------------------------------------------------------------------------------ -- -- -- 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) 2004-2014, 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 -- -- . -- ------------------------------------------------------------------------------ -- 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 with Pure, SPARK_Mode is pragma Annotate (GNATprove, External_Axiomatization); type Set (Capacity : Count_Type; Modulus : Hash_Type) is private with Iterable => (First => First, Next => Next, Has_Element => Has_Element, Element => Element), Default_Initial_Condition; 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 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); 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;