  
  [1X4 [33X[0;0YQueues and Deques[133X[101X
  
  
  [1X4.1 [33X[0;0YAPI[133X[101X
  
  [1X4.1-1 IsQueue[101X
  
  [33X[1;0Y[29X[2XIsQueue[102X( [3Xarg[103X ) [32X filter[133X
  [6XReturns:[106X  [33X[0;10Y[10Xtrue[110X or [10Xfalse[110X[133X
  
  [33X[0;0YThe category of queues.[133X
  
  [1X4.1-2 IsDeque[101X
  
  [33X[1;0Y[29X[2XIsDeque[102X( [3Xarg[103X ) [32X filter[133X
  [6XReturns:[106X  [33X[0;10Y[10Xtrue[110X or [10Xfalse[110X[133X
  
  [33X[0;0YThe category of deques.[133X
  
  [1X4.1-3 PushBack[101X
  
  [33X[1;0Y[29X[2XPushBack[102X( [3Xdeque[103X, [3Xobject[103X ) [32X operation[133X
  
  [33X[0;0YAdd [3Xobject[103X to the back of [3Xdeque[103X.[133X
  
  [1X4.1-4 PushFront[101X
  
  [33X[1;0Y[29X[2XPushFront[102X( [3Xdeque[103X, [3Xobject[103X ) [32X operation[133X
  
  [33X[0;0YAdd [3Xobject[103X to the front of [3Xdeque[103X.[133X
  
  [1X4.1-5 PopBack[101X
  
  [33X[1;0Y[29X[2XPopBack[102X( [3Xdeque[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Yobject[133X
  
  [33X[0;0YRemove an element from the back of [3Xdeque[103X and return it.[133X
  
  [1X4.1-6 PopFront[101X
  
  [33X[1;0Y[29X[2XPopFront[102X( [3Xdeque[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Yobject[133X
  
  [33X[0;0YRemove an element from the front of [3Xdeque[103X and return it.[133X
  
  [33X[0;0YFor queues, this is just an alias for PushBack[133X
  
  [1X4.1-7 Enqueue[101X
  
  [33X[1;0Y[29X[2XEnqueue[102X( [3Xqueue[103X, [3Xobject[103X ) [32X operation[133X
  
  [33X[0;0YAdd [3Xobject[103X to [3Xqueue[103X.[133X
  
  [1X4.1-8 Dequeue[101X
  
  [33X[1;0Y[29X[2XDequeue[102X( [3Xqueue[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10Yobject[133X
  
  [33X[0;0YRemove an object from the front of [3Xqueue[103X and return it.[133X
  
  [1X4.1-9 Capacity[101X
  
  [33X[1;0Y[29X[2XCapacity[102X( [3Xarg[103X ) [32X attribute[133X
  
  [33X[0;0YAllocated storage capacity of [3Xqueue[103X.[133X
  
  [1X4.1-10 Capacity[101X
  
  [33X[1;0Y[29X[2XCapacity[102X( [3Xarg[103X ) [32X attribute[133X
  
  [33X[0;0YAllocated storage capacity of [3Xdeque[103X.[133X
  
  [1X4.1-11 Length[101X
  
  [33X[1;0Y[29X[2XLength[102X( [3Xarg[103X ) [32X attribute[133X
  
  [33X[0;0YNumber of elements in [3Xqueue[103X.[133X
  
  [1X4.1-12 Length[101X
  
  [33X[1;0Y[29X[2XLength[102X( [3Xarg[103X ) [32X attribute[133X
  
  [33X[0;0YNumber of elements in [3Xdeque[103X.[133X
  
  
  [1X4.2 [33X[0;0YDeques implemented using plain lists[133X[101X
  
  [33X[0;0Y[5Xdatastructures[105X  implements  deques using a circular buffer stored in a [5XGAP[105X a
  plain   list,   wrapped   in   a  positional  object  ([2XIsPositionalObjectRep[102X
  ([14XIsPositionalObjectRep???[114X)).[133X
  
  [33X[0;0YThe five positions in such a deque [10XQ[110X have the following purpose[133X
  
  [30X    [33X[0;6Y[10XQ![1][110X - head, the index in [10XQ![5][110X of the first element in the deque[133X
  
  [30X    [33X[0;6Y[10XQ![2][110X - tail, the index in [10XQ![5][110X of the last element in the deque[133X
  
  [30X    [33X[0;6Y[10XQ![3][110X - capacity, the allocated capacity in the deque[133X
  
