

(= (+ x (+ y z)) (+ (+ x y) z))





x + (y + z) = (x + y) + z.





f(g(a,b), h(c))





f/g/a/b/h/c





f/open/g/open/a/b/close/h/open/c/close/close



Some representations are easier to use than others. Ease of use also seems to depend on purpose and inclination. S-expressions are excellent for many purposes, but the associative law is far easier to read in an infix notation. CompareandMy taste puts S-expressions far above XML, but given the relative popularity of the two, I presume for some it is the exact opposite.Ezra Cooper and I observed the importance of the pain of representation in connection with mapping function calls into path names. If every function takes a fixed number of arguments, one can map a call directly into a path name. For example,becomesalthough the second is less clear to read. We could map open and close brackets into the pathbut this so painful as to be worse than useless.There must be a psychological theory that can underpin such choices. A quick web search failed to turn up anything apposite, suggestions for the correct terms to search on would be welcome.