;;; "wttree.scm" Weight balanced trees			-*-Scheme-*-
;;; Copyright (c) 1993-1994 Stephen Adams
;;;
;;; References:
;;;
;;;   Stephen Adams, Implemeting Sets Efficiently in a Functional
;;;      Language, CSTR 92-10, Department of Electronics and Computer
;;;      Science, University of Southampton, 1992
;;;
;;;
;;; Copyright (c) 1993-94 Massachusetts Institute of Technology
;;;
;;; This material was developed by the Scheme project at the
;;; Massachusetts Institute of Technology, Department of Electrical
;;; Engineering and Computer Science.  Permission to copy and modify
;;; this software, to redistribute either the original software or a
;;; modified version, and to use this software for any purpose is
;;; granted, subject to the following restrictions and understandings.
;;;
;;; 1. Any copy made of this software must include this copyright
;;; notice in full.
;;;
;;; 2. Users of this software agree to make their best efforts (a) to
;;; return to the MIT Scheme project any improvements or extensions
;;; that they make, so that these may be included in future releases;
;;; and (b) to inform MIT of noteworthy uses of this software.
;;;
;;; 3. All materials developed as a consequence of the use of this
;;; software shall duly acknowledge such use, in accordance with the
;;; usual standards of acknowledging credit in academic research.
;;;
;;; 4. MIT has made no warrantee or representation that the operation
;;; of this software will be error-free, and MIT is under no
;;; obligation to provide any services, by way of maintenance, update,
;;; or otherwise.
;;;
;;; 5. In conjunction with products arising from the use of this
;;; material, there shall be no use of the name of the Massachusetts
;;; Institute of Technology nor of any adaptation thereof in any
;;; advertising, promotional, or sales literature without prior
;;; written consent from MIT in each case.

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;;  Weight Balanced Binary Trees
;;
;;
;;
;;  This file has been modified from the MIT-Scheme library version to
;;  make it more standard. The main changes are
;;
;;   . The whole thing has been put in a LET as R4RS Scheme has no module
;;     system.
;;   . The MIT-Scheme define structure operations have been written out by
;;     hand.
;;
;;  It has been tested on MIT-Scheme, scheme48 and scm4e1
;;
;;  If your system has a compiler and you want this code to run fast, you
;;  should do whatever is necessary to inline all of the structure accessors.
;;
;;  This is MIT-Scheme's way of saying that +, car etc should all be inlined.
;;
;;(declare (usual-integrations))

(define error:error
  (case (scheme-implementation-type)
    ((MITScheme) error)
    (else slib:error)))
(define error:wrong-type-argument
  (case (scheme-implementation-type)
    ((MITScheme) error:wrong-type-argument)
    (else (lambda (arg1 arg2 arg3)
	    (slib:error 'wrong-type-argument arg1 arg2 arg3)))))
(define error:bad-range-argument
  (case (scheme-implementation-type)
    ((MITScheme) error:bad-range-argument)
    (else (lambda (arg1 arg2)
	    (slib:error 'bad-range-argument arg1 arg2)))))

;;;
;;; Interface to this package.
;;;
;;; ONLY these procedures (and TEST at the end of the file) will be
;;; (re)defined in your system.
;;;

(define make-wt-tree-type #f)
(define number-wt-type #f)
(define string-wt-type #f)

(define make-wt-tree #f)
(define singleton-wt-tree #f)
(define alist->wt-tree #f)
(define wt-tree/empty? #f)
(define wt-tree/size #f)
(define wt-tree/add #f)
(define wt-tree/delete #f)
(define wt-tree/add! #f)
(define wt-tree/delete! #f)
(define wt-tree/member? #f)
(define wt-tree/lookup #f)
(define wt-tree/split< #f)
(define wt-tree/split> #f)
(define wt-tree/union #f)
(define wt-tree/intersection #f)
(define wt-tree/difference #f)
(define wt-tree/subset? #f)
(define wt-tree/set-equal? #f)
(define wt-tree/fold #f)
(define wt-tree/for-each #f)
(define wt-tree/index #f)
(define wt-tree/index-datum #f)
(define wt-tree/index-pair #f)
(define wt-tree/rank #f)
(define wt-tree/min #f)
(define wt-tree/min-datum #f)
(define wt-tree/min-pair #f)
(define wt-tree/delete-min #f)
(define wt-tree/delete-min! #f)


;; This LET sets all of the above variables.

