380 lines
11 KiB
Python
380 lines
11 KiB
Python
#!/usr/bin/env python
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# encoding: utf-8
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from .generic import Stack, flatten_list, expand_list
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from .operator import Operator
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from .fraction import Fraction
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from .renders import txt, post2in_fix, tex
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__all__ = ['Expression']
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class Expression(object):
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"""A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""
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PRIORITY = {"^": 5, "*" : 3, "/": 4, ":": 3, "+": 2, "-":2, "(": 1}
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STR_RENDER = tex
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def __init__(self, exp):
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""" Initiate the expression
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:param exp: the expression. It can be a string or a list of tokens. It can be infix or postfix expression
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"""
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if type(exp) == str:
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self._exp = exp
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self.tokens = self.str2tokens(exp) # les tokens seront alors stockés dans self.tokens temporairement
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elif type(exp) == list:
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self.tokens = exp
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self._infix_tokens = None
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self._postfix_tokens = None
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self.feed_fix() # Determine le fix et range la liste dans self.[fix]_tokens
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def __str__(self):
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"""
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Overload str
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If you want to changer render set Expression.RENDER
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"""
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return self.STR_RENDER(self.postfix_tokens)
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def render(self, render = lambda x:str(x)):
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""" Same as __str__ but accept render as argument
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:param render: function which render the list of token (postfix form) to string
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"""
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# TODO: I don't like the name of this method |ven. janv. 17 12:48:14 CET 2014
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return render(self.postfix_tokens)
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## ---------------------
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## Mechanism functions
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def simplify(self):
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""" Generator which return steps for computing the expression """
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if not self.can_go_further():
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yield self.STR_RENDER(self.postfix_tokens)
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else:
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self.compute_exp()
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old_s = ''
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for s in self.steps:
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new_s = self.STR_RENDER(s)
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# Astuce pour éviter d'avoir deux fois la même étape (par exemple pour la transfo d'une division en fraction)
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if new_s != old_s:
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old_s = new_s
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yield new_s
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for s in self.child.simplify():
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if old_s != s:
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yield s
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def can_go_further(self):
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"""Check whether it's a last step or not. If not create self.child the next expression.
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:returns: 1 if it's not the last step, 0 otherwise
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"""
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if len(self.tokens) == 1:
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return 0
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else:
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return 1
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def compute_exp(self):
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""" Create self.child with self.steps to go up to it """
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self.steps = [self.postfix_tokens]
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tokenList = self.postfix_tokens.copy()
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tmpTokenList = []
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while len(tokenList) > 2:
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# on va chercher les motifs du genre A B +, quad l'operateur est d'arité 2, pour les calculer
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if self.isNumber(tokenList[0]) and self.isNumber(tokenList[1]) \
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and type(tokenList[2]) == Operator and tokenList[2].arity == 2 :
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# S'il y a une opération à faire
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op1 = tokenList[0]
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op2 = tokenList[1]
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operator = tokenList[2]
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res = operator(op1, op2)
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tmpTokenList.append(res)
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# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
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del tokenList[0:3]
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elif self.isNumber(tokenList[0]) \
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and type(tokenList[1]) == Operator and tokenList[1].arity == 1 :
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# S'il y a une opération à faire
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op1 = tokenList[0]
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operator = tokenList[1]
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res = operator(op1)
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tmpTokenList.append(res)
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# Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
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del tokenList[0:2]
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else:
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tmpTokenList.append(tokenList[0])
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del tokenList[0]
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tmpTokenList += tokenList
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steps = expand_list(tmpTokenList)
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if len(steps[:-1]) > 0:
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self.steps += [flatten_list(s) for s in steps[:-1]]
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self.child = Expression(steps[-1])
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## ---------------------
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## "fix" recognition
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#@classmethod
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#def get_fix(self, tokens):
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# """ Give the "fix" of an expression
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# [A, +, B] -> infix, or if there is parenthesis it is infix
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# [+, A, B] -> prefix
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# [A, B, +] -> postfix
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# /!\ does not verify if the expression is correct/computable!
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# :param exp: the expression (list of token)
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# :returns: the "fix" (infix, postfix, prefix)
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# """
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# if self.isOperator(tokens[0]):
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# return "prefix"
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# elif "(" in tokens:
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# return "infix"
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# elif not self.isOperator(tokens[0]) and not self.isOperator(tokens[1]):
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# return "postfix"
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# else:
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# return "infix"
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#def feed_fix(self):
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# """ Recognize the fix of self.tokens and stock tokens in self.[fix]_tokens """
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# if len(self.tokens) > 1:
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# fix = self.get_fix(self.tokens)
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# else:
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# fix = "postfix" # Completement arbitraire mais on s'en fiche!
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# setattr(self, fix+"_tokens", self.tokens)
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# ----------------------
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# Expressions - tokens manipulation
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@property
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def infix_tokens(self):
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""" Return infix list of tokens. Verify if it has already been computed and compute it if not
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:returns: infix list of tokens
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"""
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if self._infix_tokens:
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return self._infix_tokens
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elif self._postfix_tokens:
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self._infix_tokens = post2in_fix(self._postfix_tokens)
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return self._infix_tokens
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else:
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raise ValueError("Unkown fix")
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@infix_tokens.setter
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def infix_tokens(self, val):
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self._infix_tokens = val
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@property
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def postfix_tokens(self):
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""" Return postfix list of tokens. Verify if it has already been computed and compute it if not
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:returns: postfix list of tokens
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"""
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if self._postfix_tokens:
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return self._postfix_tokens
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elif self._infix_tokens:
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self._postfix_tokens = self.in2post_fix(self._infix_tokens)
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return self._postfix_tokens
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else:
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raise ValueError("Unkown fix")
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@postfix_tokens.setter
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def postfix_tokens(self, val):
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self._postfix_tokens = val
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# ----------------------
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# "fix" tranformations
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@classmethod
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def in2post_fix(cls, infix_tokens):
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""" From the infix_tokens list compute the corresponding postfix_tokens list
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@param infix_tokens: the infix list of tokens to transform into postfix form.
