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14 '''This module implements a Finite State Machine (FSM).
15 In addition to state this FSM also maintains a user defined "something".
16 This "something" is effectively memory, so this FSM could be considered
17 a Push-down Automata (PDA) since a PDA is a FSM + memory.
18
19 The following describes how the FSM works, but you will probably also need
20 to see the example function to understand how the FSM is used in practice.
21
22 You define an FSM by building tables of transitions.
23 For a given input symbol the process() method uses these tables
24 to decide what action to call and what the next state will be.
25 The FSM has a table of transitions that associate:
26 (input_symbol, current_state) --> (action, next_state)
27 where "action" is a function you define. The symbols and states
28 can be any objects. You use the add_transition() and add_transition_list()
29 methods to add to the transition table. The FSM also has a table
30 of transitions that associate:
31 (current_state) --> (action, next_state)
32 You use the add_transition_any() method to add to this transition table.
33 The FSM also has one default transition that is not associated
34 with any specific input_symbol or state. You use the
35 set_default_transition() method to set the default transition.
36
37 When an action function is called it is passed a reference to the FSM.
38 The action function may then access attributes of the FSM such as
39 input_symbol, current_state, or "something". The "something" attribute
40 can be any object that you want to pass along to the action functions.
41 It is not used by the FSM. For parsing you would typically pass a list
42 to be used as a stack.
43
44 The processing sequence is as follows.
45 The process() method is given an input_symbol to process.
46 The FSM will search the table of transitions that associate:
47 (input_symbol, current_state) --> (action, next_state)
48 If the pair (input_symbol, current_state) is found then
49 process() will call the associated action function and then set the
50 current state to the next_state.
51
52 If the FSM cannot find a match for (input_symbol, current_state)
53 it will then search the table of transitions that associate:
54 (current_state) --> (action, next_state)
55 If the current_state is found then the process() method will call
56 the associated action function and then set the current state to
57 the next_state. Notice that this table lacks an input_symbol.
58 It lets you define transitions for a current_state and ANY input_symbol.
59 Hence, it is called the "any" table. Remember, it is always checked
60 after first searching the table for a specific (input_symbol, current_state).
61
62 For the case where the FSM did not match either of the previous two cases
63 the FSM will try to use the default transition. If the default transition
64 is defined then the process() method will call the associated action function
65 and then set the current state to the next_state. This lets you define
66 a default transition as a catch-all case. You can think of it as an
67 exception handler. There can be only one default transition.
68
69 Finally, if none of the previous cases are defined for an input_symbol
70 and current_state then the FSM will raise an exception.
71 This may be desirable, but you can always prevent this just by
72 defining a default transition.
73
74 Noah Spurrier 20020822
75 '''
76
78 '''This is the FSM Exception class.'''
83
85 '''This is a Finite State Machine (FSM).
86 '''
87
88 - def __init__(self, initial_state, something):
89 '''This creates the FSM.
90 You set the initial state here. The "something" attribute is any
91 object that you want to pass along to the action functions.
92 It is not used by the FSM. For parsing you would typically pass
93 a list to be used as a stack.
94 '''
95
96 self.state_transitions = {}
97
98 self.state_transitions_any = {}
99 self.default_transition = None
100
101 self.input_symbol = None
102 self.initial_state = initial_state
103 self.current_state = self.initial_state
104 self.something = something
105
107 '''This sets the current_state to the initial_state and
108 sets input_symbol to None.
109 The initial state was set by the constructor __init__().
110 '''
111 self.current_state = self.initial_state
112 self.input_symbol = None
113
115 '''This adds a transition that associates
116 (input_symbol, current_state) --> (action, next_state)
117 The action may be set to None in which case the process() method
118 will ignore the action and only set the next_state.
119
120 You can also set transitions for a list of symbols by using
121 add_transition_list().
122 '''
123 self.state_transitions[(input_symbol, state)] = (action, next_state)
124
126 '''This adds the same transition for lots of different input symbols.
127 You can pass a list or a string. Note that it is handy to use
128 string.digits, string.whitespace, string.letters, etc. to add
129 transitions that match character classes.
130 '''
131 for input_symbol in list_input_symbols:
132 self.add_transition (input_symbol, state, action, next_state)
133
135 '''This adds a transition that associates
136 (current_state) --> (action, next_state)
137 The process() method checks these associations if it cannot
138 first find a match of an (input_symbol, current_state).
