tt: logical tools for logic

Welcome to the documentation site for tt!


tt is heavily tested and fully usable, but is still pre-1.0/stable software with no guarantees of avoiding breaking API changes until hitting version 1.0.

tt's PyPI page tt runs on Python 3.6, 3.7, and 3.8 tt documentation site Linux build on Travis CI Windows build on AppVeyor


tt (truth table) is a library aiming to provide a Pythonic toolkit for working with Boolean expressions and truth tables. Please see the project site for guides and documentation, or check out for a simple web application powered by this library.


tt is tested on CPython 3.6, 3.7, and 3.8. You can get the latest release from PyPI with:

pip install ttable


Parse expressions:

>>> from tt import BooleanExpression
>>> b = BooleanExpression('A impl not (B nand C)')
>>> b.tokens
['A', 'impl', 'not', '(', 'B', 'nand', 'C', ')']
>>> print(b.tree)

Evaluate expressions:

>>> b = BooleanExpression('(A /\ B) -> (C \/ D)')
>>> b.evaluate(A=1, B=1, C=0, D=0)
>>> b.evaluate(A=1, B=1, C=1, D=0)

Interact with expression structure:

>>> b = BooleanExpression('(A and ~B and C) or (~C and D) or E')
>>> b.is_dnf
>>> for clause in b.iter_dnf_clauses():
...     print(clause)
A and ~B and C
~C and D

Apply expression transformations:

>>> from tt import to_primitives, to_cnf
>>> to_primitives('A xor B')
<BooleanExpression "(A and not B) or (not A and B)">
>>> to_cnf('(A nand B) impl (C or D)')
<BooleanExpression "(A or C or D) and (B or C or D)">

Or create your own:

>>> from tt import tt_compose, apply_de_morgans, coalesce_negations, twice
>>> b = BooleanExpression('not (not (A or B))')
>>> f = tt_compose(apply_de_morgans, twice)
>>> f(b)
<BooleanExpression "not not A or not not B">
>>> g = tt_compose(f, coalesce_negations)
>>> g(b)
<BooleanExpression "A or B">

Exhaust SAT solutions:

>>> b = BooleanExpression('~(A or B) xor C')
>>> for sat_solution in b.sat_all():
...     print(sat_solution)
A=0, B=1, C=1
A=1, B=0, C=1
A=1, B=1, C=1
A=0, B=0, C=0

Find just a few:

>>> with b.constrain(A=1):
...     for sat_solution in b.sat_all():
...         print(sat_solution)
A=1, B=0, C=1
A=1, B=1, C=1

Or just one:

>>> b.sat_one()
<BooleanValues [A=0, B=1, C=1]>

Build truth tables:

>>> from tt import TruthTable
>>> t = TruthTable('A iff B')
>>> print(t)
| A | B |   |
| 0 | 0 | 1 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |

And much more!


tt uses the MIT License.

Want to learn more?

If you’re just getting started and looking for tutorial-style documentation, head on over to the User Guide. If you would prefer a comprehensive view of this library’s functionality, check out the API docs: