def _check_rule_typing(hierarchy, rule_id, graph_id, lhs_mapping, rhs_mapping):
all_paths = nx.all_pairs_shortest_path(hierarchy)
paths_from_target = {}
for s in hierarchy.nodes():
if s == graph_id:
for key in all_paths[graph_id].keys():
paths_from_target[key] = all_paths[graph_id][key]
for t in paths_from_target.keys():
if t != graph_id:
new_lhs_h = compose(
lhs_mapping,
hierarchy.compose_path_typing(paths_from_target[t]))
new_rhs_h = compose(
rhs_mapping,
hierarchy.compose_path_typing(paths_from_target[t]))
try:
# find homomorphisms from s to t via other paths
s_t_paths = nx.all_shortest_paths(hierarchy, rule_id, t)
for path in s_t_paths:
lhs_h, rhs_h = hierarchy.compose_path_typing(path)
if lhs_h != new_lhs_h:
raise HierarchyError(
"Invalid lhs typing: homomorphism does not "
"commute with an existing "
"path from '%s' to '%s'!" % (s, t))
if rhs_h != new_rhs_h:
raise HierarchyError(
"Invalid rhs typing: homomorphism does not "
"commute with an existing " +
"path from '%s' to '%s'!" % (s, t))
except (nx.NetworkXNoPath):
pass
return
def __rmul__(self, other):
"""Right multiplication."""
if isinstance(other, Typing):
return RuleTyping(compose(self.lhs_mapping, other.mapping),
compose(self.rhs_mapping, other.mapping),
self.lhs_total and other.total, self.rhs_total
and other.total, self.attrs)
else:
return NotImplemented
def __mul__(self, other):
"""Multiplication operation."""
if isinstance(other, Typing):
return Typing(compose(other.mapping, self.mapping))
elif isinstance(other, RuleTyping):
return RuleTyping(compose(other.lhs_mapping, self.mapping),
compose(other.rhs_mapping, self.mapping),
other.lhs_total, other.rhs_total)
else:
return NotImplemented
def _check_consistency(hierarchy, source, target, mapping=None):
all_paths = nx.all_pairs_shortest_path(hierarchy)
paths_to_source = {}
paths_from_target = {}
for s in hierarchy.nodes():
if source in all_paths[s].keys():
paths_to_source[s] = all_paths[s][source]
if s == target:
for key in all_paths[target].keys():
paths_from_target[key] = all_paths[target][key]
for s in paths_to_source.keys():
if hierarchy._path_from_rule(paths_to_source[s]):
for t in paths_from_target.keys():
# find homomorphism from s to t via new path
if s == source:
raise HierarchyError(
"Found a rule typing some node in the hierarchy!")
new_lhs_h, new_rhs_h = hierarchy.compose_path_typing(
paths_to_source[s])
new_lhs_h = compose(new_lhs_h, mapping)
new_rhs_h = compose(new_rhs_h, mapping)
if t != target:
new_lhs_h = compose(
new_lhs_h,
hierarchy.compose_path_typing(paths_from_target[t]))
new_rhs_h = compose(
new_rhs_h,
hierarchy.compose_path_typing(paths_from_target[t]),
)
try:
# find homomorphisms from s to t via other paths
s_t_paths = nx.all_shortest_paths(hierarchy, s, t)
for path in s_t_paths:
lhs_h, rhs_h = hierarchy.compose_path_typing(path)
if lhs_h != new_lhs_h:
raise HierarchyError(
"Invalid lhs typing: homomorphism does "
"not commute with an existing " +
"path from '%s' to '%s'!" % (s, t))
if rhs_h != new_rhs_h:
raise HierarchyError(
"Invalid rhs typing: homomorphism does "
"not commute with an existing " +
"path from '%s' to '%s'!" % (s, t))
except (nx.NetworkXNoPath):
pass
else:
for t in paths_from_target.keys():
# find homomorphism from s to t via new path
if s != source:
new_homomorphism = hierarchy.compose_path_typing(
paths_to_source[s])
else:
new_homomorphism = dict([(key, key)
for key, _ in mapping.items()])
new_homomorphism = compose(new_homomorphism, mapping)
if t != target:
new_homomorphism = compose(
new_homomorphism,
hierarchy.compose_path_typing(paths_from_target[t]))
# find homomorphisms from s to t via other paths
s_t_paths = nx.all_shortest_paths(hierarchy, s, t)
try:
# check only the first path
for path in s_t_paths:
path_homomorphism = hierarchy.compose_path_typing(path)
if path_homomorphism != new_homomorphism:
raise HierarchyError(
"Homomorphism does not commute with an " +
"existing path from '%s' to '%s'!" % (s, t))
except (nx.NetworkXNoPath):
pass
def _propagate_down(hierarchy,
origin_id,
origin_construct,
rule,
instance,
rhs_typing_rels,
inplace=False):
"""Propagate changes down the hierarchy."""
