From patchwork Thu Apr 27 09:28:36 2017 Content-Type: text/plain; charset="utf-8" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit X-Patchwork-Submitter: Arnaud Charlet X-Patchwork-Id: 755913 Return-Path: X-Original-To: incoming@patchwork.ozlabs.org Delivered-To: patchwork-incoming@bilbo.ozlabs.org Received: from sourceware.org (server1.sourceware.org [209.132.180.131]) (using TLSv1.2 with cipher ECDHE-RSA-AES256-GCM-SHA384 (256/256 bits)) (No client certificate requested) by ozlabs.org (Postfix) with ESMTPS id 3wDBTn30Ykz9s8G for ; Thu, 27 Apr 2017 19:29:00 +1000 (AEST) Authentication-Results: ozlabs.org; dkim=pass (1024-bit key; unprotected) header.d=gcc.gnu.org header.i=@gcc.gnu.org header.b="n6eGWuDH"; dkim-atps=neutral DomainKey-Signature: a=rsa-sha1; c=nofws; d=gcc.gnu.org; h=list-id :list-unsubscribe:list-archive:list-post:list-help:sender:date :from:to:cc:subject:message-id:mime-version:content-type; q=dns; s=default; b=H4Lsg06z6N2bBxIOfPfEaHn/DZrK+fxMznmNd9dNFXSGLTJpaA To4p+Ie0y/1HCumLS/f8deUyzeDEM93HUAm55Ky7G5V5VoAfF+sT1j+L5Af5YtAI d6bGqQ4HB2GY4TllK3uy1/91BmiGi2XVLVwj2xqaspX521ENJ3sRCCCJc= DKIM-Signature: v=1; a=rsa-sha1; c=relaxed; d=gcc.gnu.org; h=list-id :list-unsubscribe:list-archive:list-post:list-help:sender:date :from:to:cc:subject:message-id:mime-version:content-type; s= default; bh=r5jFywgfmThIWMJi/r5zlSOln8c=; b=n6eGWuDH7fGkefAgjD4U mqhQAWl5wqY/UPIdehsJdjrmuhW0SmUaxxGPfsrEL3ymD/Oo/c7OQiiSHrNCLQC2 ztC4YgXhZfOG6yKocXrge7LLc9RM7kEWZweNM4m6RFbgRNsG6T073Q6GwfY5gQSB A6mdhy0j0u8C7AUy/rOggyE= Received: (qmail 14255 invoked by alias); 27 Apr 2017 09:28:45 -0000 Mailing-List: contact gcc-patches-help@gcc.gnu.org; run by ezmlm Precedence: bulk List-Id: List-Unsubscribe: List-Archive: List-Post: List-Help: Sender: gcc-patches-owner@gcc.gnu.org Delivered-To: mailing list gcc-patches@gcc.gnu.org Received: (qmail 14177 invoked by uid 89); 27 Apr 2017 09:28:43 -0000 Authentication-Results: sourceware.org; auth=none X-Virus-Found: No X-Spam-SWARE-Status: No, score=-10.2 required=5.0 tests=AWL, BAYES_00, FILL_THIS_FORM, GIT_PATCH_2, GIT_PATCH_3, KAM_ASCII_DIVIDERS, RCVD_IN_DNSWL_NONE, SPF_PASS, T_FILL_THIS_FORM_LOAN autolearn=ham version=3.3.2 spammy=proofs, Every, Capacity, bellow X-HELO: rock.gnat.com Received: from rock.gnat.com (HELO rock.gnat.com) (205.232.38.15) by sourceware.org (qpsmtpd/0.93/v0.84-503-g423c35a) with ESMTP; Thu, 27 Apr 2017 09:28:36 +0000 Received: from localhost (localhost.localdomain [127.0.0.1]) by filtered-rock.gnat.com (Postfix) with ESMTP id B3E395A5A7; Thu, 27 Apr 2017 05:28:36 -0400 (EDT) Received: from rock.gnat.com ([127.0.0.1]) by localhost (rock.gnat.com [127.0.0.1]) (amavisd-new, port 10024) with LMTP id gqAGxt19bfp1; Thu, 27 Apr 2017 05:28:36 -0400 (EDT) Received: from tron.gnat.com (tron.gnat.com [205.232.38.10]) by rock.gnat.com (Postfix) with ESMTP id 910E25A5A2; Thu, 27 Apr 2017 05:28:36 -0400 (EDT) Received: by tron.gnat.com (Postfix, from userid 4192) id 8C7B14F9; Thu, 27 Apr 2017 05:28:36 -0400 (EDT) Date: Thu, 27 Apr 2017 05:28:36 -0400 From: Arnaud Charlet To: gcc-patches@gcc.gnu.org Cc: Claire Dross Subject: [Ada] Provide extended contracts for formal doubly linked lists Message-ID: <20170427092836.GA131260@adacore.com> MIME-Version: 1.0 Content-Disposition: inline User-Agent: Mutt/1.5.23 (2014-03-12) Primitives of doubly linked lists are now annotated with precise contracts which can be used for formal verification with GNATprove. Tested on x86_64-pc-linux-gnu, committed on trunk 2017-04-27 Claire Dross * a-cfdlli.adb, a-cfdlli.ads (=): Generic parameter removed to allow the use of regular equality over elements in contracts. (Cursor): Type is now public