package mopsa

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package mopsa
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Types

type ('node_data, 'edge_data) graph

Type of graphs. Custom arbitrary data of type 'node_data and 'edge_data can be stored, respectively, in nodes and edges.

type ('node_data, 'edge_data) node

A node in the graph.

type ('node_data, 'edge_data) edge

An (hyper)-edge in the graph.

module P : P
type node_id = P.NodeId.t
type edge_id = P.EdgeId.t
type port = P.Port.t

Export back types from the functor parameter.

module NodeSet : SetExtSig.S with type elt = node_id
module EdgeSet : SetExtSig.S with type elt = edge_id

Sets constructed from ordered type parameters.

module NodeMap : MapExtSig.S with type key = node_id
module EdgeMap : MapExtSig.S with type key = edge_id

Maps constructed from ordered type parameters.

Construction

val create : unit -> ('n, 'e) graph

Creates an empty graph.

val add_node : ('n, 'e) graph -> node_id -> ?inc:(port * ('n, 'e) edge) list -> ?out:(port * ('n, 'e) edge) list -> ?entry:port -> ?exit:port -> 'n -> ('n, 'e) node

Adds a node to the graph. Optionally connects the node to incoming or outgoing edges. Optionally sets as an entry or exit node on a port (defaults to None, i.e., not entry nor exit). The node identifier must be unique among the node in the graph; raises Invalid_argument otherwise.

val add_edge : ('n, 'e) graph -> edge_id -> ?src:(port * ('n, 'e) node) list -> ?dst:(port * ('n, 'e) node) list -> 'e -> ('n, 'e) edge

Adds an edge to the graph. Optionally connects the edge to source or destination nodes. The edge identifier must be unique among the edges in the graph; raises Invalid_argument otherwise.

val remove_node : ('n, 'e) graph -> ('n, 'e) node -> unit

Removes a node if it exists in the graph; otherwise, do nothing. All connections to incoming and outgoing edges are removed.

val remove_edge : ('n, 'e) graph -> ('n, 'e) edge -> unit

Removes an edge if it exists in the graph; otherwise, do nothing. All connections to source and destination nodes are removed.

val node_set_entry : ('n, 'e) graph -> ('n, 'e) node -> port option -> unit

Sets whether a node is an entry node on some port, or not (None). A given node can be entry for a single port at a time; previous entry ports are removed.

val node_set_exit : ('n, 'e) graph -> ('n, 'e) node -> port option -> unit

Sets whether a node is an exit node on some port, or not (None). A given node can be exit on a single port at a time; previous exit ports are removed.

val node_add_in : ('n, 'e) node -> port -> ('n, 'e) edge -> unit

Adds an incoming edge to the node, on the given port. A node can be connected to the same edge several times, on different or equal ports. Use the _unique version to ensure that a node is connected to an given edge on a given port only once.

val node_add_out : ('n, 'e) node -> port -> ('n, 'e) edge -> unit

Adds an outgoing edge to the node, on the given port.

val node_add_in_list : ('n, 'e) node -> (port * ('n, 'e) edge) list -> unit

Adds incoming edges to the node, on the given ports.

val node_add_out_list : ('n, 'e) node -> (port * ('n, 'e) edge) list -> unit

Adds outgoing edges to the node, on the given ports.

val edge_add_src : ('n, 'e) edge -> port -> ('n, 'e) node -> unit

Adds a source node to the edge, on the given port.

val edge_add_dst : ('n, 'e) edge -> port -> ('n, 'e) node -> unit

Adds a destination node to the edge, on the given port.

val edge_add_src_list : ('n, 'e) edge -> (port * ('n, 'e) node) list -> unit

Adds source nodes to the edge, on the given ports.

val edge_add_dst_list : ('n, 'e) edge -> (port * ('n, 'e) node) list -> unit

Adds destination nodes to the edge, on the given ports.

val node_add_in_unique : ('n, 'e) node -> port -> ('n, 'e) edge -> unit

Adds an incoming edge to the node, on the given port, but only if not already present on this port. Does not prevent the node to be connected to the edge on other ports.

val node_add_out_unique : ('n, 'e) node -> port -> ('n, 'e) edge -> unit

Adds an outgoing edge to the node, on the given port, but only if not already present on this port.

