a -> b) -> b -> Steps f a -> b # foldr1 :: (a -> a -> a) -> Steps f a -> a # foldl1 :: (a -> a -> a) -> Steps f a -> a # elem :: Eq a => a -> Steps f a -> Bool # maximum :: Ord a => Steps f a -> a # minimum :: Ord a => Steps f a -> a # | |
| Traversable f => Traversable (Steps f) Source # | |
| Eq1 f => Eq1 (Steps f) Source # | |
| Ord1 f => Ord1 (Steps f) Source # | |
Defined in Control.Applicative.Step | |
| Read1 f => Read1 (Steps f) Source # | |
Defined in Control.Applicative.Step | |
| Show1 f => Show1 (Steps f) Source # | |
| Foldable1 f => Foldable1 (Steps f) Source # | |
| Pointed f => Pointed (Steps f) Source # | |
Defined in Control.Applicative.Step | |
| Traversable1 f => Traversable1 (Steps f) Source # | |
| Functor f => Alt (Steps f) Source # | Left-biased untion |
| Eq (f a) => Eq (Steps f a) Source # | |
| (Typeable a, Typeable f, Typeable k, Data (f a)) => Data (Steps f a) Source # | |
Defined in Control.Applicative.Step Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Steps f a -> c (Steps f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Steps f a) # toConstr :: Steps f a -> Constr # dataTypeOf :: Steps f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Steps f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Steps f a)) # gmapT :: (forall b. Data b => b -> b) -> Steps f a -> Steps f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Steps f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Steps f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Steps f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Steps f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Steps f a -> m (Steps f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Steps f a -> m (Steps f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Steps f a -> m (Steps f a) # | |
| Ord (f a) => Ord (Steps f a) Source # | |
| Read (f a) => Read (Steps f a) Source # | |
| Show (f a) => Show (Steps f a) Source # | |
| Generic (Steps f a) Source # | |
| Semigroup (Steps f a) Source # | Appends the items back-to-back, shifting all of the items in the
second map. Matches the behavior as the fixed-point of |
| type C (Steps :: (Type -> Type) -> Type -> Type) Source # | |
| type Rep (Steps f a) Source # | |
Defined in Control.Applicative.Step | |
The functor combinator that forgets all structure in the input. Ignores the input structure and stores no information.
Acts like the "zero" with respect to functor combinator composition.
ComposeTProxyF f ~ ProxyFComposeTf ProxyF ~ ProxyF
It can be injected into (losing all information), but it is impossible
to ever retract or
interpret it.
This is essentially ConstF ()
Constructors
| ProxyF |
Instances
| HFunctor (ProxyF :: (k1 -> Type) -> k2 -> Type) Source # | |
| HBind (ProxyF :: (k -> Type) -> k -> Type) Source # | |
| Inject (ProxyF :: (k -> Type) -> k -> Type) Source # | |
| Interpret (ProxyF :: (Type -> Type) -> Type -> Type) Source # | The only way for this to obey |
| Functor (ProxyF f :: Type -> Type) Source # | |
| Foldable (ProxyF f :: Type -> Type) Source # | |
Defined in Data.HFunctor Methods fold :: Monoid m => ProxyF f m -> m # foldMap :: Monoid m => (a -> m) -> ProxyF f a -> m # foldr :: (a -> b -> b) -> b -> ProxyF f a -> b # foldr' :: (a -> b -> b) -> b -> ProxyF f a -> b # foldl :: (b -> a -> b) -> b -> ProxyF f a -> b # foldl' :: (b -> a -> b) -> b -> ProxyF f a -> b # foldr1 :: (a -> a -> a) -> ProxyF f a -> a # foldl1 :: (a -> a -> a) -> ProxyF f a -> a # elem :: Eq a => a -> ProxyF f a -> Bool # maximum :: Ord a => ProxyF f a -> a # minimum :: Ord a => ProxyF f a -> a # | |
| Traversable (ProxyF f :: Type -> Type) Source # | |
| Eq1 (ProxyF f :: Type -> Type) Source # | |
| Ord1 (ProxyF f :: Type -> Type) Source # | |
Defined in Data.HFunctor | |
| Read1 (ProxyF f :: Type -> Type) Source # | |
Defined in Data.HFunctor | |
| Show1 (ProxyF f :: Type -> Type) Source # | |
| Eq (ProxyF f a) Source # | |
| (Typeable f, Typeable a, Typeable k1, Typeable k2) => Data (ProxyF f a) Source # | |
Defined in Data.HFunctor Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ProxyF f a -> c (ProxyF f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (ProxyF f a) # toConstr :: ProxyF f a -> Constr # dataTypeOf :: ProxyF f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (ProxyF f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (ProxyF f a)) # gmapT :: (forall b. Data b => b -> b) -> ProxyF f a -> ProxyF f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ProxyF f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ProxyF f a -> r # gmapQ :: (forall d. Data d => d -> u) -> ProxyF f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> ProxyF f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> ProxyF f a -> m (ProxyF f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ProxyF f a -> m (ProxyF f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ProxyF f a -> m (ProxyF f a) # | |
| Ord (ProxyF f a) Source # | |
| Read (ProxyF f a) Source # | |
| Show (ProxyF f a) Source # | |
| Generic (ProxyF f a) Source # | |
| type C (ProxyF :: (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HFunctor.Interpret | |
| type Rep (ProxyF f a) Source # | |
Functor combinator that forgets all structure on the input, and
instead stores a value of type e.
Like ProxyF, acts like a "zero" with functor combinator composition.
It can be injected into (losing all information), but it is impossible
to ever retract or
interpret it.