so that it can be used in model functions. (Formal_Model): Ghost package containing model functions that are used in subprogram contracts. (Current_To_Last): Removed, model functions should be used instead. (First_To_Previous): Removed, model functions should be used instead. (Strict_Equal): Removed, model functions should be used instead. (Append): Default parameter value replaced by new wrapper to allow more precise contracts. (Insert): Default parameter value replaced by new wrapper to allow more precise contracts. (Delete): Default parameter value replaced by new wrapper to allow more precise contracts. (Prepend): Default parameter value replaced by new wrapper to allow more precise contracts. (Delete_First): Default parameter value replaced by new wrapper to allow more precise contracts. (Delete_Last): Default parameter value replaced by new wrapper to allow more precise contracts. Index: a-cfdlli.adb =================================================================== --- a-cfdlli.adb (revision 247293) +++ a-cfdlli.adb (working copy) @@ -6,7 +6,7 @@ -- -- -- B o d y -- -- -- --- Copyright (C) 2010-2016, Free Software Foundation, Inc. -- +-- Copyright (C) 2010-2017, Free Software Foundation, Inc. -- -- -- -- 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- -- @@ -40,10 +40,6 @@ New_Item : Element_Type; New_Node : out Count_Type); - procedure Allocate - (Container : in out List; - New_Node : out Count_Type); - procedure Free (Container : in out List; X : Count_Type); @@ -109,31 +105,22 @@ end if; end Allocate; - procedure Allocate - (Container : in out List; - New_Node : out Count_Type) - is - N : Node_Array renames Container.Nodes; - - begin - if Container.Free >= 0 then - New_Node := Container.Free; - Container.Free := N (New_Node).Next; - - else - New_Node := abs Container.Free; - Container.Free := Container.Free - 1; - end if; - end Allocate; - ------------ -- Append -- ------------ procedure Append (Container : in out List; + New_Item : Element_Type) + is + begin + Insert (Container, No_Element, New_Item, 1); + end Append; + + procedure Append + (Container : in out List; New_Item : Element_Type; - Count : Count_Type := 1) + Count : Count_Type) is begin Insert (Container, No_Element, New_Item, Count); @@ -161,7 +148,7 @@ J := Source.First; while J /= 0 loop - Append (Target, N (J).Element); + Append (Target, N (J).Element, 1); J := N (J).Next; end loop; end Assign; @@ -259,44 +246,24 @@ return P; end Copy; - --------------------- - -- Current_To_Last -- - --------------------- - - function Current_To_Last - (Container : List; - Current : Cursor) return List is - Curs : Cursor := First (Container); - C : List (Container.Capacity) := Copy (Container, Container.Capacity); - Node : Count_Type; - - begin - if Curs = No_Element then - Clear (C); - return C; - end if; - - if Current /= No_Element and not Has_Element (Container, Current) then - raise Constraint_Error; - end if; - - while Curs.Node /= Current.Node loop - Node := Curs.Node; - Delete (C, Curs); - Curs := Next (Container, (Node => Node)); - end loop; - - return C; - end Current_To_Last; - ------------ -- Delete -- ------------ procedure Delete (Container : in out List; + Position : in out Cursor) + is + begin + Delete (Container => Container, + Position => Position, + Count => 1); + end Delete; + + procedure Delete + (Container : in out List; Position : in out Cursor; - Count : Count_Type := 1) + Count : Count_Type) is N : Node_Array renames Container.Nodes; X : Count_Type; @@ -357,9 +324,16 @@ -- Delete_First -- ------------------ + procedure Delete_First (Container : in out List) + is + begin + Delete_First (Container => Container, + Count => 1); + end Delete_First; + procedure Delete_First (Container : in out List; - Count : Count_Type := 1) + Count : Count_Type) is N : Node_Array renames Container.Nodes; X : Count_Type; @@ -391,9 +365,16 @@ -- Delete_Last -- ----------------- + procedure Delete_Last (Container : in out List) + is + begin + Delete_Last (Container => Container, + Count => 1); + end Delete_Last; + procedure Delete_Last (Container : in out List; - Count : Count_Type := 1) + Count : Count_Type) is N : Node_Array renames Container.Nodes; X : Count_Type; @@ -503,36 +484,356 @@ end if; end First_Element; - ----------------------- - -- First_To_Previous -- - ----------------------- + ------------------ + -- Formal_Model -- + ------------------ - function First_To_Previous - (Container : List; - Current : Cursor) return List - is - Curs : Cursor := Current; - C : List (Container.Capacity) := Copy (Container, Container.Capacity); - Node : Count_Type; + package body Formal_Model is - begin - if Curs = No_Element then - return C; + ---------------------------- + -- Lift_Abstraction_Level -- + ---------------------------- - elsif not Has_Element (Container, Curs) then - raise Constraint_Error; + procedure Lift_Abstraction_Level (Container : List) is null; - else - while Curs.Node /= 0 loop - Node := Curs.Node; - Delete (C, Curs); - Curs := Next (Container, (Node => Node)); + ------------------------- + -- M_Elements_Contains -- + ------------------------- + + function M_Elements_Contains + (S : M.Sequence; + Fst : Positive_Count_Type; + Lst : Count_Type; + E : Element_Type) + return Boolean + is + begin + for I in Fst .. Lst loop + if Element (S, I) = E then + return True; + end if; end loop; + return False; + end M_Elements_Contains; - return C; - end if; - end First_To_Previous; + -------------------- + -- M_Elements_Cst -- + -------------------- + function M_Elements_Cst + (S : M.Sequence; + Fst : Positive_Count_Type; + Lst : Count_Type; + E : Element_Type) + return Boolean + is + begin + for I in Fst .. Lst loop + if Element (S, I) /= E then + return False; + end if; + end loop; + return True; + end M_Elements_Cst; + + ---------------------- + -- M_Elements_Equal -- + ---------------------- + + function M_Elements_Equal + (S1, S2 : M.Sequence; + Fst : Positive_Count_Type; + Lst : Count_Type) + return Boolean + is + begin + return M_Elements_Shifted (S1, S2, Fst, Lst, 0); + end M_Elements_Equal; + + ------------------------- + -- M_Elements_Reversed -- + ------------------------- + + function M_Elements_Reversed (S1, S2 : M.Sequence) return Boolean is + L : constant Count_Type := M.Length (S1); + begin + if L /= M.Length (S2) then + return False; + end if; + + for I in 1 .. L loop + if Element (S1, I) /= Element (S2, L - I + 1) + then + return False; + end if; + end loop; + + return True; + end M_Elements_Reversed; + + ------------------------ + -- M_Elements_Shifted -- + ------------------------ + + function M_Elements_Shifted + (S1, S2 : M.Sequence; + Fst : Positive_Count_Type; + Lst : Count_Type; + Offset : Count_Type'Base := 1) + return Boolean + is + begin + for I in Fst .. Lst loop + if Element (S1, I) /= Element (S2, I + Offset) then + return False; + end if; + end loop; + return True; + end M_Elements_Shifted; + + ------------------------- + -- M_Elements_Shuffled -- + ------------------------- + + function M_Elements_Shuffle + (S1, S2 : M.Sequence; + Fst : Positive_Count_Type; + Lst : Count_Type; + Offset : Count_Type'Base) + return Boolean + is + begin + for I in Fst .. Lst loop + declare + Found : Boolean := False; + J : Count_Type := Fst; + begin + while not Found and J <= Lst loop + if Element (S1, I) = Element (S2, J + Offset) then + Found := True; + end if; + J := J + 1; + end loop; + + if not Found then + return False; + end if; + end; + end loop; + return True; + end M_Elements_Shuffle; + + ------------------------ + -- M_Elements_Swapted -- + ------------------------ + + function M_Elements_Swapped + (S1, S2 : M.Sequence; + X, Y : Positive_Count_Type) + return Boolean + is + begin + if M.Length (S1) /= M.Length (S2) + or else Element (S1, X) /= Element (S2, Y) + or else Element (S1, Y) /= Element (S2, X) + then + return False; + end if; + + for I in 1 .. M.Length (S1) loop + if I /= X and then I /= Y + and then Element (S1, I) /= Element (S2, I) + then + return False; + end if; + end loop; + + return True; + end M_Elements_Swapped; + + ----------- + -- Model -- + ----------- + + function Model (Container : List) return M.Sequence is + Position : Count_Type := Container.First; + R : M.Sequence; + begin + -- Can't use First, Next or Element here, since they depend + -- on models for their postconditions + while Position /= 0 loop + R := M.Add (R, Container.Nodes (Position).Element); + Position := Container.Nodes (Position).Next; + end loop; + return R; + end Model; + + ----------------------- + -- Mapping_preserved -- + ----------------------- + + function Mapping_Preserved + (S1, S2 : M.Sequence; + M1, M2 : P.Map) return Boolean is + + begin + for C of M1 loop + if not P.Mem (M2, C) + or else P.Get (M1, C) > M.Length (S1) + or else P.Get (M2, C) > M.Length (S2) + or else M.Get (S1, P.Get (M1, C)) /= M.Get (S2, P.Get (M2, C)) + then + return False; + end if; + end loop; + + for C of M2 loop + if not P.Mem (M1, C) then + return False; + end if; + end loop; + + return True; + end Mapping_Preserved; + + ------------------------- + -- P_Positions_Shifted -- + ------------------------- + + function P_Positions_Shifted + (Small : P.Map; + Big : P.Map; + Cut : Positive_Count_Type; + Count : Count_Type := 1) return Boolean + is + begin + for Cu of Small loop + if not P.Mem (Big, Cu) then + return False; + end if; + end loop; + + for Cu of Big loop + declare + Pos : constant Positive_Count_Type := P.Get (Big, Cu); + begin + if Pos < Cut then + if not P.Mem (Small, Cu) or else Pos /= P.Get (Small, Cu) + then + return False; + end if; + elsif Pos >= Cut + Count then + if not P.Mem (Small, Cu) + or else Pos /= P.Get (Small, Cu) + Count + then + return False; + end if; + else + if P.Mem (Small, Cu) then + return False; + end if; + end if; + end; + end loop; + return True; + end P_Positions_Shifted; + + ------------------------- + -- P_Positions_Swapped -- + ------------------------- + + function P_Positions_Swapped + (M1, M2 : P.Map; + C1, C2 : Cursor) return Boolean + is + begin + if not P.Mem (M1, C1) or not P.Mem (M1, C2) + or not P.Mem (M2, C1) or not P.Mem (M2, C2) + then + return False; + end if; + + if P.Get (M1, C1) /= P.Get (M2, C2) + or P.Get (M1, C2) /= P.Get (M2, C1) + then + return False; + end if; + + for C of M1 loop + if not P.Mem (M2, C) then + return False; + end if; + end loop; + + for C of M2 loop + if not P.Mem (M1, C) + or else (C /= C1 and C /= C2 and P.Get (M1, C) /= P.Get (M2, C)) + then + return False; + end if; + end loop; + + return True; + end P_Positions_Swapped; + + --------------------------- + -- P_Positions_Truncated -- + --------------------------- + + function P_Positions_Truncated + (Small : P.Map; + Big : P.Map; + Cut : Positive_Count_Type; + Count : Count_Type := 1) return Boolean + is + begin + for Cu of Small loop + if not P.Mem (Big, Cu) then + return False; + end if; + end loop; + + for Cu of Big loop + declare + Pos : constant Positive_Count_Type := P.Get (Big, Cu); + begin + if Pos < Cut then + if