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| " Fixpoint computation implemented using the work list algorithm.\n This module makes writing data-flow analysis easy.\n\n One of the simplest fixpoint analysis is that of reachability.\n Given a directed graph module [G], its analysis can be implemented\n as follows:\n\n {[\n module Reachability = Graph.Fixpoint.Make(G)\n (struct\n type vertex = G.E.vertex\n type edge = G.E.t\n type g = G.t\n type data = bool\n let direction = Graph.Fixpoint.Forward\n let equal = (=)\n let join = (||)\n let analyze _ = (fun x -> x)\n end)\n ]}\n\n The types for [vertex], [edge] and [g] are those of the graph to be\n analyzed. The [data] type is [bool]: It will tell if the\n vertex is reachable from the start vertex. The [equal] operation\n for [bool] is simply structural equality; the [join] operation is\n logical or. The [analyze] function is very simple, too: If the\n predecessor vertex is reachable, so is the successor vertex of the\n edge.\n\n To use the analysis, an instance of a graph [g] is required. For\n this analysis a predicate [is_root_vertex : G.E.vertex -> bool] is\n required to initialize the reachability of the root vertex to\n [true] and of all other vertices to [false].\n\n {[\n let g = ...\n let result = Reachability.analyze is_root_vertex g\n ]}\n\n The [result] is a map of type [G.E.vertex -> bool] that can be\n queried for every vertex to tell if the vertex is reachable from\n the root vertex.\n\n @author Markus W. Weissmann\n @see \"Introduction to Lattices and Order\" B. A. Davey and H. A. Priestley, Cambridge University Press, 2002\n @see \"Fixed Point Theory\" Andrzej Granas and James Dugundji, Springer, 2003\n @see \"Principles of Program Analysis\" Flemming Nielson, Hanne Riis Nielson and Chris Hankin, Springer, 2005\n @see \"Ubersetzerbau 3: Analyse und Transformation\" Reinhard Wilhelm and Helmut Seidl, Springer, 2010\n", | |
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