Mapytex/pymath/expression.py

#!/usr/bin/env python
# encoding: utf-8

from .generic import Stack, flatten_list, expand_list
from .operator import Operator
from .fraction import Fraction
from .renders import txt, post2in_fix, tex

__all__ = ['Expression']

class Expression(object):
    """A calculus expression. Today it can andle only expression with numbers later it will be able to manipulate unknown"""

    PRIORITY = {"^": 5, "*" : 3, "/": 4, ":": 3, "+": 2, "-":2, "(": 1}
    STR_RENDER = tex

    def __init__(self, exp):
        """ Initiate the expression

        :param exp: the expression. It can be a string or a list of tokens. It can be infix or postfix expression
        """
        if type(exp) == str:
            self._exp = exp
            self.tokens = self.str2tokens(exp) # les tokens seront alors stockés dans self.tokens temporairement
        elif type(exp) == list:
            self.tokens = exp

        self._infix_tokens = None
        self._postfix_tokens = None

        self.feed_fix() # Determine le fix et range la liste dans self.[fix]_tokens

    def __str__(self):
        """
        Overload str
        If you want to changer render set Expression.RENDER
        """
        return self.STR_RENDER(self.postfix_tokens)

    def render(self, render = lambda  x:str(x)):
        """ Same as __str__ but accept render as argument
        :param render: function which render the list of token (postfix form) to string

        """
        # TODO: I don't like the name of this method |ven. janv. 17 12:48:14 CET 2014
        return render(self.postfix_tokens)

    ## ---------------------
    ## Mechanism functions

    def simplify(self):
        """ Generator which return steps for computing the expression  """
        if not self.can_go_further():
            yield self.STR_RENDER(self.postfix_tokens) 
        else:
            self.compute_exp() 
            old_s = ''
            for s in self.steps:
                new_s = self.STR_RENDER(s)
                # Astuce pour éviter d'avoir deux fois la même étape (par exemple pour la transfo d'une division en fraction)
                if new_s != old_s:
                    old_s = new_s
                    yield new_s
            for s in self.child.simplify():
                if old_s != s:
                    yield s

    def can_go_further(self):
        """Check whether it's a last step or not. If not create self.child the next expression.
        :returns: 1 if it's not the last step, 0 otherwise
        """
        if len(self.tokens) == 1:
            return 0
        else:
            return 1

    def compute_exp(self):
        """ Create self.child with self.steps to go up to it """
        self.steps = [self.postfix_tokens]

        tokenList = self.postfix_tokens.copy()
        tmpTokenList = []

        while len(tokenList) > 2: 
            # on va chercher les motifs du genre A B +, quad l'operateur est d'arité 2, pour les calculer 
            if self.isNumber(tokenList[0]) and self.isNumber(tokenList[1]) \
                    and type(tokenList[2]) == Operator and tokenList[2].arity == 2 :
                
                # S'il y a une opération à faire
                op1 = tokenList[0]
                op2 = tokenList[1]
                operator = tokenList[2]

                res = operator(op1, op2)

                tmpTokenList.append(res)

                # Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
                del tokenList[0:3]

            elif self.isNumber(tokenList[0]) \
                    and type(tokenList[1]) == Operator and tokenList[1].arity == 1 :
                
                # S'il y a une opération à faire
                op1 = tokenList[0]
                operator = tokenList[1]

                res = operator(op1)

                tmpTokenList.append(res)

                # Comme on vient de faire le calcul, on peut détruire aussi les deux prochains termes
                del tokenList[0:2]

            else:
                tmpTokenList.append(tokenList[0])

                del tokenList[0]
        tmpTokenList += tokenList

        steps = expand_list(tmpTokenList)

        if len(steps[:-1]) > 0:
            self.steps += [flatten_list(s) for s in steps[:-1]]

        self.child = Expression(steps[-1])

    ## ---------------------
    ## String parsing

    @classmethod
    def str2tokens(self, exp):
        """ Parse the expression, ie tranform a string into a list of tokens

        /!\ float are not availiable yet!