(let ()

  ;; We use the folowing MIT-Scheme operation on fixnums (small
  ;; integers).  R4RS compatible (but less efficient) definitions.
  ;; You should replace these with something that is efficient in your
  ;; system.

  (define fix:fixnum? (lambda (x) (and (exact? x) (integer? x))))
  (define fix:+ +)
  (define fix:- -)
  (define fix:< <)
  (define fix:<= <=)
  (define fix:> >)
  (define fix:* *)

  ;;  A TREE-TYPE is a collection of those procedures that depend on the
  ;;  ordering relation.

  ;; MIT-Scheme structure definition
  ;;(define-structure
  ;;    (tree-type
  ;;     (conc-name tree-type/)
  ;;     (constructor %make-tree-type))
  ;;  (key<?       #F read-only true)
  ;;  (alist->tree #F read-only true)
  ;;  (add         #F read-only true)
  ;;  (insert!     #F read-only true)
  ;;  (delete      #F read-only true)
  ;;  (delete!     #F read-only true)
  ;;  (member?     #F read-only true)
  ;;  (lookup      #F read-only true)
  ;;  (split-lt    #F read-only true)
  ;;  (split-gt    #F read-only true)
  ;;  (union       #F read-only true)
  ;;  (intersection #F read-only true)
  ;;  (difference  #F read-only true)
  ;;  (subset?     #F read-only true)
  ;;  (rank        #F read-only true)
  ;;)

  ;; Written out by hand, using vectors:
  ;;
  ;; If possible, you should teach your system to print out something
  ;; like #[tree-type <] instread of the whole vector.

  (define tag:tree-type (string->symbol "#[(runtime wttree)tree-type]"))

  (define (%make-tree-type key<?       alist->tree
                           add         insert!
                           delete      delete!
                           member?     lookup
                           split-lt    split-gt
                           union       intersection
                           difference  subset?
                           rank        )
    (vector tag:tree-type
            key<?       alist->tree   add         insert!
            delete      delete!       member?     lookup
            split-lt    split-gt      union       intersection
            difference  subset?       rank        ))

  (define (tree-type? tt)
    (and (vector? tt)
         (eq? (vector-ref tt 0) tag:tree-type)))

  (define (tree-type/key<?        tt) (vector-ref tt 1))
  (define (tree-type/alist->tree  tt) (vector-ref tt 2))
  (define (tree-type/add          tt) (vector-ref tt 3))
  (define (tree-type/insert!      tt) (vector-ref tt 4))
  (define (tree-type/delete       tt) (vector-ref tt 5))
  (define (tree-type/delete!      tt) (vector-ref tt 6))
  (define (tree-type/member?      tt) (vector-ref tt 7))
  (define (tree-type/lookup       tt) (vector-ref tt 8))
  (define (tree-type/split-lt     tt) (vector-ref tt 9))
  (define (tree-type/split-gt     tt) (vector-ref tt 10))
  (define (tree-type/union        tt) (vector-ref tt 11))
  (define (tree-type/intersection tt) (vector-ref tt 12))
  (define (tree-type/difference   tt) (vector-ref tt 13))
  (define (tree-type/subset?      tt) (vector-ref tt 14))
  (define (tree-type/rank         tt) (vector-ref tt 15))

  ;;  User level tree representation.
  ;;
  ;;  WT-TREE is a wrapper for trees of nodes.
  ;;
  ;;MIT-Scheme:
  ;;(define-structure
  ;;    (wt-tree
  ;;     (conc-name tree/)
  ;;     (constructor %make-wt-tree))
  ;;  (type  #F read-only true)
  ;;  (root  #F read-only false))

  ;; If possible, you should teach your system to print out something
  ;; like #[wt-tree] instread of the whole vector.

