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  3 How HPC-GAP organizes shared memory: Regions
  
  HPC-GAP allows multiple threads to access data shared between them; to avoid
  common  concurrency  errors,  such  as  race  conditions,  it partitions GAP
  objects  into regions. Access to regions is regulated so that no two threads
  can  modify  objects in the same region at the same time and so that objects
  that  are  being  read  by  one  thread  cannot  concurrently be modified by
  another.
  
  
  3.1 Thread-local regions
  
  Each  thread has an associated thread-local region. When a thread implicitly
  or  explicitly  creates  a  new object, that object initially belongs to the
  thread's thread-local region.
  
  Only  the  thread can read or modify objects in its thread-local region. For
  other  threads  to  access  an object, that object has to be migrated into a
  different region first.
  
  
  3.2 Shared regions
  
  Shared  regions  are  explicitly  created  through  the ShareObj (3.9-9) and
  ShareSingleObj  (3.9-15) primitives (see below). Multiple threads can access
  them  concurrently, but accessing them requires that a thread uses an atomic
  statement to acquire a read or write lock beforehand.
  
  See the section on atomic statements (3.9-43) for details.
  
  
  3.3 Ordering of shared regions
  
  Shared  regions are by default ordered; each shared region has an associated
  numeric  precedence  level. Regions can generally only be locked in order of
  descending  precedence. The purpose of this mechanism is to avoid accidental
  deadlocks.
  
  The  ordering  requirement  can  be  overridden  in two ways: regions with a
  negative precedence are excluded from it. This exception should be used with
  care, as it can lead to deadlocks.
  
  Alternatively,  two  or  more  regions  can be locked simultaneously via the
  atomic  statement.  In  this case, the ordering of these regions relative to
  each other can be arbitrary.
  
  
  3.4 The public region
  
  A special public region contains objects that only permit atomic operations.
  These  include, in particular, all immutable objects (immutable in the sense
  that their in-memory representation cannot change).
  
  All  threads  can  access  objects in the public region at all times without
  needing to acquire a read- or write-lock beforehand.
  
  
  3.5 The read-only region
  
  The  read-only  region  is another special region that contains objects that
  are  only  meant  to  be read; attempting to modify an object in that region
  will  result  in  a  runtime  error.  To obtain a modifiable copy of such an
  object, the CopyRegion (3.9-29) primitive can be used.
  
  
  3.6 Migrating objects between regions
  
  Objects  can  be  migrated  between  regions using a number of functions. In
  order to migrate an object, the current thread must have exclusive access to
  that  object; the object must be in its thread-local region or it must be in
  a shared region for which the current thread holds a write lock.
  
  The  ShareObj  (3.9-9)  and  ShareSingleObj  (3.9-15) functions create a new
  shared region and migrate their respective argument to that region; ShareObj
  will  also  migrate  all  subobjects  that are within the same region, while
  ShareSingleObj will leave the subobjects unaffected.
  
  The  MigrateObj  (3.9-21)  and  MigrateSingleObj  (3.9-22) functions migrate
  objects  to an existing region. The first argument of either function is the
  object  to  be  migrated;  the second is either a region (as returned by the
  RegionOf  (3.9-7)  function)  or an object whose containing region the first
  argument is to be migrated to.
  
  The  current  thread needs exclusive access to the target region (denoted by
  the  second argument) for the operation to succeed. If successful, the first
  argument  will  be  in the same region as the second argument afterwards. In
  the  case  of  MigrateObj (3.9-21), all subobjects within the same region as
  the first argument will also be migrated to the target region.
  
  Finally,  AdoptObj (3.9-26) and AdoptSingleObj (3.9-27) are special cases of
  MigrateObj  (3.9-21)  and MigrateSingleObj (3.9-22), where the target region
  is the thread-local region of the current thread.
  
  To  migrate  objects  to  the  read-only region, one can use MakeReadOnlyObj
  (3.9-35) and MakeReadOnlySingleObj (3.9-36). The first migrates its argument
  and  all  its  subjobjects  that are within the same region to the read-only
  region;   the  second  migrates  only  the  argument  itself,  but  not  its
  subobjects.
  
