Evaluation of Boolean Formulas

AUTHORS:

  • Chris Gorecki (2006): initial version

  • Paul Scurek (2013-08-05): updated docstring formatting

EXAMPLES:

We can assign values to the variables and evaluate a formula:

sage: import sage.logic.booleval as booleval
sage: t = ['|', ['&', 'a', 'b'], ['&', 'a', 'c']]
sage: d = {'a' : True, 'b' : False, 'c' : True}
sage: booleval.eval_formula(t, d)
True

>>> from sage.all import *
>>> import sage.logic.booleval as booleval
>>> t = ['|', ['&', 'a', 'b'], ['&', 'a', 'c']]
>>> d = {'a' : True, 'b' : False, 'c' : True}
>>> booleval.eval_formula(t, d)
True

We can change our assignment of values by modifying the dictionary:

sage: d['a'] = False
sage: booleval.eval_formula(t, d)
False

>>> from sage.all import *
>>> d['a'] = False
>>> booleval.eval_formula(t, d)
False
sage.logic.booleval.eval_f(tree)[source]

Evaluate the tree.

INPUT:

  • tree – list of three elements corresponding to a branch of a parse tree

OUTPUT: the result of the evaluation as a boolean value

EXAMPLES:

This example illustrates how to evaluate a parse tree:

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

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

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

>>> from sage.all import *
>>> import sage.logic.booleval as booleval
>>> booleval.eval_f(['&', True, False])
False

>>> booleval.eval_f(['^', True, True])
False

>>> booleval.eval_f(['|', False, True])
True
sage.logic.booleval.eval_formula(tree, vdict)[source]

Evaluate the tree and return a boolean value.

INPUT:

  • tree – list of three elements corresponding to a branch of a parse tree

  • vdict – dictionary containing variable keys and boolean values

OUTPUT: the result of the evaluation as a boolean value

EXAMPLES:

This example illustrates evaluating a boolean formula:

sage: import sage.logic.booleval as booleval
sage: t = ['|', ['&', 'a', 'b'], ['&', 'a', 'c']]
sage: d = {'a' : True, 'b' : False, 'c' : True}
sage: booleval.eval_formula(t, d)
True

>>> from sage.all import *
>>> import sage.logic.booleval as booleval
>>> t = ['|', ['&', 'a', 'b'], ['&', 'a', 'c']]
>>> d = {'a' : True, 'b' : False, 'c' : True}
>>> booleval.eval_formula(t, d)
True


sage: d['a'] = False
sage: booleval.eval_formula(t, d)
False

>>> from sage.all import *
>>> d['a'] = False
>>> booleval.eval_formula(t, d)
False
sage.logic.booleval.eval_op(op, lv, rv)[source]

Evaluate lv and rv according to the operator op.

INPUT:

  • op – string or character representing a boolean operator

  • lv – boolean or variable

  • rv – boolean or variable

OUTPUT: the evaluation of lv op rv as a boolean value

EXAMPLES:

We can evaluate an operator given the values on either side:

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

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

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

>>> from sage.all import *
>>> import sage.logic.booleval as booleval
>>> booleval.eval_op('&', True, False)
False

>>> booleval.eval_op('^', True, True)
False

>>> booleval.eval_op('|', False, True)
True