val node_add_in_list_unique : ('n, 'e) node -> (port * ('n, 'e) edge) list -> unit

Adds incoming edges to the node, on the given ports, but only if not already present on this port.

val node_add_out_list_unique : ('n, 'e) node -> (port * ('n, 'e) edge) list -> unit

Adds outgoing edges to the node, on the given ports, but only if not already present on this port.

val edge_add_src_unique : ('n, 'e) edge -> port -> ('n, 'e) node -> unit

Adds a source node to the edge, on the given port, but only if not already present on this port.

val edge_add_dst_unique : ('n, 'e) edge -> port -> ('n, 'e) node -> unit

Adds a destination node to the edge, on the given port, but only if not already present on this port.

val edge_add_src_list_unique : ('n, 'e) edge -> (port * ('n, 'e) node) list -> unit

Adds source nodes to the edge, on the given ports, but only if not already present on this port.

val edge_add_dst_list_unique : ('n, 'e) edge -> (port * ('n, 'e) node) list -> unit

Adds destination nodes to the edge, on the given ports, but only if not already present on this port.

val node_remove_in_port : ('n, 'e) node -> port -> ('n, 'e) edge -> unit

Removes all the connections to the node incoming from the edge on the given port. No edge nor node is deleted.

val node_remove_out_port : ('n, 'e) node -> port -> ('n, 'e) edge -> unit

Removes all the connections from the node outgoing into the edge on the given port. No edge nor node is deleted.

val node_remove_in : ('n, 'e) node -> ('n, 'e) edge -> unit

Removes all the connections to the node incoming into from the edge, on all ports. No edge nor node is deleted.

val node_remove_out : ('n, 'e) node -> ('n, 'e) edge -> unit

Removes all the connections from the node incoming into the edge, on all ports. No edge nor node is deleted.

val node_remove_all_in : ('n, 'e) node -> unit

Removes all the connections incoming into the node, for all edges and ports. No edge nor node is deleted.

val node_remove_all_out : ('n, 'e) node -> unit

Removes all the connections outgoing from the node, for all edges and ports. No edge nor node is deleted.

val edge_remove_src_port : ('n, 'e) edge -> port -> ('n, 'e) node -> unit

Removes all the connections to the edge from the node on the given port. No edge nor node is deleted.

val edge_remove_dst_port : ('n, 'e) edge -> port -> ('n, 'e) node -> unit

Removes all the connections from the edge to the node on the given port. No edge nor node is deleted.

val edge_remove_src : ('n, 'e) edge -> ('n, 'e) node -> unit

Removes all the connections to the edge from the node, on all ports. No edge nor node is deleted.

val edge_remove_dst : ('n, 'e) edge -> ('n, 'e) node -> unit

Removes all the connections from the edge to the node on all ports. No edge nor node is deleted.

val edge_remove_all_src : ('n, 'e) edge -> unit

Removes all the connections at the source of the edge, for all nodes and ports. No edge nor node is deleted.

val edge_remove_all_dst : ('n, 'e) edge -> unit

Removes all the connections at the destination of the edge, for all nodes and ports. No edge nor node is deleted

val node_set_in : ('n, 'e) node -> (port * ('n, 'e) edge) list -> unit

Sets the incoming edges to the node, on the given ports.

val node_set_out : ('n, 'e) node -> (port * ('n, 'e) edge) list -> unit

Sets the outgoing edges to the node, on the given ports.

val edge_set_src : ('n, 'e) edge -> (port * ('n, 'e) node) list -> unit

Sets the source nodes to the edge, on the given ports.

val edge_set_dst : ('n, 'e) edge -> (port * ('n, 'e) node) list -> unit

Sets destination nodes to the edge, on the given ports.

val node_set_in_unique : ('n, 'e) node -> (port * ('n, 'e) edge) list -> unit

Sets the incoming edges to the node, on the given ports.

val node_set_out_unique : ('n, 'e) node -> (port * ('n, 'e) edge) list -> unit

Sets the outgoing edges to the node, on the given ports.

val edge_set_src_unique : ('n, 'e) edge -> (port * ('n, 'e) node) list -> unit

Sets the source nodes to the edge, on the given ports.

val edge_set_dst_unique : ('n, 'e) edge -> (port * ('n, 'e) node) list -> unit

Sets destination nodes to the edge, on the given ports.

