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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 _ V E C T O R 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_Vectors 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, Previous, Iterate,
+-- Has_Element, 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.
+
+-- There are three new functions:
+
+-- function Strict_Equal (Left, Right : Vector) return Boolean;
+-- function First_To_Previous (Container : Vector; Current : Cursor)
+-- return Vector;
+-- function Current_To_Last (Container : Vector; Current : Cursor)
+-- return Vector;
+
+-- See detailed specifications for these subprograms
+
+with Ada.Containers;
+use Ada.Containers;
+
+generic
+ type Index_Type is range <>;
+ type Element_Type is private;
+
+ with function "=" (Left, Right : Element_Type) return Boolean is <>;
+
+package Ada.Containers.Formal_Vectors is
+ pragma Annotate (GNATprove, External_Axiomatization);
+ pragma Pure;
+
+ subtype Extended_Index is Index_Type'Base
+ range Index_Type'First - 1 ..
+ Index_Type'Min (Index_Type'Base'Last - 1, Index_Type'Last) + 1;
+
+ No_Index : constant Extended_Index := Extended_Index'First;
+
+ subtype Capacity_Range is
+ Count_Type range 0 .. Count_Type (Index_Type'Last - Index_Type'First + 1);
+
+ type Vector (Capacity : Capacity_Range) is private with
+ Iterable => (First => First,
+ Next => Next,
+ Has_Element => Has_Element,
+ Element => Element);
+
+ type Cursor is private;
+ pragma Preelaborable_Initialization (Cursor);
+
+ Empty_Vector : constant Vector;
+
+ No_Element : constant Cursor;
+
+ function "=" (Left, Right : Vector) return Boolean with
+ Global => null;
+
+ function To_Vector
+ (New_Item : Element_Type;
+ Length : Count_Type) return Vector
+ with
+ Global => null;
+
+ function "&" (Left, Right : Vector) return Vector with
+ Global => null,
+ Pre => Capacity_Range'Last - Length (Left) >= Length (Right);
+
+ function "&" (Left : Vector; Right : Element_Type) return Vector with
+ Global => null,
+ Pre => Length (Left) < Capacity_Range'Last;
+
+ function "&" (Left : Element_Type; Right : Vector) return Vector with
+ Global => null,
+ Pre => Length (Right) < Capacity_Range'Last;
+
+ function "&" (Left, Right : Element_Type) return Vector with
+ Global => null,
+ Pre => Capacity_Range'Last >= 2;
+
+ function Capacity (Container : Vector) return Count_Type with
+ Global => null;
+
+ procedure Reserve_Capacity
+ (Container : in out Vector;
+ Capacity : Count_Type)
+ with
+ Global => null,
+ Pre => Capacity <= Container.Capacity;
+
+ function Length (Container : Vector) return Count_Type with
+ Global => null;
+
+ procedure Set_Length
+ (Container : in out Vector;
+ New_Length : Count_Type)
+ with
+ Global => null,
+ Pre => New_Length <= Length (Container);
+
+ function Is_Empty (Container : Vector) return Boolean with
+ Global => null;
+
+ procedure Clear (Container : in out Vector) with
+ Global => null;
+
+ procedure Assign (Target : in out Vector; Source : Vector) with
+ Global => null,
+ Pre => Length (Source) <= Target.Capacity;
+
+ function Copy
+ (Source : Vector;
+ Capacity : Count_Type := 0) return Vector
+ with
+ Global => null,
+ Pre => Length (Source) <= Capacity and then Capacity in Capacity_Range;
+
+ function To_Cursor
+ (Container : Vector;
+ Index : Extended_Index) return Cursor
+ with
+ Global => null;
+
+ function To_Index (Position : Cursor) return Extended_Index with
+ Global => null;
+
+ function Element
+ (Container : Vector;
+ Index : Index_Type) return Element_Type
+ with
+ Global => null,
+ Pre => First_Index (Container) <= Index
+ and then Index <= Last_Index (Container);
+
+ function Element
+ (Container : Vector;
+ Position : Cursor) return Element_Type
+ with
+ Global => null,
+ Pre => Has_Element (Container, Position);
+
+ procedure Replace_Element
+ (Container : in out Vector;
+ Index : Index_Type;
+ New_Item : Element_Type)
+ with
+ Global => null,
+ Pre => First_Index (Container) <= Index
+ and then Index <= Last_Index (Container);
+
+ procedure Replace_Element
+ (Container : in out Vector;
+ Position : Cursor;
+ New_Item : Element_Type)
+ with
+ Global => null,
+ Pre => Has_Element (Container, Position);
+
+ procedure Move (Target : in out Vector; Source : in out Vector) with
+ Global => null,
+ Pre => Length (Source) <= Target.Capacity;
+
+ procedure Insert
+ (Container : in out Vector;
+ Before : Extended_Index;
+ New_Item : Vector)
+ with
+ Global => null,
+ Pre => First_Index (Container) <= Before
+ and then Before <= Last_Index (Container) + 1
+ and then Length (Container) < Container.Capacity;
+
+ procedure Insert
+ (Container : in out Vector;
+ Before : Cursor;
+ New_Item : Vector)
+ with
+ Global => null,
+ Pre => Length (Container) < Container.Capacity
+ and then (Has_Element (Container, Before)
+ or else Before = No_Element);
+
+ procedure Insert
+ (Container : in out Vector;
+ Before : Cursor;
+ New_Item : Vector;
+ Position : out Cursor)
+ with
+ Global => null,
+ Pre => Length (Container) < Container.Capacity
+ and then (Has_Element (Container, Before)
+ or else Before = No_Element);
+
+ procedure Insert
+ (Container : in out Vector;
+ Before : Extended_Index;
+ New_Item : Element_Type;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => First_Index (Container) <= Before
+ and then Before <= Last_Index (Container) + 1
