A.18.7 Sets
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The language-defined generic packages Containers.Hashed_Sets
and Containers.Ordered_Sets provide private types Set and Cursor, and
a set of operations for each type. A set container allows elements of
an arbitrary type to be stored without duplication. A hashed set uses
a hash function to organize elements, while an ordered set orders its
element per a specified relation.{set
container} {container
(set)} 2/2
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This section describes the declarations that are
common to both kinds of sets. See A.18.8
for a description of the semantics specific to Containers.Hashed_Sets
and A.18.9 for a description of the semantics
specific to Containers.Ordered_Sets. Static Semantics
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The actual function for the generic formal function
"=" on Element_Type values is expected to define a reflexive
and symmetric relationship and return the same result value each time
it is called with a particular pair of values. If it behaves in some
other manner, the function "=" on set values returns an unspecified
value. The exact arguments and number of calls of this generic formal
function by the function "=" on set values are unspecified.{unspecified
[partial]} 3.a/2
Ramification: If
the actual function for "=" is not symmetric and consistent,
the result returned by the "=" for Set objects cannot be predicted.
The implementation is not required to protect against "=" raising
an exception, or returning random results, or any other “bad”
behavior. And it can call "=" in whatever manner makes sense.
But note that only the result of "=" for Set objects is unspecified;
other subprograms are not allowed to break if "=" is bad (they
aren't expected to use "=").
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The type Set is used to represent sets. The type
Set needs finalization (see 7.6).5/2
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A set contains elements. Set cursors designate
elements. There exists an equivalence relation on elements, whose definition
is different for hashed sets and ordered sets. A set never contains two
or more equivalent elements. The length of a set is the number
of elements it contains.{length (of a
set)} 6/2
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{first element
(of a set)} {last
element (of a set)} {successor
element (of a set)} Each nonempty set
has two particular elements called the first element and the last
element (which may be the same). Each element except for the last
element has a successor element. If there are no other intervening
operations, starting with the first element and repeatedly going to the
successor element will visit each element in the set exactly once until
the last element is reached. The exact definition of these terms is different
for hashed sets and ordered sets.7/2
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[Some operations of these generic packages have
access-to-subprogram parameters. To ensure such operations are well-defined,
they guard against certain actions by the designated subprogram. In particular,
some operations check for “tampering with cursors” of a container
because they depend on the set of elements of the container remaining
constant, and others check for “tampering with elements”
of a container because they depend on elements of the container not being
replaced.]8/2
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{tamper with cursors
(of a set)} A subprogram is said to tamper
with cursors of a set object S if:9/2
- it inserts or
deletes elements of S, that is, it calls the Insert, Include,
Clear, Delete, Exclude, or Replace_Element procedures with S as
a parameter; or
9.a/2
To be honest: Operations
which are defined to be equivalent to a call on one of these operations
also are included. Similarly, operations which call one of these as part
of their definition are included.
9.b/2
Discussion: We
have to include Replace_Element here because it might delete and reinsert
the element if it moves in the set. That could change the order of iteration,
which is what this check is designed to prevent. Replace is also included,
as it is defined in terms of Replace_Element.
10/2
11/2
- it calls the
Move procedure with S as a parameter; or
12/2
- it calls one
of the operations defined to tamper with cursors of S.
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{tamper with elements
(of a set)} A subprogram is said to tamper
with elements of a set object S if:14/2
- it tampers with
cursors of S.
14.a/2
Reason: Complete
replacement of an element can cause its memory to be deallocated while
another operation is holding onto a reference to it. That can't be allowed.
However, a simple modification of (part of) an element is not a problem,
so Update_Element_Preserving_Key does not cause a problem.
14.b/2
We don't need to list
Replace and Replace_Element here because they are covered by “tamper
with cursors”. For Set, “tamper with cursors” and “tamper
with elements” are the same. We leave both terms so that the rules
for routines like Iterate and Query_Element are consistent across all
containers.
