Forms, Boxes, and Formats¶
In the introduction to this section we gave the 3-step process converting the input you type into output produced:
the input string is parsed to a
FullFormM-expression is evaluated giving another M-expression
The result is formatted to the kind of output desired. Formatting can cause additional evaluations to occur.
Here, we are going to go in more detail over the last step which broadly is formatting.
At the top-level, the kind of output you get is dictated by the Form specified either explicitly or implicitly. See Forms of Input and Output.
Formatting a “Form” can cause parts of the expression to be “boxed” as the M-expression is traversed. This is sort of like adding parenthesis around infix expressions at certain places, but we’ll explain in more detail below.
The Box Model¶
Ever since the typesetting system TeX was developed, most full-fledged formatters follow a two-level approach to formatting output. The current HTML has a box model that follows this approach.
In the Box-Formatting model, groups of items of a similar category are “boxed”, before final layout. In “Box”ing, object details which are not relevant for formatting are hidden. This is good because the objects themself can have wildly different attributes and properties.
On the other hand, common layout formatting properties, such as the box dimensions are exposed. Therefore layout is simplified, and we have the ability to move large collections of items around by simply positioning the enclosing box.
As with M-Expressions, Boxes can be sequenced and nested.
Within a box, once it is given its initial parameters such as the dimensions or style attributes, the layout is largely independent of other boxes in the system.
In the Python code then for each distinct kind of entity, like
CompiledCode or a
Graphics3D object, there will typically be
another class with the the same name but with word
Box added at
the end. This convention ties to an entity to methods for how to Box
the entity. For example, the
CompiledCodeBox handles boxing for
Graphics3DBox handles boxing for
How an object is boxed may be influenced by context in which the expression appears formatted. For example, if an an image is used inside of a list, we might choose to show the image as a thumbnail rather than a full-size image.
For each Box type, such as a
CircleBox there can be a formatter for
the kind of output format you want, such as
If a Box is not defined for a particular entity, there will be an enclosing entity which does define a Boxing routine, and that will need to be be to handle all of the objects inside it whether or not those objects are boxed.