= The `GraphSCCFn` functor
:Author: John Reppy
:Date: {release-date}
:stem: latexmath
:source-highlighter: pygments
:VERSION: {smlnj-version}

The `GraphSCCFn` functor implements an algorithm for
calculating the strongly-connected components of a directed graph.
The resulting components are topologically-sorted; _i.e._, if a component
_A_ comes before a component _B_ in the result, then there is no
path from _B_ to _A_ (but there might be a path from _A_ to _B_).

== Synopsis

[source,sml]
------------
functor GraphSCCFn (Nd: ORD_KEY) :> GRAPH_SCC where Nd = Nd
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== Arguments

[source,sml]
------------
Nd: ORD_KEY
------------
* `Nd : xref:sig-ORD_KEY.adoc[ORD_KEY]`::
  The argument structure `Nd` defines the type of graph nodes paired with
  a comparison function that is used by the algorithm to implement finite
  maps keyed by nodes.

== Interface

[source,sml]
------------
structure Nd : ORD_KEY

type node = Nd.ord_key

datatype component
  = SIMPLE of node
  | RECURSIVE of node list

val topOrder' : digraph -> component list

val topOrder : digraph -> component list
------------

== Description

`structure Nd : ORD_KEY`::
  The argument structure.

`[.kw]#type# node = Nd.ord_key`::
  The type of a node in the graph.

`[.kw]#datatype# component`::
  The type of a component in the result.  Components are either
  `SIMPLE`, consisting of a single node, or `RECURSIVE`, consisting
  of a list of nodes that are all connected by cyclic paths.
  A single node with a self loop is represented by the `RECURSIVE`
  constructor.

`[.kw]#val# topOrder': { roots: node list, follow: node \-> node list } \-> component list`::
  `topOrder` {roots, follow}` returns a topologically-sorted list of
  strongly-connected components for a directed graph.  The graph is specified
  by a list of root nodes and a _follow_ (or _successor_) function that returns
  the list of successors for a node.  The first component in the result will
  contain the first node in the `roots` list.

`[.kw]#val# topOrder : { root: node, follow: node \-> node list } \-> component list`::
  `topOrder {root, follow}` is equivalent to the expression
[source,sml]
------------
topOrder' {roots = [root], follow = follow}
------------

== See Also

xref:smlnj-lib.adoc[__The Util Library__]