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Empty_Set represents the empty Set object. It has
a length of 0. If an object of type Set is not otherwise initialized,
it is initialized to the same value as Empty_Set.16/2
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No_Element represents a cursor that designates
no element. If an object of type Cursor is not otherwise initialized,
it is initialized to the same value as No_Element.17/2
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The predefined "=" operator for type
Cursor returns True if both cursors are No_Element, or designate the
same element in the same container.18/2
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Execution of the default implementation of the
Input, Output, Read, or Write attribute of type Cursor raises Program_Error.18.a/2
Reason: A cursor
will probably be implemented in terms of one or more access values, and
the effects of streaming access values is unspecified. Rather than letting
the user stream junk by accident, we mandate that streaming of cursors
raise Program_Error by default. The attributes can always be specified
if there is a need to support streaming.
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function "=" (Left, Right : Set) return Boolean;
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If Left and Right denote the same set object, then
the function returns True. If Left and Right have different lengths,
then the function returns False. Otherwise, for each element E
in Left, the function returns False if an element equal to E (using
the generic formal equality operator) is not present in Right. If the
function has not returned a result after checking all of the elements,
it returns True. Any exception raised during evaluation of element equality
is propagated. 20.a/2
Implementation Note:
This wording describes the canonical semantics. However, the order
and number of calls on the formal equality function is unspecified for
all of the operations that use it in this package, so an implementation
can call it as many or as few times as it needs to get the correct answer.
Specifically, there is no requirement to call the formal equality additional
times once the answer has been determined.
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function Equivalent_Sets (Left, Right : Set) return Boolean;
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If Left and Right denote the same set object, then
the function returns True. If Left and Right have different lengths,
then the function returns False. Otherwise, for each element E
in Left, the function returns False if an element equivalent to E
is not present in Right. If the function has not returned a result after
checking all of the elements, it returns True. Any exception raised during
evaluation of element equivalence is propagated.23/2
function To_Set (New_Item : Element_Type) return Set;
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Returns a set containing the single element New_Item.25/2
function Length (Container : Set) return Count_Type;
26/2
27/2
function Is_Empty (Container : Set) return Boolean;
28/2
29/2
procedure Clear (Container : in out Set);
30/2
31/2
function Element (Position : Cursor) return Element_Type;
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If Position equals No_Element, then Constraint_Error
is propagated. Otherwise, Element returns the element designated by Position.33/2
procedure Replace_Element (Container : in out Set;
Position : in Cursor;
New_Item : in Element_Type);
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If Position equals No_Element, then Constraint_Error
is propagated; if Position does not designate an element in Container,
then Program_Error is propagated. If an element equivalent to New_Item
is already present in Container at a position other than Position, Program_Error
is propagated. Otherwise, Replace_Element assigns New_Item to the element
designated by Position. Any exception raised by the assignment is propagated.34.a/2
Implementation Note:
The final assignment may require that the node of the element be
moved in the Set's data structures. That could mean that implementing
this operation exactly as worded above could require the overhead of
searching twice. Implementations are encouraged to avoid this extra overhead
when possible, by prechecking if the old element is equivalent to the
new one, by inserting a placeholder node while checking for an equivalent
element, and similar optimizations.
34.b/2
The cursor still designates
the same element after this operation; only the value of that element
has changed. Cursors cannot include information about the relative position
of an element in a Set (as they must survive insertions and deletions
of other elements), so this should not pose an implementation hardship.
35/2
procedure Query_Element
(Position : in Cursor;
Process : not null access procedure (Element : in Element_Type));
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If Position equals No_Element, then Constraint_Error
is propagated. Otherwise, Query_Element calls Process.all with
the element designated by Position as the argument. Program_Error is
propagated if Process.all tampers with the elements of Container.
