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sagemath
GitHub Repository: sagemath/sagelib
 Path: blob/master/sage/logic/booleval.py
4078 views
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r"""

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Evaluate Boolean Formulas

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Perform boolean evaluation of boolean formulas.

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AUTHORS:

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- Chris Gorecki

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EXAMPLES::

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    sage: import sage.logic.booleval as booleval

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    sage: t = ['|', ['&', 'a', 'b'], ['&', 'a', 'c']]

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    sage: d = {'a' : True, 'b' : False, 'c' : True}

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    sage: booleval.eval_formula(t, d)

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    True

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    sage: d['a'] = False

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    sage: booleval.eval_formula(t, d)

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    False

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Classes and functions

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=====================

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"""

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import logicparser

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# dictionary containing variable keys and boolean values

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__vars = {}

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def eval_formula(tree, vdict):

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    r"""

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    Evaluates the tree using the boolean values contained in dictionary

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    and returns a single boolean value.

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    INPUT:

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    - ``tree`` -- a list of three elements corresponding to a branch of a

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      parse tree.

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    - ``vdict`` -- a dictionary containing variable keys and boolean values.

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    OUTPUT:

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    - Returns the boolean evaluation of a boolean formula.

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    EXAMPLES::

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        sage: import sage.logic.booleval as booleval

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        sage: t = ['|', ['&', 'a', 'b'], ['&', 'a', 'c']]

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        sage: d = {'a' : True, 'b' : False, 'c' : True}

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        sage: booleval.eval_formula(t, d)

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        True

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        sage: d['a'] = False

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        sage: booleval.eval_formula(t, d)

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        False

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    """

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    global __vars

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    __vars = vdict

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    b = logicparser.apply_func(tree, eval_f)

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    return b

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def eval_f(tree):

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    r"""

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    This function can be applied to a parse tree to evaluate it.

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    INPUT:

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    - ``tree`` -- a list of three elements corresponding to a branch of a

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      parse tree.

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    OUTPUT:

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    - Returns a boolean evaluation of the tree.

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    EXAMPLES::

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         sage: import sage.logic.booleval as booleval

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         sage: booleval.eval_f(['&', True, False])

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         False

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         sage: booleval.eval_f(['^', True, True])

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         False

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         sage: booleval.eval_f(['|', False, True])

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         True

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    """

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    return eval_op(tree[0], tree[1], tree[2])

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def eval_op(op, lv, rv):

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    r"""

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    This function evaluates ``lv`` and ``rv`` according to the operator ``op``.

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    INPUT:

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    - ``op`` -- a string or character representing a boolean operator.

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    - ``lv`` -- a boolean or variable.

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    - ``rv`` -- a boolean or variable.

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    OUTPUT:

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    - Returns the evaluation of ``lv op rv``.

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    EXAMPLES::

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        sage: import sage.logic.booleval as booleval

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        sage: booleval.eval_op('&', True, False)

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        False

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        sage: booleval.eval_op('^', True, True)

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        False

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        sage: booleval.eval_op('|', False, True)

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        True

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    """

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    lval = rval = None

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    if lv == False:

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        lval = False

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    elif lv == True:

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        lval = True

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    elif lv is not None:

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        lval = __vars[lv]

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    if rv == False:

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        rval = False

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    elif rv == True:

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        rval = True

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    elif rv is not None:

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        rval = __vars[rv]

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    if op == '~':

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        return not lval

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    elif op == '&':

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        return lval and rval

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    elif op == '|':

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        return lval or rval

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    elif op == '^':

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        return lval ^ rval

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    elif op == '->':

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        return (not lval) or rval

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    elif op == '<->':

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        return (not lval or rval) and (not rval or lval)

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    else:  # one variable

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        return __vars[op]

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