Instances
| HFunctor (ConstF e :: (k1 -> Type) -> k2 -> Type) Source # | |
| Monoid e => Inject (ConstF e :: (k -> Type) -> k -> Type) Source # | |
| Monoid e => Interpret (ConstF e :: (Type -> Type) -> Type -> Type) Source # | The only way for this to obey |
| Functor (ConstF e f :: Type -> Type) Source # | |
| Foldable (ConstF e f :: Type -> Type) Source # | |
Defined in Data.HFunctor Methods fold :: Monoid m => ConstF e f m -> m # foldMap :: Monoid m => (a -> m) -> ConstF e f a -> m # foldr :: (a -> b -> b) -> b -> ConstF e f a -> b # foldr' :: (a -> b -> b) -> b -> ConstF e f a -> b # foldl :: (b -> a -> b) -> b -> ConstF e f a -> b # foldl' :: (b -> a -> b) -> b -> ConstF e f a -> b # foldr1 :: (a -> a -> a) -> ConstF e f a -> a # foldl1 :: (a -> a -> a) -> ConstF e f a -> a # toList :: ConstF e f a -> [a] # null :: ConstF e f a -> Bool # length :: ConstF e f a -> Int # elem :: Eq a => a -> ConstF e f a -> Bool # maximum :: Ord a => ConstF e f a -> a # minimum :: Ord a => ConstF e f a -> a # | |
| Traversable (ConstF e f :: Type -> Type) Source # | |
Defined in Data.HFunctor | |
| Eq e => Eq1 (ConstF e f :: Type -> Type) Source # | |
| Ord e => Ord1 (ConstF e f :: Type -> Type) Source # | |
Defined in Data.HFunctor | |
| Read e => Read1 (ConstF e f :: Type -> Type) Source # | |
Defined in Data.HFunctor Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (ConstF e f a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [ConstF e f a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (ConstF e f a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [ConstF e f a] # | |
| Show e => Show1 (ConstF e f :: Type -> Type) Source # | |
| Eq e => Eq (ConstF e f a) Source # | |
| (Typeable f, Typeable a, Typeable k1, Typeable k2, Data e) => Data (ConstF e f a) Source # | |
Defined in Data.HFunctor Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> ConstF e f a -> c (ConstF e f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (ConstF e f a) # toConstr :: ConstF e f a -> Constr # dataTypeOf :: ConstF e f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (ConstF e f a)) # dataCast2 :: Typeable t => (forall d e0. (Data d, Data e0) => c (t d e0)) -> Maybe (c (ConstF e f a)) # gmapT :: (forall b. Data b => b -> b) -> ConstF e f a -> ConstF e f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> ConstF e f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> ConstF e f a -> r # gmapQ :: (forall d. Data d => d -> u) -> ConstF e f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> ConstF e f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> ConstF e f a -> m (ConstF e f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> ConstF e f a -> m (ConstF e f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> ConstF e f a -> m (ConstF e f a) # | |
| Ord e => Ord (ConstF e f a) Source # | |
Defined in Data.HFunctor | |
| Read e => Read (ConstF e f a) Source # | |
| Show e => Show (ConstF e f a) Source # | |
| Generic (ConstF e f a) Source # | |
| type C (ConstF e :: (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HFunctor.Interpret | |
| type Rep (ConstF e f a) Source # | |
Defined in Data.HFunctor | |
data EnvT e (w :: Type -> Type) a #
Constructors
| EnvT e (w a) |
Instances
| ComonadTrans (EnvT e) | |
Defined in Control.Comonad.Trans.Env | |
| ComonadHoist (EnvT e) | |
| Monoid e => Interpret (EnvT e) Source # | |
| Monoid e => HBind (EnvT e :: (Type -> Type) -> Type -> Type) Source # | Combines the accumulators, Writer-style |
| Monoid e => Inject (EnvT e :: (Type -> Type) -> Type -> Type) Source # | |
| HFunctor (EnvT e :: (Type -> Type) -> Type -> Type) Source # | |
| Functor w => Functor (EnvT e w) | |
| (Monoid e, Applicative m) => Applicative (EnvT e m) | |
| Foldable w => Foldable (EnvT e w) | |
Defined in Control.Comonad.Trans.Env Methods fold :: Monoid m => EnvT e w m -> m # foldMap :: Monoid m => (a -> m) -> EnvT e w a -> m # foldr :: (a -> b -> b) -> b -> EnvT e w a -> b # foldr' :: (a -> b -> b) -> b -> EnvT e w a -> b # foldl :: (b -> a -> b) -> b -> EnvT e w a -> b # foldl' :: (b -> a -> b) -> b -> EnvT e w a -> b # foldr1 :: (a -> a -> a) -> EnvT e w a -> a # foldl1 :: (a -> a -> a) -> EnvT e w a -> a # elem :: Eq a => a -> EnvT e w a -> Bool # maximum :: Ord a => EnvT e w a -> a # minimum :: Ord a => EnvT e w a -> a # | |
| Traversable w => Traversable (EnvT e w) | |
Defined in Control.Comonad.Trans.Env | |
| Comonad w => Comonad (EnvT e w) | |
| (Semigroup e, ComonadApply w) => ComonadApply (EnvT e w) | |
| (Semigroup e, Apply w) => Apply (EnvT e w) | |
| (Data e, Typeable w, Data (w a), Data a) => Data (EnvT e w a) | |
Defined in Control.Comonad.Trans.Env Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> EnvT e w a -> c (EnvT e w a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (EnvT e w a) # toConstr :: EnvT e w a -> Constr # dataTypeOf :: EnvT e w a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (EnvT e w a)) # dataCast2 :: Typeable t => (forall d e0. (Data d, Data e0) => c (t d e0)) -> Maybe (c (EnvT e w a)) # gmapT :: (forall b. Data b => b -> b) -> EnvT e w a -> EnvT e w a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> EnvT e w a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> EnvT e w a -> r # gmapQ :: (forall d. Data d => d -> u) -> EnvT e w a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> EnvT e w a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> EnvT e w a -> m (EnvT e w a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> EnvT e w a -> m (EnvT e w a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> EnvT e w a -> m (EnvT e w a) # | |
| type C (EnvT e) Source # | |
Defined in Data.HFunctor.Interpret | |
newtype ReaderT r (m :: k -> Type) (a :: k) :: forall k. Type -> (k -> Type) -> k -> Type #
The reader monad transformer, which adds a read-only environment to the given monad.
The return function ignores the environment, while >>= passes
the inherited environment to both subcomputations.
Constructors
| ReaderT | |
Fields
| |
Instances
An f a, along with a Bool flag
Flaggedf a ~ (Bool, f a) Flagged f ~ ((,) Bool):.:f -- functor composition
Creation with inject or pure uses False as the
boolean.
You can think of it as an f a that is "flagged" with a boolean value,
and that value can indicuate whether or not it is "pure" (made with
inject or pure) as False, or "impure"
(made from some other source) as True. However, False may be always
created directly, of course, using the constructor.
You can think of it like a Step that is either 0 or 1, as well.
interpreting it requires no constraint on the
target context.
This type is equivalent (along with its instances) to:
Constructors
| Flagged | |
Fields
| |
Instances
| HFunctor (Flagged :: (k -> Type) -> k -> Type) Source # | |
| HBind (Flagged :: (k -> Type) -> k -> Type) Source # | |
| Inject (Flagged :: (k -> Type) -> k -> Type) Source # | Injects with |
| Interpret (Flagged :: (Type -> Type) -> Type -> Type) Source # | |
| Functor f => Functor (Flagged f) Source # | |
| Applicative f => Applicative (Flagged f) Source # | |
Defined in Control.Applicative.Step | |
| Foldable f => Foldable (Flagged f) Source # | |
Defined in Control.Applicative.Step Methods fold :: Monoid m => Flagged f m -> m # foldMap :: Monoid m => (a -> m) -> Flagged f a -> m # foldr :: (a -> b -> b) -> b -> Flagged f a -> b # foldr' :: (a -> b -> b) -> b -> Flagged f a -> b # foldl :: (b -> a -> b) -> b -> Flagged f a -> b # foldl' :: (b -> a -> b) -> b -> Flagged f a -> b # foldr1 :: (a -> a -> a) -> Flagged f a -> a # foldl1 :: (a -> a -> a) -> Flagged f a -> a # toList :: Flagged f a -> [a] # length :: Flagged f a -> Int # elem :: Eq a => a -> Flagged f a -> Bool # maximum :: Ord a => Flagged f a -> a # minimum :: Ord a => Flagged f a -> a # | |
| Traversable f => Traversable (Flagged f) Source # | |
Defined in Control.Applicative.Step | |
| Eq1 f => Eq1 (Flagged f) Source # | |
| Ord1 f => Ord1 (Flagged f) Source # | |
Defined in Control.Applicative.Step | |
| Read1 f => Read1 (Flagged f) Source # | |
Defined in Control.Applicative.Step | |
| Show1 f => Show1 (Flagged f) Source # | |
| Foldable1 f => Foldable1 (Flagged f) Source # | |
| Pointed f => Pointed (Flagged f) Source # | |
Defined in Control.Applicative.Step | |
| Traversable1 f => Traversable1 (Flagged f) Source # | |
| Eq (f a) => Eq (Flagged f a) Source # | |
| (Typeable a, Typeable f, Typeable k, Data (f a)) => Data (Flagged f a) Source # | |
Defined in Control.Applicative.Step Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Flagged f a -> c (Flagged f a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Flagged f a) # toConstr :: Flagged f a -> Constr # dataTypeOf :: Flagged f a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Flagged f a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Flagged f a)) # gmapT :: (forall b. Data b => b -> b) -> Flagged f a -> Flagged f a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Flagged f a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Flagged f a -> r # gmapQ :: (forall d. Data d => d -> u) -> Flagged f a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Flagged f a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Flagged f a -> m (Flagged f a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Flagged f a -> m (Flagged f a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Flagged f a -> m (Flagged f a) # | |
| Ord (f a) => Ord (Flagged f a) Source # | |
Defined in Control.Applicative.Step | |
| Read (f a) => Read (Flagged f a) Source # | |
| Show (f a) => Show (Flagged f a) Source # | |
| Generic (Flagged f a) Source # | |
| type C (Flagged :: (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HFunctor.Interpret type C (Flagged :: (Type -> Type) -> Type -> Type) = (Unconstrained :: (Type -> Type) -> Constraint) | |
| type Rep (Flagged f a) Source # | |
Defined in Control.Applicative.Step type Rep (Flagged f a) = D1 (MetaData "Flagged" "Control.Applicative.Step" "functor-combinators-0.1.1.1-B2oyFu2GVTM8ySAuzVPoNk" False) (C1 (MetaCons "Flagged" PrefixI True) (S1 (MetaSel (Just "flaggedFlag") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Bool) :*: S1 (MetaSel (Just "flaggedVal") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a)))) | |
newtype IdentityT (f :: k -> Type) (a :: k) :: forall k. (k -> Type) -> k -> Type #
The trivial monad transformer, which maps a monad to an equivalent monad.