  (define tag:wt-tree (string->symbol "#[(runtime wttree)wt-tree]"))

  (define (%make-wt-tree type root)
    (vector tag:wt-tree type root))

  (define (wt-tree? t)
    (and (vector? t)
         (eq? (vector-ref t 0) tag:wt-tree)))

  (define (tree/type t) (vector-ref t 1))
  (define (tree/root t) (vector-ref t 2))
  (define (set-tree/root! t v) (vector-set! t 2 v))

  ;;  Nodes are the thing from which the real trees are built.  There are
  ;;  lots of these and the uninquisitibe user will never see them, so
  ;;  they are represented as untagged to save the slot that would be
  ;;  used for tagging structures.
  ;;  In MIT-Scheme these were all DEFINE-INTEGRABLE

  (define (make-node k v l r w) (vector w l k r v))
  (define (node/k node) (vector-ref node 2))
  (define (node/v node) (vector-ref node 4))
  (define (node/l node) (vector-ref node 1))
  (define (node/r node) (vector-ref node 3))
  (define (node/w node) (vector-ref node 0))

  (define empty  'empty)
  (define (empty? x) (eq? x 'empty))

  (define (node/size node)
    (if (empty? node) 0  (node/w node)))

  (define (node/singleton k v) (make-node k v empty empty 1))

  (define (with-n-node node receiver)
    (receiver (node/k node) (node/v node) (node/l node) (node/r node)))

  ;;
  ;;  Constructors for building node trees of various complexity
  ;;

  (define (n-join k v l r)
    (make-node k v l r (fix:+ 1 (fix:+ (node/size l) (node/size r)))))

  (define (single-l a.k a.v x r)
    (with-n-node r
      (lambda (b.k b.v y z) (n-join b.k b.v (n-join a.k a.v x y) z))))

  (define (double-l a.k a.v x r)
    (with-n-node r
      (lambda (c.k c.v r.l z)
        (with-n-node r.l
          (lambda (b.k b.v y1 y2)
            (n-join b.k b.v
                    (n-join a.k a.v x y1)
                    (n-join c.k c.v y2 z)))))))

  (define (single-r b.k b.v l z)
    (with-n-node l
      (lambda (a.k a.v x y) (n-join a.k a.v x (n-join b.k b.v y z)))))

  (define (double-r c.k c.v l z)
    (with-n-node l
      (lambda (a.k a.v x l.r)
        (with-n-node l.r
          (lambda (b.k b.v y1 y2)
            (n-join b.k b.v
                    (n-join a.k a.v x y1)
                    (n-join c.k c.v y2 z)))))))

  ;; (define-integrable wt-tree-ratio 5)
  (define wt-tree-ratio 5)

  (define (t-join k v l r)
    (define (simple-join) (n-join k v l r))
    (let ((l.n  (node/size l))
          (r.n  (node/size r)))
      (cond ((fix:< (fix:+ l.n r.n) 2)   (simple-join))
            ((fix:> r.n (fix:* wt-tree-ratio l.n))
             ;; right is too big
             (let ((r.l.n  (node/size (node/l r)))
                   (r.r.n  (node/size (node/r r))))
               (if (fix:< r.l.n r.r.n)
                   (single-l k v l r)
                   (double-l k v l r))))
            ((fix:> l.n (fix:* wt-tree-ratio r.n))
             ;; left is too big
             (let ((l.l.n  (node/size (node/l l)))
                   (l.r.n  (node/size (node/r l))))
               (if (fix:< l.r.n l.l.n)
                   (single-r k v l r)
                   (double-r k v l r))))
            (else
             (simple-join)))))
  ;;
  ;;  Node tree procedures that are independent of key<?
  ;;

  (define (node/min node)
    (cond  ((empty? node)          (error:empty 'min))
           ((empty? (node/l node)) node)
           (else                   (node/min (node/l node)))))

  (define (node/delmin node)
    (cond ((empty? node)           (error:empty 'delmin))
          ((empty? (node/l node))  (node/r node))
          (else   (t-join (node/k node) (node/v node)
                          (node/delmin (node/l node)) (node/r node)))))

