xref: /seL4-l4v-master/HOL4/examples/dev/sw/int-binary-map.sml

(*
 *  extended by functions:
 *    update, findSome
 *)

(* int-binary-map.sml
 *
 * COPYRIGHT (c) 1993 by AT&T Bell Laboratories.  See COPYRIGHT file for details.
 *
 * This code was adapted from Stephen Adams' binary tree implementation
 * of applicative integer sets.
 *
 *   Copyright 1992 Stephen Adams.
 *
 *    This software may be used freely provided that:
 *      1. This copyright notice is attached to any copy, derived work,
 *         or work including all or part of this software.
 *      2. Any derived work must contain a prominent notice stating that
 *         it has been altered from the original.
 *
 *
 *   Name(s): Stephen Adams.
 *   Department, Institution: Electronics & Computer Science,
 *      University of Southampton
 *   Address:  Electronics & Computer Science
 *             University of Southampton
 *           Southampton  SO9 5NH
 *           Great Britian
 *   E-mail:   sra@ecs.soton.ac.uk
 *
 *   Comments:
 *
 *     1.  The implementation is based on Binary search trees of Bounded
 *         Balance, similar to Nievergelt & Reingold, SIAM J. Computing
 *         2(1), March 1973.  The main advantage of these trees is that
 *         they keep the size of the tree in the node, giving a constant
 *         time size operation.
 *
 *     2.  The bounded balance criterion is simpler than N&R's alpha.
 *         Simply, one subtree must not have more than `weight' times as
 *         many elements as the opposite subtree.  Rebalancing is
 *         guaranteed to reinstate the criterion for weight>2.23, but
 *         the occasional incorrect behaviour for weight=2 is not
 *         detrimental to performance.
 *
 *  Altered to work as a geneal intmap - Emden Gansner
 *
 *  Extended by two functions "update" and "findSome" - Martin Erwig
 *)

structure IntBinaryMapUpd : ORD_MAP_UPD =
  struct

    structure Key =
      struct
        type ord_key = int
        val compare = Int.compare
      end

    (*
    **  val weight = 3
    **  fun wt i = weight * i
    *)
    fun wt (i : int) = i + i + i

    datatype 'a map
      = E
      | T of {
          key : int,
          value : 'a,
          cnt : int,
          left : 'a map,
          right : 'a map
        }

    fun numItems E = 0
      | numItems (T{cnt,...}) = cnt

local
    fun N(k,v,E,E) = T{key=k,value=v,cnt=1,left=E,right=E}
      | N(k,v,E,r as T n) = T{key=k,value=v,cnt=1+(#cnt n),left=E,right=r}
      | N(k,v,l as T n,E) = T{key=k,value=v,cnt=1+(#cnt n),left=l,right=E}
      | N(k,v,l as T n,r as T n') =
          T{key=k,value=v,cnt=1+(#cnt n)+(#cnt n'),left=l,right=r}

    fun single_L (a,av,x,T{key=b,value=bv,left=y,right=z,...}) =
          N(b,bv,N(a,av,x,y),z)
      | single_L _ = raise Match
    fun single_R (b,bv,T{key=a,value=av,left=x,right=y,...},z) =
          N(a,av,x,N(b,bv,y,z))
      | single_R _ = raise Match
    fun double_L (a,av,w,T{key=c,value=cv,left=T{key=b,value=bv,left=x,right=y,...},right=z,...}) =
          N(b,bv,N(a,av,w,x),N(c,cv,y,z))
      | double_L _ = raise Match
    fun double_R (c,cv,T{key=a,value=av,left=w,right=T{key=b,value=bv,left=x,right=y,...},...},z) =
          N(b,bv,N(a,av,w,x),N(c,cv,y,z))
      | double_R _ = raise Match

    fun T' (k,v,E,E) = T{key=k,value=v,cnt=1,left=E,right=E}
      | T' (k,v,E,r as T{right=E,left=E,...}) =
          T{key=k,value=v,cnt=2,left=E,right=r}
      | T' (k,v,l as T{right=E,left=E,...},E) =
          T{key=k,value=v,cnt=2,left=l,right=E}

      | T' (p as (_,_,E,T{left=T _,right=E,...})) = double_L p
      | T' (p as (_,_,T{left=E,right=T _,...},E)) = double_R p

