335 lines
13 KiB
Python
335 lines
13 KiB
Python
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#!/usr/bin/env python
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'''This module implements a Finite State Machine (FSM). In addition to state
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this FSM also maintains a user defined "memory". So this FSM can be used as a
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Push-down Automata (PDA) since a PDA is a FSM + memory.
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The following describes how the FSM works, but you will probably also need to
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see the example function to understand how the FSM is used in practice.
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You define an FSM by building tables of transitions. For a given input symbol
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the process() method uses these tables to decide what action to call and what
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the next state will be. The FSM has a table of transitions that associate:
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(input_symbol, current_state) --> (action, next_state)
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Where "action" is a function you define. The symbols and states can be any
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objects. You use the add_transition() and add_transition_list() methods to add
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to the transition table. The FSM also has a table of transitions that
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associate:
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(current_state) --> (action, next_state)
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You use the add_transition_any() method to add to this transition table. The
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FSM also has one default transition that is not associated with any specific
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input_symbol or state. You use the set_default_transition() method to set the
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default transition.
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When an action function is called it is passed a reference to the FSM. The
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action function may then access attributes of the FSM such as input_symbol,
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current_state, or "memory". The "memory" attribute can be any object that you
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want to pass along to the action functions. It is not used by the FSM itself.
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For parsing you would typically pass a list to be used as a stack.
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The processing sequence is as follows. The process() method is given an
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input_symbol to process. The FSM will search the table of transitions that
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associate:
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(input_symbol, current_state) --> (action, next_state)
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If the pair (input_symbol, current_state) is found then process() will call the
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associated action function and then set the current state to the next_state.
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If the FSM cannot find a match for (input_symbol, current_state) it will then
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search the table of transitions that associate:
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(current_state) --> (action, next_state)
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If the current_state is found then the process() method will call the
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associated action function and then set the current state to the next_state.
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Notice that this table lacks an input_symbol. It lets you define transitions
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for a current_state and ANY input_symbol. Hence, it is called the "any" table.
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Remember, it is always checked after first searching the table for a specific
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(input_symbol, current_state).
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For the case where the FSM did not match either of the previous two cases the
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FSM will try to use the default transition. If the default transition is
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defined then the process() method will call the associated action function and
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then set the current state to the next_state. This lets you define a default
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transition as a catch-all case. You can think of it as an exception handler.
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There can be only one default transition.
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Finally, if none of the previous cases are defined for an input_symbol and
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current_state then the FSM will raise an exception. This may be desirable, but
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you can always prevent this just by defining a default transition.
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Noah Spurrier 20020822
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PEXPECT LICENSE
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This license is approved by the OSI and FSF as GPL-compatible.
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http://opensource.org/licenses/isc-license.txt
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Copyright (c) 2012, Noah Spurrier <noah@noah.org>
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PERMISSION TO USE, COPY, MODIFY, AND/OR DISTRIBUTE THIS SOFTWARE FOR ANY
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PURPOSE WITH OR WITHOUT FEE IS HEREBY GRANTED, PROVIDED THAT THE ABOVE
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COPYRIGHT NOTICE AND THIS PERMISSION NOTICE APPEAR IN ALL COPIES.
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THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
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ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
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ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
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OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
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'''
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class ExceptionFSM(Exception):
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'''This is the FSM Exception class.'''
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def __init__(self, value):
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self.value = value
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def __str__(self):
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return 'ExceptionFSM: ' + str(self.value)
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class FSM:
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'''This is a Finite State Machine (FSM).
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'''
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def __init__(self, initial_state, memory=None):
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'''This creates the FSM. You set the initial state here. The "memory"
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attribute is any object that you want to pass along to the action
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functions. It is not used by the FSM. For parsing you would typically
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pass a list to be used as a stack. '''
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# Map (input_symbol, current_state) --> (action, next_state).
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self.state_transitions = {}
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# Map (current_state) --> (action, next_state).
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self.state_transitions_any = {}
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self.default_transition = None
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self.input_symbol = None
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self.initial_state = initial_state
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self.current_state = self.initial_state
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self.next_state = None
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self.action = None
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self.memory = memory
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def reset (self):
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'''This sets the current_state to the initial_state and sets
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input_symbol to None. The initial state was set by the constructor
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__init__(). '''
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self.current_state = self.initial_state
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self.input_symbol = None
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def add_transition (self, input_symbol, state, action=None, next_state=None):
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'''This adds a transition that associates:
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(input_symbol, current_state) --> (action, next_state)
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The action may be set to None in which case the process() method will
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ignore the action and only set the next_state. The next_state may be
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set to None in which case the current state will be unchanged.
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You can also set transitions for a list of symbols by using
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add_transition_list(). '''
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if next_state is None:
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next_state = state
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self.state_transitions[(input_symbol, state)] = (action, next_state)
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def add_transition_list (self, list_input_symbols, state, action=None, next_state=None):
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'''This adds the same transition for a list of input symbols.
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You can pass a list or a string. Note that it is handy to use
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string.digits, string.whitespace, string.letters, etc. to add
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transitions that match character classes.
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The action may be set to None in which case the process() method will
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ignore the action and only set the next_state. The next_state may be
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set to None in which case the current state will be unchanged. '''
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if next_state is None:
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next_state = state
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for input_symbol in list_input_symbols:
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self.add_transition (input_symbol, state, action, next_state)
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def add_transition_any (self, state, action=None, next_state=None):
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'''This adds a transition that associates:
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(current_state) --> (action, next_state)
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That is, any input symbol will match the current state.
