# The contents of this file are subject to the Mozilla Public License # (MPL) Version 1.1 (the "License"); you may not use this file except # in compliance with the License. You may obtain a copy of the License # at http://www.mozilla.org/MPL/ # # Software distributed under the License is distributed on an "AS IS" # basis, WITHOUT WARRANTY OF ANY KIND, either express or implied. See # the License for the specific language governing rights and # limitations under the License. # # The Original Code is LEPL (http://www.acooke.org/lepl) # The Initial Developer of the Original Code is Andrew Cooke. # Portions created by the Initial Developer are Copyright (C) 2009-2010 # Andrew Cooke (andrew@acooke.org). All Rights Reserved. # # Alternatively, the contents of this file may be used under the terms # of the LGPL license (the GNU Lesser General Public License, # http://www.gnu.org/licenses/lgpl.html), in which case the provisions # of the LGPL License are applicable instead of those above. # # If you wish to allow use of your version of this file only under the # terms of the LGPL License and not to allow others to use your version # of this file under the MPL, indicate your decision by deleting the # provisions above and replace them with the notice and other provisions # required by the LGPL License. If you do not delete the provisions # above, a recipient may use your version of this file under either the # MPL or the LGPL License. ''' A simple regular expression engine in pure Python. This takes a set of regular expressions (only the most basic functionality is supported) and generates a finite state machines that can match them against a stream of values. Although simple (and slow compared to a C version), it has some advantages from being implemented in Python. * It can use a variety of alphabets - it is not restricted to strings. It could, for example, match lists of integers, or sequences of tokens. * The NFA implementation can yield intermediate matches. * It is extensible. The classes here form a layered series of representations for regular expressions. The first layer contains the classes `Sequence`, `Option`, `Repeat`, `Choice`, `Labelled` and `Regexp`. These are a high level representation that will typically be constructed by an alphabet-specific parser. The second layer encodes the regular expression as a non-deterministic finite automaton (NFA) with empty transitions. This is a "natural" representation of the transitions that can be generated by the first layer. The third layer encodes the regular expression as a deterministic finite automaton (DFA). This is a more "machine friendly" representation that allows for more efficient matching. It is generated by transforming a representation from the second layer. ''' from abc import ABCMeta, abstractmethod from collections import deque from itertools import chain from lepl.stream.core import s_next, s_empty, s_line from lepl.support.graph import ConstructorWalker, clone, Clone from lepl.support.node import Node from lepl.regexp.interval import Character, TaggedFragments, IntervalMap,\ _Character from lepl.support.lib import fmt, basestring, str, LogMixin # pylint: disable-msg=C0103 # Python 2.6 #class Alphabet(metaclass=ABCMeta): _Alphabet = ABCMeta('_Alphabet', (object, ), {}) # pylint: disable-msg=E1002 # pylint can't find ABCs class Alphabet(LogMixin, _Alphabet): ''' Regular expressions are generalised over alphabets, which describe the set of acceptable characters. The characters in an alphabet must have an order, which is defined by `__lt__` on the character instances themselves (equality and inequality are also assumed to be defined). In addition, `before(c)` and `after(c)` below should give the previous and subsequent characters in the ordering and `min` and `max` should give the two most extreme characters. Internally, within the routines here, ranges of characters are used. These are encoded as pairs of values `(a, b)` which are inclusive. Each pair is called an "interval". Alphabets include additional methods used for display and may also have methods specific to a given instance (typically named with an initial underscore). ''' def __init__(self, min_, max_): self.__min = min_ self.