Modulealgebraic-graphs-0.8Haskell2010

Algebra.Graph.Internal

Alga is a library for algebraic construction and manipulation of graphs in Haskell. See this paper for the motivation behind the library, the underlying theory, and implementation details.

This module defines various internal utilities and data structures used throughout the library, such as lists with fast concatenation. The API is unstable and unsafe, and is exposed only for documentation.

2 types
13 values

Packagealgebraic-graphs-0.8
Exports15
LanguageHaskell2010
LicenceMIT
SourceInternal.hs

Data structures

1 declaration

newtypenewtype List a

An abstract list data type with O(1) time concatenation (the current implementation uses difference lists). Here a is the type of list elements. List a is a Monoid: mempty corresponds to the empty list and two lists can be concatenated with mappend (or operator Data.Semigroup.<>). Singleton lists can be constructed using the function pure from the Applicative instance. List a is also an instance of IsList, therefore you can use list literals, e.g. [1,4] :: List Int is the same as pure 1 Data.Semigroup.<> pure 4; note that this requires the OverloadedLists GHC extension. To extract plain Haskell lists you can use the toList function from the Foldable instance.

Instances11Monad, Functor, Applicative, Foldable, IsList, Eq, …

Monad ListDefined in algebraic-graphs-0.8 · Algebra.Graph.Internal
Functor ListDefined in algebraic-graphs-0.8 · Algebra.Graph.Internal
Applicative ListDefined in algebraic-graphs-0.8 · Algebra.Graph.Internal
Foldable ListDefined in algebraic-graphs-0.8 · Algebra.Graph.Internal
IsList (List a)Defined in algebraic-graphs-0.8 · Algebra.Graph.Internal
Eq a => Eq (List a)Defined in algebraic-graphs-0.8 · Algebra.Graph.Internal
Ord a => Ord (List a)Defined in algebraic-graphs-0.8 · Algebra.Graph.Internal
Show a => Show (List a)Defined in algebraic-graphs-0.8 · Algebra.Graph.Internal
Semigroup (List a)Defined in algebraic-graphs-0.8 · Algebra.Graph.Internal
Monoid (List a)Defined in algebraic-graphs-0.8 · Algebra.Graph.Internal
type Item (List a) = aDefined in algebraic-graphs-0.8 · Algebra.Graph.Internal

Graph traversal

7 declarations

datadata Focus a

The focus of a graph expression is a flattened representation of the subgraph under focus, its context, as well as the list of all encountered vertices. See removeEdge for a use-case example.

Constructors

Focus
- ok :: Bool
  True if focus on the specified subgraph is obtained.
- is :: List a
  Inputs into the focused subgraph.
- os :: List a
  Outputs out of the focused subgraph.
- vs :: List a
  All vertices (leaves) of the graph expression.

valueemptyFocus :: Focus a

Focus on the empty graph.

valuevertexFocus :: (a -> Bool) -> a -> Focus a

Focus on the graph with a single vertex, given a predicate indicating whether the vertex is of interest.

valueoverlayFoci :: Focus a -> Focus a -> Focus a

Overlay two foci.

valueconnectFoci :: Focus a -> Focus a -> Focus a

Connect two foci.

valuefoldr1Safe :: (a -> a -> a) -> [a] -> Maybe a

A safe version of foldr1.

valuemaybeF :: (a -> b -> a) -> a -> Maybe b -> Maybe a

An auxiliary function that tries to apply a function to a base case and a Maybe value and returns Just the result or Just the base case.

Utilities

7 declarations

valuecartesianProductWith :: Ord c => (a -> b -> c) -> Set a -> Set b -> Set c

Compute the Cartesian product of two sets, applying a function to each resulting pair.

valuecoerce00 :: Coercible f g => f x -> g x