To start using Fōrmulæ, you will need the following:

  • Your computer must have installed either a Windows, Linux or MacOS operating system
  • Your computer must have installed Java version 7+

Download the file from the Downloads section of this site and unpack it to a new a new directory/folder.

Run the desktop.jar file, simply double-clicking over it.

The program looks as follows:

Editing expressions

The edition is done in a point-and-click interface. It works with the concept of the selected expression. There is always one and only one selected expression. It is shown in dark background. The null expression shown above is currently the selected expression. The operations in the left panel works on the selected expression. As an example, select the "Addition" operation on the left. The small figure indicates that an addition expression will be created, the current selected expression will become the left addend, and a new null expression will be created to become the second addend, as shown below:

Now move the cursor arrow over the new expression, you will notice that a blue box is shown depending on where the cursor is over. This box indicated the highlighted expression. If you left click the current highlighted expression becomes the selected expression.

In our example, there are now three possibilities to choose the selected expression, the left addend, the right addend, or the entire addition. Choose whatever you want.

Now select the  division expression from the left area (or press the '/' key on your keyboard) and see that the result depends on which expressions was the selected one:

There are also other actions, such as the insert key (to create a new subexpression when a expression can contain several of them, i.e. an addition), the delete key (the opposite), cut-copy-paste operations, undo-redo actions, etc.

With this method you can edit complex expressions.

Reducing expressions

With the desktop program you not only can create beautiful expressions, it is intended to reduce them. Reduction is the transformation of an expression in another equivalent expression, usually simpler, or more useful.

The desktop program works in a question-answer fashion, much like a command-line environment (a Unix shell or a MSDOS command window), but it is much more graphic.

As an example, substitute the null expressions for numbers. For each null expression, select it and choose "Number" from the left panel, and a dialog window will splash to ask you for the number.

Once you have finished the expression, simply press the <ENTER> key and the program will show the reduced expression, (in grey) and will show a new null expression (a new "question"), see the example below:

You can edit a new expression, or edit one of the previous.

How does reduction work ? The packages you have downloaded, also contains a set of transformation rules that can be applied to expressions in order to reduce them. The "answer" expression is the result of applying these rules on the given expression (and its subexpressions) repeatedly until no transformation rule can be applied.

In order to show the applied reduction rules, press <ALT><ENTER> instead of <ENTER>. See the following example:


The magic happens when you combine expressions from different packages. They work cooperatively to be visualized, edited and reduced together, even when their expression packages were written by different persons, at different times, and in different places of the world.

So your desktop program becomes "smarter" when you install new packages. An expression package is also a simple file that can be downloaded or sent by email.