  (define (node/concat2 node1 node2)
    (cond ((empty? node1)   node2)
          ((empty? node2)   node1)
          (else
           (let ((min-node (node/min node2)))
             (t-join (node/k min-node) (node/v min-node)
                     node1 (node/delmin node2))))))

  (define (node/inorder-fold procedure base node)
    (define (fold base node)
      (if (empty? node)
          base
          (with-n-node node
            (lambda (k v l r)
              (fold (procedure k v (fold base r)) l)))))
    (fold base node))

  (define (node/for-each procedure node)
    (if (not (empty? node))
        (with-n-node node
          (lambda (k v l r)
            (node/for-each procedure l)
            (procedure k v)
            (node/for-each procedure r)))))

  (define (node/height node)
    (if (empty? node)
        0
        (+ 1 (max (node/height (node/l node))
                  (node/height (node/r node))))))

  (define (node/index node index)
    (define (loop node index)
      (let ((size.l  (node/size (node/l node))))
        (cond ((fix:< index size.l)  (loop (node/l node) index))
              ((fix:> index size.l)  (loop (node/r node)
                                           (fix:- index (fix:+ 1 size.l))))
              (else                  node))))
    (let ((bound  (node/size node)))
      (if (or (< index 0)
              (>= index bound)
              (not (fix:fixnum? index)))
          (error:bad-range-argument index 'node/index)
          (loop node index))))

  (define (error:empty owner)
    (error:error "Operation requires non-empty tree:" owner))


  (define (local:make-wt-tree-type key<?)

    ;; MIT-Scheme definitions:
    ;;(declare (integrate key<?))
    ;;(define-integrable (key>? x y)  (key<? y x))

    (define (key>? x y)  (key<? y x))

    (define (node/find k node)
      ;; Returns either the node or #f.
      ;; Loop takes D comparisons where D is the depth of the tree
      ;; rather than the traditional compare-low, compare-high which
      ;; takes on average 1.5(D-1) comparisons
      (define (loop this best)
        (cond ((empty? this)  best)
              ((key<? k (node/k this))   (loop (node/l this) best))
              (else (loop (node/r this) this))))
      (let ((best (loop node #f)))
        (cond ((not best)               #f)
              ((key<? (node/k best) k)  #f)
              (else                     best))))

    (define (node/rank k node rank)
      (cond ((empty? node)             #f)
            ((key<? k (node/k node))  (node/rank k (node/l node) rank))
            ((key>? k (node/k node))
             (node/rank k (node/r node)
                        (fix:+ 1 (fix:+ rank (node/size (node/l node))))))
            (else                     (fix:+ rank (node/size (node/l node))))))

    (define (node/add node k v)
      (if (empty? node)
          (node/singleton k v)
          (with-n-node node
            (lambda (key val l r)
              (cond ((key<? k key)   (t-join key val (node/add l k v) r))
                    ((key<? key k)   (t-join key val l (node/add r k v)))
                    (else            (n-join key v   l r)))))))

    (define (node/delete x node)
      (if (empty? node)
          empty
          (with-n-node node
            (lambda (key val l r)
              (cond ((key<? x key)   (t-join key val (node/delete x l) r))
                    ((key<? key x)   (t-join key val l (node/delete x r)))
                    (else            (node/concat2 l r)))))))

    (define (node/concat tree1 tree2)
      (cond ((empty? tree1)  tree2)
            ((empty? tree2)  tree1)
            (else
             (let ((min-node (node/min tree2)))
               (node/concat3 (node/k min-node) (node/v min-node) tree1
                             (node/delmin tree2))))))

    (define (node/concat3 k v l r)
      (cond ((empty? l)   (node/add r k v))
            ((empty? r)   (node/add l k v))
            (else
             (let ((n1  (node/size l))
                   (n2  (node/size r)))
               (cond ((fix:< (fix:* wt-tree-ratio n1) n2)
                      (with-n-node r
                        (lambda (k2 v2 l2 r2)
                          (t-join k2 v2 (node/concat3 k v l l2) r2))))
                     ((fix:< (fix:* wt-tree-ratio n2) n1)
                      (with-n-node l
                        (lambda (k1 v1 l1 r1)
                          (t-join k1 v1 l1 (node/concat3 k v r1 r)))))
                     (else
                      (n-join k v l r)))))))