Constructors
| IdentityT | |
Fields
| |
Instances
Void2 a ba and b.
Instances
| HFunctor (Void2 :: (k1 -> Type) -> k2 -> Type) Source # | |
| Functor (Void2 a :: Type -> Type) Source # | |
| Foldable (Void2 a :: Type -> Type) Source # | |
Defined in Control.Applicative.Step Methods fold :: Monoid m => Void2 a m -> m # foldMap :: Monoid m => (a0 -> m) -> Void2 a a0 -> m # foldr :: (a0 -> b -> b) -> b -> Void2 a a0 -> b # foldr' :: (a0 -> b -> b) -> b -> Void2 a a0 -> b # foldl :: (b -> a0 -> b) -> b -> Void2 a a0 -> b # foldl' :: (b -> a0 -> b) -> b -> Void2 a a0 -> b # foldr1 :: (a0 -> a0 -> a0) -> Void2 a a0 -> a0 # foldl1 :: (a0 -> a0 -> a0) -> Void2 a a0 -> a0 # toList :: Void2 a a0 -> [a0] # elem :: Eq a0 => a0 -> Void2 a a0 -> Bool # maximum :: Ord a0 => Void2 a a0 -> a0 # minimum :: Ord a0 => Void2 a a0 -> a0 # | |
| Traversable (Void2 a :: Type -> Type) Source # | |
Defined in Control.Applicative.Step | |
| Eq1 (Void2 a :: Type -> Type) Source # | |
| Ord1 (Void2 a :: Type -> Type) Source # | |
Defined in Control.Applicative.Step | |
| Read1 (Void2 a :: Type -> Type) Source # | |
Defined in Control.Applicative.Step Methods liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Void2 a a0) # liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Void2 a a0] # liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Void2 a a0) # liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Void2 a a0] # | |
| Show1 (Void2 a :: Type -> Type) Source # | |
| Apply (Void2 a :: Type -> Type) Source # | |
| Alt (Void2 a :: Type -> Type) Source # | |
| Bind (Void2 a :: Type -> Type) Source # | |
| Eq (Void2 a b) Source # | |
| (Typeable a, Typeable b, Typeable k1, Typeable k2) => Data (Void2 a b) Source # | |
Defined in Control.Applicative.Step Methods gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Void2 a b -> c (Void2 a b) # gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Void2 a b) # toConstr :: Void2 a b -> Constr # dataTypeOf :: Void2 a b -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Void2 a b)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Void2 a b)) # gmapT :: (forall b0. Data b0 => b0 -> b0) -> Void2 a b -> Void2 a b # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Void2 a b -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Void2 a b -> r # gmapQ :: (forall d. Data d => d -> u) -> Void2 a b -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Void2 a b -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Void2 a b -> m (Void2 a b) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Void2 a b -> m (Void2 a b) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Void2 a b -> m (Void2 a b) # | |
| Ord (Void2 a b) Source # | |
| Read (Void2 a b) Source # | |
| Show (Void2 a b) Source # | |
| Generic (Void2 a b) Source # | |
| Semigroup (Void2 a b) Source # | |
| type Rep (Void2 a b) Source # | |
A simple way to inject/reject into any eventual typeclass.
In a way, this is the "ultimate" multi-purpose Interpret instance.
You can use this to inject an f into a free structure of any
typeclass. If you want f to have a Monad instance, for example,
just use
inject:: f a ->FinalMonadf a
When you want to eventually interpret out the data, use:
interpret:: (f~>g) ->Finalc f a -> g a
Essentially, Final cFinal MonadMonad, etc.
Final can theoretically replace Ap, Ap1, ListF, NonEmptyF,
MaybeF, Free, Identity, Coyoneda, and
other instances of FreeOf, if you don't care about being able to
pattern match on explicit structure.
However, it cannot replace Interpret instances that are not free
structures, like Step,
Steps,
Backwards, etc.
Note that this doesn't have instances for all the typeclasses you
could lift things into; you probably have to define your own if you want
to use Final cc (using liftFinal0,
liftFinal1, liftFinal2 for help).
Instances
class Interpret t => FreeOf c t | t -> c where Source #
A typeclass associating a free structure with the typeclass it is free on.
This essentially lists instances of Interpret where a "trip" through
Final will leave it unchanged.
fromFree.toFree== idtoFree.fromFree== id
This can be useful because Final doesn't have a concrete structure
that you can pattern match on and inspect, but t might. This lets you
work on a concrete structure if you desire.
Minimal complete definition
Nothing
Methods
fromFree :: t f ~> Final c f Source #
toFree :: Functor f => Final c f ~> t f Source #
Instances
| FreeOf Monad Free Source # | |
| FreeOf Functor Coyoneda Source # | |
| FreeOf Applicative Ap Source # | |
| FreeOf Applicative Ap Source # | |
| FreeOf Alternative Alt Source # | |
| FreeOf Apply Ap1 Source # | |
| FreeOf Pointed MaybeApply Source # | |
| FreeOf Pointed Lift Source # | |
| FreeOf Plus ListF Source # | |
| FreeOf Alt NonEmptyF Source # | |
| FreeOf Bind Free1 Source # | |
| FreeOf (Unconstrained :: (Type -> Type) -> Constraint) (IdentityT :: (Type -> Type) -> Type -> Type) Source # | |
newtype ComposeT (f :: (Type -> Type) -> Type -> Type) (g :: (Type -> Type) -> Type -> Type) (m :: Type -> Type) a infixr 9 #
Composition of monad transformers.
