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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) 2004-2021, 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.
with Ada.Containers.Functional_Vectors;
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 with
SPARK_Mode
is
-- Contracts in this unit are meant for analysis only, not for run-time
-- checking.
pragma Assertion_Policy (Pre => Ignore);
pragma Assertion_Policy (Post => Ignore);
pragma Annotate (CodePeer, Skip_Analysis);
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;
Last_Count : constant Count_Type :=
(if Index_Type'Last < Index_Type'First then
0
elsif Index_Type'Last < -1
or else Index_Type'Pos (Index_Type'First) >
Index_Type'Pos (Index_Type'Last) - Count_Type'Last
then
Index_Type'Pos (Index_Type'Last) -
Index_Type'Pos (Index_Type'First) + 1
else
Count_Type'Last);
-- Maximal capacity of any vector. It is the minimum of the size of the
-- index range and the last possible Count_Type.
subtype Capacity_Range is Count_Type range 0 .. Last_Count;
type Vector (Capacity : Capacity_Range) is private with
Default_Initial_Condition => Is_Empty (Vector),
Iterable => (First => Iter_First,
Has_Element => Iter_Has_Element,
Next => Iter_Next,
Element => Element);
function Length (Container : Vector) return Capacity_Range with
Global => null,
Post => Length'Result <= Capacity (Container);
pragma Unevaluated_Use_Of_Old (Allow);
package Formal_Model with Ghost is
package M is new Ada.Containers.Functional_Vectors
(Index_Type => Index_Type,
Element_Type => Element_Type);
function "="
(Left : M.Sequence;
Right : M.Sequence) return Boolean renames M."=";
function "<"
(Left : M.Sequence;
Right : M.Sequence) return Boolean renames M."<";
function "<="
(Left : M.Sequence;
Right : M.Sequence) return Boolean renames M."<=";
function M_Elements_In_Union
(Container : M.Sequence;
Left : M.Sequence;
Right : M.Sequence) return Boolean
-- The elements of Container are contained in either Left or Right
with
Global => null,
Post =>
M_Elements_In_Union'Result =
(for all I in Index_Type'First .. M.Last (Container) =>
(for some J in Index_Type'First .. M.Last (Left) =>
Element (Container, I) = Element (Left, J))
or (for some J in Index_Type'First .. M.Last (Right) =>
Element (Container, I) = Element (Right, J)));
pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_In_Union);
function M_Elements_Included
(Left : M.Sequence;
L_Fst : Index_Type := Index_Type'First;
L_Lst : Extended_Index;
Right : M.Sequence;
R_Fst : Index_Type := Index_Type'First;
R_Lst : Extended_Index) return Boolean
-- The elements of the slice from L_Fst to L_Lst in Left are contained
-- in the slide from R_Fst to R_Lst in Right.
with
Global => null,
Pre => L_Lst <= M.Last (Left) and R_Lst <= M.Last (Right),
Post =>
M_Elements_Included'Result =
(for all I in L_Fst .. L_Lst =>
(for some J in R_Fst .. R_Lst =>
Element (Left, I) = Element (Right, J)));
pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Included);
function M_Elements_Reversed
(Left : M.Sequence;
Right : M.Sequence) return Boolean
-- Right is Left in reverse order
with
Global => null,
Post =>
M_Elements_Reversed'Result =
(M.Length (Left) = M.Length (Right)
and (for all I in Index_Type'First .. M.Last (Left) =>
Element (Left, I) =
Element (Right, M.Last (Left) - I + 1))
and (for all I in Index_Type'First .. M.Last (Right) =>
Element (Right, I) =
Element (Left, M.Last (Left) - I + 1)));
pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Reversed);
function M_Elements_Swapped
(Left : M.Sequence;
Right : M.Sequence;
X : Index_Type;
Y : Index_Type) return Boolean
-- Elements stored at X and Y are reversed in Left and Right
with
Global => null,
Pre => X <= M.Last (Left) and Y <= M.Last (Left),
Post =>
M_Elements_Swapped'Result =
(M.Length (Left) = M.Length (Right)
and Element (Left, X) = Element (Right, Y)
and Element (Left, Y) = Element (Right, X)
and M.Equal_Except (Left, Right, X, Y));
pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Swapped);
function Model (Container : Vector) return M.Sequence with
-- The high-level model of a vector is a sequence of elements. The
-- sequence really is similar to the vector itself. However, it is not
-- limited which allows usage of 'Old and 'Loop_Entry attributes.
