Controls from the expression

notatio draws a control for a variable without being told how. The free symbols of an expression each get a control, chosen from what is known about the symbol, and the same choice serves a Manipulate, a prose panel and a worksheet.

What decides a control

For each symbol, in order of precedence:

1. The author's hint: a control tuple in params ({n, 1, 20}, {b, Boolean}).
2. The engine's declared type or assumption: integer steps by one, boolean is a checkbox, complex a 2D pad, and a bounded type such as integer<1..> (what an assumption n > 0 leaves) gives the bounds.
3. A letter convention, where a host turns it on (worksheets do): n, m and k are integers, z is complex.
4. A real slider from −10 to 10, widened only as far as a starting value needs.

A control-type hint (slider, stepper, knob) applies only when it suits the symbol's domain.

Domain	Control
real, integer	slider
boolean	checkbox
string	input field
complex	2D pad
finite list of values	setter bar (up to five), else popup menu
bare symbols (Natural, Adic)	the same choices, binding the symbol itself
lattice point (Gaussian or Eisenstein integers)	integer 2D pad, binding Tuple(a, b)

Manipulate without tuples

Manipulate(body) with no control tuples gives every free symbol of the body a control. A bare symbol after the body names just that one.

#Sliders for a and b

source · editable

<notatio-out format="epsil" value="Manipulate(Plot(a * Sin(b * x), (x, -6.283, 6.283)))" />

#Only b is a control

source · editable

<notatio-out format="epsil" value="Manipulate(Plot(a * Sin(b * x), (x, -6.283, 6.283)), b)" />

In params, {b, Boolean}, {s, String} and {z, Complex} are the non-numeric tuples. The lowering itself has no engine, so it writes real sliders. <notatio-manipulate> then refines the symbols named in its infer attribute against the engine's declarations: a symbol declared integer gets a whole-number slider, one declared boolean a checkbox.

Scope

Inference reads the declarations of the enclosing notebook or dynamic module. A declaration made in one notebook types the controls there and nowhere else.

Prose panels

A prose panel with Variables -> Automatic gives each hole in the sentence the control its type calls for: a whole-number knob for an integer, a toggler for a boolean, a 2D pad for a complex variable, an integer pad for a lattice point. A hole over bare-name choices binds the symbol, and a knob option on it scrubs through the names.

Worksheets

A worksheet takes integer-ness and bounds from a declared type or, with letter conventions (on in worksheets, off elsewhere), from the symbol's letter. A value-based range is unchanged, and n := 3 gets a whole-number slider.

From a signature

A head's typed signature and an example of it make controls too: this is the Try it panel on every symbol page. The record fields it reads are in Reference records.