| ------------------------------------------------------------------------------ |
| -- -- |
| -- GNAT LIBRARY COMPONENTS -- |
| -- -- |
| -- 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 _ S E T S -- |
| -- -- |
| -- S p e c -- |
| -- -- |
| -- Copyright (C) 2004-2015, 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_Ordered_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: Key, Element, Next, Query_Element, Previous, |
| -- Has_Element, Iterate, 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. The operators "<" and ">" that could not be modified that way |
| -- have been removed. |
| |
| -- 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.Red_Black_Trees; |
| |
| generic |
| type Element_Type is private; |
| |
| with function "<" (Left, Right : Element_Type) return Boolean is <>; |
| with function "=" (Left, Right : Element_Type) return Boolean is <>; |
| |
| package Ada.Containers.Formal_Ordered_Sets with |
| Pure, |
| SPARK_Mode |
| is |
| pragma Annotate (GNATprove, External_Axiomatization); |
| |
| function Equivalent_Elements (Left, Right : Element_Type) return Boolean |
| with |
| Global => null; |
| |
| type Set (Capacity : Count_Type) is private with |
| Iterable => (First => First, |
| Next => Next, |
| Has_Element => Has_Element, |
| Element => Element), |
| Default_Initial_Condition => Is_Empty (Set); |
| 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 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 |
| 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 Delete_First (Container : in out Set) with |
| Global => null; |
| |
| procedure Delete_Last (Container : in out Set) with |
| Global => null; |
| |
| 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 First_Element (Container : Set) return Element_Type with |
| Global => null, |
| Pre => not Is_Empty (Container); |
| |
| function Last (Container : Set) return Cursor; |
| |
| function Last_Element (Container : Set) return Element_Type with |
| Global => null, |
| Pre => not Is_Empty (Container); |
| |
| 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 Previous (Container : Set; Position : Cursor) return Cursor with |
| Global => null, |
| Pre => Has_Element (Container, Position) or else Position = No_Element; |
| |
| procedure Previous (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 Floor (Container : Set; Item : Element_Type) return Cursor with |
| Global => null; |
| |
| function Ceiling (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; |
| |
| generic |
| type Key_Type (<>) is private; |
| |
| with function Key (Element : Element_Type) return Key_Type; |
| |
| with function "<" (Left, Right : Key_Type) return Boolean is <>; |
| |
| package Generic_Keys is |
| |
| function Equivalent_Keys (Left, Right : Key_Type) return Boolean with |
| Global => null; |
| |
| 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 Floor (Container : Set; Key : Key_Type) return Cursor with |
| Global => null; |
| |
| function Ceiling (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); |
| pragma Inline (Previous); |
| |
| type Node_Type is record |
| Has_Element : Boolean := False; |
| Parent : Count_Type := 0; |
| Left : Count_Type := 0; |
| Right : Count_Type := 0; |
| Color : Red_Black_Trees.Color_Type; |
| Element : Element_Type; |
| end record; |
| |
| package Tree_Types is |
| new Red_Black_Trees.Generic_Bounded_Tree_Types (Node_Type); |
| |
| type Set (Capacity : Count_Type) is |
| new Tree_Types.Tree_Type (Capacity) with null record; |
| |
| use Red_Black_Trees; |
| |
| type Cursor is record |
| Node : Count_Type; |
| end record; |
| |
| No_Element : constant Cursor := (Node => 0); |
| |
| Empty_Set : constant Set := (Capacity => 0, others => <>); |
| |
| end Ada.Containers.Formal_Ordered_Sets; |