        (* these cases almost never happen with small weight*)
      | T' (p as (_,_,E,T{left=T{cnt=ln,...},right=T{cnt=rn,...},...})) =
          if ln < rn then single_L p else double_L p
      | T' (p as (_,_,T{left=T{cnt=ln,...},right=T{cnt=rn,...},...},E)) =
          if ln > rn then single_R p else double_R p

      | T' (p as (_,_,E,T{left=E,...})) = single_L p
      | T' (p as (_,_,T{right=E,...},E)) = single_R p

      | T' (p as (k,v,l as T{cnt=ln,left=ll,right=lr,...},
                      r as T{cnt=rn,left=rl,right=rr,...})) =
          if rn >= wt ln then (*right is too big*)
            let val rln = numItems rl
                val rrn = numItems rr
            in
              if rln < rrn then  single_L p  else  double_L p
            end

          else if ln >= wt rn then  (*left is too big*)
            let val lln = numItems ll
                val lrn = numItems lr
            in
              if lrn < lln then  single_R p  else  double_R p
            end

          else T{key=k,value=v,cnt=ln+rn+1,left=l,right=r}

    local
      fun min (T{left=E,key,value,...}) = (key,value)
        | min (T{left,...}) = min left
        | min _ = raise Match

      fun delmin (T{left=E,right,...}) = right
        | delmin (T{key,value,left,right,...}) = T'(key,value,delmin left,right)
        | delmin _ = raise Match
    in
      fun delete' (E,r) = r
        | delete' (l,E) = l
        | delete' (l,r) = let val (mink,minv) = min r in
            T'(mink,minv,l,delmin r)
          end
    end
in
    val empty = E

    fun insert (E,x,v) = T{key=x,value=v,cnt=1,left=E,right=E}
      | insert (T(set as {key,left,right,value,...}),x,v) =
          if key > x then T'(key,value,insert(left,x,v),right)
          else if key < x then T'(key,value,left,insert(right,x,v))
          else T{key=x,value=v,left=left,right=right,cnt= #cnt set}

    fun update (E,_,_) = raise Binaryset.NotFound
      | update (T(set as {key,left,right,value,...}),x,f) =
          if key > x then T'(key,value,update(left,x,f),right)
          else if key < x then T'(key,value,left,update(right,x,f))
          else T{key=x,value=f(value),left=left,right=right,cnt= #cnt set}

    fun find (set, x) = let
          fun mem E = NONE
            | mem (T(n as {key,left,right,...})) =
                if x > key then mem right
                else if x < key then mem left
                else SOME(#value n)
          in
            mem set
          end

    fun findSome E = NONE
     |  findSome (T{key,value,...}) = SOME (key,value)

    fun remove (E,x) = raise Binaryset.NotFound
      | remove (set as T{key,left,right,value,...},x) =
          if key > x then
            let val (left',v) = remove(left,x)
            in (T'(key,value,left',right),v) end
          else if key < x then
            let val (right',v) = remove(right,x)
            in (T'(key,value,left,right'),v) end
          else (delete'(left,right),value)

    fun listItems d = let
          fun d2l (E, l) = l
            | d2l (T{key,value,left,right,...}, l) =
                d2l(left, value::(d2l(right,l)))
          in
            d2l (d,[])
          end

    fun listItemsi d = let
          fun d2l (E, l) = l
            | d2l (T{key,value,left,right,...}, l) =
                d2l(left, (key,value)::(d2l(right,l)))
          in
            d2l (d,[])
          end

    local
      fun next ((t as T{right, ...})::rest) = (t, left(right, rest))
        | next _ = (E, [])
      and left (E, rest) = rest
        | left (t as T{left=l, ...}, rest) = left(l, t::rest)
    in
    fun collate cmpRng (s1, s2) = let
          fun cmp (t1, t2) = (case (next t1, next t2)
                 of ((E, _), (E, _)) => EQUAL
                  | ((E, _), _) => LESS
                  | (_, (E, _)) => GREATER
                  | ((T{key=x1, value=y1, ...}, r1), (T{key=x2, value=y2, ...}, r2)) => (
                      case Key.compare(x1, x2)
                       of EQUAL => (case cmpRng(y1, y2)
                             of EQUAL => cmp (r1, r2)
                              | order => order
                            (* end case *))
                        | order => order
                      (* end case *))
                (* end case *))
          in
            cmp (left(s1, []), left(s2, []))
          end
    end (* local *)