Any exception raised by Process.all is propagated.37/2
procedure Move (Target : in out Set;
Source : in out Set);
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If Target denotes the same object as Source, then
Move has no effect. Otherwise, Move first clears Target. Then, each element
from Source is removed from Source and inserted into Target. The length
of Source is 0 after a successful call to Move.39/2
procedure Insert (Container : in out Set;
New_Item : in Element_Type;
Position : out Cursor;
Inserted : out Boolean);
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Insert checks if an element equivalent to New_Item
is already present in Container. If a match is found, Inserted is set
to False and Position designates the matching element. Otherwise, Insert
adds New_Item to Container; Inserted is set to True and Position designates
the newly-inserted element. Any exception raised during allocation is
propagated and Container is not modified.41/2
procedure Insert (Container : in out Set;
New_Item : in Element_Type);
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Insert inserts New_Item into Container as per the
four-parameter Insert, with the difference that if an element equivalent
to New_Item is already in the set, then Constraint_Error is propagated.42.a/2
Discussion:
This is equivalent to:
42.b/2
declare
Inserted : Boolean; C : Cursor;
begin
Insert (Container, New_Item, C, Inserted);
if not Inserted then
raise Constraint_Error;
end if;
end;
42.c/2
but doesn't require the
hassle of out parameters.
43/2
procedure Include (Container : in out Set;
New_Item : in Element_Type);
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Include inserts New_Item into Container as per
the four-parameter Insert, with the difference that if an element equivalent
to New_Item is already in the set, then it is replaced. Any exception
raised during assignment is propagated.45/2
procedure Replace (Container : in out Set;
New_Item : in Element_Type);
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Replace checks if an element equivalent to New_Item
is already in the set. If a match is found, that element is replaced
with New_Item; otherwise, Constraint_Error is propagated.47/2
procedure Exclude (Container : in out Set;
Item : in Element_Type);
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Exclude checks if an element equivalent to Item
is present in Container. If a match is found, Exclude removes the element
from the set.49/2
procedure Delete (Container : in out Set;
Item : in Element_Type);
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Delete checks if an element equivalent to Item
is present in Container. If a match is found, Delete removes the element
from the set; otherwise, Constraint_Error is propagated.51/2
procedure Delete (Container : in out Set;
Position : in out Cursor);
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If Position equals No_Element, then Constraint_Error
is propagated. If Position does not designate an element in Container,
then Program_Error is propagated. Otherwise, Delete removes the element
designated by Position from the set. Position is set to No_Element on
return.52.a/2
Ramification: The
check on Position checks that the cursor does not belong to some other
set. This check implies that a reference to the set is included in the
cursor value. This wording is not meant to require detection of dangling
cursors; such cursors are defined to be invalid, which means that execution
is erroneous, and any result is allowed (including not raising an exception).
53/2
procedure Union (Target : in out Set;
Source : in Set);
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Union inserts into Target the elements of Source
that are not equivalent to some element already in Target.54.a/2
Implementation Note:
If the objects are the same, the result is the same as the original
object. The implementation needs to take care so that aliasing effects
do not make the result trash; Union (S, S); must work.
55/2
function Union (Left, Right : Set) return Set;
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Returns a set comprising all of the elements of
Left, and the elements of Right that are not equivalent to some element
of Left.57/2
procedure Intersection (Target : in out Set;
Source : in Set);
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Union deletes from Target the elements of Target
that are not equivalent to some element of Source.58.a/2
Implementation Note:
If the objects are the same, the result is the same as the original
object. The implementation needs to take care so that aliasing effects
do not make the result trash; Intersection (S, S); must work.