    (define (node/split-lt node x)
      (cond ((empty? node)  empty)
            ((key<? x (node/k node))
             (node/split-lt (node/l node) x))
            ((key<? (node/k node) x)
             (node/concat3 (node/k node) (node/v node) (node/l node)
                           (node/split-lt (node/r node) x)))
            (else (node/l node))))

    (define (node/split-gt node x)
      (cond ((empty? node)  empty)
            ((key<? (node/k node) x)
             (node/split-gt (node/r node) x))
            ((key<? x (node/k node))
             (node/concat3 (node/k node) (node/v node)
                           (node/split-gt (node/l node) x) (node/r node)))
            (else (node/r node))))

    (define (node/union tree1 tree2)
      (cond ((empty? tree1)  tree2)
            ((empty? tree2)  tree1)
            (else
             (with-n-node tree2
               (lambda (ak av l r)
                 (let ((l1  (node/split-lt tree1 ak))
                       (r1  (node/split-gt tree1 ak)))
                   (node/concat3 ak av (node/union l1 l) (node/union r1 r))))))))

    (define (node/difference tree1 tree2)
      (cond ((empty? tree1)   empty)
            ((empty? tree2)   tree1)
            (else
             (with-n-node tree2
               (lambda (ak av l r)
                 (let ((l1  (node/split-lt tree1 ak))
                       (r1  (node/split-gt tree1 ak)))
                   av
                   (node/concat (node/difference l1 l)
                                (node/difference r1 r))))))))

    (define (node/intersection tree1 tree2)
      (cond ((empty? tree1)   empty)
            ((empty? tree2)   empty)
            (else
             (with-n-node tree2
               (lambda (ak av l r)
                 (let ((l1  (node/split-lt tree1 ak))
                       (r1  (node/split-gt tree1 ak)))
                   (if (node/find ak tree1)
                       (node/concat3 ak av (node/intersection l1 l)
                                     (node/intersection r1 r))
                       (node/concat (node/intersection l1 l)
                                    (node/intersection r1 r)))))))))

    (define (node/subset? tree1 tree2)
      (or (empty? tree1)
          (and (fix:<= (node/size tree1) (node/size tree2))
               (with-n-node tree1
                 (lambda (k v l r)
                   v
                   (cond ((key<? k (node/k tree2))
                          (and (node/subset? l (node/l tree2))
                               (node/find k tree2)
                               (node/subset? r tree2)))
                         ((key>? k (node/k tree2))
                          (and (node/subset? r (node/r tree2))
                               (node/find k tree2)
                               (node/subset? l tree2)))
                         (else
                          (and (node/subset? l (node/l tree2))
                               (node/subset? r (node/r tree2))))))))))


    ;;; Tree interface: stripping off or injecting the tree types

    (define (tree/map-add tree k v)
      (%make-wt-tree (tree/type tree)
                     (node/add (tree/root tree) k v)))

    (define (tree/insert! tree k v)
      (set-tree/root! tree (node/add (tree/root tree) k v)))

    (define (tree/delete tree k)
      (%make-wt-tree (tree/type tree)
                     (node/delete k (tree/root tree))))

    (define (tree/delete! tree k)
      (set-tree/root! tree (node/delete k (tree/root tree))))

    (define (tree/split-lt tree key)
      (%make-wt-tree (tree/type tree)
                     (node/split-lt (tree/root tree) key)))

    (define (tree/split-gt tree key)
      (%make-wt-tree (tree/type tree)
                     (node/split-gt (tree/root tree) key)))

    (define (tree/union tree1 tree2)
      (%make-wt-tree (tree/type tree1)
                     (node/union (tree/root tree1) (tree/root tree2))))

    (define (tree/intersection tree1 tree2)
      (%make-wt-tree (tree/type tree1)
                     (node/intersection (tree/root tree1) (tree/root tree2))))

    (define (tree/difference tree1 tree2)
      (%make-wt-tree (tree/type tree1)
                     (node/difference (tree/root tree1) (tree/root tree2))))

