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Ada

------------------------------------------------------------------------------
-- --
-- GNAT LIBRARY COMPONENTS --
-- --
-- A D A . C O N T A I N E R S . F O R M A L _ O R D E R E D _ S E T S --
-- --
-- S p e c --
-- --
-- Copyright (C) 2004-2015, Free Software Foundation, Inc. --
-- --
-- This specification is derived from the Ada Reference Manual for use with --
-- GNAT. The copyright notice above, and the license provisions that follow --
-- apply solely to the contents of the part following the private keyword. --
-- --
-- GNAT is free software; you can redistribute it and/or modify it under --
-- terms of the GNU General Public License as published by the Free Soft- --
-- ware Foundation; either version 3, or (at your option) any later ver- --
-- sion. GNAT is distributed in the hope that it will be useful, but WITH- --
-- OUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY --
-- or FITNESS FOR A PARTICULAR PURPOSE. --
-- --
-- As a special exception under Section 7 of GPL version 3, you are granted --
-- additional permissions described in the GCC Runtime Library Exception, --
-- version 3.1, as published by the Free Software Foundation. --
-- --
-- You should have received a copy of the GNU General Public License and --
-- a copy of the GCC Runtime Library Exception along with this program; --
-- see the files COPYING3 and COPYING.RUNTIME respectively. If not, see --
-- <http://www.gnu.org/licenses/>. --
------------------------------------------------------------------------------
-- This spec is derived from package Ada.Containers.Bounded_Ordered_Sets in
-- the Ada 2012 RM. The modifications are meant to facilitate formal proofs by
-- making it easier to express properties, and by making the specification of
-- this unit compatible with SPARK 2014. Note that the API of this unit may be
-- subject to incompatible changes as SPARK 2014 evolves.
-- The modifications are:
-- A parameter for the container is added to every function reading the
-- content of a container: Key, Element, Next, Query_Element, Previous,
-- Has_Element, Iterate, Reverse_Iterate. This change is motivated by the
-- need to have cursors which are valid on different containers (typically
-- a container C and its previous version C'Old) for expressing properties,
-- which is not possible if cursors encapsulate an access to the underlying
-- container. The operators "<" and ">" that could not be modified that way
-- have been removed.
-- There are three new functions:
-- function Strict_Equal (Left, Right : Set) return Boolean;
-- function First_To_Previous (Container : Set; Current : Cursor)
-- return Set;
-- function Current_To_Last (Container : Set; Current : Cursor)
-- return Set;
-- See detailed specifications for these subprograms
private with Ada.Containers.Red_Black_Trees;
generic
type Element_Type is private;
with function "<" (Left, Right : Element_Type) return Boolean is <>;
with function "=" (Left, Right : Element_Type) return Boolean is <>;
package Ada.Containers.Formal_Ordered_Sets with
Pure,
SPARK_Mode
is
pragma Annotate (GNATprove, External_Axiomatization);
pragma Annotate (CodePeer, Skip_Analysis);
function Equivalent_Elements (Left, Right : Element_Type) return Boolean
with
Global => null;
type Set (Capacity : Count_Type) is private with
Iterable => (First => First,
Next => Next,
Has_Element => Has_Element,
Element => Element),
Default_Initial_Condition => Is_Empty (Set);
pragma Preelaborable_Initialization (Set);
type Cursor is private;
pragma Preelaborable_Initialization (Cursor);
Empty_Set : constant Set;
No_Element : constant Cursor;
function "=" (Left, Right : Set) return Boolean with
Global => null;
function Equivalent_Sets (Left, Right : Set) return Boolean with
Global => null;
function To_Set (New_Item : Element_Type) return Set with
Global => null;
function Length (Container : Set) return Count_Type with
Global => null;
function Is_Empty (Container : Set) return Boolean with
Global => null;
procedure Clear (Container : in out Set) with
Global => null;
procedure Assign (Target : in out Set; Source : Set) with
Pre => Target.Capacity >= Length (Source);
function Copy (Source : Set; Capacity : Count_Type := 0) return Set with
Global => null,
Pre => Capacity = 0 or else Capacity >= Source.Capacity;
function Element
(Container : Set;
Position : Cursor) return Element_Type
with
Global => null,
Pre => Has_Element (Container, Position);
procedure Replace_Element
(Container : in out Set;
Position : Cursor;
New_Item : Element_Type)
with
Global => null,
Pre => Has_Element (Container, Position);
procedure Move (Target : in out Set; Source : in out Set) with
Global => null,
Pre => Target.Capacity >= Length (Source);
procedure Insert
(Container : in out Set;
New_Item : Element_Type;
Position : out Cursor;
Inserted : out Boolean)
with
Global => null,
Pre => Length (Container) < Container.Capacity;
procedure Insert
(Container : in out Set;
New_Item : Element_Type)
with
Global => null,
Pre => Length (Container) < Container.Capacity
and then (not Contains (Container, New_Item));
procedure Include
(Container : in out Set;
New_Item : Element_Type)
with
Global => null,
Pre => Length (Container) < Container.Capacity;
procedure Replace
(Container : in out Set;
New_Item : Element_Type)
with
Global => null,
Pre => Contains (Container, New_Item);
procedure Exclude
(Container : in out Set;
Item : Element_Type)
with
Global => null;
procedure Delete
(Container : in out Set;
Item : Element_Type)
with
Global => null,
Pre => Contains (Container, Item);
procedure Delete
(Container : in out Set;
Position : in out Cursor)
with
Global => null,
Pre => Has_Element (Container, Position);
procedure Delete_First (Container : in out Set) with