59/2
function Intersection (Left, Right : Set) return Set;
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Returns a set comprising all the elements of Left
that are equivalent to the some element of Right.61/2
procedure Difference (Target : in out Set;
Source : in Set);
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If Target denotes the same object as Source, then
Difference clears Target. Otherwise, it deletes from Target the elements
that are equivalent to some element of Source.63/2
function Difference (Left, Right : Set) return Set;
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Returns a set comprising the elements of Left that
are not equivalent to some element of Right.65/2
procedure Symmetric_Difference (Target : in out Set;
Source : in Set);
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If Target denotes the same object as Source, then
Symmetric_Difference clears Target. Otherwise, it deletes from Target
the elements that are equivalent to some element of Source, and inserts
into Target the elements of Source that are not equivalent to some element
of Target.67/2
function Symmetric_Difference (Left, Right : Set) return Set;
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Returns a set comprising the elements of Left that
are not equivalent to some element of Right, and the elements of Right
that are not equivalent to some element of Left.69/2
function Overlap (Left, Right : Set) return Boolean;
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If an element of Left is equivalent to some element
of Right, then Overlap returns True. Otherwise it returns False.70.a/2
Discussion: This
operation is commutative. If Overlap returns False, the two sets are
disjoint.
71/2
function Is_Subset (Subset : Set;
Of_Set : Set) return Boolean;
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If an element of Subset is not equivalent to some
element of Of_Set, then Is_Subset returns False. Otherwise it returns
True.72.a/2
Discussion: This
operation is not commutative, so we use parameter names that make it
clear in named notation which set is which.
73/2
function First (Container : Set) return Cursor;
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If Length (Container) = 0, then First returns No_Element.
Otherwise, First returns a cursor that designates the first element in
Container.75/2
function Next (Position : Cursor) return Cursor;
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Returns a cursor that designates the successor
of the element designated by Position. If Position designates the last
element, then No_Element is returned. If Position equals No_Element,
then No_Element is returned.77/2
procedure Next (Position : in out Cursor);
78/2
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Equivalent to Find (Container, Item) /= No_Element.80/2
function Find (Container : Set;
Item : Element_Type) return Cursor;
81/2
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If Length (Container) equals 0, then Find returns
No_Element. Otherwise, Find checks if an element equivalent to Item is
present in Container. If a match is found, a cursor designating the matching
element is returned; otherwise, No_Element is returned.82/2
function Contains (Container : Set;
Item : Element_Type) return Boolean;
83/2
function Has_Element (Position : Cursor) return Boolean;
84/2
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Returns True if Position designates an element,
and returns False otherwise.84.a/2
To be honest: This
function may not detect cursors that designate deleted elements; such
cursors are invalid (see below); the result of Has_Element for invalid
cursors is unspecified (but not erroneous).
85/2
procedure Iterate
(Container : in Set;
Process : not null access procedure (Position : in Cursor));
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Iterate calls Process.all with a cursor
that designates each element in Container, starting with the first element
and moving the cursor according to the successor relation. Program_Error
is propagated if Process.all tampers with the cursors of Container.
Any exception raised by Process.all is propagated.86.a/2
Implementation Note:
The “tamper with cursors” check takes place when the
operations that insert or delete elements, and so on are called.
86.b/2
See Iterate for vectors
(A.18.2) for a suggested implementation
of the check.
87/2
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Both Containers.Hashed_Set and Containers.Ordered_Set
declare a nested generic package Generic_Keys, which provides operations
that allow set manipulation in terms of a key (typically, a portion of
an element) instead of a complete element. The formal function Key of
Generic_Keys extracts a key value from an element. It is expected to
return the same value each time it is called with a particular element.