__max = max_ super(Alphabet, self).__init__() @property def min(self): ''' The "smallest" character. ''' return self.__min @property def max(self): ''' The "largest" character. ''' return self.__max @abstractmethod def before(self, c): ''' Must return the character before c in the alphabet. Never called with min (assuming input data are in range). ''' @abstractmethod def after(self, c): ''' Must return the character after c in the alphabet. Never called with max (assuming input data are in range). ''' @abstractmethod def fmt_intervals(self, intervals): ''' This must fully describe the data in the intervals (it is used to hash the data). ''' def invert(self, intervals): ''' Return a list of intervals that describes the complement of the given interval. Note - the input interval must be ordered (and the result will be ordered too). ''' if not intervals: return [(self.min, self.max)] inverted = [] (a, last) = intervals[0] if a != self.min: inverted.append((self.min, self.before(a))) for (a, b) in intervals[1:]: inverted.append((self.after(last), self.before(a))) last = b if last != self.max: inverted.append((self.after(last), self.max)) self._debug(fmt('invert {0} -> {1}', intervals, inverted)) return inverted def extension(self, text): ''' This is called for extensions for the form (*NAME) where NAME is any sequence of capitals. It should return a character range. Further uses of (*...) are still to be decided. ''' raise RegexpError(fmt('Extension {0!r} not supported by {1!s}', text, self.__class__)) @abstractmethod def fmt_sequence(self, children): ''' This must fully describe the data in the children (it is used to hash the data). ''' @abstractmethod def fmt_repeat(self, children): ''' This must fully describe the data in the children (it is used to hash the data). ''' @abstractmethod def fmt_choice(self, children): ''' This must fully describe the data in the children (it is used to hash the data). ''' @abstractmethod def fmt_option(self, children): ''' This must fully describe the data in the children (it is used to hash the data). ''' @abstractmethod def fmt_label(self, label, child): ''' This must fully describe the data in the child (it is used to hash the data). ''' @abstractmethod def join(self, chars): ''' Join a list of characters into a string (or the equivalent). ''' @abstractmethod def parse(self, regexp): ''' Generate a Sequence from the given regexp text. ''' class Sequence(Node): ''' A sequence of Characters, etc. ''' def __init__(self, alphabet, *children): assert isinstance(alphabet, Alphabet) # pylint: disable-msg=W0142 # have to disable this assertion to embed error nodes # for child in children: # assert isinstance(child, RegexpGraphNode), type(child) super(Sequence, self).__init__(*children) self.alphabet = alphabet self.state = None self.__str = self._build_str() def _build_str(self): ''' Construct a string representation of self. ''' return self.alphabet.fmt_sequence(self) def __str__(self): return self.__str def __hash__(self): return hash(self.__str) def build(self, graph, before, after): ''' Connect in sequence. ''' if self: src = before last = self[-1] for child in self: dest = after if child is last else graph.new_node() child.build(graph, src, dest) src = dest else: graph.connect(before, after) @staticmethod def __clone(node, args, kargs): try: args = list(args) args.insert(0, node.alphabet) except AttributeError: pass return clone(node, args, kargs) def clone(self): return ConstructorWalker(self, RegexpGraphNode)(Clone(self.__clone)) #class RegexpGraphNode(metaclass=ABCMeta): RegexpGraphNode = ABCMeta('RegexpGraphNode', (object, ), {}) RegexpGraphNode.register(_Character) RegexpGraphNode.register(Sequence) class Option(Sequence): ''' An optional sequence of Characters (or sequences). ''' def _build_str(self): ''' Construct a string representation of self. ''' return self.alphabet.fmt_option(self) def build(self, graph, before, after): ''' Connect as sequence and also directly from start to end ''' super(Option, self).build(graph, before, after) graph.connect(before, after) class Empty(Sequence): ''' Matches an empty sequence. ''' def _build_str(self): ''' Construct a string representation of self. ''' return self.alphabet.fmt_sequence([]) def