Ghost,
Global => null,
Post => M.Length (Model'Result) = Length (Container);
pragma Annotate (GNATprove, Iterable_For_Proof, "Model", Model);
function Element
(S : M.Sequence;
I : Index_Type) return Element_Type renames M.Get;
-- To improve readability of contracts, we rename the function used to
-- access an element in the model to Element.
end Formal_Model;
use Formal_Model;
function Empty_Vector return Vector with
Global => null,
Post => Length (Empty_Vector'Result) = 0;
function "=" (Left, Right : Vector) return Boolean with
Global => null,
Post => "="'Result = (Model (Left) = Model (Right));
function To_Vector
(New_Item : Element_Type;
Length : Capacity_Range) return Vector
with
Global => null,
Post =>
Formal_Vectors.Length (To_Vector'Result) = Length
and M.Constant_Range
(Container => Model (To_Vector'Result),
Fst => Index_Type'First,
Lst => Last_Index (To_Vector'Result),
Item => New_Item);
function Capacity (Container : Vector) return Capacity_Range with
Global => null,
Post =>
Capacity'Result = Container.Capacity;
pragma Annotate (GNATprove, Inline_For_Proof, Capacity);
procedure Reserve_Capacity
(Container : in out Vector;
Capacity : Capacity_Range)
with
Global => null,
Pre => Capacity <= Container.Capacity,
Post => Model (Container) = Model (Container)'Old;
function Is_Empty (Container : Vector) return Boolean with
Global => null,
Post => Is_Empty'Result = (Length (Container) = 0);
procedure Clear (Container : in out Vector) with
Global => null,
Post => Length (Container) = 0;
procedure Assign (Target : in out Vector; Source : Vector) with
Global => null,
Pre => Length (Source) <= Target.Capacity,
Post => Model (Target) = Model (Source);
function Copy
(Source : Vector;
Capacity : Capacity_Range := 0) return Vector
with
Global => null,
Pre => (Capacity = 0 or Length (Source) <= Capacity),
Post =>
Model (Copy'Result) = Model (Source)
and (if Capacity = 0 then
Copy'Result.Capacity = Length (Source)
else
Copy'Result.Capacity = Capacity);
procedure Move (Target : in out Vector; Source : in out Vector)
with
Global => null,
Pre => Length (Source) <= Capacity (Target),
Post => Model (Target) = Model (Source)'Old and Length (Source) = 0;
function Element
(Container : Vector;
Index : Index_Type) return Element_Type
with
Global => null,
Pre => Index in First_Index (Container) .. Last_Index (Container),
Post => Element'Result = Element (Model (Container), Index);
pragma Annotate (GNATprove, Inline_For_Proof, Element);
procedure Replace_Element
(Container : in out Vector;
Index : Index_Type;
New_Item : Element_Type)
with
Global => null,
Pre => Index in First_Index (Container) .. Last_Index (Container),
Post =>
Length (Container) = Length (Container)'Old
-- Container now has New_Item at index Index
and Element (Model (Container), Index) = New_Item
-- All other elements are preserved
and M.Equal_Except
(Left => Model (Container)'Old,
Right => Model (Container),
Position => Index);
function At_End (E : access constant Vector) return access constant Vector
is (E)
with Ghost,
Annotate => (GNATprove, At_End_Borrow);
function At_End
(E : access constant Element_Type) return access constant Element_Type
is (E)
with Ghost,
Annotate => (GNATprove, At_End_Borrow);
function Constant_Reference
(Container : aliased Vector;
Index : Index_Type) return not null access constant Element_Type
with
Global => null,
Pre => Index in First_Index (Container) .. Last_Index (Container),
Post =>
Constant_Reference'Result.all = Element (Model (Container), Index);
function Reference
(Container : not null access Vector;
Index : Index_Type) return not null access Element_Type
with
Global => null,
Pre =>
Index in First_Index (Container.all) .. Last_Index (Container.all),
Post =>
Length (Container.all) = Length (At_End (Container).all)
-- Container will have Result.all at index Index
and At_End (Reference'Result).all =