Constructors
| ComposeT infixr 9 | |
Fields
| |
Instances
| MonadRWS r w s (f (g m)) => MonadRWS r w s (ComposeT f g m) | |
Defined in Control.Monad.Trans.Compose | |
| MonadReader r (f (g m)) => MonadReader r (ComposeT f g m) | |
| MonadState s (f (g m)) => MonadState s (ComposeT f g m) | |
| MonadWriter w (f (g m)) => MonadWriter w (ComposeT f g m) | |
| MonadError e (f (g m)) => MonadError e (ComposeT f g m) | |
Defined in Control.Monad.Trans.Compose Methods throwError :: e -> ComposeT f g m a # catchError :: ComposeT f g m a -> (e -> ComposeT f g m a) -> ComposeT f g m a # | |
| (HFunctor s, HFunctor t) => HFunctor (ComposeT s t :: (Type -> Type) -> Type -> Type) Source # | |
| (MFunctor f, MFunctor g, forall (m :: Type -> Type). Monad m => Monad (g m)) => MFunctor (ComposeT f g :: (Type -> Type) -> Type -> Type) | |
| (Inject s, Inject t) => Inject (ComposeT s t :: (Type -> Type) -> Type -> Type) Source # | |
| (MFunctor f, MonadTrans f, MonadTrans g) => MonadTrans (ComposeT f g) | |
Defined in Control.Monad.Trans.Compose | |
| (Interpret s, Interpret t) => Interpret (ComposeT s t) Source # | |
| Monad (f (g m)) => Monad (ComposeT f g m) | |
| Functor (f (g m)) => Functor (ComposeT f g m) | |
| MonadFail (f (g m)) => MonadFail (ComposeT f g m) | |
Defined in Control.Monad.Trans.Compose | |
| Applicative (f (g m)) => Applicative (ComposeT f g m) | |
Defined in Control.Monad.Trans.Compose Methods pure :: a -> ComposeT f g m a # (<*>) :: ComposeT f g m (a -> b) -> ComposeT f g m a -> ComposeT f g m b # liftA2 :: (a -> b -> c) -> ComposeT f g m a -> ComposeT f g m b -> ComposeT f g m c # (*>) :: ComposeT f g m a -> ComposeT f g m b -> ComposeT f g m b # (<*) :: ComposeT f g m a -> ComposeT f g m b -> ComposeT f g m a # | |
| Foldable (f (g m)) => Foldable (ComposeT f g m) | |
Defined in Control.Monad.Trans.Compose Methods fold :: Monoid m0 => ComposeT f g m m0 -> m0 # foldMap :: Monoid m0 => (a -> m0) -> ComposeT f g m a -> m0 # foldr :: (a -> b -> b) -> b -> ComposeT f g m a -> b # foldr' :: (a -> b -> b) -> b -> ComposeT f g m a -> b # foldl :: (b -> a -> b) -> b -> ComposeT f g m a -> b # foldl' :: (b -> a -> b) -> b -> ComposeT f g m a -> b # foldr1 :: (a -> a -> a) -> ComposeT f g m a -> a # foldl1 :: (a -> a -> a) -> ComposeT f g m a -> a # toList :: ComposeT f g m a -> [a] # null :: ComposeT f g m a -> Bool # length :: ComposeT f g m a -> Int # elem :: Eq a => a -> ComposeT f g m a -> Bool # maximum :: Ord a => ComposeT f g m a -> a # minimum :: Ord a => ComposeT f g m a -> a # | |
| Traversable (f (g m)) => Traversable (ComposeT f g m) | |
Defined in Control.Monad.Trans.Compose Methods traverse :: Applicative f0 => (a -> f0 b) -> ComposeT f g m a -> f0 (ComposeT f g m b) # sequenceA :: Applicative f0 => ComposeT f g m (f0 a) -> f0 (ComposeT f g m a) # mapM :: Monad m0 => (a -> m0 b) -> ComposeT f g m a -> m0 (ComposeT f g m b) # sequence :: Monad m0 => ComposeT f g m (m0 a) -> m0 (ComposeT f g m a) # | |
| Alternative (f (g m)) => Alternative (ComposeT f g m) | |
| MonadPlus (f (g m)) => MonadPlus (ComposeT f g m) | |
| MonadIO (f (g m)) => MonadIO (ComposeT f g m) | |
Defined in Control.Monad.Trans.Compose | |
| MonadCont (f (g m)) => MonadCont (ComposeT f g m) | |
| Eq (f (g m) a) => Eq (ComposeT f g m a) | |
| Ord (f (g m) a) => Ord (ComposeT f g m a) | |
Defined in Control.Monad.Trans.Compose Methods compare :: ComposeT f g m a -> ComposeT f g m a -> Ordering # (<) :: ComposeT f g m a -> ComposeT f g m a -> Bool # (<=) :: ComposeT f g m a -> ComposeT f g m a -> Bool # (>) :: ComposeT f g m a -> ComposeT f g m a -> Bool # (>=) :: ComposeT f g m a -> ComposeT f g m a -> Bool # max :: ComposeT f g m a -> ComposeT f g m a -> ComposeT f g m a # min :: ComposeT f g m a -> ComposeT f g m a -> ComposeT f g m a # | |
| Read (f (g m) a) => Read (ComposeT f g m a) | |
| Show (f (g m) a) => Show (ComposeT f g m a) | |
| type C (ComposeT s t) Source # | |
Multi
data Day (f :: Type -> Type) (g :: Type -> Type) a where #
The Day convolution of two covariant functors.
Constructors
| Day :: forall (f :: Type -> Type) (g :: Type -> Type) a b c. f b -> g c -> (b -> c -> a) -> Day f g a |
Instances
data ((f :: k -> Type) :*: (g :: k -> Type)) (p :: k) :: forall k. (k -> Type) -> (k -> Type) -> k -> Type infixr 6 #
Products: encode multiple arguments to constructors
Constructors
| (f p) :*: (g p) infixr 6 |
Instances
| HBifunctor ((:*:) :: (k -> Type) -> (k -> Type) -> k -> Type) Source # | |
| HFunctor ((:*:) f :: (k -> Type) -> k -> Type) Source # | |
| Generic1 (f :*: g :: k -> Type) | |
| Semigroupoidal ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HBifunctor.Associative Methods appendSF :: (SF (:*:) f :*: SF (:*:) f) ~> SF (:*:) f Source # matchSF :: Functor f => SF (:*:) f ~> (f :+: (f :*: SF (:*:) f)) Source # consSF :: (f :*: SF (:*:) f) ~> SF (:*:) f Source # toSF :: (f :*: f) ~> SF (:*:) f Source # biretract :: CS (:*:) f => (f :*: f) ~> f Source # binterpret :: CS (:*:) h => (f ~> h) -> (g ~> h) -> (f :*: g) ~> h Source # | |
| Associative ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Matchable ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Monoidal ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HBifunctor.Tensor Methods appendMF :: (MF (:*:) f :*: MF (:*:) f) ~> MF (:*:) f Source # splitSF :: SF (:*:) f ~> (f :*: MF (:*:) f) Source # splittingMF :: MF (:*:) f <~> (I (:*:) :+: (f :*: MF (:*:) f)) Source # toMF :: (f :*: f) ~> MF (:*:) f Source # fromSF :: SF (:*:) f ~> MF (:*:) f Source # pureT :: CM (:*:) f => I (:*:) ~> f Source # upgradeC :: CM (:*:) f => proxy f -> (CS (:*:) f -> r) -> r Source # | |
| Tensor ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Plus f => HBind ((:*:) f :: (Type -> Type) -> Type -> Type) Source # | |
| Plus f => Inject ((:*:) f :: (Type -> Type) -> Type -> Type) Source # | Only uses |
| Plus f => Interpret ((:*:) f) Source # | |
| (Monad f, Monad g) => Monad (f :*: g) | Since: base-4.9.0.0 |
| (Functor f, Functor g) => Functor (f :*: g) | Since: base-4.9.0.0 |
| (MonadFix f, MonadFix g) => MonadFix (f :*: g) | Since: base-4.9.0.0 |
Defined in Control.Monad.Fix | |
| (Applicative f, Applicative g) => Applicative (f :*: g) | Since: base-4.9.0.0 |
| (Foldable f, Foldable g) => Foldable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :*: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :*: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :*: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :*: g) a -> b # foldr1 :: (a -> a -> a) -> (f :*: g) a -> a # foldl1 :: (a -> a -> a) -> (f :*: g) a -> a # toList :: (f :*: g) a -> [a] # length :: (f :*: g) a -> Int # elem :: Eq a => a -> (f :*: g) a -> Bool # maximum :: Ord a => (f :*: g) a -> a # minimum :: Ord a => (f :*: g) a -> a # | |
| (Traversable f, Traversable g) => Traversable (f :*: g) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| (Contravariant f, Contravariant g) => Contravariant (f :*: g) | |
| (Representable f, Representable g) => Representable (f :*: g) | |
| (Alternative f, Alternative g) => Alternative (f :*: g) | Since: base-4.9.0.0 |
| (MonadPlus f, MonadPlus g) => MonadPlus (f :*: g) | Since: base-4.9.0.0 |
