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