Element (Model (At_End (Container).all), Index)
-- All other elements are preserved
and M.Equal_Except
(Left => Model (Container.all),
Right => Model (At_End (Container).all),
Position => Index);
procedure Insert
(Container : in out Vector;
Before : Extended_Index;
New_Item : Vector)
with
Global => null,
Pre =>
Length (Container) <= Capacity (Container) - Length (New_Item)
and (Before in Index_Type'First .. Last_Index (Container)
or (Before /= No_Index
and then Before - 1 = Last_Index (Container))),
Post =>
Length (Container) = Length (Container)'Old + Length (New_Item)
-- Elements located before Before in Container are preserved
and M.Range_Equal
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Index_Type'First,
Lst => Before - 1)
-- Elements of New_Item are inserted at position Before
and (if Length (New_Item) > 0 then
M.Range_Shifted
(Left => Model (New_Item),
Right => Model (Container),
Fst => Index_Type'First,
Lst => Last_Index (New_Item),
Offset => Count_Type (Before - Index_Type'First)))
-- Elements located after Before in Container are shifted
and M.Range_Shifted
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Before,
Lst => Last_Index (Container)'Old,
Offset => Length (New_Item));
procedure Insert
(Container : in out Vector;
Before : Extended_Index;
New_Item : Element_Type)
with
Global => null,
Pre =>
Length (Container) < Capacity (Container)
and then (Before in Index_Type'First .. Last_Index (Container) + 1),
Post =>
Length (Container) = Length (Container)'Old + 1
-- Elements located before Before in Container are preserved
and M.Range_Equal
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Index_Type'First,
Lst => Before - 1)
-- Container now has New_Item at index Before
and Element (Model (Container), Before) = New_Item
-- Elements located after Before in Container are shifted by 1
and M.Range_Shifted
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Before,
Lst => Last_Index (Container)'Old,
Offset => 1);
procedure Insert
(Container : in out Vector;
Before : Extended_Index;
New_Item : Element_Type;
Count : Count_Type)
with
Global => null,
Pre =>
Length (Container) <= Capacity (Container) - Count
and (Before in Index_Type'First .. Last_Index (Container)
or (Before /= No_Index
and then Before - 1 = Last_Index (Container))),
Post =>
Length (Container) = Length (Container)'Old + Count
-- Elements located before Before in Container are preserved
and M.Range_Equal
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Index_Type'First,
Lst => Before - 1)
-- New_Item is inserted Count times at position Before
and (if Count > 0 then
M.Constant_Range
(Container => Model (Container),
Fst => Before,
Lst => Before + Index_Type'Base (Count - 1),
Item => New_Item))
-- Elements located after Before in Container are shifted
and M.Range_Shifted
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Before,
Lst => Last_Index (Container)'Old,
Offset => Count);
procedure Prepend (Container : in out Vector; New_Item : Vector) with
Global => null,
Pre => Length (Container) <= Capacity (Container) - Length (New_Item),
Post =>
Length (Container) = Length (Container)'Old + Length (New_Item)
-- Elements of New_Item are inserted at the beginning of Container
and M.Range_Equal
(Left => Model (New_Item),
Right => Model (Container),
Fst => Index_Type'First,
Lst => Last_Index (New_Item))
-- Elements of Container are shifted
and M.Range_Shifted
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Index_Type'First,
Lst => Last_Index (Container)'Old,
Offset => Length (New_Item));
procedure Prepend (Container : in out Vector; New_Item : Element_Type) with
Global => null,
Pre => Length (Container) < Capacity (Container),
Post =>
Length (Container) = Length (Container)'Old + 1
-- Container now has New_Item at Index_Type'First
and Element (Model (Container), Index_Type'First) = New_Item
-- Elements of Container are shifted by 1