| (Foldable1 f, Foldable1 g) => Foldable1 (f :*: g) | |
| (Apply f, Apply g) => Apply (f :*: g) | |
| (Pointed f, Pointed g) => Pointed (f :*: g) | |
Defined in Data.Pointed | |
| (Traversable1 f, Traversable1 g) => Traversable1 (f :*: g) | |
| (Plus f, Plus g) => Plus (f :*: g) | |
Defined in Data.Functor.Plus | |
| (Alt f, Alt g) => Alt (f :*: g) | |
| (GIndex f, GIndex g) => GIndex (f :*: g) | |
Defined in Data.Functor.Rep | |
| (GTabulate f, GTabulate g) => GTabulate (f :*: g) | |
Defined in Data.Functor.Rep Methods gtabulate' :: (GRep' (f :*: g) -> a) -> (f :*: g) a | |
| (GDefault a, GDefault b) => GDefault (a :*: b) | |
Defined in Data.Default.Class | |
| (Eq (f p), Eq (g p)) => Eq ((f :*: g) p) | Since: base-4.7.0.0 |
| (Typeable f, Typeable g, Data p, Data (f p), Data (g p)) => Data ((f :*: g) p) | Since: base-4.9.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> (f :*: g) p -> c ((f :*: g) p) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c ((f :*: g) p) # toConstr :: (f :*: g) p -> Constr # dataTypeOf :: (f :*: g) p -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c ((f :*: g) p)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c ((f :*: g) p)) # gmapT :: (forall b. Data b => b -> b) -> (f :*: g) p -> (f :*: g) p # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (f :*: g) p -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (f :*: g) p -> r # gmapQ :: (forall d. Data d => d -> u) -> (f :*: g) p -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> (f :*: g) p -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> (f :*: g) p -> m ((f :*: g) p) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (f :*: g) p -> m ((f :*: g) p) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (f :*: g) p -> m ((f :*: g) p) # | |
| (Ord (f p), Ord (g p)) => Ord ((f :*: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| (Read (f p), Read (g p)) => Read ((f :*: g) p) | Since: base-4.7.0.0 |
| (Show (f p), Show (g p)) => Show ((f :*: g) p) | Since: base-4.7.0.0 |
| Generic ((f :*: g) p) | |
| (Semigroup (f p), Semigroup (g p)) => Semigroup ((f :*: g) p) | Since: base-4.12.0.0 |
| (Monoid (f p), Monoid (g p)) => Monoid ((f :*: g) p) | Since: base-4.12.0.0 |
| type Rep1 (f :*: g :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics type Rep1 (f :*: g :: k -> Type) = D1 (MetaData ":*:" "GHC.Generics" "base" False) (C1 (MetaCons ":*:" (InfixI RightAssociative 6) False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 g))) | |
| type SF ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| type MF ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| type I ((:*:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| type C ((:*:) f) Source # | |
Defined in Data.HFunctor.Interpret | |
| type Rep (f :*: g) | |
| type GRep' (f :*: g) | |
Defined in Data.Functor.Rep | |
| type Rep ((f :*: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics type Rep ((f :*: g) p) = D1 (MetaData ":*:" "GHC.Generics" "base" False) (C1 (MetaCons ":*:" (InfixI RightAssociative 6) False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f p)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (g p)))) | |
data ((f :: k -> Type) :+: (g :: k -> Type)) (p :: k) :: forall k. (k -> Type) -> (k -> Type) -> k -> Type infixr 5 #
Sums: encode choice between constructors
Instances
| HBifunctor ((:+:) :: (k -> Type) -> (k -> Type) -> k -> Type) Source # | |
| HFunctor ((:+:) f :: (k -> Type) -> k -> Type) Source # | |
| HBind ((:+:) f :: (k -> Type) -> k -> Type) Source # | |
| Inject ((:+:) f :: (k -> Type) -> k -> Type) Source # | |
| Generic1 (f :+: g :: k -> Type) | |
| (GSum arity a, GSum arity b) => GSum arity (a :+: b) | |
| Semigroupoidal ((:+:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HBifunctor.Associative Methods appendSF :: (SF (:+:) f :+: SF (:+:) f) ~> SF (:+:) f Source # matchSF :: Functor f => SF (:+:) f ~> (f :+: (f :+: SF (:+:) f)) Source # consSF :: (f :+: SF (:+:) f) ~> SF (:+:) f Source # toSF :: (f :+: f) ~> SF (:+:) f Source # biretract :: CS (:+:) f => (f :+: f) ~> f Source # binterpret :: CS (:+:) h => (f ~> h) -> (g ~> h) -> (f :+: g) ~> h Source # | |
| Associative ((:+:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Matchable ((:+:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Monoidal ((:+:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HBifunctor.Tensor Methods appendMF :: (MF (:+:) f :+: MF (:+:) f) ~> MF (:+:) f Source # splitSF :: SF (:+:) f ~> (f :+: MF (:+:) f) Source # splittingMF :: MF (:+:) f <~> (I (:+:) :+: (f :+: MF (:+:) f)) Source # toMF :: (f :+: f) ~> MF (:+:) f Source # fromSF :: SF (:+:) f ~> MF (:+:) f Source # pureT :: CM (:+:) f => I (:+:) ~> f Source # upgradeC :: CM (:+:) f => proxy f -> (CS (:+:) f -> r) -> r Source # | |
| Tensor ((:+:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Interpret ((:+:) f) Source # | Technically, |
| (Functor f, Functor g) => Functor (f :+: g) | Since: base-4.9.0.0 |
| (Foldable f, Foldable g) => Foldable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => (f :+: g) m -> m # foldMap :: Monoid m => (a -> m) -> (f :+: g) a -> m # foldr :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldr' :: (a -> b -> b) -> b -> (f :+: g) a -> b # foldl :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldl' :: (b -> a -> b) -> b -> (f :+: g) a -> b # foldr1 :: (a -> a -> a) -> (f :+: g) a -> a # foldl1 :: (a -> a -> a) -> (f :+: g) a -> a # toList :: (f :+: g) a -> [a] # length :: (f :+: g) a -> Int # elem :: Eq a => a -> (f :+: g) a -> Bool # maximum :: Ord a => (f :+: g) a -> a # minimum :: Ord a => (f :+: g) a -> a # | |
| (Traversable f, Traversable g) => Traversable (f :+: g) | Since: base-4.9.0.0 |
Defined in Data.Traversable | |
| (Contravariant f, Contravariant g) => Contravariant (f :+: g) | |
| (Foldable1 f, Foldable1 g) => Foldable1 (f :+: g) | |
| (Traversable1 f, Traversable1 g) => Traversable1 (f :+: g) | |
| (SumSize a, SumSize b) => SumSize (a :+: b) | |
Defined in Data.Hashable.Generic.Instances | |
| (GSumGet a, GSumGet b) => GSumGet (a :+: b) | |
| (SumSize a, SumSize b) => SumSize (a :+: b) | |
Defined in Data.Binary.Generic | |
| (GSumPut a, GSumPut b) => GSumPut (a :+: b) | |
| (Eq (f p), Eq (g p)) => Eq ((f :+: g) p) | Since: base-4.7.0.0 |
| (Typeable f, Typeable g, Data p, Data (f p), Data (g p)) => Data ((f :+: g) p) | Since: base-4.9.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> (f :+: g) p -> c ((f :+: g) p) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c ((f :+: g) p) # toConstr :: (f :+: g) p -> Constr # dataTypeOf :: (f :+: g) p -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c ((f :+: g) p)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c ((f :+: g) p)) # gmapT :: (forall b. Data b => b -> b) -> (f :+: g) p -> (f :+: g) p # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> (f :+: g) p -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> (f :+: g) p -> r # gmapQ :: (forall d. Data d => d -> u) -> (f :+: g) p -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> (f :+: g) p -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> (f :+: g) p -> m ((f :+: g) p) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> (f :+: g) p -> m ((f :+: g) p) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> (f :+: g) p -> m ((f :+: g) p) # | |
