package grenier

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A library to compute graph dominators using "A Simple, Fast Dominance Algorithm" by Keith D. Cooper, Timothy J. Harvey, Ken Kennedy.

Graph representation

type 'a graph = {

memoize : 'b. ('a -> 'b) -> 'a -> 'b;
(*
memoize f memoizes a function f over nodes of the graph. The function returned must evaluate f x at most once for each node x. If f raises an exception, the same exception must be propagated to the caller but it is not necessary to memoize it.
*)
successors : 'b. ('b -> 'a -> 'b) -> 'b -> 'a -> 'b;
(*
successors f acc n fold over the successors of node n, threading and updating the acc value.
*)

}

Abstraction of graphs with nodes of type 'a. Instance of graph must be provided by the user of the library.

type 'a t

Dominance information for a vertex of type 'a

val node : 'a t -> 'a

The node to which this information applies.

val dominator : 'a t -> 'a t

dominator (node n) returns the information associated to the dominator of n. If n is its own dominator, then dominator (node n) == node n.

val is_reachable : 'a t -> bool

is_reachable (node n) returns true iff n is reachable from entrypoint following the successors relation.

val postorder_index : 'a t -> int

postorder_index (node n) is the index of n in the postorder traversal of the graph (see dominance), starting from 0.

If n was not reachable from the entrypoint, post_order_index (node n) = -1

Though in this case, it is better to use is_reachable before to check the validity of the node.

val predecessors : 'a t -> 'a t list

Reverse the successors relation (on the subset of the graph reachable from entrypoint).

val dominance : 'a graph -> 'a -> 'a t array * ('a -> 'a t)

dominance graph entrypoint = (info, map) computes the dominators of graph starting from entrypoint.

The info array is indexed by the postorder index of a vertex, see postorder_index.

map n is the dominance information of node n. If n is not reachable from entrypoint, then is_reachable (map n) = false.