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A simple way to evaluate Boolean Algebra.

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Caesium is a simple language built to help myself (and others) learn about and understand how Boolean algebra works. It does this by providing an interpreter for Boolean algebra.


  1. Ensure that you have a working version of python (You can get python3 from the official site if you don't have it or want to upgrade). Any python version >= 3.6.0 is officially supported so it should work. Older versions of python3 will probably work but they are not officially supported so use them at your own risk.
  2. Install caesium using pip by running pip install caesium-lang from the command line.
  3. Test it out by running the command caesium in your command line.


Starting the Prompt

You can start the prompt by typing the word caesium into your terminal and pressing Enter. The caesium prompt should start and print something out to the screen like so:

$ caesium
caesium version 1.3.1 running on win32.
Press Ctrl+C or type "exit" to quit.

If you wish to close the interpreter now, scroll down to the Exiting header or press here to learn how to do that.


An expression is any valid code which can be turned into a single value. All valid code is made up of expressions (except the exit keyword which exits the prompt). Expressions are evaluated right to left by default unless brackets (()) are used.


There are only 2 built-in values: True (or 1) and False (or 0). Caesium is case-insensitive, so it will accept them in upper, lower or even mixed case.

There is also the random keyword which randomly evaluates to either True or False whenever it is used.

Cs> False
Cs> tRuE
Cs> 0
Cs> 1
Cs> random


You can bind a name to a value by putting a valid name, then a = and any valid expression. A valid name is made up of any number of alphanumeric characters and underscores.Valid names also cannot be keywords. Assignments can be chained together to define more than one variable at once. Since assignments are expressions, they can be nested within larger expressions. I wouldn't recommend this though, it makes the line quite unreadable.

Cs> foo = True
Cs> quux = coco = (True ^ (bar = True)) & False


In Boolean algebra,there are 2 types of operators, basic operators and derived operators.

Basic Operators

Basic operators, together with the 2 Boolean values, are the building blocks of Boolean algebra. Without them, Boolean algebra simply wouldn't exist. There are only 3 basic operators:

1. NOT

not takes a value and flips its value. It can also be written as !. Its operations can be summarised as:

Expression Result
not True False
not False True
2. AND

and takes 2 arguments and checks if both of them evaluate to True. and can also be written as & or &&. and operations can be summarised as:

Expression Result
True and True True
True and False False
False and True False
False and False False
3. OR

or also takes 2 arguments and checks if both of them evaluate to False. or can also be written as | or ||. or operations can be summarised as:

Expression Result
True or True True
True or False True
False or True True
False or False False

Derived Operators

Derived operators are called "derived" because they are derived from the basic operators (they can be re-written as basic operators). Since we ,as programmers, are too lazy to write them out in full, we made them as a kind of shorthand.

1. XOR

xor (eXclusive OR) works just like or, but where both values cannot be True. xor can also be written as ^. xor operations can be represented in a table as:

Expression Result
True xor True False
True xor False True
False xor True True
False xor False False
2. NOR

nor (Not OR) also works just like or, but it negates what or returns. It can also be written as ~.nandnor operations can be represented in a table as:

Expression Result
True nor True False
True nor False False
False nor True False
False nor False True

nand (Not AND) works exactly like and, but it negates what and returns. It can also be written as @. nand operations can be represented in a table as:

Expression Result
True nand True False
True nand False True
False nand True True
False nand False True


Rather than having to refer to the README every single time you don't remember what an operator does, caesium comes with the help command. It is used to print out a line of explanation about the operator passed to it.

It is useed by typing help then the operator in question like so:

Cs> help or
or checks if at least one value is true.


Comments are lines of text meant for other people to read, rather than for the interpreter to run. Everything that comes after a # character is treated by the interpreter as if it is not there. So for example, if a line starts with a #, the entire line will be treated as if it were blank.


When you try to run code which has a mistake (like a missing bracket), the interpreter complains about your code instead of running it. This is an error. An error is basically the interpreter alerting you that there was something wrong with the code and so it can't run it. Once an error is thrown, you will have to fix whatever is wrong with your expression then rerun it.


Cs> quux
Error: Undefined name "quux".
Cs> random/  # Here I'm supposed to write "random"
Error: Invalid syntax: "/".


Either pressing Control + C or typing in exit and hitting Enter will cause the interpreter to stop instantly and take you back to the normal shell.

Cs> exit


Development Setup

  1. Install development packages by running pip install -r requirements-dev.txt inside a fresh virtualenv (for this project, we use the .venv folder).
  2. Assert everything is working by running pytest from the project's root dir.


  1. Create your feature branch by forking the develop branch.
  2. Commit your changes.
  3. Push to origin/develop.
  4. Open a pull request.


Just like the element Caesium, this app may break down. In case it does, please contact me or if you want to, fix it yourself.


This project is licensed under the BSD 3-Clause License. Please see the license file for more information.

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