| (Ord (f p), Ord (g p)) => Ord ((f :+: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics | |
| (Read (f p), Read (g p)) => Read ((f :+: g) p) | Since: base-4.7.0.0 |
| (Show (f p), Show (g p)) => Show ((f :+: g) p) | Since: base-4.7.0.0 |
| Generic ((f :+: g) p) | |
| type Rep1 (f :+: g :: k -> Type) | Since: base-4.9.0.0 |
Defined in GHC.Generics type Rep1 (f :+: g :: k -> Type) = D1 (MetaData ":+:" "GHC.Generics" "base" False) (C1 (MetaCons "L1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)) :+: C1 (MetaCons "R1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 g))) | |
| type SF ((:+:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| type MF ((:+:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| type I ((:+:) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| type C ((:+:) f) Source # | |
Defined in Data.HFunctor.Interpret | |
| type Rep ((f :+: g) p) | Since: base-4.7.0.0 |
Defined in GHC.Generics type Rep ((f :+: g) p) = D1 (MetaData ":+:" "GHC.Generics" "base" False) (C1 (MetaCons "L1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f p))) :+: C1 (MetaCons "R1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (g p)))) | |
data V1 (p :: k) :: forall k. k -> Type #
Void: used for datatypes without constructors
Instances
| Generic1 (V1 :: k -> Type) | |
| Functor (V1 :: Type -> Type) | Since: base-4.9.0.0 |
| Foldable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
Defined in Data.Foldable Methods fold :: Monoid m => V1 m -> m # foldMap :: Monoid m => (a -> m) -> V1 a -> m # foldr :: (a -> b -> b) -> b -> V1 a -> b # foldr' :: (a -> b -> b) -> b -> V1 a -> b # foldl :: (b -> a -> b) -> b -> V1 a -> b # foldl' :: (b -> a -> b) -> b -> V1 a -> b # foldr1 :: (a -> a -> a) -> V1 a -> a # foldl1 :: (a -> a -> a) -> V1 a -> a # elem :: Eq a => a -> V1 a -> Bool # maximum :: Ord a => V1 a -> a # | |
| Traversable (V1 :: Type -> Type) | Since: base-4.9.0.0 |
| Contravariant (V1 :: Type -> Type) | |
| Foldable1 (V1 :: Type -> Type) | |
| Apply (V1 :: Type -> Type) | |
| Traversable1 (V1 :: Type -> Type) | |
| Alt (V1 :: Type -> Type) | |
| Bind (V1 :: Type -> Type) | |
| Eq (V1 p) | Since: base-4.9.0.0 |
| Data p => Data (V1 p) | Since: base-4.9.0.0 |
Defined in Data.Data Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> V1 p -> c (V1 p) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (V1 p) # dataTypeOf :: V1 p -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (V1 p)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (V1 p)) # gmapT :: (forall b. Data b => b -> b) -> V1 p -> V1 p # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> V1 p -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> V1 p -> r # gmapQ :: (forall d. Data d => d -> u) -> V1 p -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> V1 p -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> V1 p -> m (V1 p) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> V1 p -> m (V1 p) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> V1 p -> m (V1 p) # | |
| Ord (V1 p) | Since: base-4.9.0.0 |
| Read (V1 p) | Since: base-4.9.0.0 |
| Show (V1 p) | Since: base-4.9.0.0 |
| Generic (V1 p) | |
| Semigroup (V1 p) | Since: base-4.12.0.0 |
| type Rep1 (V1 :: k -> Type) | Since: base-4.9.0.0 |
| type Rep (V1 p) | Since: base-4.9.0.0 |
data These1 (f :: Type -> Type) (g :: Type -> Type) a #
Instances
| Semigroupoidal These1 Source # | Ideally here |
Defined in Data.HBifunctor.Associative Methods appendSF :: These1 (SF These1 f) (SF These1 f) ~> SF These1 f Source # matchSF :: Functor f => SF These1 f ~> (f :+: These1 f (SF These1 f)) Source # consSF :: These1 f (SF These1 f) ~> SF These1 f Source # toSF :: These1 f f ~> SF These1 f Source # biretract :: CS These1 f => These1 f f ~> f Source # binterpret :: CS These1 h => (f ~> h) -> (g ~> h) -> These1 f g ~> h Source # | |
| Associative These1 Source # | |
| Monoidal These1 Source # | |
Defined in Data.HBifunctor.Tensor Methods appendMF :: These1 (MF These1 f) (MF These1 f) ~> MF These1 f Source # splitSF :: SF These1 f ~> These1 f (MF These1 f) Source # splittingMF :: MF These1 f <~> (I These1 :+: These1 f (MF These1 f)) Source # toMF :: These1 f f ~> MF These1 f Source # fromSF :: SF These1 f ~> MF These1 f Source # pureT :: CM These1 f => I These1 ~> f Source # upgradeC :: CM These1 f => proxy f -> (CS These1 f -> r) -> r Source # | |
| Tensor These1 Source # | |
| Interpret (These1 f) Source # | Technically, |
| Alt f => HBind (These1 f :: (Type -> Type) -> Type -> Type) Source # | |
| Inject (These1 f :: (Type -> Type) -> Type -> Type) Source # | |
| HFunctor (These1 f :: (Type -> Type) -> Type -> Type) Source # | |
| HBifunctor These1 Source # | |
| Generic1 (These1 f g :: Type -> Type) | |
| (Functor f, Functor g) => Functor (These1 f g) | |
| (Foldable f, Foldable g) => Foldable (These1 f g) | |
Defined in Data.Functor.These Methods fold :: Monoid m => These1 f g m -> m # foldMap :: Monoid m => (a -> m) -> These1 f g a -> m # foldr :: (a -> b -> b) -> b -> These1 f g a -> b # foldr' :: (a -> b -> b) -> b -> These1 f g a -> b # foldl :: (b -> a -> b) -> b -> These1 f g a -> b # foldl' :: (b -> a -> b) -> b -> These1 f g a -> b # foldr1 :: (a -> a -> a) -> These1 f g a -> a # foldl1 :: (a -> a -> a) -> These1 f g a -> a # toList :: These1 f g a -> [a] # null :: These1 f g a -> Bool # length :: These1 f g a -> Int # elem :: Eq a => a -> These1 f g a -> Bool # maximum :: Ord a => These1 f g a -> a # minimum :: Ord a => These1 f g a -> a # | |
| (Traversable f, Traversable g) => Traversable (These1 f g) | |
Defined in Data.Functor.These | |
| (Arbitrary1 f, Arbitrary1 g) => Arbitrary1 (These1 f g) | |
Defined in Data.Functor.These Methods liftArbitrary :: Gen a -> Gen (These1 f g a) # liftShrink :: (a -> [a]) -> These1 f g a -> [These1 f g a] # | |
| (ToJSON1 f, ToJSON1 g) => ToJSON1 (These1 f g) | |
Defined in Data.Functor.These Methods liftToJSON :: (a -> Value) -> ([a] -> Value) -> These1 f g a -> Value # liftToJSONList :: (a -> Value) -> ([a] -> Value) -> [These1 f g a] -> Value # liftToEncoding :: (a -> Encoding) -> ([a] -> Encoding) -> These1 f g a -> Encoding # liftToEncodingList :: (a -> Encoding) -> ([a] -> Encoding) -> [These1 f g a] -> Encoding # | |
| (FromJSON1 f, FromJSON1 g) => FromJSON1 (These1 f g) | |
| (Eq1 f, Eq1 g) => Eq1 (These1 f g) | |
| (Ord1 f, Ord1 g) => Ord1 (These1 f g) | |
Defined in Data.Functor.These | |
| (Read1 f, Read1 g) => Read1 (These1 f g) | |
Defined in Data.Functor.These Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (These1 f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [These1 f g a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (These1 f g a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [These1 f g a] # | |
| (Show1 f, Show1 g) => Show1 (These1 f g) | |
| (NFData1 f, NFData1 g) => NFData1 (These1 f g) | This instance is available only with |
Defined in Data.Functor.These | |
| (Eq1 f, Eq1 g, Eq a) => Eq (These1 f g a) | |
| (Typeable f, Typeable g, Typeable a, Data (f a), Data (g a)) => Data (These1 f g a) | |