The behavior of Generic_Keys is unspecified if Key behaves in some other
manner.{unspecified [partial]}
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A key is expected to unambiguously determine a
single equivalence class for elements. The behavior of Generic_Keys is
unspecified if the formal parameters of this package behave in some other
manner.{unspecified [partial]}
89/2
function Key (Position : Cursor) return Key_Type;
90/2
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The subprograms in package Generic_Keys named Contains,
Find, Element, Delete, and Exclude, are equivalent to the corresponding
subprograms in the parent package, with the difference that the Key parameter
is used to locate an element in the set.92/2
procedure Replace (Container : in out Set;
Key : in Key_Type;
New_Item : in Element_Type);
93/2
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Equivalent to Replace_Element (Container, Find
(Container, Key), New_Item).94/2
procedure Update_Element_Preserving_Key
(Container : in out Set;
Position : in Cursor;
Process : not null access procedure
(Element : in out Element_Type));
95/2
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If Position equals No_Element, then Constraint_Error
is propagated; if Position does not designate an element in Container,
then Program_Error is propagated. Otherwise, Update_Element_Preserving_Key
uses Key to save the key value K of the element designated by
Position. Update_Element_Preserving_Key then calls Process.all
with that element as the argument. Program_Error is propagated if Process.all
tampers with the elements of Container. Any exception raised by Process.all
is propagated. After Process.all returns, Update_Element_Preserving_Key
checks if K determines the same equivalence class as that for
the new element; if not, the element is removed from the set and Program_Error
is propagated.95.a/2
Reason: The key
check ensures that the invariants of the set are preserved by the modification.
The “tampers with the elements” check prevents data loss
(if Element_Type is by-copy) or erroneous execution (if element type
is unconstrained and indefinite).
96/2
If
Element_Type is unconstrained and definite, then the actual Element parameter
of Process.all shall be unconstrained.
96.a/2
Ramification: This
means that the elements cannot be directly allocated from the heap; it
must be possible to change the discriminants of the element in place.
Erroneous Execution
97/2
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A Cursor value is invalid if any of the
following have occurred since it was created:{invalid
cursor (of a set)} {cursor
(invalid) [partial]} 98/2
- The set that
contains the element it designates has been finalized;
99/2
- The set that
contains the element it designates has been used as the Source or Target
of a call to Move; or
100/2
- The element
it designates has been deleted from the set.
101/2
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The result of "=" or Has_Element is unspecified
if these functions are called with an invalid cursor parameter.{unspecified
[partial]} Execution is erroneous if any
other subprogram declared in Containers.Hashed_Sets or Containers.Ordered_Sets
is called with an invalid cursor parameter.{erroneous
execution (cause) [partial]} 101.a/2
Discussion: The
list above is intended to be exhaustive. In other cases, a cursor value
continues to designate its original element. For instance, cursor values
survive the insertion and deletion of other elements.
101.b/2
While it is possible to
check for these cases, in many cases the overhead necessary to make the
check is substantial in time or space. Implementations are encouraged
to check for as many of these cases as possible and raise Program_Error
if detected.
Implementation Requirements
102/2
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No storage associated with a Set object shall be
lost upon assignment or scope exit.103/2
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The execution of an assignment_statement
for a set shall have the effect of copying the elements from the source
set object to the target set object.103.a/2
Implementation Note:
An assignment of a Set is a “deep” copy; that is the
elements are copied as well as the data structures. We say “effect
of” in order to allow the implementation to avoid copying elements
immediately if it wishes. For instance, an implementation that avoided
copying until one of the containers is modified would be allowed.
Implementation Advice
104/2
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Move should not copy elements, and should minimize
copying of internal data structures. 104.a/2
Implementation Advice:
Move for sets should not copy elements,
and should minimize copying of internal data structures.
104.b/2
Implementation Note:
Usually that can be accomplished simply by moving the pointer(s)
to the internal data structures from the Source container to the Target
container.
105/2
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If an exception is propagated from a set operation,
no storage should be lost, nor any elements removed from a set unless
specified by the operation. 105.a/2
Implementation Advice:
If an exception is propagated from a
set operation, no storage should be lost, nor any elements removed from
a set unless specified by the operation.
105.b/2
Reason: This is
important so that programs can recover from errors. But we don't want
to require heroic efforts, so we just require documentation of cases
where this can't be accomplished.
Wording Changes from Ada 95
105.c/2
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This description of sets is new; the extensions
are documented with the specific packages.
Sponsored by Ada-Europe