fun numFields [r ::: {Type}] (fl : folder r) (r : $r) : int =
    @fold [fn _ => int] (fn [nm ::_] [u ::_] [r ::_] [[nm] ~ r] acc => acc+1) 0 fl

fun mem [a ::: Type] [ns ::: {Unit}] (_ : eq a) (fl : folder ns) (x : a) (r : $(mapU a ns)) : bool =
    @foldUR [a] [fn _ => bool]
     (fn [nm ::_] [r ::_] [[nm] ~ r] y acc =>
         acc || x = y)
     False fl r