and M.Range_Shifted
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Index_Type'First,
Lst => Last_Index (Container)'Old,
Offset => 1);
procedure Prepend
(Container : in out Vector;
New_Item : Element_Type;
Count : Count_Type)
with
Global => null,
Pre => Length (Container) <= Capacity (Container) - Count,
Post =>
Length (Container) = Length (Container)'Old + Count
-- New_Item is inserted Count times at the beginning of Container
and M.Constant_Range
(Container => Model (Container),
Fst => Index_Type'First,
Lst => Index_Type'First + Index_Type'Base (Count - 1),
Item => New_Item)
-- Elements of Container are shifted
and M.Range_Shifted
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Index_Type'First,
Lst => Last_Index (Container)'Old,
Offset => Count);
procedure Append (Container : in out Vector; New_Item : Vector) with
Global => null,
Pre =>
Length (Container) <= Capacity (Container) - Length (New_Item),
Post =>
Length (Container) = Length (Container)'Old + Length (New_Item)
-- The elements of Container are preserved
and Model (Container)'Old <= Model (Container)
-- Elements of New_Item are inserted at the end of Container
and (if Length (New_Item) > 0 then
M.Range_Shifted
(Left => Model (New_Item),
Right => Model (Container),
Fst => Index_Type'First,
Lst => Last_Index (New_Item),
Offset =>
Count_Type
(Last_Index (Container)'Old - Index_Type'First + 1)));
procedure Append (Container : in out Vector; New_Item : Element_Type) with
Global => null,
Pre => Length (Container) < Capacity (Container),
Post =>
Length (Container) = Length (Container)'Old + 1
-- Elements of Container are preserved
and Model (Container)'Old < Model (Container)
-- Container now has New_Item at the end of Container
and Element
(Model (Container), Last_Index (Container)'Old + 1) = New_Item;
procedure Append
(Container : in out Vector;
New_Item : Element_Type;
Count : Count_Type)
with
Global => null,
Pre => Length (Container) <= Capacity (Container) - Count,
Post =>
Length (Container) = Length (Container)'Old + Count
-- Elements of Container are preserved
and Model (Container)'Old <= Model (Container)
-- New_Item is inserted Count times at the end of Container
and (if Count > 0 then
M.Constant_Range
(Container => Model (Container),
Fst => Last_Index (Container)'Old + 1,
Lst =>
Last_Index (Container)'Old + Index_Type'Base (Count),
Item => New_Item));
procedure Delete (Container : in out Vector; Index : Extended_Index) with
Global => null,
Pre => Index in First_Index (Container) .. Last_Index (Container),
Post =>
Length (Container) = Length (Container)'Old - 1
-- Elements located before Index in Container are preserved
and M.Range_Equal
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Index_Type'First,
Lst => Index - 1)
-- Elements located after Index in Container are shifted by 1
and M.Range_Shifted
(Left => Model (Container),
Right => Model (Container)'Old,
Fst => Index,
Lst => Last_Index (Container),
Offset => 1);
procedure Delete
(Container : in out Vector;
Index : Extended_Index;
Count : Count_Type)
with
Global => null,
Pre =>
Index in First_Index (Container) .. Last_Index (Container),
Post =>
Length (Container) in
Length (Container)'Old - Count .. Length (Container)'Old
-- The elements of Container located before Index are preserved.
and M.Range_Equal
(Left => Model (Container)'Old,
Right => Model (Container),
Fst => Index_Type'First,
Lst => Index - 1),
Contract_Cases =>
-- All the elements after Position have been erased
(Length (Container) - Count <= Count_Type (Index - Index_Type'First) =>
Length (Container) = Count_Type (Index - Index_Type'First),
others =>
Length (Container) = Length (Container)'Old - Count
-- Other elements are shifted by Count
and M.Range_Shifted
(Left => Model (Container),
Right => Model (Container)'Old,
Fst => Index,
Lst => Last_Index (Container),
Offset => Count));
procedure Delete_First (Container : in out Vector) with