  It  is  generally  not  possible to migrate objects explicitly to the public
  region;  only  objects  with purely atomic operations can be made public and
  that is done automatically when they are created.
  
  The   exception   are  immutable  objects.  When  MakeImmutable  (Reference:
  MakeImmutable)  is  used,  its argument is automatically moved to the public
  region.
  
    Example  
    gap> RegionOf(MakeImmutable([1,2,3]));
    <public region>
  
  
  
  3.7 Region names
  
  Regions  can be given names, either explicitly via SetRegionName (3.9-38) or
  when  they  are  created  via  ShareObj (3.9-9) and ShareSingleObj (3.9-15).
  Thread-local regions, the public, and the readonly region are given names by
  default.
  
  Multiple regions can have the same name.
  
  
  3.8 Controlling access to regions
  
  If  either  GAP code or a kernel primitive attempts to access an object that
  it  is  not  allowed to access according to these semantics, either a "write
  guard  error"  (for  a  failed  write access) or a "read guard error" (for a
  failed  read  access)  will  be raised. The global variable LastInaccessible
  will contain the object that caused such an error.
  
  One  exception  is that threads can modify objects in regions that they have
  only  read access (but not write access) to using write-once functions - see
  section 3.11.
  
  To inspect objects whose contents lie in other regions (and therefore cannot
  be  displayed  by  PrintObj  (Reference:  PrintObj)  or  ViewObj (Reference:
  ViewObj),  the functions ViewShared (3.9-41) and UNSAFE_VIEW (3.9-42) can be
  used.
  
  
  3.9 Functions relating to regions
  
  3.9-1 NewRegion
  
  NewRegion( [name, ]prec )  function
  
  The function NewRegion creates a new shared region. If the optional argument
  name is provided, then the name of the new region will be set to name.
  
    Example  
    gap> NewRegion("example region");
    <region: example region>
  
  
  NewRegion  will create a region with a high precedence level. It is intended
  to  be  called by user code. The exact precedence level can be adjusted with
  prec,  which  must  be  an  integer in the range [-1000..1000]; prec will be
  added to the normal precedence level.
  
  3.9-2 NewLibraryRegion
  
  NewLibraryRegion( [name, ]prec )  function
  
  NewLibraryRegion   functions   like   NewRegion  (3.9-1),  except  that  the
  precedence  of  the region it creates is below that of NewRegion (3.9-1). It
  is intended to be used by user libraries and GAP packages.
  
  3.9-3 NewSystemRegion
  
  NewSystemRegion( [name, ]prec )  function
  
  NewSystemRegion functions like NewRegion (3.9-1), except that the precedence
  of  the  region  it creates is below that of NewLibraryRegion (3.9-2). It is
  intended to be used by the standard GAP library.
  
  3.9-4 NewKernelRegion
  
  NewKernelRegion( [name, ]prec )  function
  
  NewKernelRegion functions like NewRegion (3.9-1), except that the precedence
  of  the  region  it  creates is below that of NewSystemRegion (3.9-3). It is
  intended  to  be used by the GAP kernel, and GAP library code that interacts
  closely with the kernel.
  
  3.9-5 NewInternalRegion
  
  NewInternalRegion( [name] )  function
  
  NewInternalRegion   functions   like  NewRegion  (3.9-1),  except  that  the
  precedence  of the region it creates is the lowest available. It is intended
  to  be  used for regions that are self-contained; i.e. no function that uses
  such  a  region  may  lock another region while accessing it. The precedence
  level of an internal region cannot be adjusted.
  
  3.9-6 NewSpecialRegion
  
  NewSpecialRegion( [name] )  function
  
  NewLibraryRegion  (3.9-2)  functions like NewRegion (3.9-1), except that the
  precedence  of  the  region  it  creates is negative. It is thus exempt from
  normal ordering and deadlock checks.
  