Global => null;
procedure Delete_Last (Container : in out Set) with
Global => null;
procedure Union (Target : in out Set; Source : Set) with
Global => null,
Pre => Length (Target) + Length (Source) -
Length (Intersection (Target, Source)) <= Target.Capacity;
function Union (Left, Right : Set) return Set with
Global => null,
Pre => Length (Left) + Length (Right) -
Length (Intersection (Left, Right)) <= Count_Type'Last;
function "or" (Left, Right : Set) return Set renames Union;
procedure Intersection (Target : in out Set; Source : Set) with
Global => null;
function Intersection (Left, Right : Set) return Set with
Global => null;
function "and" (Left, Right : Set) return Set renames Intersection;
procedure Difference (Target : in out Set; Source : Set) with
Global => null;
function Difference (Left, Right : Set) return Set with
Global => null;
function "-" (Left, Right : Set) return Set renames Difference;
procedure Symmetric_Difference (Target : in out Set; Source : Set) with
Global => null,
Pre => Length (Target) + Length (Source) -
2 * Length (Intersection (Target, Source)) <= Target.Capacity;
function Symmetric_Difference (Left, Right : Set) return Set with
Global => null,
Pre => Length (Left) + Length (Right) -
2 * Length (Intersection (Left, Right)) <= Count_Type'Last;
function "xor" (Left, Right : Set) return Set renames Symmetric_Difference;
function Overlap (Left, Right : Set) return Boolean with
Global => null;
function Is_Subset (Subset : Set; Of_Set : Set) return Boolean with
Global => null;
function First (Container : Set) return Cursor with
Global => null;
function First_Element (Container : Set) return Element_Type with
Global => null,
Pre => not Is_Empty (Container);
function Last (Container : Set) return Cursor;
function Last_Element (Container : Set) return Element_Type with
Global => null,
Pre => not Is_Empty (Container);
function Next (Container : Set; Position : Cursor) return Cursor with
Global => null,
Pre => Has_Element (Container, Position) or else Position = No_Element;
procedure Next (Container : Set; Position : in out Cursor) with
Global => null,
Pre => Has_Element (Container, Position) or else Position = No_Element;
function Previous (Container : Set; Position : Cursor) return Cursor with
Global => null,
Pre => Has_Element (Container, Position) or else Position = No_Element;
procedure Previous (Container : Set; Position : in out Cursor) with
Global => null,
Pre => Has_Element (Container, Position) or else Position = No_Element;
function Find (Container : Set; Item : Element_Type) return Cursor with
Global => null;
function Floor (Container : Set; Item : Element_Type) return Cursor with
Global => null;
function Ceiling (Container : Set; Item : Element_Type) return Cursor with
Global => null;
function Contains (Container : Set; Item : Element_Type) return Boolean with
Global => null;
function Has_Element (Container : Set; Position : Cursor) return Boolean
with
Global => null;
generic
type Key_Type (<>) is private;
with function Key (Element : Element_Type) return Key_Type;
with function "<" (Left, Right : Key_Type) return Boolean is <>;
package Generic_Keys with SPARK_Mode is
function Equivalent_Keys (Left, Right : Key_Type) return Boolean with
Global => null;
function Key (Container : Set; Position : Cursor) return Key_Type with
Global => null;
function Element (Container : Set; Key : Key_Type) return Element_Type
with
Global => null;
procedure Replace
(Container : in out Set;
Key : Key_Type;
New_Item : Element_Type)
with
Global => null;
procedure Exclude (Container : in out Set; Key : Key_Type) with
Global => null;
procedure Delete (Container : in out Set; Key : Key_Type) with
Global => null;
function Find (Container : Set; Key : Key_Type) return Cursor with
Global => null;
function Floor (Container : Set; Key : Key_Type) return Cursor with
Global => null;
function Ceiling (Container : Set; Key : Key_Type) return Cursor with
Global => null;
function Contains (Container : Set; Key : Key_Type) return Boolean with
Global => null;
end Generic_Keys;
function Strict_Equal (Left, Right : Set) return Boolean with
Ghost,
Global => null;
-- Strict_Equal returns True if the containers are physically equal, i.e.
-- they are structurally equal (function "=" returns True) and that they
-- have the same set of cursors.
function First_To_Previous (Container : Set; Current : Cursor) return Set
with
Ghost,
Global => null,
Pre => Has_Element (Container, Current) or else Current = No_Element;
function Current_To_Last (Container : Set; Current : Cursor) return Set
with
Ghost,
Global => null,
Pre => Has_Element (Container, Current) or else Current = No_Element;
-- First_To_Previous returns a container containing all elements preceding
-- Current (excluded) in Container. Current_To_Last returns a container
-- containing all elements following Current (included) in Container.
-- These two new functions can be used to express invariant properties in
-- loops which iterate over containers. First_To_Previous returns the part
-- of the container already scanned and Current_To_Last the part not
-- scanned yet.
private
pragma SPARK_Mode (Off);
pragma Inline (Next);
pragma Inline (Previous);
type Node_Type is record
Has_Element : Boolean := False;
Parent : Count_Type := 0;
Left : Count_Type := 0;
Right : Count_Type := 0;
Color : Red_Black_Trees.Color_Type;
Element : Element_Type;
end record;
package Tree_Types is
new Red_Black_Trees.Generic_Bounded_Tree_Types (Node_Type);
type Set (Capacity : Count_Type) is
new Tree_Types.Tree_Type (Capacity) with null record;
use Red_Black_Trees;
type Cursor is record
Node : Count_Type;
end record;
No_Element : constant Cursor := (Node => 0);
Empty_Set : constant Set := (Capacity => 0, others => <>);
end Ada.Containers.Formal_Ordered_Sets;