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+------------------------------------------------------------------------------
+-- --
+-- GNAT LIBRARY COMPONENTS --
+-- --
+-- A D A . C O N T A I N E R S . F O R M A L _ H A S H E D _ S E T S --
+-- --
+-- S p e c --
+-- --
+-- Copyright (C) 2004-2013, 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_Hashed_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: Element, Next, Query_Element, Has_Element, Key,
+-- Iterate, Equivalent_Elements. 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.
+
+-- 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.Hash_Tables;
+
+generic
+ type Element_Type is private;
+
+ with function Hash (Element : Element_Type) return Hash_Type;
+
+ with function Equivalent_Elements (Left, Right : Element_Type)
+ return Boolean;
+
+ with function "=" (Left, Right : Element_Type) return Boolean is <>;
+
+package Ada.Containers.Formal_Hashed_Sets is
+ pragma Annotate (GNATprove, External_Axiomatization);
+ pragma Pure;
+
+ type Set (Capacity : Count_Type; Modulus : Hash_Type) is private with
+ Iterable => (First => First,
+ Next => Next,
+ Has_Element => Has_Element,
+ Element => Element);
+ 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 Capacity (Container : Set) return Count_Type with
+ Global => null;
+
+ procedure Reserve_Capacity
+ (Container : in out Set;
+ Capacity : Count_Type)
+ with
+ Global => null,
+ Pre => Capacity <= Container.Capacity;
+
+ 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
+ Global => null,
+ 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 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 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 Find
+ (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;
+
+ function Equivalent_Elements (Left : Set; CLeft : Cursor;
+ Right : Set; CRight : Cursor) return Boolean
+ with
+ Global => null;
+
+ function Equivalent_Elements
+ (Left : Set; CLeft : Cursor;
+ Right : Element_Type) return Boolean
+ with
+ Global => null;
+
+ function Equivalent_Elements
+ (Left : Element_Type;
+ Right : Set; CRight : Cursor) return Boolean
+ with
+ Global => null;
+
+ function Default_Modulus (Capacity : Count_Type) return Hash_Type with
+ Global => null;
+
+ generic
+ type Key_Type (<>) is private;
+
+ with function Key (Element : Element_Type) return Key_Type;
+
+ with function Hash (Key : Key_Type) return Hash_Type;
+
+ with function Equivalent_Keys (Left, Right : Key_Type) return Boolean;
+
+ package Generic_Keys is
+
+ 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 Contains (Container : Set; Key : Key_Type) return Boolean with
+ Global => null;
+
+ end Generic_Keys;
+
+ function Strict_Equal (Left, Right : Set) return Boolean with
+ 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
+ Global => null,
+ Pre => Has_Element (Container, Current) or else Current = No_Element;
+ function Current_To_Last (Container : Set; Current : Cursor) return Set
+ with
+ 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 Inline (Next);
+
+ type Node_Type is
+ record
+ Element : Element_Type;
+ Next : Count_Type;
+ Has_Element : Boolean := False;
+ end record;
+
+ package HT_Types is new
+ Ada.Containers.Hash_Tables.Generic_Bounded_Hash_Table_Types (Node_Type);
+
+ type Set (Capacity : Count_Type; Modulus : Hash_Type) is
+ new HT_Types.Hash_Table_Type (Capacity, Modulus) with null record;
+
+ use HT_Types;
+
+ type Cursor is record
+ Node : Count_Type;
+ end record;
+
+ No_Element : constant Cursor := (Node => 0);
+
+ Empty_Set : constant Set := (Capacity => 0, Modulus => 0, others => <>);
+
+end Ada.Containers.Formal_Hashed_Sets;