Defined in Data.Functor.These Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> These1 f g a -> c (These1 f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (These1 f g a) # toConstr :: These1 f g a -> Constr # dataTypeOf :: These1 f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (These1 f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (These1 f g a)) # gmapT :: (forall b. Data b => b -> b) -> These1 f g a -> These1 f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> These1 f g a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> These1 f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> These1 f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> These1 f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> These1 f g a -> m (These1 f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> These1 f g a -> m (These1 f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> These1 f g a -> m (These1 f g a) # | |
| (Ord1 f, Ord1 g, Ord a) => Ord (These1 f g a) | |
Defined in Data.Functor.These | |
| (Read1 f, Read1 g, Read a) => Read (These1 f g a) | |
| (Show1 f, Show1 g, Show a) => Show (These1 f g a) | |
| Generic (These1 f g a) | |
| (Arbitrary1 f, Arbitrary1 g, Arbitrary a) => Arbitrary (These1 f g a) | |
| (ToJSON1 f, ToJSON1 g, ToJSON a) => ToJSON (These1 f g a) | |
Defined in Data.Functor.These | |
| (FromJSON1 f, FromJSON1 g, FromJSON a) => FromJSON (These1 f g a) | |
| (NFData1 f, NFData1 g, NFData a) => NFData (These1 f g a) | This instance is available only with |
Defined in Data.Functor.These | |
| type SF These1 Source # | |
| type MF These1 Source # | |
| type I These1 Source # | |
| type C (These1 f) Source # | |
Defined in Data.HFunctor.Interpret | |
| type Rep1 (These1 f g :: Type -> Type) | |
Defined in Data.Functor.These type Rep1 (These1 f g :: Type -> Type) = D1 (MetaData "These1" "Data.Functor.These" "these-1-37K73wV69xaJpdXmERtoQz" False) (C1 (MetaCons "This1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f)) :+: (C1 (MetaCons "That1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 g)) :+: C1 (MetaCons "These1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 f) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec1 g)))) | |
| type Rep (These1 f g a) | |
Defined in Data.Functor.These type Rep (These1 f g a) = D1 (MetaData "These1" "Data.Functor.These" "these-1-37K73wV69xaJpdXmERtoQz" False) (C1 (MetaCons "This1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a))) :+: (C1 (MetaCons "That1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (g a))) :+: C1 (MetaCons "These1" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (f a)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (g a))))) | |
data Comp f g a where Source #
Functor composition. Comp f g af (g a), and
the Comp pattern synonym is a way of getting the f (g a) in
a Comp f g a
For example, Maybe (IO Bool)Comp Maybe IO Bool
This is mostly useful for its typeclass instances: in particular,
Functor, Applicative, HBifunctor, and
Monoidal.
This is essentially a version of :.: and
Compose that allows for an
HBifunctor instance.
It is slightly less performant. Using comp . unCompComp value (if you have Functor f
The "free monoid" over Comp is Free, and the "free semigroup" over
Comp is Free1.
Bundled Patterns
| pattern Comp :: Functor f => f (g a) -> Comp f g a | Pattern match on and construct a |
Instances
An HBifunctor that ignores its second input. Like
a :+: with no R1/right branch.
This is Joker from Data.Bifunctors.Joker, but
given a more sensible name for its purpose.
Instances
| HBifunctor (LeftF :: (k2 -> Type) -> (k1 -> Type) -> k2 -> Type) Source # | |
| HFunctor (LeftF f :: (k -> Type) -> k -> Type) Source # | |
| Semigroupoidal (LeftF :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HBifunctor.Associative Methods appendSF :: LeftF (SF LeftF f) (SF LeftF f) ~> SF LeftF f Source # matchSF :: Functor f => SF LeftF f ~> (f :+: LeftF f (SF LeftF f)) Source # consSF :: LeftF f (SF LeftF f) ~> SF LeftF f Source # toSF :: LeftF f f ~> SF LeftF f Source # biretract :: CS LeftF f => LeftF f f ~> f Source # binterpret :: CS LeftF h => (f ~> h) -> (g ~> h) -> LeftF f g ~> h Source # | |
| Associative (LeftF :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Functor f => Bifunctor (LeftF f :: Type -> Type -> Type) Source # | |
| Traversable f => Bitraversable (LeftF f :: Type -> Type -> Type) Source # | |
Defined in Data.HBifunctor Methods bitraverse :: Applicative f0 => (a -> f0 c) -> (b -> f0 d) -> LeftF f a b -> f0 (LeftF f c d) # | |
| Foldable f => Bifoldable (LeftF f :: Type -> Type -> Type) Source # | |
| Applicative f => Biapplicative (LeftF f :: Type -> Type -> Type) Source # | |
| Functor f => Functor (LeftF f g) Source # | |
| Foldable f => Foldable (LeftF f g) Source # | |
Defined in Data.HBifunctor Methods fold :: Monoid m => LeftF f g m -> m # foldMap :: Monoid m => (a -> m) -> LeftF f g a -> m # foldr :: (a -> b -> b) -> b -> LeftF f g a -> b # foldr' :: (a -> b -> b) -> b -> LeftF f g a -> b # foldl :: (b -> a -> b) -> b -> LeftF f g a -> b # foldl' :: (b -> a -> b) -> b -> LeftF f g a -> b # foldr1 :: (a -> a -> a) -> LeftF f g a -> a # foldl1 :: (a -> a -> a) -> LeftF f g a -> a # toList :: LeftF f g a -> [a] # length :: LeftF f g a -> Int # elem :: Eq a => a -> LeftF f g a -> Bool # maximum :: Ord a => LeftF f g a -> a # minimum :: Ord a => LeftF f g a -> a # | |
| Traversable f => Traversable (LeftF f g) Source # | |
Defined in Data.HBifunctor | |
| Eq1 f => Eq1 (LeftF f g) Source # | |
| Ord1 f => Ord1 (LeftF f g) Source # | |
Defined in Data.HBifunctor | |
| Read1 f => Read1 (LeftF f g) Source # | |
Defined in Data.HBifunctor | |
| Show1 f => Show1 (LeftF f g) Source # | |
| Eq (f a) => Eq (LeftF f g a) Source # | |
| (Typeable g, Typeable a, Typeable f, Typeable k2, Typeable k1, Data (f a)) => Data (LeftF f g a) Source # | |
Defined in Data.HBifunctor Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> LeftF f g a -> c (LeftF f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (LeftF f g a) # toConstr :: LeftF f g a -> Constr # dataTypeOf :: LeftF f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (LeftF f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (LeftF f g a)) # gmapT :: (forall b. Data b => b -> b) -> LeftF f g a -> LeftF f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> LeftF f g a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> LeftF f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> LeftF f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> LeftF f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> LeftF f g a -> m (LeftF f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> LeftF f g a -> m (LeftF f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> LeftF f g a -> m (LeftF f g a) # | |
| Ord (f a) => Ord (LeftF f g a) Source # | |
Defined in Data.HBifunctor | |
| Read (f a) => Read (LeftF f g a) Source # | |
| Show (f a) => Show (LeftF f g a) Source # | |
| Generic (LeftF f g a) Source # | |
| type SF (LeftF :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| type Rep (LeftF f g a) Source # | |
Defined in Data.HBifunctor | |
An HBifunctor that ignores its first input. Like
a :+: with no L1/left branch.
