10.14.3 How purity is defined and stored

Purity is defined in LilyPond with the creation of an unpure-pure container (unpure is not a word, but hey, neither was LilyPond until the 90s). For example:

#(define (foo grob)
  '(-1 . 1))

#(define (bar grob start end)
  '(-2 . 2))

\override Stem.length = #(ly:make-unpure-pure-container foo bar)

Note that items can only ever have two pure heights: their actual pure height if they are between ‘start’ and ‘end’, or an empty interval if they are not. Thus, their pure property is cached to speed LilyPond up. Pure heights for spanners are generally not cached as they change depending on the start and end values. They are only cached in certain particular cases. Before writing a lot of caching code, make sure that it is a value that will be reused a lot.