build(self, graph, before, after): ''' Connect directly from start to end. ''' graph.connect(before, after) class Repeat(Sequence): ''' A sequence of Characters (or sequences) that can repeat 0 or more times. ''' def _build_str(self): ''' Construct a string representation of self. ''' return self.alphabet.fmt_repeat(self) def build(self, graph, before, after): ''' Connect in loop from before to before, and also directly from start to end. ''' node = graph.new_node() graph.connect(before, node) super(Repeat, self).build(graph, node, node) graph.connect(node, after) def Choice(alphabet, *children): ''' Encase a choice in a sequence so that it can be treated in the same way as other components (if we don't do this, then passing it to another sequence will split it into constituents and then sequence them). ''' return Sequence(alphabet, _Choice(alphabet, *children)) class _Choice(Sequence): ''' A set of alternative Characters (or sequences). ''' def _build_str(self): ''' Construct a string representation of self. ''' return self.alphabet.fmt_choice(self) def build(self, graph, before, after): ''' Connect in parallel from start to end, but add extra nodes so that the sequence is tried in order (because evaluation tries empty transitions last) and that loops don't return to start. ''' if self: last = self[-1] for child in self: # this places numbering first, so empty transition chosen in order if child is not last: node = graph.new_node() child.build(graph, before, after) if child is not last: graph.connect(before, node) before = node # if self: # last = self[-1] # for child in self: # node = graph.new_node() # graph.connect(before, node) # child.build(graph, node, after) # if child is not last: # node = graph.new_node() # graph.connect(before, node) # before = node class Labelled(Sequence): ''' A labelled sequence. Within our limited implementation these are restricted to (1) being children of Regexp and (2) not being followed by any other sequence. Their termination defines terminal nodes. ''' def __init__(self, alphabet, label, *children): self.label = label super(Labelled, self).__init__(alphabet, *children) def _build_str(self): ''' Construct a string representation of self. ''' return self.alphabet.fmt_label(self.label, self.alphabet.fmt_sequence(self)) def build(self, graph, before, after): ''' A sequence, but with an extra final empty transition to force any loops before termination. ''' node = graph.new_node() super(Labelled, self).build(graph, before, node) graph.connect(node, after) graph.terminate(node, [self.label]) class RegexpError(Exception): ''' An error associated with (problems in) the regexp implementation. ''' pass class Compiler(LogMixin): ''' Compile an expression. ''' def __init__(self, expression, alphabet): super(Compiler, self).__init__() self.expression = expression self.alphabet = alphabet def nfa(self): ''' Generate a NFA-based matcher. ''' self._debug(fmt('compiling to nfa: {0}', self)) graph = NfaGraph(self.alphabet) self.expression.build(graph, graph.new_node(), graph.new_node()) self._debug(fmt('nfa graph: {0}', graph)) return NfaPattern(graph, self.alphabet) def dfa(self): ''' Generate a DFA-based matcher (faster than NFA, but returns only a single, greedy match). ''' self._debug(fmt('compiling to dfa: {0}', self)) ngraph = NfaGraph(self.alphabet) self.expression.build(ngraph, ngraph.new_node(), ngraph.new_node()) self._debug(fmt('nfa graph: {0}', ngraph)) dgraph = NfaToDfa(ngraph, self.alphabet).dfa self._debug(fmt('dfa graph: {0}', dgraph)) return DfaPattern(dgraph, self.alphabet) def re(self): ''' Generate a matcher that wraps the standard "re" package. ''' return RePattern(str(self), self.alphabet) def __str__(self): ''' Show the expression itself. ''' return str(self.expression) @staticmethod def _coerce(regexp, alphabet): ''' Coerce to a regexp. ''' if isinstance(regexp, basestring): coerced = alphabet.parse(regexp) if not coerced: raise RegexpError(fmt('Cannot parse regexp {0!r} using {1}', regexp, alphabet)) return coerced else: return regexp @staticmethod def single(alphabet, regexp, label='label'): ''' Generate an instance for a single expression or sequence. ''' return Compiler(Labelled(alphabet, label, *Compiler._coerce(regexp, alphabet)), alphabet) @staticmethod def multiple(alphabet, regexps): ''' Generate an instance for several expressions. ''' return Compiler( Choice(alphabet, *[Labelled(alphabet, label, *Compiler._coerce(regexp, alphabet)) for (label, regexp) in regexps]), alphabet) class BaseGraph(object): ''' Describes a collection of connected nodes. ''' def __init__(self, alphabet): super(BaseGraph, self).