        :param exp: The expression (a string)
        :returns: list of token

        """
        tokens = ['']

        for character in exp:
            if character.isdigit():
                # for "big" numbers (like 2345)
                if type(tokens[-1]) == int:
                    if tokens[-1] > 0:
                        tokens[-1] = tokens[-1]*10 + int(character)
                    else:
                        tokens[-1] = tokens[-1]*10 - int(character)


                # Special case for "-" at the begining of an expression or before "("
                elif tokens[-1] == "-" and \
                        str(tokens[-2]) in " (+-*/:":
                    tokens[-1] = - int(character)
                else:
                    tokens.append(int(character))

            elif character in "+-*/):^":
                tokens.append(character)

            elif character in "(":
                # If "3(", ")("
                if self.isNumber(tokens[-1]) \
                        or tokens[-1] == ")" :
                    tokens.append("*")
                tokens.append(character)

            elif character == ".":
                raise ValueError("No float number please")

            elif character != " ":
                raise ValueError("{} is an unvalid character".format(character))

        return tokens[1:]

    # ---------------------
    # "fix" recognition

    @classmethod
    def get_fix(self, tokens):
        """ Give the "fix" of an expression
        [A, +, B] -> infix, or if there is parenthesis it is infix
        [+, A, B] -> prefix
        [A, B, +] -> postfix
        /!\ does not verify if the expression is correct/computable!

        :param exp: the expression (list of token)
        :returns: the "fix" (infix, postfix, prefix)

        """
        if self.isOperator(tokens[0]):
            return "prefix"
        elif "(" in tokens:
            return "infix"
        elif not self.isOperator(tokens[0]) and not self.isOperator(tokens[1]):
            return "postfix"
        else:
            return "infix"

    def feed_fix(self):
        """ Recognize the fix of self.tokens and stock tokens in self.[fix]_tokens """
        if len(self.tokens) > 1:
            fix = self.get_fix(self.tokens)
        else:
            fix = "postfix" # Completement arbitraire mais on s'en fiche!

        setattr(self, fix+"_tokens", self.tokens)


    # ----------------------
    # Expressions - tokens manipulation

    @property
    def infix_tokens(self):
        """ Return infix list of tokens. Verify if it has already been computed and compute it if not

        :returns: infix list of tokens
        """
        if self._infix_tokens:
            return self._infix_tokens

        elif self._postfix_tokens:
            self._infix_tokens = post2in_fix(self._postfix_tokens)
            return self._infix_tokens

        else:
            raise ValueError("Unkown fix")

    @infix_tokens.setter
    def infix_tokens(self, val):
        self._infix_tokens = val

    @property
    def postfix_tokens(self):
        """ Return postfix list of tokens. Verify if it has already been computed and compute it if not

        :returns: postfix list of tokens
        """
        if self._postfix_tokens:
            return self._postfix_tokens

        elif self._infix_tokens:
            self._postfix_tokens = self.in2post_fix(self._infix_tokens)
            return self._postfix_tokens

        else:
            raise ValueError("Unkown fix")

    @postfix_tokens.setter
    def postfix_tokens(self, val):
        self._postfix_tokens = val

    # ----------------------
    # "fix" tranformations

    @classmethod
    def in2post_fix(cls, infix_tokens):
        """ From the infix_tokens list compute the corresponding postfix_tokens list
        
        @param infix_tokens: the infix list of tokens to transform into postfix form.
        @return: the corresponding postfix list of tokens.

        >>> Expression.in2post_fix(['(', 2, '+', 5, '-', 1, ')', '/', '(', 3, '*', 4, ')'])
        [2, 5, '+', 1, '-', 3, 4, '*', '/']
        >>> Expression.in2post_fix(['-', '(', '-', 2, ')'])
        [2, '-', '-']
        >>> Expression.in2post_fix(['-', '(', '-', 2, '+', 3, "*", 4, ')'])
        [2, '-', 3, 4, '*', '+', '-']
        """
        # Stack where operator will be stocked
        opStack = Stack()
        # final postfix list of tokens
        postfix_tokens = []
        # stack with the nbr of tokens still to compute in postfix_tokens
        arity_Stack = Stack()
        arity_Stack.push(0)

        for (pos_token,token) in enumerate(infix_tokens):