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The process() method checks the "any" state associations after it first
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checks for an exact match of (input_symbol, current_state).
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The action may be set to None in which case the process() method will
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ignore the action and only set the next_state. The next_state may be
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set to None in which case the current state will be unchanged. '''
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if next_state is None:
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next_state = state
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self.state_transitions_any [state] = (action, next_state)
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def set_default_transition (self, action, next_state):
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'''This sets the default transition. This defines an action and
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next_state if the FSM cannot find the input symbol and the current
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state in the transition list and if the FSM cannot find the
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current_state in the transition_any list. This is useful as a final
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fall-through state for catching errors and undefined states.
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The default transition can be removed by setting the attribute
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default_transition to None. '''
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self.default_transition = (action, next_state)
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def get_transition (self, input_symbol, state):
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'''This returns (action, next state) given an input_symbol and state.
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This does not modify the FSM state, so calling this method has no side
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effects. Normally you do not call this method directly. It is called by
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process().
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The sequence of steps to check for a defined transition goes from the
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most specific to the least specific.
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1. Check state_transitions[] that match exactly the tuple,
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(input_symbol, state)
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2. Check state_transitions_any[] that match (state)
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In other words, match a specific state and ANY input_symbol.
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3. Check if the default_transition is defined.
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This catches any input_symbol and any state.
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This is a handler for errors, undefined states, or defaults.
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4. No transition was defined. If we get here then raise an exception.
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'''
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if (input_symbol, state) in self.state_transitions:
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return self.state_transitions[(input_symbol, state)]
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elif state in self.state_transitions_any:
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return self.state_transitions_any[state]
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elif self.default_transition is not None:
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return self.default_transition
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else:
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raise ExceptionFSM ('Transition is undefined: (%s, %s).' %
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(str(input_symbol), str(state)) )
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def process (self, input_symbol):
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'''This is the main method that you call to process input. This may
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cause the FSM to change state and call an action. This method calls
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get_transition() to find the action and next_state associated with the
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input_symbol and current_state. If the action is None then the action
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is not called and only the current state is changed. This method
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processes one complete input symbol. You can process a list of symbols
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(or a string) by calling process_list(). '''
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self.input_symbol = input_symbol
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(self.action, self.next_state) = self.get_transition (self.input_symbol, self.current_state)
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if self.action is not None:
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self.action (self)
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self.current_state = self.next_state
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self.next_state = None
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def process_list (self, input_symbols):
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'''This takes a list and sends each element to process(). The list may
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be a string or any iterable object. '''
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for s in input_symbols:
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self.process (s)
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##############################################################################
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# The following is an example that demonstrates the use of the FSM class to
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# process an RPN expression. Run this module from the command line. You will
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# get a prompt > for input. Enter an RPN Expression. Numbers may be integers.
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# Operators are * / + - Use the = sign to evaluate and print the expression.
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# For example:
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#
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# 167 3 2 2 * * * 1 - =
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#
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# will print:
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#
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# 2003
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##############################################################################
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import sys
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import string
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PY3 = (sys.version_info[0] >= 3)
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#
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# These define the actions.
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# Note that "memory" is a list being used as a stack.
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#
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def BeginBuildNumber (fsm):
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fsm.memory.append (fsm.input_symbol)
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def BuildNumber (fsm):
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s = fsm.memory.pop ()
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s = s + fsm.input_symbol
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fsm.memory.append (s)
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def EndBuildNumber (fsm):
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s = fsm.memory.pop ()
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fsm.memory.append (int(s))
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def DoOperator (fsm):
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ar = fsm.memory.pop()
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al = fsm.memory.pop()
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if fsm.input_symbol == '+':
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fsm.memory.append (al + ar)
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elif fsm.input_symbol == '-':
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fsm.memory.append (al - ar)
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elif fsm.input_symbol == '*':
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fsm.memory.append (al * ar)
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elif fsm.input_symbol == '/':
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fsm.memory.append (al / ar)
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def DoEqual (fsm):
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print(str(fsm.memory.pop()))
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def Error (fsm):
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print('That does not compute.')
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print(str(fsm.input_symbol))
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def main():
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'''This is where the example starts and the FSM state transitions are
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defined. Note that states are strings (such as 'INIT'). This is not
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necessary, but it makes the example easier to read. '''
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f = FSM ('INIT', [])
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f.set_default_transition (Error, 'INIT')
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f.add_transition_any ('INIT', None, 'INIT')
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f.add_transition ('=', 'INIT', DoEqual, 'INIT')
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f.add_transition_list (string.digits, 'INIT', BeginBuildNumber, 'BUILDING_NUMBER')
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f.add_transition_list (string.digits, 'BUILDING_NUMBER', BuildNumber, 'BUILDING_NUMBER')
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f.add_transition_list (string.whitespace, 'BUILDING_NUMBER', EndBuildNumber, 'INIT')
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f.add_transition_list ('+-*/', 'INIT', DoOperator, 'INIT')
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print()
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print('Enter an RPN Expression.')
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print('Numbers may be integers. Operators are * / + -')
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print('Use the = sign to evaluate and print the expression.')
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print('For example: ')
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print(' 167 3 2 2 * * * 1 - =')
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inputstr = (input if PY3 else raw_input)('> ') # analysis:ignore
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f.process_list(inputstr)
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if __name__ == '__main__':
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main()
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