__init__() self._alphabet = alphabet self._next_node = 0 self._transitions = {} # map from source to (dest, edge) self._terminals = {} # node to label def terminate(self, node, labels): ''' Indicate that the node terminates with the given labels. ''' assert node < self._next_node if node not in self._terminals: self._terminals[node] = set() self._terminals[node].update(labels) def new_node(self): ''' Get a new node. ''' node = self._next_node self._next_node += 1 return node def connect(self, src, dest, edge): ''' Define a connection between src and dest, with an edge value (a character). ''' assert src < self._next_node assert dest < self._next_node if src not in self._transitions: self._transitions[src] = [] self._transitions[src].append((dest, edge)) def __iter__(self): ''' An iterator over all nodes. ''' return iter(range(self._next_node)) def transitions(self, src): ''' An iterator over all non-empty transitions from src - returns (dest, edge) pairs. ''' return iter(self._transitions.get(src, [])) def terminals(self, node): ''' An iterator over the terminals for the give node. ''' return iter(self._terminals.get(node, [])) def __len__(self): return self._next_node class NfaGraph(BaseGraph): ''' Describes a NFA with epsilon (empty) transitions. ''' def __init__(self, alphabet): super(NfaGraph, self).__init__(alphabet) self._empty_transitions = {} # map from source to set(dest) def new_node(self): ''' Get a new (unconnected) node. ''' node = super(NfaGraph, self).new_node() self._empty_transitions[node] = set() return node def connect(self, src, dest, edge=None): ''' Define a connection between src and dest, with an optional edge value (a character). ''' if edge: super(NfaGraph, self).connect(src, dest, edge) else: assert src < self._next_node assert dest < self._next_node assert src not in self._terminals, 'Source is terminal' self._empty_transitions[src].add(dest) def empty_transitions(self, src): ''' An iterator over all empty transitions from src. ''' return iter(self._empty_transitions.get(src, [])) def connected(self, nodes): ''' Return all nodes connected to the given node. ''' connected = set() stack = deque(nodes) while stack: src = stack.pop() connected.add(src) for dest in self.empty_transitions(src): if dest not in connected: connected.add(dest) stack.append(dest) return (frozenset(connected), chain(*[self.terminals(node) for node in connected])) def terminal(self, node): ''' The NFA graph has single terminal. ''' terminals = list(self.terminals(node)) if terminals: assert len(terminals) == 1, 'Multiple terminals in NFA' return terminals[0] else: return None def __str__(self): ''' Example: 0: 3, 4; 1: 2; 2(Tk1); 3: [{u'\x00'}-`b-{u'\U0010ffff'}]->3, 1; 4: {$}->5, 7; 5: 6; 6($); 7: {^}->10; 8: 9; 9(^); 10: 11; 11: [ ]->11, 8 Node 0 leads to 3 and 4 (both empty) Node 1 leads to 2 (empty) Node 2 is terminal, labelled with "Tk1" Node 3 loops back to 3 for a character in the given range, or to 1 etc. ''' lines = [] for node in self: edges = [] for (dest, edge) in self.transitions(node): edges.append(fmt('{0}->{1}', edge, dest)) for dest in self.empty_transitions(node): edges.append(str(dest)) label = '' if self.terminal(node) is None \ else fmt('({0})', self.terminal(node)) if edges: lines.append( fmt('{0}{1}: {2}', node, label, ', '.join(edges))) else: lines.append(fmt('{0}{1}', node, label)) return '; '.join(lines) class NfaPattern(LogMixin): ''' Given a graph this constructs a transition table and an associated matcher. The matcher attempts to find longest matches but does not guarantee termination (if a possible empty match is repeated). Note that the matcher returns a triple, including label. This is not the same interface as the matchers used in recursive descent parsing. Evaluation order for transition: - Transition with character, if defined - Empty transition to largest numbered node these ensure we do deepest match first. ''' def __init__(self, graph, alphabet): super(NfaPattern, self).