In its polykinded form (on f), it is essentially a higher-order
version of Tagged.
Instances
| HBifunctor (RightF :: (k1 -> Type) -> (k2 -> Type) -> k2 -> Type) Source # | |
| HFunctor (RightF f :: (k1 -> Type) -> k1 -> Type) Source # | |
| HFunctor (RightF f :: (k -> Type) -> k -> Type) Source # | |
| HBind (RightF f :: (k1 -> Type) -> k1 -> Type) Source # | |
| Inject (RightF f :: (k1 -> Type) -> k1 -> Type) Source # | |
| Semigroupoidal (RightF :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HBifunctor.Associative Methods appendSF :: RightF (SF RightF f) (SF RightF f) ~> SF RightF f Source # matchSF :: Functor f => SF RightF f ~> (f :+: RightF f (SF RightF f)) Source # consSF :: RightF f (SF RightF f) ~> SF RightF f Source # toSF :: RightF f f ~> SF RightF f Source # biretract :: CS RightF f => RightF f f ~> f Source # binterpret :: CS RightF h => (f ~> h) -> (g ~> h) -> RightF f g ~> h Source # | |
| Associative (RightF :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| Interpret (RightF f :: (Type -> Type) -> Type -> Type) Source # | |
| Functor g => Functor (RightF f g) Source # | |
| Foldable g => Foldable (RightF f g) Source # | |
Defined in Data.HBifunctor Methods fold :: Monoid m => RightF f g m -> m # foldMap :: Monoid m => (a -> m) -> RightF f g a -> m # foldr :: (a -> b -> b) -> b -> RightF f g a -> b # foldr' :: (a -> b -> b) -> b -> RightF f g a -> b # foldl :: (b -> a -> b) -> b -> RightF f g a -> b # foldl' :: (b -> a -> b) -> b -> RightF f g a -> b # foldr1 :: (a -> a -> a) -> RightF f g a -> a # foldl1 :: (a -> a -> a) -> RightF f g a -> a # toList :: RightF f g a -> [a] # null :: RightF f g a -> Bool # length :: RightF f g a -> Int # elem :: Eq a => a -> RightF f g a -> Bool # maximum :: Ord a => RightF f g a -> a # minimum :: Ord a => RightF f g a -> a # | |
| Traversable g => Traversable (RightF f g) Source # | |
Defined in Data.HBifunctor | |
| Eq1 g => Eq1 (RightF f g) Source # | |
| Ord1 g => Ord1 (RightF f g) Source # | |
Defined in Data.HBifunctor | |
| Read1 g => Read1 (RightF f g) Source # | |
Defined in Data.HBifunctor Methods liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (RightF f g a) # liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [RightF f g a] # liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (RightF f g a) # liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [RightF f g a] # | |
| Show1 g => Show1 (RightF f g) Source # | |
| Eq (g a) => Eq (RightF f g a) Source # | |
| (Typeable f, Typeable a, Typeable g, Typeable k1, Typeable k2, Data (g a)) => Data (RightF f g a) Source # | |
Defined in Data.HBifunctor Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> RightF f g a -> c (RightF f g a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (RightF f g a) # toConstr :: RightF f g a -> Constr # dataTypeOf :: RightF f g a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (RightF f g a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (RightF f g a)) # gmapT :: (forall b. Data b => b -> b) -> RightF f g a -> RightF f g a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> RightF f g a -> r # gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> RightF f g a -> r # gmapQ :: (forall d. Data d => d -> u) -> RightF f g a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> RightF f g a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> RightF f g a -> m (RightF f g a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> RightF f g a -> m (RightF f g a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> RightF f g a -> m (RightF f g a) # | |
| Ord (g a) => Ord (RightF f g a) Source # | |
Defined in Data.HBifunctor | |
| Read (g a) => Read (RightF f g a) Source # | |
| Show (g a) => Show (RightF f g a) Source # | |
| Generic (RightF f g a) Source # | |
| type SF (RightF :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Source # | |
| type C (RightF f :: (Type -> Type) -> Type -> Type) Source # | |
Defined in Data.HBifunctor type C (RightF f :: (Type -> Type) -> Type -> Type) = (Unconstrained :: (Type -> Type) -> Constraint) | |
| type Rep (RightF f g a) Source # | |
Defined in Data.HBifunctor | |
Combinator Combinators
An "HFunctor combinator" that enhances an HFunctor with the
ability to hold a single f a. This is the higher-order analogue of
Lift.
You can think of it as a free Inject for any f.
Instances
| HFunctor t => HFunctor (HLift t :: (k -> Type) -> k -> Type) Source # | |
| (HBind t, Inject t) => HBind (HLift t :: (k -> Type) -> k -> Type) Source # | |
| HFunctor t => Inject (HLift t :: (k -> Type) -> k -> Type) Source # | |
| Interpret t => Interpret (HLift t) Source # | Never uses |
| (Functor f, Functor (t f)) => Functor (HLift t f) Source # | |
| (Eq1 (t f), Eq1 f) => Eq1 (HLift t f) Source # | |
| (Ord1 (t f), Ord1 f) => Ord1 (HLift t f) Source # | |
Defined in Data.HFunctor | |
| (Show1 (t f), Show1 f) => Show1 (HLift t f) Source # | |
| (Eq (f a), Eq (t f a)) => Eq (HLift t f a) Source # | |
| (Ord (f a), Ord (t f a)) => Ord (HLift t f a) Source # | |
Defined in Data.HFunctor | |
| (Read (f a), Read (t f a)) => Read (HLift t f a) Source # | |
| (Show (f a), Show (t f a)) => Show (HLift t f a) Source # | |
| type C (HLift t) Source # | |
Defined in Data.HFunctor.Interpret | |
An "HFunctor combinator" that turns an HFunctor into potentially
infinite nestings of that HFunctor.
An HFree t f af a, t f a, t (t f) a, t (t (t f))
a, etc.
This effectively turns t into a tree with t branches.
One particularly useful usage is with MapF. For example if you had
a data type representing a command line command parser:
data Command a
You could represent "many possible named commands" using
type Commands =MapFStringCommand
And you can represent multiple nested named commands using:
type NestedCommands =HFree(MapFString)
This has an Interpret instance, but it can be
more useful to use via direct pattern matching, or through
foldHFree::HBifunctort => f~>g -> t g ~> g -> HFree t f ~> g
which requires no extra constriant on g, and lets you consider each
branch separately.
This can be considered the higher-oder analogue of
Free; it is the free HBind for any HFunctor
t
Instances
| HFunctor t => HFunctor (HFree t :: (k -> Type) -> k -> Type) Source # | |
| HFunctor t => HBind (HFree t :: (k -> Type) -> k -> Type) Source # | |
| HFunctor t => Inject (HFree t :: (k -> Type) -> k -> Type) Source # | |
| Interpret t => Interpret (HFree t) Source # | Never uses |
| (Functor f, Functor (t (HFree t f))) => Functor (HFree t f) Source # | |
| (Show1 (t (HFree t f)), Show1 f) => Show1 (HFree t f) Source # | |
| (Show1 (t (HFree t f)), Show1 f, Show a) => Show (HFree t f a) Source # | |
| type C (HFree t) Source # | |
Defined in Data.HFunctor.Interpret | |
Util
Natural Transformations
generalize :: Applicative f => Identity ~> f Source #
Turn Identity into any Applicative fhmap, hbimap, or interpret.
It is a more general form of generalize from
mmorph.