Global => null,
Pre => Length (Container) > 0,
Post =>
Length (Container) = Length (Container)'Old - 1
-- Elements of Container are shifted by 1
and M.Range_Shifted
(Left => Model (Container),
Right => Model (Container)'Old,
Fst => Index_Type'First,
Lst => Last_Index (Container),
Offset => 1);
procedure Delete_First (Container : in out Vector; Count : Count_Type) with
Global => null,
Contract_Cases =>
-- All the elements of Container have been erased
(Length (Container) <= Count => Length (Container) = 0,
others =>
Length (Container) = Length (Container)'Old - Count
-- Elements of Container are shifted by Count
and M.Range_Shifted
(Left => Model (Container),
Right => Model (Container)'Old,
Fst => Index_Type'First,
Lst => Last_Index (Container),
Offset => Count));
procedure Delete_Last (Container : in out Vector) with
Global => null,
Pre => Length (Container) > 0,
Post =>
Length (Container) = Length (Container)'Old - 1
-- Elements of Container are preserved
and Model (Container) < Model (Container)'Old;
procedure Delete_Last (Container : in out Vector; Count : Count_Type) with
Global => null,
Contract_Cases =>
-- All the elements after Position have been erased
(Length (Container) <= Count => Length (Container) = 0,
others =>
Length (Container) = Length (Container)'Old - Count
-- The elements of Container are preserved
and Model (Container) <= Model (Container)'Old);
procedure Reverse_Elements (Container : in out Vector) with
Global => null,
Post => M_Elements_Reversed (Model (Container)'Old, Model (Container));
procedure Swap
(Container : in out Vector;
I : Index_Type;
J : Index_Type)
with
Global => null,
Pre =>
I in First_Index (Container) .. Last_Index (Container)
and then J in First_Index (Container) .. Last_Index (Container),
Post =>
M_Elements_Swapped (Model (Container)'Old, Model (Container), I, J);
function First_Index (Container : Vector) return Index_Type with
Global => null,
Post => First_Index'Result = Index_Type'First;
pragma Annotate (GNATprove, Inline_For_Proof, First_Index);
function First_Element (Container : Vector) return Element_Type with
Global => null,
Pre => not Is_Empty (Container),
Post =>
First_Element'Result = Element (Model (Container), Index_Type'First);
pragma Annotate (GNATprove, Inline_For_Proof, First_Element);
function Last_Index (Container : Vector) return Extended_Index with
Global => null,
Post => Last_Index'Result = M.Last (Model (Container));
pragma Annotate (GNATprove, Inline_For_Proof, Last_Index);
function Last_Element (Container : Vector) return Element_Type with
Global => null,
Pre => not Is_Empty (Container),
Post =>
Last_Element'Result =
Element (Model (Container), Last_Index (Container));
pragma Annotate (GNATprove, Inline_For_Proof, Last_Element);
function Find_Index
(Container : Vector;
Item : Element_Type;
Index : Index_Type := Index_Type'First) return Extended_Index
with
Global => null,
Contract_Cases =>
-- If Item is not contained in Container after Index, Find_Index
-- returns No_Index.
(Index > Last_Index (Container)
or else not M.Contains
(Container => Model (Container),
Fst => Index,
Lst => Last_Index (Container),
Item => Item)
=>
Find_Index'Result = No_Index,
-- Otherwise, Find_Index returns a valid index greater than Index
others =>
Find_Index'Result in Index .. Last_Index (Container)
-- The element at this index in Container is Item
and Element (Model (Container), Find_Index'Result) = Item
-- It is the first occurrence of Item after Index in Container
and not M.Contains
(Container => Model (Container),
Fst => Index,
Lst => Find_Index'Result - 1,
Item => Item));
function Reverse_Find_Index
(Container : Vector;
Item : Element_Type;
Index : Index_Type := Index_Type'Last) return Extended_Index
with
Global => null,
Contract_Cases =>
-- If Item is not contained in Container before Index,
-- Reverse_Find_Index returns No_Index.