updated_graphs = dict()
updated_homomorphisms = dict()
updated_relations = []
(origin_m, origin_m_origin, origin_prime, origin_m_origin_prime,
rhs_origin_prime) = origin_construct
if rule.is_relaxing():
for graph in nx.bfs_tree(hierarchy, origin_id):
if graph != origin_id:
relation_g_rhs = set()
for key, values in rhs_typing_rels[graph].items():
for v in values:
relation_g_rhs.add((v, key))
(g_prime, g_g_prime, rhs_g_prime) =\
pushout_from_relation(
hierarchy.node[graph].graph, rule.rhs,
relation_g_rhs, inplace)
updated_graphs[graph] = (g_prime, g_g_prime, rhs_g_prime)
graph_predecessors = hierarchy.predecessors(graph)
if origin_id in graph_predecessors:
updated_homomorphisms[(origin_id, graph)] =\
get_unique_map_from_pushout(
origin_prime.nodes(),
origin_m_origin_prime,
rhs_origin_prime,
compose_chain(
[origin_m_origin,
hierarchy.edge[origin_id][graph].mapping,
g_g_prime]),
rhs_g_prime)
if len(rule.added_nodes()) > 0 or\
len(rule.merged_nodes()) > 0:
for pred in hierarchy.predecessors(graph):
if pred in updated_graphs.keys():
if pred != origin_id:
updated_homomorphisms[(pred, graph)] =\
get_unique_map_from_pushout(
updated_graphs[pred][0].nodes(),
updated_graphs[pred][1],
updated_graphs[pred][2],
compose(
hierarchy.edge[pred][graph].mapping,
g_g_prime),
rhs_g_prime)
for suc in hierarchy.successors(graph):
if suc in updated_graphs.keys():
updated_homomorphisms[(graph, suc)] =\
get_unique_map_from_pushout(
g_prime.nodes(),
g_g_prime,
rhs_g_prime,
compose(
hierarchy.edge[graph][suc].mapping,
updated_graphs[suc][1]),
updated_graphs[suc][2])
if len(rule.merged_nodes()) > 0:
# propagate changes to adjacent relations
for related_g in hierarchy.adjacent_relations(graph):
updated_relations.append((graph, related_g))
else:
for suc in hierarchy.successors(origin_id):
updated_homomorphisms[(origin_id, suc)] =\
compose(
origin_m_origin,
hierarchy.edge[origin_id][suc].mapping)
return {
"graphs": updated_graphs,
"homomorphisms": updated_homomorphisms,
"relations": updated_relations
}
def _propagate_up(hierarchy,
graph_id,
rule,
instance,
p_origin_m,
origin_m_origin_prime,
inplace=False):
updated_graphs = dict()
updated_homomorphisms = dict()
updated_relations = set()
updated_rules = dict()
updated_rule_h = dict()
if rule.is_restrictive():
for graph in nx.bfs_tree(hierarchy, graph_id, reverse=True):
if graph != graph_id:
if isinstance(hierarchy.node[graph], hierarchy.graph_node_cls):
origin_typing = hierarchy.get_typing(graph, graph_id)
(graph_prime, graph_prime_graph, graph_prime_origin) =\
_propagate_rule_to(
hierarchy.node[graph].graph,
origin_typing, rule, instance,
p_origin_m, inplace)
updated_graphs[graph] =\
(graph_prime, graph_prime_graph, None, graph_prime_origin)
