Introduction

Axis is a language that compiles to Desmos graphs. A .axis file goes in; the expressions, folders, tables and settings a graph is made of come out, ready for a calculator to draw. Nothing in the file runs: it describes a graph, the way an HTML file describes a page.

"A parabola and a wave"

f(x) = x ^ 2 - 4x + 3 @ color: RED
a = 1 @ slider: 0..5 step 0.5
y = a sin(x) @ color: BLUE, lineStyle: DASHED

Open in playground →

Each line is a statement: a note, a function, a slider, an equation. Anything after an @ is metadata - how the statement looks and behaves - so the colour, the slider’s range and the dashed line are written beside the thing they belong to rather than set afterwards in a menu.

Why write a graph

Desmos is built to be clicked. That is the right way to explore an idea and a hard way to keep a large graph in order: a long expression list has no comments, no way to reuse a piece of it in another graph, and no history but the undo stack. Axis keeps the graph as text instead, which buys the things text already has.

• A graph is a file. It can be diffed, reviewed, and kept in git beside whatever else it belongs to. A comment explains a line to whoever reads it next, and never reaches the graph.
• Graphs can be built out of other graphs. import "./lib/waves" drops a whole file into this one as a folder, so a long graph can live in several files and a useful one can be reused.
• Repetition has names. A macro names an expression and a style names a set of properties. Both are resolved away before Desmos sees anything, so the graph is the one you would have written out by hand.
• Mistakes are reported, not drawn. Desmos reads a misspelt sine(x) as a product of variables and color: red as r·e·d, and never calls either a mistake. Axis reports each as a diagnostic with a code and the place it was written.
• The editor knows the language. The VSCode extension completes, hovers, formats and checks as you type, and previews the graph beside the file. Drag a point or move a slider in the preview and the statement that drew it is rewritten in the editor.

Nothing about Desmos is hidden to make this work. Every statement becomes an ordinary expression, folder, table or note, and a compiled graph is one anybody can open, change and save at desmos.com. It also runs the other way: the decompiler reads a Desmos graph back into a file.

A slightly longer example

config { showGrid: true; xmin: -7; xmax: 7 }

style guide { color: BLACK; lineOpacity: 0.3; lineStyle: DASHED }

"Sine, and a point riding it"

folder "Controls" { @ collapsed
    amp = 2 @ slider: 0..4 step 0.1
    t = 0 @ slider: 0..2pi, playing
}

y = amp sin(x) @ color: BLUE, lineWidth: 3
(t, amp sin(t)) @ color: RED, pointSize: 16
y = amp @ use: guide
y = -amp @ use: guide

Open in playground →

config sets the calculator up, style names a look to use: twice, the folder keeps the sliders out of the way, and playing sets t moving the moment the graph opens.

Where to go next

• Getting started installs the editor extension, the in-browser playground and the command-line harness.
• The language is a tour, statement by statement. The rest of the guide takes one topic at a time.
• The reference lists every function, property, setting and diagnostic, generated from the language itself.
• The specification is the contract the implementation is built against: where the two disagree, one of them is a bug.