(not M.Contains
(Container => Model (Container),
Fst => Index_Type'First,
Lst => (if Index <= Last_Index (Container) then Index
else Last_Index (Container)),
Item => Item)
=>
Reverse_Find_Index'Result = No_Index,
-- Otherwise, Reverse_Find_Index returns a valid index smaller than
-- Index
others =>
Reverse_Find_Index'Result in Index_Type'First .. Index
and Reverse_Find_Index'Result <= Last_Index (Container)
-- The element at this index in Container is Item
and Element (Model (Container), Reverse_Find_Index'Result) = Item
-- It is the last occurrence of Item before Index in Container
and not M.Contains
(Container => Model (Container),
Fst => Reverse_Find_Index'Result + 1,
Lst =>
(if Index <= Last_Index (Container) then
Index
else
Last_Index (Container)),
Item => Item));
function Contains
(Container : Vector;
Item : Element_Type) return Boolean
with
Global => null,
Post =>
Contains'Result =
M.Contains
(Container => Model (Container),
Fst => Index_Type'First,
Lst => Last_Index (Container),
Item => Item);
function Has_Element
(Container : Vector;
Position : Extended_Index) return Boolean
with
Global => null,
Post =>
Has_Element'Result =
(Position in Index_Type'First .. Last_Index (Container));
pragma Annotate (GNATprove, Inline_For_Proof, Has_Element);
generic
with function "<" (Left, Right : Element_Type) return Boolean is <>;
package Generic_Sorting with SPARK_Mode is
package Formal_Model with Ghost is
function M_Elements_Sorted (Container : M.Sequence) return Boolean
with
Global => null,
Post =>
M_Elements_Sorted'Result =
(for all I in Index_Type'First .. M.Last (Container) =>
(for all J in I .. M.Last (Container) =>
Element (Container, I) = Element (Container, J)
or Element (Container, I) < Element (Container, J)));
pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Sorted);
end Formal_Model;
use Formal_Model;
function Is_Sorted (Container : Vector) return Boolean with
Global => null,
Post => Is_Sorted'Result = M_Elements_Sorted (Model (Container));
procedure Sort (Container : in out Vector) with
Global => null,
Post =>
Length (Container) = Length (Container)'Old
and M_Elements_Sorted (Model (Container))
and M_Elements_Included
(Left => Model (Container)'Old,
L_Lst => Last_Index (Container),
Right => Model (Container),
R_Lst => Last_Index (Container))
and M_Elements_Included
(Left => Model (Container),
L_Lst => Last_Index (Container),
Right => Model (Container)'Old,
R_Lst => Last_Index (Container));
procedure Merge (Target : in out Vector; Source : in out Vector) with
-- Target and Source should not be aliased
Global => null,
Pre => Length (Source) <= Capacity (Target) - Length (Target),
Post =>
Length (Target) = Length (Target)'Old + Length (Source)'Old
and Length (Source) = 0
and (if M_Elements_Sorted (Model (Target)'Old)
and M_Elements_Sorted (Model (Source)'Old)
then
M_Elements_Sorted (Model (Target)))
and M_Elements_Included
(Left => Model (Target)'Old,
L_Lst => Last_Index (Target)'Old,
Right => Model (Target),
R_Lst => Last_Index (Target))
and M_Elements_Included
(Left => Model (Source)'Old,
L_Lst => Last_Index (Source)'Old,
Right => Model (Target),
R_Lst => Last_Index (Target))
and M_Elements_In_Union
(Model (Target),
Model (Source)'Old,
Model (Target)'Old);
end Generic_Sorting;
---------------------------
-- Iteration Primitives --
---------------------------
function Iter_First (Container : Vector) return Extended_Index with
Global => null;
function Iter_Has_Element
(Container : Vector;
Position : Extended_Index) return Boolean
with
Global => null,
Post =>
Iter_Has_Element'Result =
(Position in Index_Type'First .. Last_Index (Container));
pragma Annotate (GNATprove, Inline_For_Proof, Iter_Has_Element);
function Iter_Next
(Container : Vector;
Position : Extended_Index) return Extended_Index
with
Global => null,
Pre => Iter_Has_Element (Container, Position);
private
pragma SPARK_Mode (Off);
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);
subtype Array_Index is Capacity_Range range 1 .. Capacity_Range'Last;
type Elements_Array is array (Array_Index range <>) of aliased Element_Type;
function "=" (L, R : Elements_Array) return Boolean is abstract;
type Vector (Capacity : Capacity_Range) is record
Last : Extended_Index := No_Index;
Elements : Elements_Array (1 .. Capacity);
end record;
function Empty_Vector return Vector is
((Capacity => 0, others => <>));
function Iter_First (Container : Vector) return Extended_Index is
(Index_Type'First);
function Iter_Next
(Container : Vector;
Position : Extended_Index) return Extended_Index
is
(if Position = Extended_Index'Last then
Extended_Index'First
else
Extended_Index'Succ (Position));
function Iter_Has_Element
(Container : Vector;
Position : Extended_Index) return Boolean
is
(Position in Index_Type'First .. Container.Last);
end Ada.Containers.Formal_Vectors;