The following is some SML code that implements the natural numbers using peano arithmetic in the SML type system. These numbers can be used to protect access to list functions. I haven't yet figured out if addition is possible, but I'm hoping that it is. It could be really handy!

signature SLIST = sig type 'a nat type Z type 'a S val S : 'a nat -> 'a S nat val P : 'a S nat -> 'a nat val Z : unit -> Z nat val zerop : 'a nat -> bool val toInt : 'a nat -> int type ('elt,'n) slist val snil : unit -> ('elt, Z nat) slist val scons : 'elt -> ('elt, 'n nat) slist -> ('elt, 'n S nat) slist val :+: : 'elt * ('elt, 'n nat) slist -> ('elt, 'n S nat) slist val shd : ('elt, 'n S nat) slist -> 'elt val stl : ('elt, 'n S nat) slist -> ('elt, 'n nat) slist val slen : ('elt, 'n…

signature SLIST = sig type 'a nat type Z type 'a S val S : 'a nat -> 'a S nat val P : 'a S nat -> 'a nat val Z : unit -> Z nat val zerop : 'a nat -> bool val toInt : 'a nat -> int type ('elt,'n) slist val snil : unit -> ('elt, Z nat) slist val scons : 'elt -> ('elt, 'n nat) slist -> ('elt, 'n S nat) slist val :+: : 'elt * ('elt, 'n nat) slist -> ('elt, 'n S nat) slist val shd : ('elt, 'n S nat) slist -> 'elt val stl : ('elt, 'n S nat) slist -> ('elt, 'n nat) slist val slen : ('elt, 'n…