A.18.7 Sets
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.
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
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.
The type Set is used to represent sets. The type
Set needs finalization (see
7.6).
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.
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.
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.
A
subprogram is said to
tamper with cursors of a set object
S
if:
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
it finalizes S; or
it calls the Move procedure with S as a
parameter; or
it calls one of the operations defined to tamper
with cursors of S.
A
subprogram is said to
tamper with elements of a set object
S
if:
it tampers with cursors of S.
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.
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.
The predefined "=" operator for type Cursor
returns True if both cursors are No_Element, or designate the same element
in the same container.
Execution of the default implementation of the Input,
Output, Read, or Write attribute of type Cursor raises Program_Error.
function "=" (Left, Right : Set) return Boolean;
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.
function Equivalent_Sets (Left, Right : Set) return Boolean;
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.
function To_Set (New_Item : Element_Type) return Set;
Returns a set containing
the single element New_Item.
function Length (Container : Set) return Count_Type;
Returns the number
of elements in Container.
function Is_Empty (Container : Set) return Boolean;
Equivalent to Length
(Container) = 0.
procedure Clear (Container : in out Set);
Removes all the
elements from Container.
function Element (Position : Cursor) return Element_Type;
If Position equals
No_Element, then Constraint_Error is propagated. Otherwise, Element returns
the element designated by Position.
procedure Replace_Element (Container : in out Set;
Position : in Cursor;
New_Item : in Element_Type);
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.
procedure Query_Element
(Position : in Cursor;
Process : not null access procedure (Element : in Element_Type));
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.
procedure Move (Target : in out Set;
Source : in out Set);
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.
procedure Insert (Container : in out Set;
New_Item : in Element_Type;
Position : out Cursor;
Inserted : out Boolean);
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.
procedure Insert (Container : in out Set;
New_Item : in Element_Type);
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.
procedure Include (Container : in out Set;
New_Item : in Element_Type);
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.
procedure Replace (Container : in out Set;
New_Item : in Element_Type);
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.
procedure Exclude (Container : in out Set;
Item : in Element_Type);
Exclude checks if
an element equivalent to Item is present in Container. If a match is
found, Exclude removes the element from the set.
procedure Delete (Container : in out Set;
Item : in Element_Type);
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.
procedure Delete (Container : in out Set;
Position : in out Cursor);
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.
procedure Union (Target : in out Set;
Source : in Set);
Union inserts into
Target the elements of Source that are not equivalent to some element
already in Target.
function Union (Left, Right : Set) return Set;
Returns a set comprising
all of the elements of Left, and the elements of Right that are not equivalent
to some element of Left.
procedure Intersection (Target : in out Set;
Source : in Set);
Union deletes from
Target the elements of Target that are not equivalent to some element
of Source.
function Intersection (Left, Right : Set) return Set;
Returns a set comprising
all the elements of Left that are equivalent to the some element of Right.
procedure Difference (Target : in out Set;
Source : in Set);
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.
function Difference (Left, Right : Set) return Set;
Returns a set comprising
the elements of Left that are not equivalent to some element of Right.
procedure Symmetric_Difference (Target : in out Set;
Source : in Set);
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.
function Symmetric_Difference (Left, Right : Set) return Set;
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.
function Overlap (Left, Right : Set) return Boolean;
If an element of
Left is equivalent to some element of Right, then Overlap returns True.
Otherwise it returns False.
function Is_Subset (Subset : Set;
Of_Set : Set) return Boolean;
If an element of
Subset is not equivalent to some element of Of_Set, then Is_Subset returns
False. Otherwise it returns True.
function First (Container : Set) return Cursor;
If Length (Container)
= 0, then First returns No_Element. Otherwise, First returns a cursor
that designates the first element in Container.
function Next (Position : Cursor) return Cursor;
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.
procedure Next (Position : in out Cursor);
Equivalent to Position
:= Next (Position).
Equivalent to Find
(Container, Item) /= No_Element.
function Find (Container : Set;
Item : Element_Type) return Cursor;
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.
function Contains (Container : Set;
Item : Element_Type) return Boolean;
function Has_Element (Position : Cursor) return Boolean;
Returns True if
Position designates an element, and returns False otherwise.
procedure Iterate
(Container : in Set;
Process : not null access procedure (Position : in Cursor));
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.
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.
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.
function Key (Position : Cursor) return Key_Type;
Equivalent to Key
(Element (Position)).
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.
procedure Replace (Container : in out Set;
Key : in Key_Type;
New_Item : in Element_Type);
Equivalent to Replace_Element
(Container, Find (Container, Key), New_Item).
procedure Update_Element_Preserving_Key
(Container : in out Set;
Position : in Cursor;
Process : not null access procedure
(Element : in out Element_Type));
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.
If Element_Type
is unconstrained and definite, then the actual Element parameter of Process.all
shall be unconstrained.
Erroneous Execution
A Cursor value is
invalid
if any of the following have occurred since it was created:
The set that contains the element it designates
has been finalized;
The set that contains the element it designates
has been used as the Source or Target of a call to Move; or
The element it designates has been deleted from
the set.
The result of "=" or Has_Element is unspecified
if these functions are called with an invalid cursor parameter.
Execution is erroneous if any other subprogram declared in Containers.Hashed_Sets
or Containers.Ordered_Sets is called with an invalid cursor parameter.
Implementation Requirements
No storage associated with a Set object shall be
lost upon assignment or scope exit.
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.
Implementation Advice
Move should not copy elements, and should minimize
copying of internal data structures.
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.
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