+ and then Length (Container) + Count <= Container.Capacity;
+
+ procedure Insert
+ (Container : in out Vector;
+ 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 Vector;
+ 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 Prepend
+ (Container : in out Vector;
+ New_Item : Vector)
+ with
+ Global => null,
+ Pre => Length (Container) < Container.Capacity;
+
+ procedure Prepend
+ (Container : in out Vector;
+ New_Item : Element_Type;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => Length (Container) + Count <= Container.Capacity;
+
+ procedure Append
+ (Container : in out Vector;
+ New_Item : Vector)
+ with
+ Global => null,
+ Pre => Length (Container) < Container.Capacity;
+
+ procedure Append
+ (Container : in out Vector;
+ New_Item : Element_Type;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => Length (Container) + Count <= Container.Capacity;
+
+ procedure Delete
+ (Container : in out Vector;
+ Index : Extended_Index;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => First_Index (Container) <= Index
+ and then Index <= Last_Index (Container) + 1;
+
+ procedure Delete
+ (Container : in out Vector;
+ Position : in out Cursor;
+ Count : Count_Type := 1)
+ with
+ Global => null,
+ Pre => Has_Element (Container, Position);
+
+ procedure Delete_First
+ (Container : in out Vector;
+ Count : Count_Type := 1)
+ with
+ Global => null;
+
+ procedure Delete_Last
+ (Container : in out Vector;
+ Count : Count_Type := 1)
+ with
+ Global => null;
+
+ procedure Reverse_Elements (Container : in out Vector) with
+ Global => null;
+
+ procedure Swap (Container : in out Vector; I, J : Index_Type) with
+ Global => null,
+ Pre => First_Index (Container) <= I
+ and then I <= Last_Index (Container)
+ and then First_Index (Container) <= J
+ and then J <= Last_Index (Container);
+
+ procedure Swap (Container : in out Vector; I, J : Cursor) with
+ Global => null,
+ Pre => Has_Element (Container, I) and then Has_Element (Container, J);
+
+ function First_Index (Container : Vector) return Index_Type with
+ Global => null;
+
+ function First (Container : Vector) return Cursor with
+ Global => null;
+
+ function First_Element (Container : Vector) return Element_Type with
+ Global => null,
+ Pre => not Is_Empty (Container);
+
+ function Last_Index (Container : Vector) return Extended_Index with
+ Global => null;
+
+ function Last (Container : Vector) return Cursor with
+ Global => null;
+
+ function Last_Element (Container : Vector) return Element_Type with
+ Global => null,
+ Pre => not Is_Empty (Container);
+
+ function Next (Container : Vector; Position : Cursor) return Cursor with
+ Global => null,
+ Pre => Has_Element (Container, Position) or else Position = No_Element;
+
+ procedure Next (Container : Vector; Position : in out Cursor) with
+ Global => null,
+ Pre => Has_Element (Container, Position) or else Position = No_Element;
+
+ function Previous (Container : Vector; Position : Cursor) return Cursor with
+ Global => null,
+ Pre => Has_Element (Container, Position) or else Position = No_Element;
+
+ procedure Previous (Container : Vector; Position : in out Cursor) with
+ Global => null,
+ Pre => Has_Element (Container, Position) or else Position = No_Element;
+
+ function Find_Index
+ (Container : Vector;
+ Item : Element_Type;
+ Index : Index_Type := Index_Type'First) return Extended_Index
+ with
+ Global => null;
+
+ function Find
+ (Container : Vector;
+ 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_Index
+ (Container : Vector;
+ Item : Element_Type;
+ Index : Index_Type := Index_Type'Last) return Extended_Index
+ with
+ Global => null;
+
+ function Reverse_Find
+ (Container : Vector;
+ 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 : Vector;
+ Item : Element_Type) return Boolean
+ with
+ Global => null;
+
+ function Has_Element (Container : Vector; 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 : Vector) return Boolean with
+ Global => null;
+
+ procedure Sort (Container : in out Vector) with
+ Global => null;
+
+ procedure Merge (Target : in out Vector; Source : in out Vector) with
+ Global => null;
+
+ end Generic_Sorting;
+
+ function Strict_Equal (Left, Right : Vector) 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 : Vector;
+ Current : Cursor) return Vector
+ with
+ Global => null,
+ Pre => Has_Element (Container, Current) or else Current = No_Element;
+ function Current_To_Last
+ (Container : Vector;
+ Current : Cursor) return Vector
+ 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 (First_Index);
+ pragma Inline (Last_Index);
+ pragma Inline (Element);
+ pragma Inline (First_Element);
+ pragma Inline (Last_Element);
+ pragma Inline (Replace_Element);
+ pragma Inline (Contains);
+ pragma Inline (Next);
+ pragma Inline (Previous);
+
+ type Elements_Array is array (Count_Type range <>) of Element_Type;
+ function "=" (L, R : Elements_Array) return Boolean is abstract;
+
+ type Vector (Capacity : Capacity_Range) is record
+ Elements : Elements_Array (1 .. Capacity);
+ Last : Extended_Index := No_Index;
+ end record;
+
+ type Cursor is record
+ Valid : Boolean := True;
+ Index : Index_Type := Index_Type'First;
+ end record;
+
+ Empty_Vector : constant Vector := (Capacity => 0, others => <>);
+
+ No_Element : constant Cursor := (Valid => False, Index => Index_Type'First);
+
+end Ada.Containers.Formal_Vectors;