            # # Pour voir ce qu'il se passe dans cette procédure
            # print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))
            if token == "(":
                opStack.push(token)
                # Set next arity counter
                arity_Stack.push(0)
            elif token == ")":
                op = opStack.pop()
                while op != "(":
                    postfix_tokens.append(op)
                    op = opStack.pop()

                # Go back to old arity 
                arity_Stack.pop()
                # Raise the arity
                arity = arity_Stack.pop()
                arity_Stack.push(arity + 1)

            elif cls.isOperator(token):
                while (not opStack.isEmpty()) and (cls.PRIORITY[opStack.peek()] >= cls.PRIORITY[token]):
                    op = opStack.pop()
                    postfix_tokens.append(op)

                arity = arity_Stack.pop() 
                opStack.push(Operator(token, arity + 1))
                # print("--", token, " -> ", str(arity + 1))
                # Reset arity to 0 in case there is other operators (the real operation would be "-op.arity + 1")
                arity_Stack.push(0)
            else:
                postfix_tokens.append(token)
                arity = arity_Stack.pop()
                arity_Stack.push(arity + 1)

        while not opStack.isEmpty():
            op = opStack.pop()
            postfix_tokens.append(op)

            # # Pour voir ce qu'il se passe dans cette procédure
            # print(str(postfix_tokens), " | ", str(opStack), " | ", str(infix_tokens[(pos_token+1):]), " | ", str(arity_Stack))

        if arity_Stack.peek() != 1:
            raise ValueError("Unvalid expression. The arity Stack is ", str(arity_Stack))

        return postfix_tokens

    ## ---------------------
    ## Recognize numbers and operators

    @staticmethod
    def isNumber(exp):
        """Check if the expression can be a number

        :param exp: an expression
        :returns: True if the expression can be a number and false otherwise

        """
        return type(exp) == int or \
                type(exp) == Fraction 

    @staticmethod
    def isOperator(exp):
        """Check if the expression is an opération in "+-*/:^"

        :param exp: an expression
        :returns: boolean

        """
        return (type(exp) == str and exp in "+-*/:^")


def test(exp):
    a = Expression(exp)
    for i in a.simplify():
        print(i)

    print("\n")

if __name__ == '__main__':
    Expression.STR_RENDER = txt
    exp = "2 ^ 3 * 5"
    test(exp)

    exp = "1 + 3 * 5"
    test(exp)

    #exp = "2 * 3 * 3 * 5"
    #test(exp)

    #exp = "2 * 3 + 3 * 5"
    #test(exp)

    #exp = "2 * ( 3 + 4 ) + 3 * 5"
    #test(exp)

    #exp = "2 * ( 3 + 4 ) + ( 3 - 4 ) * 5"
    #test(exp)
    #
    #exp = "2 * ( 2 - ( 3 + 4 ) ) + ( 3 - 4 ) * 5"
    #test(exp)
    #
    #exp = "2 * ( 2 - ( 3 + 4 ) ) + 5 * ( 3 - 4 )"
    #test(exp)
    #
    #exp = "2 + 5 * ( 3 - 4 )"
    #test(exp)

    #exp = "( 2 + 5 ) * ( 3 - 4 )^4"
    #test(exp)

    #exp = "( 2 + 5 ) * ( 3 * 4 )"
    #test(exp)

    #exp = "( 2 + 5 - 1 ) / ( 3 * 4 )"
    #test(exp)

    #exp = "( 2 + 5 ) / ( 3 * 4 ) + 1 / 12"
    #test(exp)

    #exp = "( 2+ 5 )/( 3 * 4 ) + 1 / 2"
    #test(exp)

    #exp="(-2+5)/(3*4)+1/12+5*5"
    #test(exp)

    #exp="-2*4(12 + 1)(3-12)"
    #test(exp)


    #exp="(-2+5)/(3*4)+1/12+5*5"
    #test(exp)

    # TODO: The next one doesn't work  |ven. janv. 17 14:56:58 CET 2014
    #exp="-2*(-a)(12 + 1)(3-12)"
    #e = Expression(exp)
    #print(e)

    ## Can't handle it yet!!
    #exp="-(-2)"
    #test(exp)

    import doctest
    doctest.testmod()

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