Module Fixpoint

module Fixpoint: sig .. end

Fixpoint computation implemented using the work list algorithm. This module makes writing data-flow analysis easy.

One of the simplest fixpoint analysis is that of reachability. Given a directed graph module G, its analysis can be implemented as follows:

module Reachability = Graph.Fixpoint.Make(G)
(struct
  type vertex = G.E.vertex
  type edge = G.E.t
  type g = G.t
  type data = bool
  let direction = Graph.Fixpoint.Forward
  let equal = (=)
  let join = (||)
  let analyze _ = (fun x -> x)
end)

The types for vertex, edge and g are those of the graph to be analyzed. The data type is bool: It will tell if the vertex is reachable from the start vertex. The equal operation for bool is simply structural equality; the join operation is logical or. The analyze function is very simple, too: If the predecessor vertex is reachable, so is the successor vertex of the edge.

To use the analysis, an instance of a graph g is required. For this analysis a predicate is_root_vertex : G.E.vertex -> bool is required to initialize the reachability of the root vertex to true and of all other vertices to false.

    let g = ...
    let result = Reachability.analyze is_root_vertex g
    

The result is a map of type G.E.vertex -> bool that can be queried for every vertex to tell if the vertex is reachable from the root vertex.
Author(s): Markus W. Weissmann
See also

• Introduction to Lattices and Order B. A. Davey and H. A. Priestley, Cambridge University Press, 2002
• Fixed Point Theory Andrzej Granas and James Dugundji, Springer, 2003
• Principles of Program Analysis Flemming Nielson, Hanne Riis Nielson and Chris Hankin, Springer, 2005
• Ubersetzerbau 3: Analyse und Transformation Reinhard Wilhelm and Helmut Seidl, Springer, 2010

module type G = sig .. end

type direction = 

module type Analysis = sig .. end

module Make: 
functor (G : G) -> 
functor (A : Analysis  with type g = G.t  with type edge = G.E.t 
                with type vertex = G.V.t) -> sig .. end