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@return: the corresponding postfix list of tokens.
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>>> Expression.in2post_fix(['(', 2, '+', 5, '-', 1, ')', '/', '(', 3, '*', 4, ')'])
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[2, 5, '+', 1, '-', 3, 4, '*', '/']
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>>> Expression.in2post_fix(['-', '(', '-', 2, ')'])
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[2, '-', '-']
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>>> Expression.in2post_fix(['-', '(', '-', 2, '+', 3, "*", 4, ')'])
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[2, '-', 3, 4, '*', '+', '-']
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"""
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# Stack where operator will be stocked
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opStack = Stack()
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# final postfix list of tokens
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postfix_tokens = []
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# stack with the nbr of tokens still to compute in postfix_tokens
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arity_Stack = Stack()
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arity_Stack.push(0)
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for (pos_token,token) in enumerate(infix_tokens):
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# # Pour voir ce qu'il se passe dans cette procédure
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# print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))
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if token == "(":
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opStack.push(token)
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# Set next arity counter
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arity_Stack.push(0)
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elif token == ")":
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op = opStack.pop()
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while op != "(":
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postfix_tokens.append(op)
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op = opStack.pop()
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# Go back to old arity
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arity_Stack.pop()
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# Raise the arity
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arity = arity_Stack.pop()
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arity_Stack.push(arity + 1)
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elif cls.isOperator(token):
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while (not opStack.isEmpty()) and (cls.PRIORITY[opStack.peek()] >= cls.PRIORITY[token]):
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op = opStack.pop()
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postfix_tokens.append(op)
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arity = arity_Stack.pop()
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opStack.push(Operator(token, arity + 1))
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# print("--", token, " -> ", str(arity + 1))
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# Reset arity to 0 in case there is other operators (the real operation would be "-op.arity + 1")
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arity_Stack.push(0)
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else:
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postfix_tokens.append(token)
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arity = arity_Stack.pop()
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arity_Stack.push(arity + 1)
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while not opStack.isEmpty():
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op = opStack.pop()
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postfix_tokens.append(op)
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# # Pour voir ce qu'il se passe dans cette procédure
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# print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))
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if arity_Stack.peek() != 1:
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raise ValueError("Unvalid expression. The arity Stack is ", str(arity_Stack))
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return postfix_tokens
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## ---------------------
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## Recognize numbers and operators
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@staticmethod
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def isNumber(exp):
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"""Check if the expression can be a number
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:param exp: an expression
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:returns: True if the expression can be a number and false otherwise
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"""
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return type(exp) == int or \
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type(exp) == Fraction
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@staticmethod
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def isOperator(exp):
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"""Check if the expression is an opération in "+-*/:^"
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:param exp: an expression
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:returns: boolean
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"""
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return (type(exp) == str and exp in "+-*/:^")
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def test(exp):
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a = Expression(exp)
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for i in a.simplify():
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print(i)
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print("\n")
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if __name__ == '__main__':
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Expression.STR_RENDER = txt
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exp = "2 ^ 3 * 5"
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test(exp)
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exp = "1 + 3 * 5"
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test(exp)
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#exp = "2 * 3 * 3 * 5"
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#test(exp)
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#exp = "2 * 3 + 3 * 5"
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#test(exp)
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#exp = "2 * ( 3 + 4 ) + 3 * 5"
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#test(exp)
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#exp = "2 * ( 3 + 4 ) + ( 3 - 4 ) * 5"
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#test(exp)
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#
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#exp = "2 * ( 2 - ( 3 + 4 ) ) + ( 3 - 4 ) * 5"
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#test(exp)
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#
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#exp = "2 * ( 2 - ( 3 + 4 ) ) + 5 * ( 3 - 4 )"
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#test(exp)
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#
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#exp = "2 + 5 * ( 3 - 4 )"
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#test(exp)
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#exp = "( 2 + 5 ) * ( 3 - 4 )^4"
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#test(exp)
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#exp = "( 2 + 5 ) * ( 3 * 4 )"
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#test(exp)
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#exp = "( 2 + 5 - 1 ) / ( 3 * 4 )"
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#test(exp)
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#exp = "( 2 + 5 ) / ( 3 * 4 ) + 1 / 12"
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#test(exp)
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#exp = "( 2+ 5 )/( 3 * 4 ) + 1 / 2"
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#test(exp)
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#exp="(-2+5)/(3*4)+1/12+5*5"
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#test(exp)
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#exp="-2*4(12 + 1)(3-12)"
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#test(exp)
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#exp="(-2+5)/(3*4)+1/12+5*5"
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#test(exp)
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# TODO: The next one doesn't work |ven. janv. 17 14:56:58 CET 2014
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#exp="-2*(-a)(12 + 1)(3-12)"
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#e = Expression(exp)
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#print(e)
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## Can't handle it yet!!
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#exp="-(-2)"
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#test(exp)
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import doctest
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doctest.testmod()
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# -----------------------------
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# Reglages pour 'vim'
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# vim:set autoindent expandtab tabstop=4 shiftwidth=4:
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# cursor: 16 del
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