not P.Mem (Small, Cu) or else Pos /= P.Get (Small, Cu) + then + return False; + end if; + elsif Pos >= Cut + Count then + return False; + elsif P.Mem (Small, Cu) then + return False; + end if; + end; + end loop; + return True; + end P_Positions_Truncated; + + --------------- + -- Positions -- + --------------- + + function Positions (Container : List) return P.Map is + Position : Count_Type := Container.First; + R : P.Map; + I : Count_Type := 1; + begin + -- Can't use First, Next or Element here, since they depend + -- on models for their postconditions + while Position /= 0 loop + R := P.Add (R, (Node => Position), I); + pragma Assert (P.Length (R) = I); + Position := Container.Nodes (Position).Next; + I := I + 1; + end loop; + return R; + end Positions; + + end Formal_Model; + ---------- -- Free -- ---------- @@ -602,6 +903,33 @@ return True; end Is_Sorted; + ----------------------- + -- M_Elements_Sorted -- + ----------------------- + + function M_Elements_Sorted (S : M.Sequence) return Boolean is + begin + if M.Length (S) = 0 then + return True; + end if; + + declare + E1 : Element_Type := Element (S, 1); + begin + for I in 2 .. M.Length (S) loop + declare + E2 : constant Element_Type := Element (S, I); + begin + if E2 < E1 then + return False; + end if; + E1 := E2; + end; + end loop; + end; + return True; + end M_Elements_Sorted; + ----------- -- Merge -- ----------- @@ -766,7 +1094,7 @@ Before : Cursor; New_Item : Element_Type; Position : out Cursor; - Count : Count_Type := 1) + Count : Count_Type) is J : Count_Type; @@ -798,8 +1126,22 @@ (Container : in out List; Before : Cursor; New_Item : Element_Type; - Count : Count_Type := 1) + Position : out Cursor) is + begin + Insert (Container => Container, + Before => Before, + New_Item => New_Item, + Position => Position, + Count => 1); + end Insert; + + procedure Insert + (Container : in out List; + Before : Cursor; + New_Item : Element_Type; + Count : Count_Type) + is Position : Cursor; begin Insert (Container, Before, New_Item, Position, Count); @@ -808,33 +1150,11 @@ procedure Insert (Container : in out List; Before : Cursor; - Position : out Cursor; - Count : Count_Type := 1) + New_Item : Element_Type) is - J : Count_Type; - + Position : Cursor; begin - if Before.Node /= 0 then - pragma Assert (Vet (Container, Before), "bad cursor in Insert"); - end if; - - if Count = 0 then - Position := Before; - return; - end if; - - if Container.Length > Container.Capacity - Count then - raise Constraint_Error with "new length exceeds capacity"; - end if; - - Allocate (Container, New_Node => J); - Insert_Internal (Container, Before.Node, New_Node => J); - Position := (Node => J); - - for Index in 2 .. Count loop - Allocate (Container, New_Node => J); - Insert_Internal (Container, Before.Node, New_Node => J); - end loop; + Insert (Container, Before, New_Item, Position, 1); end Insert; --------------------- @@ -1046,8 +1366,16 @@ procedure Prepend (Container : in out List; + New_Item : Element_Type) + is + begin + Insert (Container, First (Container), New_Item, 1); + end Prepend; + + procedure Prepend + (Container : in out List; New_Item : Element_Type; - Count : Count_Type := 1) + Count : Count_Type) is begin Insert (Container, First (Container), New_Item, Count); @@ -1377,29 +1705,6 @@ pragma Assert (N (Container.Last).Next = 0); end Splice; - ------------------ - -- Strict_Equal -- - ------------------ - - function Strict_Equal (Left, Right : List) return Boolean is - CL : Count_Type := Left.First; - CR : Count_Type := Right.First; - - begin - while CL /= 0 or CR /= 0 loop - if CL /= CR or else - Left.Nodes (CL).Element /= Right.Nodes (CL).Element - then - return