(* 5. A size function on terms *)

(* Can add to arith/syntax.ml *)
let rec size t = match t with
    TmTrue(_) -> 1
  | TmFalse(_) -> 1
  | TmIf(_,b,t1,t2) -> size b + size t1 + size t2 + 1
  | TmZero(_) -> 1
  | TmSucc(_,t) -> size t + 1
  | TmPred(_,t) -> size t + 1
  | TmIsZero(_,t) -> size t + 1


(* 6. Pierce 4.2.2 : big-step evaluation  *)

(* This replaces existing eval and eval1 functions in arith/core.ml *)
let rec eval t = match t with
    _ when isval t -> t
  | TmIf(_,t1,t2,t3) ->
      (match eval t1 with
         TmTrue(_) -> eval t2
       | TmFalse(_) -> eval t3
       | _ -> raise NoRuleApplies)
  | TmSucc(fi,t1) -> 
      (match eval t1 with
         nv1 when isnumericval nv1 -> TmSucc(fi,nv1)
       | _ -> raise NoRuleApplies)
  | TmPred(fi,t1) ->
      (match eval t1 with
         TmZero(_) -> TmZero(dummyinfo)
       | TmSucc(_,nv1) when isnumericval nv1 -> nv1
       | _ -> raise NoRuleApplies)
  | TmIsZero(_,t1) ->
      (match eval t1 with
         TmZero(_) -> TmTrue(dummyinfo)
      |	 TmSucc(_,nv1) when isnumericval nv1 -> TmFalse(dummyinfo)
      |	 _ -> raise NoRuleApplies)