Macros

A macro is an expression with a name. Wherever the name appears it is replaced by that expression before anything is compiled, so Desmos never learns that a macro was involved - the graph is the one you would have written by hand.

Two kinds. Without a parameter list it stands for one expression:

macro TAU = 6.283185

With one, it takes arguments and puts them into its body:

macro LERP(a, b, t) = a + (b - a) * t

A macro stands for an expression and nothing else - never a statement, a block or a run of metadata. Reusable styling is a different thing, a style, and 19-styles.axis is about those; the end of this file shows the two side by side.

examples/17-macros.axis

config {
    xmin: -7
    xmax: 7
    ymin: -3
    ymax: 3
}

macro TAU = 6.283185
macro WAVE(k, phase) = sin(k * x + phase)

"Constants"

// A macro is not a variable: nothing named TAU reaches the graph, and the
// number is written into each expression that used it.
y = sin(TAU * x / 4) @ color: RED, lineWidth: 3
period = TAU / 4 @ color: RED

"Arguments"

// An argument may be anything an expression may hold - a number, a name, an
// expression, another macro.
y = WAVE(1, 0) @ color: BLUE
y = WAVE(2, TAU / 4) @ color: GREEN
y = WAVE(1, 0) + WAVE(2, TAU / 4) @ color: PURPLE, lineWidth: 3

// The substitution is made on the parsed expression, not on its text, so an
// argument keeps its own grouping without brackets: this is sin((1 + 2) * x),
// never sin(1 + 2 * x).
y = WAVE(1 + 2, 0) @ color: ORANGE, lineOpacity: 0.4

// A macro is in scope for the whole file, wherever it is written and whatever
// it is written above - so it belongs at the top level, outside every block. Its
// body may be a whole equation, which then stands as a statement of its own.
macro CIRCLE(size) = x ^ 2 + y ^ 2 = size ^ 2

folder "Everywhere an expression goes" {
    // Inside a block is no different: the substitution happens first, and
    // what comes out of it is read as the folder's entries.
    CIRCLE(1) @ color: BLACK, lineStyle: DASHED
    CIRCLE(2) @ color: BLACK, lineOpacity: 0.3
}

"Macros and styles"

// Metadata is not an expression, so no macro can stand for it. A run of
// properties written once and used on many statements is a style instead: it
// has a name of its own, and `use:` applies it. Macros make expressions, styles
// make metadata, and each is checked as what it is.
style swatch { pointSize: 14; showLabel }
style faint { color: #7b7b7b; lineOpacity: 0.35; lineStyle: DOTTED }

(-2, 1) @ use: swatch, color: RED, label: "one"
(0, 1) @ use: swatch, color: BLUE, label: "two"
(2, 1) @ use: swatch, color: GREEN, label: "three"

y = x @ use: faint
y = -x @ use: faint

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