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The rendering done by the default renderer resembles the macro expander defined by the base page. Just like the macro expander works with a macro state, the renderer works with a rendering state. The rendering state, however, is a bit more complicated than the macro state.
A macro state has form 
where 
is a recipe for macro expanding subterms expressed as a function and 
can be used for passing down data from root to leaf in the parse tree being expanded. In contrast, a rendering state has form 
where is a recipe for rendering subterms, 
is an accumulating state and 
is a pass down state.
The macro state is not used by macros described here. In contrast, the accumulating state and the pass down state are used a lot.
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