  3.9-7 RegionOf
  
  RegionOf( obj )  function
  
    Example  
    gap> RegionOf(1/2);
    <public region>
    gap> RegionOf([1,2,3]);
    <region: thread region #0>
    gap> RegionOf(ShareObj([1,2,3]));
    <region 0x45deaa0>
    gap> RegionOf(ShareObj([1,2,3]));
    <region 0x45deaa0>
    gap> RegionOf(ShareObj([1,2,3], "test region"));
    <region: test region>
  
  
  Note  that  the  unique  number  that  each  region  is  identified  with is
  system-specific  and  can  change  each  time  the code is being run. Region
  objects returned by RegionOf can be compared:
  
    Example  
    gap> RegionOf([1,2,3]) = RegionOf([4,5,6]);
    true
  
  
  The  result  in  this  example  is  true  because both lists are in the same
  thread-local region.
  
  3.9-8 RegionPrecedence
  
  RegionPrecedence( obj )  function
  
  RegionPrecedence will return the precedence of the region of obj.
  
    Example  
    gap> RegionPrecedence(NewRegion("Test"));
    30000
    gap> RegionPrecedence(NewRegion("Test2", 1));
    30001
    gap> RegionPrecedence(NewLibraryRegion("LibTest", -1));
    19999
  
  
  3.9-9 ShareObj
  
  ShareObj( obj[[, name], prec] )  function
  
  The  ShareObj  function  creates a new shared region and migrates the object
  and  all  its  subobjects  to  that region. If the optional argument name is
  provided, then the name of the new region is set to name.
  
  ShareObj  will  create a region with a high precedence level. It is intended
  to  be  called  by user code. The actual precedence level can be adjusted by
  the optional prec argument in the same way as for NewRegion (3.9-1).
  
  3.9-10 ShareLibraryObj
  
  ShareLibraryObj( obj[[, name], prec] )  function
  
  ShareLibraryObj  functions like ShareObj (3.9-9), except that the precedence
  of  the  region it creates is below that of ShareObj (3.9-9). It is intended
  to be used by user libraries and GAP packages.
  
  3.9-11 ShareSystemObj
  
  ShareSystemObj( obj[[, name], prec] )  function
  
  ShareSystemObj  functions  like ShareObj (3.9-9), except that the precedence
  of  the  region  it creates is below that of ShareLibraryObj (3.9-10). It is
  intended to be used by the standard GAP library.
  
  3.9-12 ShareKernelObj
  
  ShareKernelObj( obj[[, name], prec] )  function
  
  ShareKernelObj  functions  like ShareObj (3.9-9), except that the precedence
  of  the  region  it  creates is below that of ShareSystemObj (3.9-11). It is
  intended  to  be used by the GAP kernel, and GAP library code that interacts
  closely with the kernel.
  
  3.9-13 ShareInternalObj
  
  ShareInternalObj( obj[, name] )  function
  
  ShareInternalObj functions like ShareObj (3.9-9), except that the precedence
  of  the region it creates is the lowest available. It is intended to be used
  for  regions  that  are  self-contained;  i.e.  no function that uses such a
  region may lock another region while accessing it.
  
  3.9-14 ShareSpecialObj
  
  ShareSpecialObj( obj[, name] )  function
  
  ShareLibraryObj  (3.9-10)  functions  like ShareObj (3.9-9), except that the
  precedence  of  the  region  it  creates is negative. It is thus exempt from
  normal ordering and deadlock checks.
  
  3.9-15 ShareSingleObj
  
  ShareSingleObj( obj[[, name], prec] )  function
  
  The  ShareSingleObj  function  creates  a new shared region and migrates the
  object,  but  not  its  subobjects, to that region. If the optional argument
  name is provided, then the name of the new region is set to name.
  
    Example  
    gap> m := [ [1, 2], [3, 4] ];;
    gap> ShareSingleObj(m);;
    gap> atomic readonly m do
    >      Display([ IsShared(m), IsShared(m[1]), IsShared(m[2]) ]);
    >    od;
    [ true, false, false ]
  
  
  ShareSingleObj  will  create  a  region  with a high precedence level. It is
  intended  to  be  called  by  user  code. The actual precedence level can be
  adjusted  by  the  optional  prec  argument in the same way as for NewRegion
  (3.9-1).
  