  [30X    [33X[0;6Y[10XQ![4][110X - factor by which storage is increased if capacity is exceeded[133X
  
  [30X    [33X[0;6Y[10XQ![5][110X - GAP plain list with storage for capacity many entries[133X
  
  [33X[0;0YGlobal  constants  [9XQHEAD[109X,  [9XQTAIL[109X, [9XQCAPACITY[109X, [9XQFACTOR[109X, and [9XQDATA[109X are bound to
  reflect the above.[133X
  
  [33X[0;0YWhen  a push fills the deque, its capacity is resized by a factor of [9XQFACTOR[109X
  using  PlistDequeExpand.  A  new  empty  plist  is allocated and all current
  entries  of  the  deque are copied into the new plist with the head entry at
  index 1.[133X
  
  [33X[0;0YThe  deque  is  empty if and only if head = tail and the entry that head and
  tail point to in the storage list is unbound.[133X
  
  [1X4.2-1 PlistDeque[101X
  
  [33X[1;0Y[29X[2XPlistDeque[102X( [[3Xcapacity[103X[, [3Xfactor[103X]] ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Ya deque[133X
  
  [33X[0;0YConstructor  for plist based deques. The optinal argument [3Xcapacity[103X must be a
  positive  integer and is the capacity of the created deque, and the optional
  argument  [3Xfactor[103X  must  be  a  rational number greater than one which is the
  factor  by  which  the  storage  of the deque is increased if it runs out of
  capacity when an object is put on the queue.[133X
  
  [1X4.2-2 PlistDequePushFront[101X
  
  [33X[1;0Y[29X[2XPlistDequePushFront[102X( [3Xdeque[103X, [3Xobject[103X ) [32X function[133X
  
  [33X[0;0YPush [3Xobject[103X to the front of [3Xdeque[103X.[133X
  
  [1X4.2-3 PlistDequePushBack[101X
  
  [33X[1;0Y[29X[2XPlistDequePushBack[102X( [3Xdeque[103X, [3Xobject[103X ) [32X function[133X
  
  [33X[0;0YPush [3Xobject[103X to the back of [3Xdeque[103X.[133X
  
  [1X4.2-4 PlistDequePopFront[101X
  
  [33X[1;0Y[29X[2XPlistDequePopFront[102X( [3Xdeque[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Yobject or fail[133X
  
  [33X[0;0YPop object from the front of [3Xdeque[103X and return it. If [3Xdeque[103X is empty, returns
  [9Xfail[109X.[133X
  
  [1X4.2-5 PlistDequePopBack[101X
  
  [33X[1;0Y[29X[2XPlistDequePopBack[102X( [3Xdeque[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Yobject or fail[133X
  
  [33X[0;0YPop  object from the back of [3Xdeque[103X and return it. If [3Xdeque[103X is empty, returns
  [9Xfail[109X.[133X
  
  [1X4.2-6 PlistDequePeekFront[101X
  
  [33X[1;0Y[29X[2XPlistDequePeekFront[102X( [3Xdeque[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Yobject or fail[133X
  
  [33X[0;0YReturns  the  object  at  the  front  [3Xdeque[103X without removing it. If [3Xdeque[103X is
  empty, returns [9Xfail[109X.[133X
  
  [1X4.2-7 PlistDequePeekBack[101X
  
  [33X[1;0Y[29X[2XPlistDequePeekBack[102X( [3Xdeque[103X ) [32X function[133X
  [6XReturns:[106X  [33X[0;10Yobject or fail[133X
  
  [33X[0;0YReturns the object at the back [3Xdeque[103X without removing it. If [3Xdeque[103X is empty,
  returns [9Xfail[109X.[133X
  
  [1X4.2-8 PlistDequeExpand[101X
  
  [33X[1;0Y[29X[2XPlistDequeExpand[102X( [3Xdeque[103X ) [32X function[133X
  
  [33X[0;0YHelper function to expand the capacity of [3Xdeque[103X by the configured factor.[133X
  
  [33X[0;0Y[13XQueues[113X  are  linear  data structure that allow adding elements at the end of
  the  queue,  and removing elements from the front. A [13Xdeque[113X is a [13Xdouble-ended
  queue[113X; a linear data structure that allows access to objects at both ends.[133X
  
  [33X[0;0YThe  API  that  objects  that  lie  in  [2XIsQueue[102X  ([14X???IsQueue???[114X) and [2XIsDeque[102X
  ([14X???IsDeque???[114X) must implement the API set out below.[133X
  
  [33X[0;0Y[5Xdatastructures[105X provides[133X
  
