# 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
```

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

```sage: d['a'] = False
sage: booleval.eval_formula(t, d)
False
```
sage.logic.booleval.eval_f(tree)#

Evaluate the tree.

INPUT:

• `tree` – a 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
```
sage.logic.booleval.eval_formula(tree, vdict)#

Evaluate the tree and return a boolean value.

INPUT:

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

• `vdict` – a 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
```
```sage: d['a'] = False
sage: booleval.eval_formula(t, d)
False
```
sage.logic.booleval.eval_op(op, lv, rv)#

Evaluate `lv` and `rv` according to the operator `op`.

INPUT:

• `op` – a string or character representing a boolean operator

• `lv` – a boolean or variable

• `rv` – a 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
```