graph_successors = hierarchy.successors(graph)
if graph_id in graph_successors:
updated_homomorphisms[(graph, graph_id)] =\
compose(
graph_prime_origin,
origin_m_origin_prime)
if len(rule.removed_nodes()) > 0 or\
len(rule.cloned_nodes()) > 0:
for suc in graph_successors:
if suc != graph_id:
if suc in updated_graphs.keys():
graph_prime_suc_prime =\
get_unique_map_to_pullback(
updated_graphs[suc][0].nodes(),
updated_graphs[suc][1],
updated_graphs[suc][3],
compose(
graph_prime_graph,
hierarchy.edge[graph][suc].mapping),
graph_prime_origin)
else:
graph_prime_suc_prime = compose(
graph_prime_graph,
hierarchy.edge[graph][suc].mapping)
updated_homomorphisms[(
graph, suc)] = graph_prime_suc_prime
for pred in hierarchy.predecessors(graph):
if pred in updated_graphs.keys():
pred_m_graph_m = get_unique_map_to_pullback(
graph_prime.nodes(), graph_prime_graph,
graph_prime_origin,
updated_graphs[pred][1],
updated_graphs[pred][3])
updated_homomorphisms[(pred,
graph)] = pred_m_graph_m
# propagate changes to adjacent relations
for related_g in hierarchy.adjacent_relations(graph):
updated_relations.add((graph, related_g))
else:
rule_to_rewrite = hierarchy.node[graph].rule
(lhs_origin_typing,
p_origin_typing,
rhs_origin_typing) =\
hierarchy.get_rule_typing(graph, graph_id)
(lhs_prime, lhs_prime_lhs, lhs_prime_origin) =\
_propagate_rule_to(
rule_to_rewrite.lhs,
lhs_origin_typing, rule, instance,
p_origin_m, inplace=False)
(pr_prime, pr_prime_pr, pr_prime_origin) =\
_propagate_rule_to(
rule_to_rewrite.p,
p_origin_typing, rule, instance,
p_origin_m, inplace=False)
(rhs_prime, rhs_prime_rhs, rhs_prime_origin) =\
_propagate_rule_to(
rule_to_rewrite.rhs,
rhs_origin_typing, rule, instance,
p_origin_m, inplace=False)
# find p_m -> lhs_m
new_p_lhs = get_unique_map_to_pullback(
lhs_prime.nodes(), lhs_prime_lhs, lhs_prime_origin,
compose(pr_prime_pr, rule_to_rewrite.p_lhs),
pr_prime_origin)
# find p_m -> rhs_m
new_p_rhs = get_unique_map_to_pullback(
rhs_prime.nodes(), rhs_prime_rhs, rhs_prime_origin,
compose(pr_prime_pr, rule_to_rewrite.p_rhs),
pr_prime_origin)
new_rule =\
Rule(pr_prime, lhs_prime, rhs_prime,
new_p_lhs, new_p_rhs)
updated_rules[graph] = new_rule
for suc in hierarchy.successors(graph):
if suc == graph_id:
lhs_prime_suc_prime =\
compose(lhs_prime_origin,
origin_m_origin_prime)
rhs_prime_suc_prime =\
compose(rhs_prime_origin,
origin_m_origin_prime)
if suc in updated_graphs.keys():
lhs_prime_suc_prime = get_unique_map_to_pullback(
updated_graphs[suc][0].nodes(),
updated_graphs[suc][1], updated_graphs[suc][3],
compose(
lhs_prime_lhs,
hierarchy.edge[graph][suc].lhs_mapping),
lhs_prime_origin)
rhs_prime_suc_prime = get_unique_map_to_pullback(
updated_graphs[suc][0].nodes(),
updated_graphs[suc][1], updated_graphs[suc][3],