  3.9-16 ShareSingleLibraryObj
  
  ShareSingleLibraryObj( obj[[, name], prec] )  function
  
  ShareSingleLibraryObj  functions  like  ShareSingleObj (3.9-15), except that
  the  precedence  of  the  region  it creates is below that of ShareSingleObj
  (3.9-15). It is intended to be used by user libraries and GAP packages.
  
  3.9-17 ShareSingleSystemObj
  
  ShareSingleSystemObj( obj[[, name], prec] )  function
  
  ShareSingleSystemObj functions like ShareSingleObj (3.9-15), except that the
  precedence  of  the region it creates is below that of ShareSingleLibraryObj
  (3.9-16). It is intended to be used by the standard GAP library.
  
  3.9-18 ShareSingleKernelObj
  
  ShareSingleKernelObj( obj[[, name], prec] )  function
  
  ShareSingleKernelObj functions like ShareSingleObj (3.9-15), except that the
  precedence  of  the  region it creates is below that of ShareSingleSystemObj
  (3.9-17).  It is intended to be used by the GAP kernel, and GAP library code
  that interacts closely with the kernel.
  
  3.9-19 ShareSingleInternalObj
  
  ShareSingleInternalObj( obj[, name] )  function
  
  ShareSingleInternalObj  functions  like ShareSingleObj (3.9-15), except that
  the  precedence  of  the  region  it  creates is the lowest available. It is
  intended  to  be  used for regions that are self-contained; i.e. no function
  that uses such a region may lock another region while accessing it.
  
  3.9-20 ShareSingleSpecialObj
  
  ShareSingleSpecialObj( obj[, name] )  function
  
  ShareSingleLibraryObj   (3.9-16)  functions  like  ShareSingleObj  (3.9-15),
  except  that the precedence of the region it creates is negative. It is thus
  exempt from normal ordering and deadlock checks.
  
  3.9-21 MigrateObj
  
  MigrateObj( obj, target )  function
  
  The  MigrateObj  function  migrates obj (and all subobjects contained within
  the  same region) to the region denoted by the target argument. Here, target
  can  either  be a region object returned by RegionOf (3.9-7) or a normal gap
  object. If target is a normal gap object, obj will be migrated to the region
  containing target.
  
  For  the operation to succeed, the current thread must have exclusive access
  to the target region and the object being migrated.
  
  3.9-22 MigrateSingleObj
  
  MigrateSingleObj( obj, target )  function
  
  The MigrateSingleObj function works like MigrateObj (3.9-21), except that it
  does not migrate the subobjects of obj.
  
  3.9-23 LockAndMigrateObj
  
  LockAndMigrateObj( obj, target )  function
  
  The  LockAndMigrateObj  function works like MigrateObj (3.9-21), except that
  it will automatically try to acquire a lock for the region containing target
  if it does not have one already.
  
  3.9-24 IncorporateObj
  
  IncorporateObj( target, index, value )  function
  
  The  IncorporateObj function allows convenient migration to a shared list or
  record. If target is a list, then IncorporateObj is equivalent to:
  
    Example  
    IncorporateObj := function(target, index, value)
      atomic value do
        target[index] := MigrateObj(value, target)
      od;
    end;
  
  
  If target is a record, then it is equivalent to:
  
    Example  
    IncorporateObj := function(target, index, value)
      atomic value do
        target.(index) := MigrateObj(value, target)
      od;
    end;
  
  
  The  intended  purpose  is  the  population  of a shared list or record with
  values after its creation. Example:
  
    Example  
    gap> list := ShareObj([]);
    gap> atomic list do
    >      IncorporateObj(list, 1, [1,2,3]);
    >      IncorporateObj(list, 2, [4,5,6]);
    >      IncorporateObj(list, 3, [7,8,9]);
    >    od;
    gap> ViewShared(list);
    [ [ 1, 2, 3 ], [ 4, 5, 6 ], [ 7, 8, 9 ] ]
  
  
  Using   plain  assignment  would  leave  the  newly  created  lists  in  the
  thread-local region.
  