Exploration

val node_list : ('n, 'e) graph -> ('n, 'e) node list

The set of nodes in the graph as a list.

val edge_list : ('n, 'e) graph -> ('n, 'e) edge list

The set of edges in the graph as a list.

val node_set : ('n, 'e) graph -> NodeSet.t

The set of nodes in the graph as a set of identifiers.

val edge_set : ('n, 'e) graph -> EdgeSet.t

The set of edges in the graph as a set of identifiers.

val node_map : ('n, 'e) graph -> ('n, 'e) node NodeMap.t

The set of nodes in the graph as a map from identifiers to nodes.

val edge_map : ('n, 'e) graph -> ('n, 'e) edge EdgeMap.t

The set of edges in the graph as a map from identifiers to edges.

val has_node : ('n, 'e) graph -> node_id -> bool

Whether the graph contains a node with this identifier.

val has_edge : ('n, 'e) graph -> edge_id -> bool

Whether the graph contains an edge with this identifier.

val get_node : ('n, 'e) graph -> node_id -> ('n, 'e) node

The node corresponding to the identifier in the graph. Raises Not_found if has_node is false.

val get_edge : ('n, 'e) graph -> edge_id -> ('n, 'e) edge

The edge corresponding to the identifier in the graph. Raises Not_found if has_edge is false.

val entries : ('n, 'e) graph -> (port * ('n, 'e) node) list

List of entry nodes, with port.

val exits : ('n, 'e) graph -> (port * ('n, 'e) node) list

List of exist nodes, with port.

val edge_id : ('n, 'e) edge -> edge_id

Edge identifier.

val edge_data : ('n, 'e) edge -> 'e

Gets custom data associated to the edge.

val edge_set_data : ('n, 'e) edge -> 'e -> unit

Sets custom data associated to the edge.

val edge_src : ('n, 'e) edge -> (port * ('n, 'e) node) list

List of edge source nodes.

val edge_dst : ('n, 'e) edge -> (port * ('n, 'e) node) list

List of edge destination nodes.

val edge_src_port : ('n, 'e) edge -> port -> ('n, 'e) node list

List of edge source nodes on the given port.

val edge_dst_port : ('n, 'e) edge -> port -> ('n, 'e) node list

List of edge destination nodes on the given port.

val edge_src_size : ('n, 'e) edge -> int

Number of edge source nodes.

val edge_dst_size : ('n, 'e) edge -> int

Number of edge destination nodes.

val edge_src_port_size : ('n, 'e) edge -> port -> int

Number of edge source nodes on the given port.

val edge_dst_port_size : ('n, 'e) edge -> port -> int

Number of edge destination nodes on the given port.

val node_id : ('n, 'e) node -> node_id

Node identifier.

val node_data : ('n, 'e) node -> 'n

Gets custom data associated to the node.

val node_set_data : ('n, 'e) node -> 'n -> unit

Sets custom data associated to the node.

val node_in : ('n, 'e) node -> (port * ('n, 'e) edge) list

List of edges incoming into the node.

val node_out : ('n, 'e) node -> (port * ('n, 'e) edge) list

List of edges outgoing from the node.

val node_in_port : ('n, 'e) node -> port -> ('n, 'e) edge list

List of edges incoming into the node on the given port.

val node_out_port : ('n, 'e) node -> port -> ('n, 'e) edge list

List of edges outgoing from the node on the given port.

val node_in_size : ('n, 'e) node -> int

Number of edges incoming into the node.

val node_out_size : ('n, 'e) node -> int

Number of edges outgoing from the node.

val node_in_port_size : ('n, 'e) node -> port -> int

Number of edges incoming into the node on the given port.

val node_out_port_size : ('n, 'e) node -> port -> int

Number of edges outgoing from the node on the given port.

val node_entry_port : ('n, 'e) graph -> ('n, 'e) node -> port option

If the node is an entry node, returns its port, otherwise None.

