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+------------------------------------------------------------------------------
+-- --
+-- GNAT LIBRARY COMPONENTS --
+-- --
+-- ADA.CONTAINERS.FORMAL_DOUBLY_LINKED_LISTS --
+-- --
+-- 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 Ada.Containers.Bounded_Doubly_Linked_Lists 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
+-- contents of a container: Next, Previous, Query_Element, Has_Element,
+-- Iterate, Reverse_Iterate, Element. 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 : List) return Boolean;
+-- function First_To_Previous (Container : List; Current : Cursor)
+-- return List;
+-- function Current_To_Last (Container : List; Current : Cursor)
+-- return List;
+
+-- See subprogram specifications that follow for details
+
+generic
+ type Element_Type is private;
+
+ with function "=" (Left, Right : Element_Type)
+ return Boolean is <>;
+
+package Ada.Containers.Formal_Doubly_Linked_Lists is
+ pragma Annotate (GNATprove, External_Axiomatization);
+ pragma Pure;
+
+ type List (Capacity : Count_Type) is private with
+ Iterable => (First => First,
+ Next => Next,
+ Has_Element => Has_Element,
+ Element => Element);
+ pragma Preelaborable_Initialization (List);
+
+ type Cursor is private;
+ pragma Preelaborable_Initialization (Cursor);
+
+ Empty_List : constant List;
+
+ No_Element : constant Cursor;
+
+ function "=" (Left, Right : List) return Boolean with
+ Global => null;
+
+ function Length (Container : List) return Count_Type with
+ Global => null;
+
+ function Is_Empty (Container : List) return Boolean with
+ Global => null;
+
+ procedure Clear (Container : in out List) with
+ Global => null;
+
+ procedure Assign (Target : in out List; Source : List) with
+ Global => null,
+ Pre => Target.Capacity >= Length (Source);
+
+ function Copy (Source : List; Capacity : Count_Type := 0) return List with
+ Global => null,
+ Pre => Capacity = 0 or else Capacity >= Source.Capacity;
+
+ function Element
+ (Container : List;
+ Position : Cursor) return Element_Type
+ with
+ Global => null,
+ Pre => Has_Element (Container, Position);
+
+ procedure Replace_Element
+ (Container : in out List;
+ Position : Cursor;
+ New_Item : Element_Type)
+ with
+ Global => null,
+ Pre => Has_Element (Container, Position);
+
+ procedure Move (Target : in out List; Source : in out List) with
+ Global => null,
+ Pre => Target.Capacity >= Length (Source);
+
+ procedure Insert
+ (Container : in out List;
+ Before : Cursor;
+ New_Item : Element_Type;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => Length (Container) + Count <= Container.Capacity
+ and then (Has_Element (Container, Before)
+ or else Before = No_Element);
+
+ procedure Insert
+ (Container : in out List;
+ Before : Cursor;
+ New_Item : Element_Type;
+ Position : out Cursor;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => Length (Container) + Count <= Container.Capacity
+ and then (Has_Element (Container, Before)
+ or else Before = No_Element);
+
+ procedure Insert
+ (Container : in out List;
+ Before : Cursor;
+ Position : out Cursor;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => Length (Container) + Count <= Container.Capacity
+ and then (Has_Element (Container, Before)
+ or else Before = No_Element);
+
+ procedure Prepend
+ (Container : in out List;
+ New_Item : Element_Type;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => Length (Container) + Count <= Container.Capacity;
+
+ procedure Append
+ (Container : in out List;
+ New_Item : Element_Type;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => Length (Container) + Count <= Container.Capacity;
+
+ procedure Delete
+ (Container : in out List;
+ Position : in out Cursor;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => Has_Element (Container, Position);
+
+ procedure Delete_First
+ (Container : in out List;
+ Count : Count_Type := 1)
+ with
+ Global => null;
+
+ procedure Delete_Last
+ (Container : in out List;
+ Count : Count_Type := 1)
+ with
+ Global => null;
+
+ procedure Reverse_Elements (Container : in out List) with
+ Global => null;
+
+ procedure Swap
+ (Container : in out List;
+ I, J : Cursor)
+ with
+ Global => null,
+ Pre => Has_Element (Container, I) and then Has_Element (Container, J);
