Derived attributes

#Read-only, recomputed every frame

Some constructs compute something as they render — a fit's slope, an integral's area, the value a reader has dragged a parameter to. Those results are published as derived attributes: read-only, recomputed every frame, and never written by the author. They are listed in their own section on the reference page of any construct that has them.

#Reading a derived value

By member access on the construct's id, written as a {{…}} group:

The fitted slope is {{#f.slope}}.

A reference written bare reaches one only where the attribute's declared type is reference — fit(of: #points), cue.trace(path: #flight), table(data: #islands). Everywhere else the text #f.slope is just those characters: a mark's label: is rich-text, so label: slope = #f.slope renders the literal words slope = #f.slope rather than a number.

The group works there, though. A rich-text attribute takes a bound expression exactly as prose does, whole or mixed into a sentence, so a mark may caption itself with a number it computes — including its own:

text(x: 0; y: 4; label: slope = {{round(#f.slope, 2)}})
curve#c(expression: sin(x); label: peaks at {{#c.max}})

A bare reading shows about four significant figures. {{round(#f.slope, 2)}} fixes the decimals, and the text functions shape it further — !format:percent{ {{#f.r2}} } for a percentage. Whatever the sentence needs, it is done to the number in the expression rather than asked for as an attribute.

#Why it must stay a binding

Reading #f.slope makes the expression around it bound: it depends on something that does not exist until the construct renders, so the compiler cannot finish it. A snapshot spliced into the source before parsing — reading the value once, while compiling — would let the prose assert a number the picture beside it later contradicts, so there is no such form. The expression tree travels to the renderer instead and is evaluated there, every frame.

#Every derived attribute

• fit — slope, intercept, r2. The slope is the fitted polynomial's derivative at zero: exact, and live under whichever degree is in force.
• curve — max and min over the plotted domain.
• integral — value, the computed area.
• The controls — slider, selector and their cue twins — value, where the parameter currently stands: the reader's setting, or the scene's sweep where they have not moved it. A selector whose values are names publishes the name itself.
• contour and surface — min and max over the visible window.
• boxplot — median, q1, q3, iqr, and the sample's min and max. A box summarising a pair of samples publishes each axis's under that axis's name — x-median, y-q3, im-iqr — and no plain median, which a sample of pairs does not have. A box grouped by a column of names publishes the plain ones only while it holds one group: each name has its own median, so a number prose needs to cite is drawn as its own box, on: its name.
• choropleth — min, max, mean and count over the values the join actually covered.
• arc — distance, the great-circle length in kilometres.

Each is published by the construct itself, from inside the renderer, once per frame. Nothing an author writes adds a derived attribute to a construct that does not declare one, and nothing sets one — an assignment is an error rather than a silent override:

fit#f(of: #points; model: polynomial; slope: 2)

Existence is still proven at compile time: a reference to a derived name the construct does not publish fails before anything renders.