  3.9-25 AtomicIncorporateObj
  
  AtomicIncorporateObj( target, index, value )  function
  
  AtomicIncorporateObj  extends  IncorporateObj  (3.9-24)  by also locking the
  target. I.e., for a list, it is equivalent to:
  
    Example  
    AtomicIncorporateObj := function(target, index, value)
      atomic target, value do
        target[index] := MigrateObj(value, target)
      od;
    end;
  
  
  If target is a record, then it is equivalent to:
  
    Example  
    AtomicIncorporateObj := function(target, index, value)
      atomic value do
        target.(index) := MigrateObj(value, target)
      od;
    end;
  
  
  3.9-26 AdoptObj
  
  AdoptObj( obj )  function
  
  The  AdoptObj function migrates obj (and all its subobjects contained within
  the  same  region)  to  the  thread's  current region. It requires exclusive
  access to obj.
  
    Example  
    gap> l := ShareObj([1,2,3]);;
    gap> IsThreadLocal(l);
    false
    gap> atomic l do AdoptObj(l); od;
    gap> IsThreadLocal(l);
    true
  
  
  3.9-27 AdoptSingleObj
  
  AdoptSingleObj( obj )  function
  
  The  AdoptSingleObj  function  works  like AdoptObj (3.9-26), except that it
  does not migrate the subobjects of obj.
  
  3.9-28 LockAndAdoptObj
  
  LockAndAdoptObj( obj )  function
  
  The  LockAndAdoptObj  function  works like AdoptObj (3.9-26), except that it
  will  attempt  acquire an exclusive lock for the region containing obj if it
  does not have one already.
  
  3.9-29 CopyRegion
  
  CopyRegion( obj )  function
  
  The  CopyRegion  function  performs  a structural copy of obj. The resulting
  objects  will  be  located  in the current thread's thread-local region. The
  function returns the copy as its result.
  
    Example  
    gap> l := MakeReadOnlyObj([1,2,3]);
    [ 1, 2, 3 ]
    gap> l2 := CopyRegion(l);
    [ 1, 2, 3 ]
    gap> RegionOf(l) = RegionOf(l2);
    false
    gap> IsIdenticalObj(l, l2);
    false
    gap> l = l2;
    true
  
  
  3.9-30 IsPublic
  
  IsPublic( obj )  function
  
  The  IsPublic  function  returns  true  if  its argument is an object in the
  public region, false otherwise.
  
    Example  
    gap> IsPublic(1/2);
    true
    gap> IsPublic([1,2,3]);
    false
    gap> IsPublic(ShareObj([1,2,3]));
    false
    gap> IsPublic(MakeImmutable([1,2,3]));
    true
  
  
  3.9-31 IsThreadLocal
  
  IsThreadLocal( obj )  function
  
  The  IsThreadLocal function returns true if its argument is an object in the
  current thread's thread-local region, false otherwise.
  
    Example  
    gap> IsThreadLocal([1,2,3]);
    true
    gap> IsThreadLocal(ShareObj([1,2,3]));
    false
    gap> IsThreadLocal(1/2);
    false
    gap> RegionOf(1/2);
    <public region>
  
  
  3.9-32 IsShared
  
  IsShared( obj )  function
  
  The  IsShared function returns true if its argument is an object in a shared
  region.  Note that if the current thread does not hold a lock on that shared
  region,  another  thread  can  migrate  obj to a different region before the
  result is being evaluated; this can lead to race conditions. The function is
  intended primarily for debugging, not to build actual program logic around.
  
  3.9-33 HaveReadAccess
  
  HaveReadAccess( obj )  function
  
  The  HaveReadAccess  function  returns  true  if the current thread has read
  access to obj.
  