139 '''
140 self.state_transitions_any [state] = (action, next_state)
141
143 '''This sets the default transition.
144 This defines an action and next_state if the FSM cannot find the
145 input symbol and the current state in the transition list and
146 if the FSM cannot find the current_state in the transition_any list.
147 This is useful for catching errors and undefined states.
148
149 The default transition can be removed by setting the attribute
150 default_transition to None.
151 '''
152 self.default_transition = (action, next_state)
153
155 '''This returns (action, next state) given an input_symbol and state.
156 This leaves the FSM unchanged. This does not update the current state
157 nor does it trigger the output action. Normally you do not call
158 this method. It is called by process().
159
160 The sequence of steps to check for a defined transition goes from
161 the most specific to the least specific.
162 1. Check state_transitions[] that match (input_symbol, state)
163 2. Check state_transitions_any[] that match (state)
164 In other words, match a specific state and ANY input_symbol.
165 3. Check if the default_transition is defined.
166 This catches any input_symbol and any state.
167 This is a handler for errors, undefined states, or defaults.
168 4. No transition was defined. If we get here then raise an exception.
169 '''
170 if self.state_transitions.has_key((input_symbol, self.current_state)):
171 return self.state_transitions[(input_symbol, self.current_state)]
172 elif self.state_transitions_any.has_key (self.current_state):
173 return self.state_transitions_any[self.current_state]
174 elif self.default_transition != None:
175 return self.default_transition
176 else:
177 raise ExceptionFSM ('Transition is undefined: (%s, %s).' %
178 (str(input_symbol), str(self.current_state)) )
179
181 '''This is the main method that you call to process input.
182 This may cause the FSM to change state and call an action.
183 This method calls get_transition() to find the action and next_state
184 associated with the input_symbol and current_state.
185 If the action is None then the action is not called and
186 only the current state is changed.
187 This method processes one input symbol. You can process a list of
188 symbols (or a string) by calling process_list().
189 '''
190 self.input_symbol = input_symbol
191 (action, next_state) = self.get_transition (self.input_symbol, self.current_state)
192 if action != None:
193 action (self)
194 self.current_state = next_state
195
197 '''This takes a list and sends each element to process().
198 The list may be a string.
199 '''
200 for c in s:
201 self.process (c)
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215
216 import string
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221
223 fsm.something.append (fsm.input_symbol)
225 s = fsm.something.pop ()
226 s = s + fsm.input_symbol
227 fsm.something.append (s)
229 s = fsm.something.pop ()
230 fsm.something.append (int(s))
232 ar = fsm.something.pop()
233 al = fsm.something.pop()
234 if fsm.input_symbol == '+':
235 fsm.something.append (al + ar)
236 elif fsm.input_symbol == '-':
237 fsm.something.append (al - ar)
238 elif fsm.input_symbol == '*':
239 fsm.something.append (al * ar)
240 elif fsm.input_symbol == '/':
241 fsm.something.append (al / ar)
243 print str(fsm.something.pop())
245 print 'That does not compute.'
246 print str(fsm.input_symbol)
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254 f = FSM ('INIT', [])
255 f.set_default_transition (Error, 'INIT')
256 f.add_transition_any ('INIT', None, 'INIT')
257 f.add_transition ('=', 'INIT', DoEqual, 'INIT')
258 f.add_transition_list (string.digits, 'INIT', BeginBuildNumber, 'BUILDING_NUMBER')
259 f.add_transition_list (string.digits, 'BUILDING_NUMBER', BuildNumber, 'BUILDING_NUMBER')
260 f.add_transition_list (string.whitespace, 'BUILDING_NUMBER', EndBuildNumber, 'INIT')
261 f.add_transition_list ('+-*/', 'INIT', DoOperator, 'INIT')
262
263 print
264 print 'Enter an RPN Expression.'
265 print 'Numbers may be integers. Operators are * / + -'
266 print 'Use the = sign to evaluate and print the expression.'
267 print 'For example: '
268 print ' 167 3 2 2 * * * 1 - ='
269 inputs = raw_input ('>')
270 for s in inputs:
271 f.process (s)
272
273 if __name__ == '__main__':
274 example ()
275