(*  ML ASSESSED EXERCISES. TICK 5* SUBMISSION *)

(* PROBLEM 1. datatype declaration *)

datatype  univ=Int of int
              |Real of real
              |Bool of bool
              |String of string
              |Pair of univ*univ
              |Named of string*univ;

(* PROBLEM 2. a function lofu such that lofu(uofl(l))=l *)

fun uofl[]=String "nil"
  | uofl(u::us)=Pair(u,uofl us);

fun lofu(String"nil")=[]
  | lofu(Pair(u,v))=u::lofu(v);

(* PROBLEM 3. a function sumreals to sum all the reals in a univ *)
(* ints returns a list of all the integers in a univ             *)

fun ints(Int n)=[n]
  | ints(Pair(u,v))=ints u @ ints v
  | ints(Named(s,u))=ints u
  | ints u=[];

fun sumreals(u)=
  let fun f(Real r,total)=total+r
        | f(Pair(u,v),total)=f(u,f(v,total))
        | f(Named(s,u),total)=f(u,total)
        | f(u,total)=total;
  in
    f(u,0.0)
  end;