    Example  
    gap> HaveReadAccess([1,2,3]);
    true
    gap> l := ShareObj([1,2,3]);;
    gap> HaveReadAccess(l);
    false
    gap> atomic readonly l do t := HaveReadAccess(l); od;; t;
    true
  
  
  3.9-34 HaveWriteAccess
  
  HaveWriteAccess( obj )  function
  
  The  HaveWriteAccess  function  returns true if the current thread has write
  access to obj.
  
    Example  
    gap> HaveWriteAccess([1,2,3]);
    true
    gap> l := ShareObj([1,2,3]);;
    gap> HaveWriteAccess(l);
    false
    gap> atomic readwrite l do t := HaveWriteAccess(l); od;; t;
    true
  
  
  3.9-35 MakeReadOnlyObj
  
  MakeReadOnlyObj( obj )  function
  
  The  MakeReadOnlyObj  function  migrates obj and all its subobjects that are
  within the same region as obj to the read-only region. It returns obj.
  
  3.9-36 MakeReadOnlySingleObj
  
  MakeReadOnlySingleObj( obj )  function
  
  The  MakeReadOnlySingleObj  function  migrates  obj,  but  not  any  of  its
  subobjects, to the read-only region. It returns obj.
  
  3.9-37 IsReadOnlyObj
  
  IsReadOnlyObj( obj )  function
  
  The  IsReadOnlyObj  function returns true if obj is in the read-only region,
  false otherwise.
  
    Example  
    gap> IsReadOnlyObj([1,2,3]);
    false
    gap> IsReadOnlyObj(MakeImmutable([1,2,3]));
    false
    gap> IsReadOnlyObj(MakeReadOnlyObj([1,2,3]));
    true
  
  
  3.9-38 SetRegionName
  
  SetRegionName( obj, name )  function
  
  The SetRegionName function sets the name of the region of obj to name.
  
  3.9-39 ClearRegionName
  
  ClearRegionName( obj )  function
  
  The ClearRegionName function clears the name of the region of obj to name.
  
  3.9-40 RegionName
  
  RegionName( obj )  function
  
  The  RegionName  function  returns  the  name  of the region of obj. If that
  region does not have a name, fail will be returned.
  
  3.9-41 ViewShared
  
  ViewShared( obj )  function
  
  The  ViewShared function allows the inspection of objects in shared regions.
  It  will  try  to  lock  the region and then call ViewObj(obj). If it cannot
  acquire a lock for the region, it will simply display the normal description
  of the object.
  
  3.9-42 UNSAFE_VIEW
  
  UNSAFE_VIEW( obj )  function
  
  The  UNSAFE_VIEW function allows the inspection of any object in the system,
  regardless of whether the current thread has access to the region containing
  it.  It  should be used with care: If the object inspected is being modified
  by another thread concurrently, the resulting behavior is undefined.
  
  Moreover,  the function works by temporarily disabling read and write guards
  for  regions,  so  other  threads  may  corrupt memory rather than producing
  errors.
  
  It is generally safe to use if all threads but the current one are paused.
  
  
  3.9-43 The atomic statement.
  
  The  atomic  statement  ensures exclusive or read-only access to one or more
  shared regions for statements within its scope. It has the following syntax:
  
    Example  
    atomic ([readwrite|readonly] expr (, expr)* )* do
      statements
    od;
  
  
  Each  expression is evaluated and the region containing the resulting object
  is  locked  with  either  a  read-write  or read-only lock, depending on the
  keyword  preceding the expression. If neither the readwrite nor the readonly
  keyword was provided, read-write locks are used by default. Examples:
  
    Example  
    gap> l := ShareObj([1,2,3]);;
    gap> atomic readwrite l do l[3] := 9; od;
    gap> atomic l do l[2] := 4; od;
    gap> atomic readonly l do Display(l); od;
    [ 1, 4, 9 ]
  
  
    Example  
    gap> l := ShareObj([1,2,3,4,5]);;
    gap> l2 := ShareObj([6,7,8]);;
    gap> atomic readwrite l, readonly l2 do
    >      for i in [1..3] do l[i] := l2[i]; od;
    >      l3 := AdoptObj(l);
    >    od;
    gap> l3;
    [ 6, 7, 8, 4, 5 ]
  
  
  Atomic  statements must observe region ordering. That means that the highest
  precedence level of a region locked by an atomic statement must be less than
  the  lowest precedene level of a region that is locked by the same thread at
  the time the atomic statement is executed.
  