    (define (tree/subset? tree1 tree2)
      (node/subset? (tree/root tree1) (tree/root tree2)))

    (define (alist->tree alist)
      (define (loop alist node)
        (cond ((null? alist)  node)
              ((pair? alist)  (loop (cdr alist)
                                    (node/add node (caar alist) (cdar alist))))
              (else
               (error:wrong-type-argument alist "alist" 'alist->tree))))
      (%make-wt-tree my-type (loop alist empty)))

    (define (tree/get tree key default)
      (let ((node  (node/find key (tree/root tree))))
        (if node
            (node/v node)
            default)))

    (define (tree/rank tree key)  (node/rank key (tree/root tree) 0))

    (define (tree/member? key tree)
      (and (node/find key (tree/root tree))
           #t))

    (define my-type #F)

    (set! my-type
          (%make-tree-type
           key<?                        ;  key<?
           alist->tree                  ;  alist->tree
           tree/map-add                 ;  add
           tree/insert!                 ;  insert!
           tree/delete                  ;  delete
           tree/delete!                 ;  delete!
           tree/member?                 ;  member?
           tree/get                     ;  lookup
           tree/split-lt                ;  split-lt
           tree/split-gt                ;  split-gt
           tree/union                   ;  union
           tree/intersection            ;  intersection
           tree/difference              ;  difference
           tree/subset?                 ;  subset?
           tree/rank                    ;  rank
           ))

    my-type)

  (define (guarantee-tree tree procedure)
    (if (not (wt-tree? tree))
        (error:wrong-type-argument tree "weight-balanced tree" procedure)))

  (define (guarantee-tree-type type procedure)
    (if (not (tree-type? type))
        (error:wrong-type-argument type "weight-balanced tree type" procedure)))

  (define (guarantee-compatible-trees tree1 tree2 procedure)
    (guarantee-tree tree1 procedure)
    (guarantee-tree tree2 procedure)
    (if (not (eq? (tree/type tree1) (tree/type tree2)))
        (error:error "The trees" tree1 'and tree2 'have 'incompatible 'types
		     (tree/type tree1) 'and (tree/type tree2))))

;;;______________________________________________________________________
;;;
;;;  Export interface
;;;
  (set! make-wt-tree-type local:make-wt-tree-type)

  (set! make-wt-tree
        (lambda (tree-type)
          (%make-wt-tree tree-type empty)))

  (set! singleton-wt-tree
        (lambda (type key value)
          (guarantee-tree-type type 'singleton-wt-tree)
          (%make-wt-tree type (node/singleton key value))))

  (set! alist->wt-tree
        (lambda (type alist)
          (guarantee-tree-type type 'alist->wt-tree)
          ((tree-type/alist->tree type) alist)))

  (set! wt-tree/empty?
        (lambda (tree)
          (guarantee-tree tree 'wt-tree/empty?)
          (empty? (tree/root tree))))

  (set! wt-tree/size
        (lambda (tree)
          (guarantee-tree tree 'wt-tree/size)
          (node/size (tree/root tree))))

  (set! wt-tree/add
        (lambda (tree key datum)
          (guarantee-tree tree 'wt-tree/add)
          ((tree-type/add (tree/type tree)) tree key datum)))

  (set! wt-tree/delete
        (lambda (tree key)
          (guarantee-tree tree 'wt-tree/delete)
          ((tree-type/delete (tree/type tree)) tree key)))

  (set! wt-tree/add!
        (lambda (tree key datum)
          (guarantee-tree tree 'wt-tree/add!)
          ((tree-type/insert! (tree/type tree)) tree key datum)))

  (set! wt-tree/delete!
        (lambda (tree key)
          (guarantee-tree tree 'wt-tree/delete!)
          ((tree-type/delete! (tree/type tree)) tree key)))

  (set! wt-tree/member?
        (lambda (key tree)
          (guarantee-tree tree 'wt-tree/member?)
          ((tree-type/member? (tree/type tree)) key tree)))

  (set! wt-tree/lookup
        (lambda (tree key default)
          (guarantee-tree tree 'wt-tree/lookup)
          ((tree-type/lookup (tree/type tree)) tree key default)))

  (set! wt-tree/split<
        (lambda (tree key)
          (guarantee-tree tree 'wt-tree/split<)
          ((tree-type/split-lt (tree/type tree)) tree key)))

  (set! wt-tree/split>
        (lambda (tree key)
          (guarantee-tree tree 'wt-tree/split>)
          ((tree-type/split-gt (tree/type tree)) tree key)))

  (set! wt-tree/union
        (lambda (tree1 tree2)
          (guarantee-compatible-trees tree1 tree2 'wt-tree/union)
          ((tree-type/union (tree/type tree1)) tree1 tree2)))

  (set! wt-tree/intersection
        (lambda (tree1 tree2)
          (guarantee-compatible-trees tree1 tree2 'wt-tree/intersection)
          ((tree-type/intersection (tree/type tree1)) tree1 tree2)))

  (set! wt-tree/difference
        (lambda (tree1 tree2)
          (guarantee-compatible-trees tree1 tree2 'wt-tree/difference)
          ((tree-type/difference (tree/type tree1)) tree1 tree2)))

  (set! wt-tree/subset?
        (lambda (tree1 tree2)
          (guarantee-compatible-trees tree1 tree2 'wt-tree/subset?)
          ((tree-type/subset? (tree/type tree1)) tree1 tree2)))

  (set! wt-tree/set-equal?
        (lambda (tree1 tree2)
          (and (wt-tree/subset? tree1 tree2)
               (wt-tree/subset? tree2 tree1))))

  (set! wt-tree/fold
        (lambda (combiner-key-datum-result init tree)
          (guarantee-tree tree 'wt-tree/fold)
          (node/inorder-fold combiner-key-datum-result
                             init
                             (tree/root tree))))

  (set! wt-tree/for-each
        (lambda (action-key-datum tree)
          (guarantee-tree tree 'wt-tree/for-each)
          (node/for-each action-key-datum (tree/root tree))))

  (set! wt-tree/index
        (lambda (tree index)
          (guarantee-tree tree 'wt-tree/index)
          (let ((node  (node/index (tree/root tree) index)))
            (and node (node/k node)))))

  (set! wt-tree/index-datum
        (lambda (tree index)
          (guarantee-tree tree 'wt-tree/index-datum)
          (let ((node  (node/index (tree/root tree) index)))
            (and node (node/v node)))))

  (set! wt-tree/index-pair
        (lambda (tree index)
          (guarantee-tree tree 'wt-tree/index-pair)
          (let ((node  (node/index (tree/root tree) index)))
            (and node (cons (node/k node) (node/v node))))))

  (set! wt-tree/rank
        (lambda (tree key)
          (guarantee-tree tree 'wt-tree/rank)
          ((tree-type/rank (tree/type tree)) tree key)))

  (set! wt-tree/min
        (lambda (tree)
          (guarantee-tree tree 'wt-tree/min)
          (node/k (node/min (tree/root tree)))))

  (set! wt-tree/min-datum
        (lambda (tree)
          (guarantee-tree tree 'wt-tree/min-datum)
          (node/v (node/min (tree/root tree)))))

  (set! wt-tree/min-pair
        (lambda (tree)
          (guarantee-tree tree 'wt-tree/min-pair)
          (let ((node  (node/min (tree/root tree))))
            (cons (node/k node) (node/v node)))))

  (set! wt-tree/delete-min
        (lambda (tree)
          (guarantee-tree tree 'wt-tree/delete-min)
          (%make-wt-tree (tree/type tree)
                         (node/delmin (tree/root tree)))))

  (set! wt-tree/delete-min!
        (lambda (tree)
          (guarantee-tree tree 'wt-tree/delete-min!)
          (set-tree/root! tree (node/delmin (tree/root tree)))))

  ;; < is a lexpr. Many compilers can open-code < so the lambda is faster
  ;; than passing <.
  (set! number-wt-type (local:make-wt-tree-type  (lambda (u v) (< u v))))
  (set! string-wt-type (local:make-wt-tree-type  string<?))

  'done)

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