__init__() self.__graph = graph self.__alphabet = alphabet self.__table = {} self.__build_table() def __build_table(self): ''' Rewrite the graph as a transition table, with appropriate ordering. ''' for src in self.__graph: # construct an interval map of possible destinations and terminals # given a character fragments = TaggedFragments(self.__alphabet) for (dest, char) in self.__graph.transitions(src): fragments.append(char, (dest, self.__graph.terminal(dest))) map_ = IntervalMap() for (interval, dts) in fragments: map_[interval] = dts # collect empty transitions empties = [(dest, self.__graph.terminal(dest)) # ordering here is reverse of what is required, which # is ok because we use empties[-1] below for dest in sorted(self.__graph.empty_transitions(src))] self.__table[src] = (map_, empties) def match(self, stream): ''' Use the table to match a stream. The stack holds the current state, which is consumed from left to right. An entry on the stack contains: - map_ - a map from character to [(dest state, terminals)] - matched - the [(dest state, terminals)] generated by the map for a given character - empties - empty transitions for this state - match - the current match, as a list of tokens consumed from the stream - stream - the current stream ''' #self._debug(str(self.__table)) stack = deque() (map_, empties) = self.__table[0] stack.append((map_, None, empties, [], stream)) while stack: #self._debug(str(stack)) (map_, matched, empties, match, stream) = stack.pop() if not map_ and not matched and not empties: # if we have no more transitions, drop pass elif map_: # re-add empties with old match stack.append((None, None, empties, match, stream)) # and try matching a character if not s_empty(stream): (value, next_stream) = s_next(stream) try: matched = map_[value] if matched: stack.append((None, matched, None, match + [value], next_stream)) except IndexError: pass elif matched: (dest, terminal) = matched[-1] # add back reduced matched if len(matched) > 1: # avoid discard iteration stack.append((map_, matched[:-1], empties, match, stream)) # and expand this destination (map_, empties) = self.__table[dest] stack.append((map_, None, empties, match, stream)) if terminal: yield (terminal, self.__alphabet.join(match), stream) else: # we must have an empty transition (dest, terminal) = empties[-1] # add back reduced empties if len(empties) > 1: # avoid discard iteration stack.append((map_, matched, empties[:-1], match, stream)) # and expand this destination (map_, empties) = self.__table[dest] stack.append((map_, None, empties, match, stream)) if terminal: yield (terminal, self.__alphabet.join(match), stream) def __repr__(self): return '' class DfaGraph(BaseGraph): ''' Describes a DFA where each node is a collection of NFA nodes. ''' def __init__(self, alphabet): super(DfaGraph, self).__init__(alphabet) self._dfa_to_nfa = {} # map from dfa node to set(nfa nodes) self._nfa_to_dfa = {} # map from set(nfa nodes) to dfa nodes def node(self, nfa_nodes): ''' Add a node, defined as a set of nfa nodes. If the set already exists, (False, old node) is returned, with the existing DFA node. Otherwise (True, new node) is returned. ''' new = nfa_nodes not in self._nfa_to_dfa if new: dfa_node = self.new_node() self._nfa_to_dfa[nfa_nodes] = dfa_node self._dfa_to_nfa[dfa_node] = nfa_nodes return (new, self._nfa_to_dfa[nfa_nodes]) def nfa_nodes(self, node): ''' An iterator over NFA nodes associated with the given DFA node. ''' return iter(self._dfa_to_nfa[node]) def __str__(self): lines = [] for node in self: edges = [] for (dest, edge) in self.transitions(node): edges.append(fmt('{0}->{1}', edge, dest)) nodes = [n for n in self.nfa_nodes(node)] edges = ' ' + ','.join(edges) if edges else '' labels = list(self.terminals(node)) labels = fmt('({0})', ','.join(str(label) for label in labels)) \ if labels else '' lines.append(fmt('{0}{1}: {2}{3}', node, labels, nodes, edges)) return '; '.join(lines) # pylint: disable-msg=R0903 # this is complex enough class NfaToDfa(object): ''' Convert a NFA graph to a DFA graph (uses the usual superset approach but does combination of states in a way that seems to fit better with the idea of character ranges). ''' def __init__(self, nfa, alphabet): super(NfaToDfa, self).