  
  3.10 Atomic functions
  
  Instead  of  atomic  regions, entire functions can be declared to be atomic.
  This  has  the same effect as though the function's body were enclosed in an
  atomic  statement.  Function  arguments  can be declared either readwrite or
  readonly;  they will be locked in the same way as for a lock statement. If a
  function  argument  is  preceded  by  neither  readwrite  nor  readonly, the
  corresponding object will not be locked. Example:
  
    Example  
    gap> AddAtomic := atomic function(readwrite list, readonly item)
    >      Add(list, item);
    >    end;
  
  
  
  3.11 Write-once functionality
  
  There  is  an  exception  to the rule that objects can only be modified if a
  thread  has  write  access  to  a  region.  A limited sets of objects can be
  modified  using  the  "bind  once"  family  of  functions.  These  allow the
  modifications  of  objects  to  which  a thread has read access in a limited
  fashion.
  
  For  reasons of implementation symmetry, these functions can also be used on
  the atomic versions of these objects.
  
  Implementation  note:  The  functionality  is  not  currently  available for
  component objects.
  
  3.11-1 BindOnce
  
  BindOnce( obj, index, value )  function
  
  BindOnce  modifies  obj, which can be a positional object, atomic positional
  object,   component   object,   or  atomic  component  object.  It  inspects
  obj![index]  for  the  positional versions or obj!.(index) for the component
  versions.  If  the respective element is not yet bound, value is assigned to
  that  element. Otherwise, no modification happens. The test and modification
  occur  as  one  atomic  step. The function returns the value of the element;
  i.e. the old value if the element was bound and value if it was unbound.
  
  The  intent  of  this  function  is  to  allow  concurrent initialization of
  objects,  where  multiple  threads  may attempt to set a value concurrently.
  Only one will succeed; all threads can then use the return value of BindOnce
  as  the  definitive  value  of  the  element.  It  also  allows for the lazy
  initialization of objects in the read-only region.
  
  The  current  thread needs to have at least read access to obj, but does not
  require write access.
  
  3.11-2 TestBindOnce
  
  TestBindOnce( obj, index, value )  function
  
  TestBindOnce  works  like  BindOnce (3.11-1), except that it returns true if
  the value could be bound and false otherwise.
  
  3.11-3 BindOnceExpr
  
  BindOnceExpr( obj, index, expr )  function
  
  BindOnceExpr  works  like  BindOnce  (3.11-1),  except that it evaluates the
  parameterless  function  expr  to determine the value. It will only evaluate
  expr if the element is not bound.
  
  For positional objects, the implementation works as follows:
  
    Example  
    BindOnceExprPosObj := function(obj, index, expr)
      if not IsBound(obj![index]) then
        return BindOnce(obj, index, expr());
      else
        return obj![index]);
      fi;
    end;
  
  
  The implementation for component objects works analogously.
  
  The  intent  is  to  avoid  unnecessary computations if the value is already
  bound.  Note  that  this  cannot be avoided entirely, because obj![index] or
  obj!.(index)  can be bound while expr is evaluated, but it can minimize such
  occurrences.
  
  3.11-4 TestBindOnceExpr
  
  TestBindOnceExpr( obj, index, expr )  function
  
  TestBindOnceExpr  works  like  BindOnceExpr (3.11-3), except that it returns
  true if the value could be bound and false otherwise.
  
  3.11-5 StrictBindOnce
  
  StrictBindOnce( obj, index, expr )  function
  
  StrictBindOnce  works like BindOnce (3.11-1), except that it raises an error
  if  the  element  is  already  bound.  This  is  intended  for cases where a
  read-only  object  is  initialized,  but  where  another  thread  trying  to
  initialize it concurrently would be an error.