compose(
rhs_prime_rhs,
hierarchy.edge[graph][suc].rhs_mapping),
rhs_prime_origin)
else:
lhs_prime_suc_prime =\
compose(
lhs_prime_lhs,
hierarchy.edge[graph][suc].lhs_mapping)
rhs_prime_suc_prime =\
compose(
rhs_prime_rhs,
hierarchy.edge[graph][suc].rhs_mapping)
updated_rule_h[(graph, suc)] =\
(lhs_prime_suc_prime, rhs_prime_suc_prime)
else:
for pred in hierarchy.predecessors(graph_id):
if isinstance(hierarchy.node[pred], hierarchy.graph_node_cls):
updated_homomorphisms[(pred, graph_id)] =\
compose(
hierarchy.edge[pred][graph_id].mapping,
origin_m_origin_prime)
else:
updated_rule_h[(pred, graph_id)] = (
compose(hierarchy.edge[pred][graph_id].lhs_mapping,
origin_m_origin_prime),
compose(hierarchy.edge[pred][graph_id].rhs_mapping,
origin_m_origin_prime))
return {
"graphs": updated_graphs,
"homomorphisms": updated_homomorphisms,
"rules": updated_rules,
"rule_homomorphisms": updated_rule_h,
"relations": updated_relations
}
def __rmul__(self, other):
"""Right multiplication operation."""
if isinstance(other, Typing):
return Typing(compose(other.mapping), self.attrs)
else:
return NotImplemented
def get_rule_projections(tx,
hierarchy,
graph_id,
rule,
instance,
rhs_typing=None):
"""Execute the query finding rule liftings."""
if rhs_typing is None:
rhs_typing = {}
projections = {}
if rule.is_relaxing():
if len(rule.lhs.nodes()) > 0:
lhs_instance = {n: instance[n] for n in rule.lhs.nodes()}
lhs_vars = {n: n for n in rule.lhs.nodes()}
match_instance_vars = {
v: lhs_instance[k]
for k, v in lhs_vars.items()
}
# Match nodes
query = "// Match nodes the instance of the rewritten graph \n"
query += "MATCH {}".format(", ".join([
"({}:{} {{id: '{}'}})".format(k, graph_id, v)
for k, v in match_instance_vars.items()
]))
query += "\n\n"
carry_vars = list(lhs_vars.values())
for k, v in lhs_vars.items():
query += ("OPTIONAL MATCH (n)<-[:typing*1..]-({})\n".format(
v
) + "WITH {} \n".format(", ".join(carry_vars + [
"collect(DISTINCT {{type:'node', origin: {}.id, id: n.id, graph:labels(n)[0], attrs: properties(n)}}) as {}_dict\n"
.format(v, v)
])))
carry_vars.append("{}_dict".format(v))
# Match edges
for (u, v) in rule.p.edges():
edge_var = "{}_{}".format(lhs_vars[u], lhs_vars[v])
query += "OPTIONAL MATCH ({}_instance)-[{}:edge]->({}_instance)\n".format(
lhs_vars[u], edge_var, lhs_vars[v])
query += "WHERE ({})<-[:typing*1..]-({}) AND ({})<-[:typing*1..]-({})\n".format(
"{}_instance".format(lhs_vars[u]), lhs_vars[u],
"{}_instance".format(lhs_vars[v]), lhs_vars[v])
query += ("WITH {} \n".format(", ".join(carry_vars + [
"collect({{type: 'edge', source: {}.id, target: {}.id, graph:labels({})[0], attrs: properties({})}}) as {}\n"
.format("{}_instance".format(lhs_vars[u]), "{}_instance".