+
+ procedure Swap_Links
+ (Container : in out List;
+ I, J : Cursor)
+ with
+ Global => null,
+ Pre => Has_Element (Container, I) and then Has_Element (Container, J);
+
+ procedure Splice
+ (Target : in out List;
+ Before : Cursor;
+ Source : in out List)
+ with
+ Global => null,
+ Pre => Length (Source) + Length (Target) <= Target.Capacity
+ and then (Has_Element (Target, Before)
+ or else Before = No_Element);
+
+ procedure Splice
+ (Target : in out List;
+ Before : Cursor;
+ Source : in out List;
+ Position : in out Cursor)
+ with
+ Global => null,
+ Pre => Length (Source) + Length (Target) <= Target.Capacity
+ and then (Has_Element (Target, Before)
+ or else Before = No_Element)
+ and then Has_Element (Source, Position);
+
+ procedure Splice
+ (Container : in out List;
+ Before : Cursor;
+ Position : Cursor)
+ with
+ Global => null,
+ Pre => 2 * Length (Container) <= Container.Capacity
+ and then (Has_Element (Container, Before)
+ or else Before = No_Element)
+ and then Has_Element (Container, Position);
+
+ function First (Container : List) return Cursor with
+ Global => null;
+
+ function First_Element (Container : List) return Element_Type with
+ Global => null,
+ Pre => not Is_Empty (Container);
+
+ function Last (Container : List) return Cursor with
+ Global => null;
+
+ function Last_Element (Container : List) return Element_Type with
+ Global => null,
+ Pre => not Is_Empty (Container);
+
+ function Next (Container : List; Position : Cursor) return Cursor with
+ Global => null,
+ Pre => Has_Element (Container, Position) or else Position = No_Element;
+
+ procedure Next (Container : List; Position : in out Cursor) with
+ Global => null,
+ Pre => Has_Element (Container, Position) or else Position = No_Element;
+
+ function Previous (Container : List; Position : Cursor) return Cursor with
+ Global => null,
+ Pre => Has_Element (Container, Position) or else Position = No_Element;
+
+ procedure Previous (Container : List; Position : in out Cursor) with
+ Global => null,
+ Pre => Has_Element (Container, Position) or else Position = No_Element;
+
+ function Find
+ (Container : List;
+ Item : Element_Type;
+ Position : Cursor := No_Element) return Cursor
+ with
+ Global => null,
+ Pre => Has_Element (Container, Position) or else Position = No_Element;
+
+ function Reverse_Find
+ (Container : List;
+ Item : Element_Type;
+ Position : Cursor := No_Element) return Cursor
+ with
+ Global => null,
+ Pre => Has_Element (Container, Position) or else Position = No_Element;
+
+ function Contains
+ (Container : List;
+ Item : Element_Type) return Boolean
+ with
+ Global => null;
+
+ function Has_Element (Container : List; Position : Cursor) return Boolean
+ with
+ Global => null;
+
+ generic
+ with function "<" (Left, Right : Element_Type) return Boolean is <>;
+ package Generic_Sorting is
+
+ function Is_Sorted (Container : List) return Boolean with
+ Global => null;
+
+ procedure Sort (Container : in out List) with
+ Global => null;
+
+ procedure Merge (Target, Source : in out List) with
+ Global => null;
+
+ end Generic_Sorting;
+
+ function Strict_Equal (Left, Right : List) 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 : List; Current : Cursor) return List
+ with
+ Global => null,
+ Pre => Has_Element (Container, Current) or else Current = No_Element;
+ function Current_To_Last (Container : List; Current : Cursor) return List
+ 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
+
+ type Node_Type is record
+ Prev : Count_Type'Base := -1;
+ Next : Count_Type;
+ Element : Element_Type;
+ end record;
+
+ function "=" (L, R : Node_Type) return Boolean is abstract;
+
+ type Node_Array is array (Count_Type range <>) of Node_Type;
+ function "=" (L, R : Node_Array) return Boolean is abstract;
+
+ type List (Capacity : Count_Type) is tagged record
+ Nodes : Node_Array (1 .. Capacity) := (others => <>);
+ Free : Count_Type'Base := -1;
+ Length : Count_Type := 0;
+ First : Count_Type := 0;
+ Last : Count_Type := 0;
+ end record;
+
+ type Cursor is record
+ Node : Count_Type := 0;
+ end record;
+
+ Empty_List : constant List := (0, others => <>);
+
+ No_Element : constant Cursor := (Node => 0);
+
+end Ada.Containers.Formal_Doubly_Linked_Lists;