val node_exit_port : ('n, 'e) graph -> ('n, 'e) node -> port option

If the node is an exit node, returns its port, otherwise None.

val node_has_out : ('n, 'e) node -> ('n, 'e) edge -> bool

Whether the given edge is outgoing from the node.

val node_has_out_port : ('n, 'e) node -> port -> ('n, 'e) edge -> bool

Whether the given edge is outgoing from the node on the given port.

val node_has_in : ('n, 'e) node -> ('n, 'e) edge -> bool

Whether the given edge is incoming into the node.

val node_has_in_port : ('n, 'e) node -> port -> ('n, 'e) edge -> bool

Whether the given edge is incoming into the node on the given port.

val edge_has_src : ('n, 'e) edge -> ('n, 'e) node -> bool

Whether the edge has the node as source.

val edge_has_src_port : ('n, 'e) edge -> port -> ('n, 'e) node -> bool

Whether the edge has the node as source on the given port.

val edge_has_dst : ('n, 'e) edge -> ('n, 'e) node -> bool

Whether the edge has the node as destination.

val edge_has_dst_port : ('n, 'e) edge -> port -> ('n, 'e) node -> bool

Whether the edge has the node as destination on the given port.

val node_out_nodes : ('n, 'e) node -> (port * ('n, 'e) edge * port * ('n, 'e) node) list

Successors nodes of a given node. Each returned element (port1,edge,port2,node) gives the port port1 connecting the argument node to an edge edge, the edge edge, the port port2 connecting the edge edge to the successor node node, and finally the successor node node.

val node_in_nodes : ('n, 'e) node -> (('n, 'e) node * port * ('n, 'e) edge * port) list

Predecessor nodes of a given node. Each returned element (node,port1,edge,port2) gives the predecessor node node, the port port1 connecting it to an edge edge, the edge edge, and finally the port port2 connecting the edge edge to the argument node.

val node_out_nodes_port : ('n, 'e) node -> port -> port -> (('n, 'e) edge * ('n, 'e) node) list

Successor nodes of a given node connected through an edge on the specified ports. node_out_nodes_port node port1 port2 returns a list of (edge,node') elements, where port1 connects the argument node to an edge edge and port2 connects the edge edge to a successor node node'.

val node_in_nodes_port : ('n, 'e) node -> port -> port -> (('n, 'e) node * ('n, 'e) edge) list

Predecessor nodes of a given node connected through an edge on the specified ports. node_in_nodes_port node port1 port2 returns a list of (node',edge) elements, where port1 connects the predecessor node' to an edge edge and port2 connects the edge edge to a the argument node node.

val node_has_node_out : ('n, 'e) node -> ('n, 'e) node -> bool

Whether the first node has an outgoing edge into the second node.

val node_has_node_in : ('n, 'e) node -> ('n, 'e) node -> bool

Whether the first node has an incoming edge from the second node.

val node_has_node_out_port : ('n, 'e) node -> port -> port -> ('n, 'e) node -> bool

Whether the first node has an outgoing edge on the first port, going into the second node on the second port.

val node_has_node_in_port : ('n, 'e) node -> port -> port -> ('n, 'e) node -> bool

Whether the first node has an incoming edge on the first port, coming from the second node on the second port.

Maps and folds

val clone : ('n, 'e) graph -> ('n, 'e) graph

Creates a copy of the graph.

val clone_map : ('n1 -> 'n2) -> ('e1 -> 'e2) -> ('n1, 'e1) graph -> ('n2, 'e2) graph

Creates a copy of the graph, applying a function to each node data and each edge data.

val transpose : ('n, 'e) graph -> unit

Reverses the direction of all edges. Also switches entry and exit nodes.

val iter_nodes : (node_id -> ('n, 'e) node -> unit) -> ('n, 'e) graph -> unit

Iterates a function on all nodes. The order in which the function is called is not specified.

val iter_edges : (edge_id -> ('n, 'e) edge -> unit) -> ('n, 'e) graph -> unit

Iterates a function on all edges. The order in which the function is called is not specified.

val map_nodes : (node_id -> ('n, 'e) node -> 'a) -> ('n, 'e) graph -> 'a NodeMap.t

Constructs a map from node identifiers, applying the given function. The order in which the function is called is not specified.

val map_edges : (edge_id -> ('n, 'e) edge -> 'a) -> ('n, 'e) graph -> 'a EdgeMap.t

Constructs a map from edge identifiers, applying the given function. The order in which the function is called is not specified.

val fold_nodes : (node_id -> ('n, 'e) node -> 'a -> 'a) -> ('n, 'e) graph -> 'a -> 'a

Accumulates a function on all nodes. The order in which the function is called is not specified.

val fold_edges : (edge_id -> ('n, 'e) edge -> 'a -> 'a) -> ('n, 'e) graph -> 'a -> 'a

Accumulates a function on all edges. The order in which the function is called is not specified.

val iter_nodes_ordered : (node_id -> ('n, 'e) node -> unit) -> ('n, 'e) graph -> unit

Iterates a function on all nodes. The function is called in increasing identifier order.

val iter_edges_ordered : (edge_id -> ('n, 'e) edge -> unit) -> ('n, 'e) graph -> unit

Iterates a function on all edges. The function is called in increasing identifier order.

val map_nodes_ordered : (node_id -> ('n, 'e) node -> 'a) -> ('n, 'e) graph -> 'a NodeMap.t

Constructs a map from node identifiers, applying the given function. The function is called in increasing identifier order.

val map_edges_ordered : (edge_id -> ('n, 'e) edge -> 'a) -> ('n, 'e) graph -> 'a EdgeMap.t

Constructs a map from edge identifiers, applying the given function. The function is called in increasing identifier order.

val fold_nodes_ordered : (node_id -> ('n, 'e) node -> 'a -> 'a) -> ('n, 'e) graph -> 'a -> 'a

Accumulates a function on all nodes. The function is called in increasing identifier order.

val fold_edges_ordered : (edge_id -> ('n, 'e) edge -> 'a -> 'a) -> ('n, 'e) graph -> 'a -> 'a

Accumulates a function on all edges. The function is called in increasing identifier order.

Simplification

val remove_orphan : ('n, 'e) graph -> unit

Removes orphan nodes and edges. Orphan nodes have no incoming nor outgoing edges, and orphan edges have no source nor destination nodes.

Topological ordering

val weak_topological_order : ('n, 'e) graph -> ('n, 'e) node nested_list list

Computes a weak topological ordering suitable to perform fixpoint iterations with widening. Implements Bourdoncle's algorithm 1. 1 Francois Bourdoncle. Efficient Chaotic Iteration Strategies With Widenings. In Proc. FMPA'93, 128-141, 1993. Springer.

val widening_points : ('n, 'e) node nested_list list -> ('n, 'e) node list

Returns an adminisible list of widening points. Given a weak topological ordering, we compute the head of every component.

Printing

Print in plain text.

type ('n, 'e) printer = {
  1. print_node : Format.formatter -> ('n, 'e) node -> unit;
  2. print_edge : Format.formatter -> ('n, 'e) edge -> unit;
  3. print_src : Format.formatter -> ('n, 'e) node -> port -> ('n, 'e) edge -> unit;
  4. print_dst : Format.formatter -> ('n, 'e) edge -> port -> ('n, 'e) node -> unit;
  5. print_entry : Format.formatter -> ('n, 'e) node -> port -> unit;
  6. print_exit : Format.formatter -> ('n, 'e) node -> port -> unit;
}
val print : ('n, 'e) printer -> Format.formatter -> ('n, 'e) graph -> unit

Print in dot graph format.

type ('n, 'e) dot_printer = {
  1. dot_pp_node : Format.formatter -> ('n, 'e) node -> unit;
  2. dot_pp_edge : Format.formatter -> ('n, 'e) edge -> unit;
  3. dot_pp_port : Format.formatter -> port -> unit;
  4. dot_filter_node : ('n, 'e) node -> bool;
  5. dot_filter_edge : ('n, 'e) edge -> bool;
  6. dot_filter_port : port -> bool;
}
val print_dot : ('n, 'e) dot_printer -> string -> Format.formatter -> ('n, 'e) graph -> unit

print_dot channel graph name printer. outputs the graph in the specified channel in dot format. In addition name gives the dot graph name. The node, edge and port printer functions are user-specified.

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