format(lhs_vars[v]), "{}_instance".format(
lhs_vars[u]), edge_var, edge_var)
])))
carry_vars.append(edge_var)
query += "RETURN {}".format(", ".join(
["{}_dict as {}".format(v, v) for v in lhs_vars.values()] + [
"{}_{}".format(lhs_vars[u], lhs_vars[v])
for u, v in rule.p.edges()
]))
result = tx.run(query)
record = result.single()
l_l_ts = {}
l_nodes = {}
l_edges = {}
for k, v in record.items():
if len(v) > 0:
if v[0]["type"] == "node":
for el in v:
l_node = keys_by_value(instance, el["origin"])[0]
if el["graph"] not in l_nodes:
l_nodes[el["graph"]] = {}
l_l_ts[el["graph"]] = {}
if el["id"] not in l_nodes[el["graph"]]:
l_nodes[el["graph"]][el["id"]] = {}
l_nodes[el["graph"]][el["id"]] = attrs_union(
l_nodes[el["graph"]][el["id"]],
attrs_intersection(
generic.convert_props_to_attrs(
el["attrs"]),
get_node(rule.lhs, l_node)))
l_l_ts[el["graph"]][l_node] = el["id"]
else:
for el in v:
l_sources = keys_by_value(l_l_ts[el["graph"]],
el["source"])
l_targets = keys_by_value(l_l_ts[el["graph"]],
el["target"])
for l_source in l_sources:
for l_target in l_targets:
if exists_edge(rule.l, l_source, l_target):
if el["graph"] not in l_edges:
l_edges[el["graph"]] = {}
if (el["source"], el["target"]
) not in l_edges[el["graph"]]:
l_edges[el["graph"]][(
el["source"],
el["target"])] = {}
l_edges[el["graph"]][(el["source"], el["target"])] =\
attrs_union(
l_edges[el["graph"]][(el["source"], el["target"])],
attrs_intersection(
generic.convert_props_to_attrs(el["attrs"]),
get_edge(rule.lhs, l_source, l_target)))
for graph, typing in hierarchy.get_descendants(graph_id).items():
if graph in l_nodes:
nodes = l_nodes[graph]
else:
nodes = {}
if graph in l_edges:
edges = l_edges[graph]
else:
edges = {}
l = nx.DiGraph()
add_nodes_from(l, [(k, v) for k, v in nodes.items()])
if graph in l_edges:
add_edges_from(l, [(s, t, v) for (s, t), v in edges.items()])
rhs, p_rhs, r_r_t = pushout(rule.p, l, rule.rhs,
compose(rule.p_lhs, l_l_ts[graph]),
rule.p_rhs)
l_t_t = {n: n for n in nodes}
# Modify P_T and R_T according to the controlling
# relation rhs_typing
if graph in rhs_typing.keys():
r_t_factorization = {
r_r_t[k]: v
for k, v in rhs_typing[graph].items()
}
added_t_nodes = set()
for n in rhs.nodes():
if n in r_t_factorization.keys():
# If corresponding R_T node is specified in
# the controlling relation add nodes of T
# that type it to P
t_nodes = r_t_factorization[n]
for t_node in t_nodes:
if t_node not in l_t_t.values() and\
t_node not in added_t_nodes:
new_p_node = generate_new_id(l.nodes(), t_node)
l.add_node(new_p_node)
added_t_nodes.add(t_node)
p_rhs[new_p_node] = n
l_t_t[new_p_node] = t_node
else:
p_rhs[keys_by_value(l_t_t, t_node)[0]] = n
projections[graph] = {
"rule": Rule(p=l, rhs=rhs, p_rhs=p_rhs),
"instance": l_t_t,
"l_l_t": l_l_ts[graph],
"p_p_t": {k: l_l_ts[graph][v]
for k, v in rule.p_lhs.items()},
"r_r_t": r_r_t
}
return projections