__init__() self.__nfa = nfa self.__alphabet = alphabet self.dfa = DfaGraph(alphabet) self.__build_graph() def __build_graph(self): ''' This is the driver for the "usual" superset algorithm - we find all states that correspond to a DFA state, then look at transitions to other states. This repeats until we have covered all the different combinations of NFA states that could occur. ''' stack = deque() # (dfa node, set(nfa nodes), set(terminals)) # start with initial node (nfa_nodes, terminals) = self.__nfa.connected([0]) (_, src) = self.dfa.node(nfa_nodes) stack.append((src, nfa_nodes, terminals)) # continue until all states covered while stack: (src, nfa_nodes, terminals) = stack.pop() self.dfa.terminate(src, terminals) fragments = self.__fragment_transitions(nfa_nodes) groups = self.__group_fragments(fragments) self.__add_groups(src, groups, stack) def __fragment_transitions(self, nfa_nodes): ''' From the given nodes we can accumulate the destination nodes and terminals associated with each transition (edge/character). At the same time we separate the character matches into non-overlapping fragments. ''' fragments = TaggedFragments(self.__alphabet) for nfa_node in nfa_nodes: for (dest, edge) in self.__nfa.transitions(nfa_node): (nodes, terminals) = self.__nfa.connected([dest]) fragments.append(edge, (nodes, list(terminals))) return fragments @staticmethod def __group_fragments(fragments): ''' For each fragment, we for the complete set of possible destinations and associated terminals. Since it is possible that more than one fragment will lead to the same set of target nodes we group all related fragments together. ''' # map from set(nfa nodes) to (set(intervals), set(terminals)) groups = {} for (interval, nts) in fragments: if len(nts) > 1: # collect all nodes and terminals for fragment (nodes, terminals) = (set(), set()) for (n, t) in nts: nodes.update(n) terminals.update(t) nodes = frozenset(nodes) else: (nodes, terminals) = nts[0] if nodes not in groups: groups[nodes] = (set(), set()) groups[nodes][0].add(interval) groups[nodes][1].update(terminals) return groups def __add_groups(self, src, groups, stack): ''' The target nfa nodes identified above are now used to create dfa nodes. ''' for nfa_nodes in groups: (intervals, terminals) = groups[nfa_nodes] char = Character(intervals, self.__alphabet) (new, dest) = self.dfa.node(nfa_nodes) self.dfa.connect(src, dest, char) if new: stack.append((dest, nfa_nodes, terminals)) class DfaPattern(LogMixin): ''' Create a lookup table for a DFA and a matcher to evaluate it. ''' def __init__(self, graph, alphabet): super(DfaPattern, self).__init__() self.__graph = graph self.__alphabet = alphabet self.__table = [None] * len(graph) self.__empty_labels = list(graph.terminals(0)) self.__build_table() def __build_table(self): ''' Construct a transition table. ''' for src in self.__graph: row = IntervalMap() for (dest, char) in self.__graph.transitions(src): # use tuple rather than list to allow hashing of tokens! labels = tuple(self.__graph.terminals(dest)) for interval in char: row[interval] = (dest, labels) self.__table[src] = row def match(self, stream_in): ''' Match against the stream. ''' try: (terminals, size, _) = self.size_match(stream_in) (value, stream_out) = s_next(stream_in, count=size) return (terminals, value, stream_out) except TypeError: # the matcher returned None return None def size_match(self, stream): ''' Match against the stream, but return the length of the match. ''' state = 0 size = 0 longest = (self.__empty_labels, 0, stream) \ if self.__empty_labels else None (line, _) = s_line(stream, True) while size < len(line): future = self.__table[state][line[size]] if future is None: break # update state (state, terminals) = future size += 1 # match is strictly increasing, so storing the length is enough # (no need to make an expensive copy) if terminals: try: (_, next_stream) = s_next(stream, count=size) longest = (terminals, size, next_stream) except StopIteration: pass return longest def __repr__(self): return ''