AlgeZip is a command-line demo program for manipulating boolean expressions. Apply various axioms from boolean algebra to transform expressions into equivalent expressions. Choose the subexpression to apply axioms to by moving a "focus" around to navigate the expression. The navigation system is powered by a zipper data structure, hence the name AlgeZip -- using zippers to manipulate a (boolean) algebraic expression.
pip install shape-warrior-t.algezip
The command-line program itself has no external dependencies, but running tests requires pytest.
Once installed, run in the command line with the command algezip.
To run tests, just clone the repository and run pytest in the proper directory.
Example run, showing the equivalence of two different formulations of XOR:
---AlgeZip---
For help, type 'help'
F
^
> help
Focus:
'^' under the current expression denotes the subexpression currently under focus
Use '^', '.', '<', '>' to move focus around (more info under Commands)
Transformations are always applied to the current subexpression under focus
Boolean expression syntax (for giving arguments to 'r!' and 'x'):
F - False, T - True
Single lowercase letters - variables
(!a) - not a, (a & b) - a and b, (a | b) - a or b
No operator precedence -- operations must be explicitly written in brackets
Allowed bracket types (interchangeable, but must be paired correctly): (), [], {}
Commands:
r! a - replace current subexpression under focus with a
^ - move focus to the parent of the current subexpression under focus
. - move focus from (!a) to its only argument a
< - move focus from (a & b) or (a | b) to the left argument a
> - move focus from (a & b) or (a | b) to the right argument b
c - [c]ommutativity -- (a | b) -> (b | a), (a & b) -> (b & a)
i - [i]dentity -- (a | F) -> a, (a & T) -> a
|F - expand via identity -- a -> (a | F)
&T - expand via identity -- a -> (a & T)
d - [d]istributivity -- (a | [b & c]) -> ([a | b] & [a | c]), (a & [b | c]) -> ([a & b] | [a & c])
f - [f]actoring -- ([a | b] & [a | c]) -> (a | [b & c]), ([a & b] | [a & c]) -> (a & [b | c])
v - complements/in[v]erses -- (a | [!a]) -> T, (a & [!a]) -> F
x a - e[x]pand into complements -- T -> (a | [!a]), F -> (a & [!a])
help - print help
q! - quit
F
^
> r! ([a | b] & [{!a} | {!b}])
([a | b] & [{!a} | {!b}])
^^^^^^^^^^^^^^^^^^^^^^^^^
> d
([{a | b} & {!a}] | [{a | b} & {!b}])
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> <
([{a | b} & {!a}] | [{a | b} & {!b}])
^^^^^^^^^^^^^^^^
> c
([{!a} & {a | b}] | [{a | b} & {!b}])
^^^^^^^^^^^^^^^^
> d
([{(!a) & a} | {(!a) & b}] | [{a | b} & {!b}])
^^^^^^^^^^^^^^^^^^^^^^^^^
> <
([{(!a) & a} | {(!a) & b}] | [{a | b} & {!b}])
^^^^^^^^^^
> c
([{a & (!a)} | {(!a) & b}] | [{a | b} & {!b}])
^^^^^^^^^^
> v
([F | {(!a) & b}] | [{a | b} & {!b}])
^
> ^
([F | {(!a) & b}] | [{a | b} & {!b}])
^^^^^^^^^^^^^^^^
> c
([{(!a) & b} | F] | [{a | b} & {!b}])
^^^^^^^^^^^^^^^^
> i
([{!a} & b] | [{a | b} & {!b}])
^^^^^^^^^^
> c
([b & {!a}] | [{a | b} & {!b}])
^^^^^^^^^^
> ^
([b & {!a}] | [{a | b} & {!b}])
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> >
([b & {!a}] | [{a | b} & {!b}])
^^^^^^^^^^^^^^^^
> c
([b & {!a}] | [{!b} & {a | b}])
^^^^^^^^^^^^^^^^
> d
([b & {!a}] | [{(!b) & a} | {(!b) & b}])
^^^^^^^^^^^^^^^^^^^^^^^^^
> >
([b & {!a}] | [{(!b) & a} | {(!b) & b}])
^^^^^^^^^^
> c
([b & {!a}] | [{(!b) & a} | {b & (!b)}])
^^^^^^^^^^
> v
([b & {!a}] | [{(!b) & a} | F])
^
> ^
([b & {!a}] | [{(!b) & a} | F])
^^^^^^^^^^^^^^^^
> i
([b & {!a}] | [{!b} & a])
^^^^^^^^^^
> c
([b & {!a}] | [a & {!b}])
^^^^^^^^^^
> ^
([b & {!a}] | [a & {!b}])
^^^^^^^^^^^^^^^^^^^^^^^^^
> c
([a & {!b}] | [b & {!a}])
^^^^^^^^^^^^^^^^^^^^^^^^^
> q!