    fun appi f d = let
          fun appf E = ()
            | appf (T{key,value,left,right,...}) = (
                appf left; f(key,value); appf right)
          in
            appf d
          end
    fun app f d = appi (fn (_, v) => f v) d

    fun mapi f d = let
          fun mapf E = E
            | mapf (T{key,value,left,right,cnt}) = let
                val left' = mapf left
                val value' = f(key, value)
                val right' = mapf right
                in
                  T{cnt=cnt, key=key, value=value', left = left', right = right'}
                end
          in
            mapf d
          end
    fun map f d = mapi (fn (_, x) => f x) d

    fun foldli f init d = let
          fun fold (E,v) = v
            | fold (T{key,value,left,right,...},v) =
                fold (right, f(key, value, fold(left, v)))
          in
            fold (d, init)
          end
    fun foldl f init d = foldli (fn (_, v, accum) => f (v, accum)) init d

    fun foldri f init d = let
          fun fold (E,v) = v
            | fold (T{key,value,left,right,...},v) =
                fold (left, f(key, value, fold(right, v)))
          in
            fold (d, init)
          end
    fun foldr f init d = foldri (fn (_, v, accum) => f (v, accum)) init d

    end (* local *)

(* the following are generic implementations of the unionWith and intersectWith
 * operetions.  These should be specialized for the internal representations
 * at some point.
 *)
    fun unionWith f (m1, m2) = let
          fun ins (key, x, m) = (case find(m, key)
                 of NONE => insert(m, key, x)
                  | (SOME x') => insert(m, key, f(x, x'))
                (* end case *))
          in
            if (numItems m1 > numItems m2)
              then foldli ins m1 m2
              else foldli ins m2 m1
          end
    fun unionWithi f (m1, m2) = let
          fun ins (key, x, m) = (case find(m, key)
                 of NONE => insert(m, key, x)
                  | (SOME x') => insert(m, key, f(key, x, x'))
                (* end case *))
          in
            if (numItems m1 > numItems m2)
              then foldli ins m1 m2
              else foldli ins m2 m1
          end

    fun intersectWith f (m1, m2) = let
        (* iterate over the elements of m1, checking for membership in m2 *)
          fun intersect (m1, m2) = let
                fun ins (key, x, m) = (case find(m2, key)
                       of NONE => m
                        | (SOME x') => insert(m, key, f(x, x'))
                      (* end case *))
                in
                  foldli ins empty m1
                end
          in
            if (numItems m1 > numItems m2)
              then intersect (m1, m2)
              else intersect (m2, m1)
          end

    fun intersectWithi f (m1, m2) = let
        (* iterate over the elements of m1, checking for membership in m2 *)
          fun intersect (m1, m2) = let
                fun ins (key, x, m) = (case find(m2, key)
                       of NONE => m
                        | (SOME x') => insert(m, key, f(key, x, x'))
                      (* end case *))
                in
                  foldli ins empty m1
                end
          in
            if (numItems m1 > numItems m2)
              then intersect (m1, m2)
              else intersect (m2, m1)
          end

  (* this is a generic implementation of filter.  It should
   * be specialized to the data-structure at some point.
   *)
    fun filter predFn m = let
          fun f (key, item, m) = if predFn item
                then insert(m, key, item)
                else m
          in
            foldli f empty m
          end
    fun filteri predFn m = let
          fun f (key, item, m) = if predFn(key, item)
                then insert(m, key, item)
                else m
          in
            foldli f empty m
          end

  (* this is a generic implementation of mapPartial.  It should
   * be specialized to the data-structure at some point.
   *)
    fun mapPartial f m = let
          fun g (key, item, m) = (case f item
                 of NONE => m
                  | (SOME item') => insert(m, key, item')
                (* end case *))
          in
            foldli g empty m
          end
    fun mapPartiali f m = let
          fun g (key, item, m) = (case f(key, item)
                 of NONE => m
                  | (SOME item') => insert(m, key, item')
                (* end case *))
          in
            foldli g empty m
          end

  end