structure IntHeap =

struct
	type item = int
	    
	val initial = 0

	fun leq(p : item, q : item) : bool = p <= q
    
	infix leq
    
	fun max(p,q) = if p leq q then q else p
	and min(p,q) = if p leq q then p else q
    

	datatype tree = L of item 
	  | N of item * tree * tree

       exception InitHeap

       fun initHeap n = 
	   if n < 1 then raise InitHeap
	   else if n = 1 then L initial
		else let val t = initHeap(n - 1)
		     in N (initial, t, t)
		     end

    
	fun top(L i) = i 
	  | top(N(i,_,_)) = i
    

	fun isHeap (L _) = true
	  | isHeap (N(i,l,r)) = 
	    i leq top l andalso
	    i leq top r andalso
	    isHeap l andalso
	    isHeap r

	fun depth (L _) = 1 
	  | depth (N(i,l,r)) = 1 + max(depth l,depth r)
	   

       fun replace (i,h) = (top h, insert(i,h))
       and insert (i, L _) = L i
	 | insert (i, N(_,l,r)) =
	   if i leq min(top l,top r)
	       then N(i,l,r)
	   else if (top l) leq (top r)
		    then N(top l,insert(i,l),r)
		else N(top r,l,insert(i,r))
	 

       fun size (L _) = 1
	 | size (N(_,l,r)) = 1 + size l + size r
	   
       fun maxHeap (L i) = i
	 | maxHeap (N(_,l,r)) = max(maxHeap l, maxHeap r)


end