Combinators for the Arrow type.
The ArrowSelect typeclass maps an arrow into any Traversable. The simplest instance of this is pure function type (->).
class Arrow a => ArrowSelect a where
select :: Traversable f => a b c -> a (f b) (f c)
instance ArrowSelect (->) where
select = fmap
ArrowRace provides a generic interface for some process to race against the other. This is intended for use in concurrency context with access to IO.
It is sufficient to implement the more generic combinator (///).
infixr 4 ///, \\\
class ArrowChoice a => ArrowRace a where
(///) :: a b c -> a d e -> a (b, d) (Either c e)
(\\\) :: a b c -> a b c -> a b c
a \\\ b = id &&& id >>> a /// b >>> id ||| id
The Algebraic type takes an algebraic approach to the arrow notation.
instance Arrow a => ArrowTransformer Algebraic a where
lift = Lift
Most notably the mapReduce :: Arrow a => Algebraic a b c -> Algebraic a b c combinator treats operators (***), (&&&), first and second as a way to express parallelism.
After using mapReduce you can the function algebraic to unlift the underlying arrow.
algebraic :: Arrow a => Algebraic a b c -> a b c
The most prominent operator in this namespace is dag. Its purpose to apply some arrow operation recursively from the bottom up, e.g. installing a dependency tree.
Given any recursive data type b that resembles a directed acyclic graph (DAG), there exists a value of type DAG k b, where k identifies a node uniquely.
data DAG k b = DAG (b -> k) (Lens' b (Map k b))
Picture a dependency tree with type Dependency that is already resolved and now needs installing. There exists a lens for each dependency to get and set its very own dependencies called dependencies. Then the corresponding dag value may be defined as follows:
dependencyTree :: DAG Identifier Dependency
dependencyTree = DAG (view identifier) dependencies
Now for an arrow (~>) that allows for side effects necessary for installation and an operator of type install :: Dependency ~> Dependency, you may now install the whole dependency tree by calling dag dependencyTree install :: Dependency ~> Dependency.