False; - end if; - - CL := Left.Nodes (CL).Next; - CR := Right.Nodes (CR).Next; - end loop; - - return True; - end Strict_Equal; - ---------- -- Swap -- ---------- Index: a-cfdlli.ads =================================================================== --- a-cfdlli.ads (revision 247293) +++ a-cfdlli.ads (working copy) @@ -6,7 +6,7 @@ -- -- -- S p e c -- -- -- --- Copyright (C) 2004-2015, Free Software Foundation, Inc. -- +-- Copyright (C) 2004-2017, 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 -- @@ -29,43 +29,14 @@ -- . -- ------------------------------------------------------------------------------ --- This spec is derived from Ada.Containers.Bounded_Doubly_Linked_Lists 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; +with Ada.Containers.Functional_Maps; --- The modifications are: - --- A parameter for the container is added to every function reading the --- contents of a container: Next, Previous, Query_Element, Has_Element, --- Iterate, Reverse_Iterate, Element. 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 : List) return Boolean; --- function First_To_Previous (Container : List; Current : Cursor) --- return List; --- function Current_To_Last (Container : List; Current : Cursor) --- return List; - --- See subprogram specifications that follow for details - generic type Element_Type is private; - - with function "=" (Left, Right : Element_Type) - return Boolean is <>; - package Ada.Containers.Formal_Doubly_Linked_Lists with - Pure, SPARK_Mode is - pragma Annotate (GNATprove, External_Axiomatization); pragma Annotate (CodePeer, Skip_Analysis); type List (Capacity : Count_Type) is private with @@ -76,39 +47,334 @@ Default_Initial_Condition => Is_Empty (List); pragma Preelaborable_Initialization (List); - type Cursor is private; - pragma Preelaborable_Initialization (Cursor); + type Cursor is record + Node : Count_Type := 0; + end record; + No_Element : constant Cursor := Cursor'(Node => 0); + Empty_List : constant List; - No_Element : constant Cursor; + function Length (Container : List) return Count_Type with + Global => null, + Post => Length'Result <= Container.Capacity; + pragma Unevaluated_Use_Of_Old (Allow); + + package Formal_Model with Ghost is + subtype Positive_Count_Type is Count_Type range 1 .. Count_Type'Last; + + package M is new Ada.Containers.Functional_Vectors + (Index_Type => Positive_Count_Type, + Element_Type => Element_Type); + function "=" (Left, Right : M.Sequence) return Boolean renames M."="; + function "<" (Left, Right : M.Sequence) return Boolean renames M."<"; + function "<=" (Left, Right : M.Sequence) return Boolean renames M."<="; + + function M_Elements_Contains + (S : M.Sequence; + Fst : Positive_Count_Type; + Lst : Count_Type; + E : Element_Type) + return Boolean + -- E appears in the slice from Fst to Lst in S + with + Global => null, + Pre => Lst <= M.Length (S), + Post => + M_Elements_Contains'Result = + (for some I in Fst .. Lst => Element (S, I) = E); + pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Contains); + + function M_Elements_Cst + (S : M.Sequence; + Fst : Positive_Count_Type; + Lst : Count_Type; + E : Element_Type) + return Boolean + -- Every element of the slice from Fst to Lst in S is E. + with + Global => null, + Pre => Lst <= M.Length (S), + Post => + M_Elements_Cst'Result = + (for all I in Fst .. Lst => Element (S, I) = E); + pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Cst); + + function M_Elements_Equal + (S1, S2 : M.Sequence; + Fst : Positive_Count_Type; + Lst : Count_Type) + return Boolean + -- The slice from Fst to Lst is the same in S1 and S2 + with + Global => null, + Pre => Lst <= M.Length (S1) and Lst <= M.Length (S2), + Post => + M_Elements_Equal'Result = + (for all I in Fst .. Lst => Element (S1, I) = Element (S2, I)); + pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Equal); + + function M_Elements_Shuffle + (S1, S2 : M.Sequence; + Fst : Positive_Count_Type; + Lst : Count_Type; + Offset : Count_Type'Base) + return Boolean + -- The slice from Fst to Lst in S1 contains the same elements than the + -- same slide shifted by Offset in S2 + with + Global => null, + Pre => + Lst <= M.Length (S1) + and Offset in 1 - Fst .. M.Length (S2) - Lst, + Post => + M_Elements_Shuffle'Result = + (for all J in Fst + Offset .. Lst + Offset => + (for some I in Fst .. Lst => + Element (S1, I) = Element (S2, J))); + pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Shuffle); + + function M_Elements_Reversed (S1, S2 : M.Sequence) return Boolean + -- S2 is S1 in reverse order + with + Global => null, + Post => + M_Elements_Reversed'Result = + (M.Length (S1) = M.Length (S2) + and (for all I in 1 .. M.Length (S1) => + Element (S1, I) = Element (S2, M.Length (S1) - I + 1)) + and (for all I in 1 .. M.Length (S1) => + Element (S2, I) = Element (S1, M.Length (S1) - I + 1))); + pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Reversed); + + function M_Elements_Shifted + (S1, S2 : M.Sequence; + Fst : Positive_Count_Type; + Lst : Count_Type; + Offset : Count_Type'Base := 1) + return Boolean + -- The slice from Fst to Lst in S1 has been shifted by Offset in S2. + with + Global => null, + Pre => + Lst <= M.Length (S1) + and Offset in 1 - Fst .. M.Length (S2) - Lst, + Post => + M_Elements_Shifted'Result = + ((for all I in Fst .. Lst => + Element (S1, I) = Element (S2, I + Offset)) + and (for all I in Fst + Offset .. Lst + Offset => + Element (S1, I - Offset) = Element (S2, I))); + pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Shifted); + + function M_Elements_Swapped + (S1, S2 : M.Sequence; + X, Y : Positive_Count_Type) + return Boolean + -- Elements stored at X and Y are reversed in S1 and S2 + with + Global => null, + Pre => X <= M.Length (S1) and Y <= M.Length (S1), + Post => + M_Elements_Swapped'Result = + (M.Length (S1) = M.Length (S2) + and Element (S1, X) = Element (S2, Y) + and Element (S1, Y) = Element (S2, X) + and + (for all I in 1 .. M.Length (S1) => + (if I /= X and I /= Y + then Element (S1, I) = Element (S2, I)))); + pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Swapped); + + package P is new Ada.Containers.Functional_Maps + (Key_Type => Cursor, + Element_Type => Positive_Count_Type, + Equivalent_Keys => "="); + function "=" (Left, Right : P.Map) return Boolean renames P."="; + function "<=" (Left, Right : P.Map) return Boolean renames P."<="; + + function P_Positions_Shifted + (Small : P.Map; + Big : P.Map; + Cut : Positive_Count_Type; + Count : Count_Type := 1) return Boolean + with + Global => null, + Post => + P_Positions_Shifted'Result = + + -- Big contains all cursors of Small + ((for all I of Small => P.Mem (Big, I)) + + -- Cursors located before Cut are not moved, cursors located after + -- are shifted by Count. + and + (for all I of Small => + (if P.Get (Small, I) < Cut + then P.Get (Big, I) = P.Get (Small, I) + else P.Get (Big, I) - Count = P.Get (Small, I))) + + -- New cursors of Big (if any) are between Cut and Cut - 1 + Count + and + (for all I of Big => + P.Mem (Small, I) + or P.Get (Big, I) - Count in Cut - Count .. Cut - 1)); + + function P_Positions_Swapped + (M1, M2 : P.Map; + C1, C2 : Cursor) return Boolean + -- M1 and M2 contain the same cursors, but the positions of C1 and C2 + -- are reversed. + with + Ghost, + Global => null, + Post => + P_Positions_Swapped'Result = + ((for all C of M1 => P.Mem (M2, C)) + and (for all C of M2 => P.Mem (M1, C)) + and + (for all C of M1 => + (if C /= C1 and C /= C2 + then P.Get (M1, C) = P.Get (M2, C))) + and P.Mem (M1, C1) and P.Mem (M1, C2) + and P.Get (M1, C1) = P.Get (M2, C2) + and P.Get (M1, C2) = P.Get (M2, C1)); + + function P_Positions_Truncated + (Small : P.Map; + Big : P.Map; + Cut : Positive_Count_Type; + Count : Count_Type := 1) return Boolean + with + Ghost, + Global => null, + Post => + P_Positions_Truncated'Result = + + -- Big contains all cursors of Small + ((for all I of Small => P.Mem (Big, I)) + + -- The cursors of Small are all bellow Cut + and (for all I of Small => P.Get (Small, I) < Cut) + + -- The cursors have the same position in Big and Small + and (for all I of Small => P.Get (Big, I) = P.Get (Small, I)) + + -- New cursors of Big (if any) are between Cut and Cut - 1 + Count + and + (for all I of Big => + P.Mem (Small, I) + or P.Get (Big, I) - Count in Cut - Count .. Cut - 1)); + + function Mapping_Preserved + (S1, S2 : M.Sequence; + M1, M2 : P.Map) return Boolean + with + Ghost, + Global => null, + Post => + (if Mapping_Preserved'Result then + + -- M1 contains all cursors of M2 + (for all I of M2 => P.Mem (M1, I)) + + -- M2 contains all cursors of M1 + and (for all I of M1 => P.Mem (M2, I)) + + -- Mappings from cursors to elements induced by S1, M1 and S2, M2 + -- are the same. + and (for all I of M1 => + M.Get (S1, P.Get (M1, I)) = M.Get (S2, P.Get (M2, I)))); + + function Model (Container : List) return M.Sequence with + -- The highlevel model of a list is a sequence of elements. Cursors are + -- not represented in this model. + + Ghost, + Global => null, + Post => M.Length (Model'Result) = Length (Container); + pragma Annotate (GNATprove, Iterable_For_Proof, "Model", Model); + + function Positions (Container : List) return P.Map with + -- The Positions map is used to model cursors. It only contains valid + -- cursors and map them to their position in the container. + + Ghost, + Global => null, + Post => not P.Mem (Positions'Result, No_Element) + -- Positions of cursors are smaller than the container's length. + and then + (for all I of Positions'Result => + P.Get (Positions'Result, I) in 1 .. Length (Container) + + -- No two cursors have the same position. Note that we do not + -- state that there is a cursor in the map for each position, + -- as it is rarely needed. + and then + (for all J of Positions'Result => + (if P.Get (Positions'Result, I) = P.Get (Positions'Result, J) + then I = J))); + + procedure Lift_Abstraction_Level (Container : List) with + -- Lift_Abstraction_Level is a ghost procedure that does nothing but + -- assume that we can access to the same elements by iterating over + -- positions or cursors. + -- This information is not generally useful except when switching from + -- a lowlevel, cursor aware view of a container, to a highlevel + -- position based view. + + Ghost, + Global => null, + Post => + (for all Elt of Model (Container) => + (for some I of Positions (Container) => + M.Get (Model (Container), P.Get (Positions (Container), I)) + = Elt)); + + function Element (S : M.Sequence; I : Count_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 "=" (Left, Right : List) return Boolean with - Global => null; + Global => null, + Post => "="'Result = (Model (Left) = Model (Right)); - function Length (Container : List) return Count_Type with - Global => null; - function Is_Empty (Container : List) return Boolean with - Global => null; + Global => null, + Post => Is_Empty'Result = (Length (Container) = 0); procedure Clear (Container : in out List) with - Global => null; + Global => null, + Post => Length (Container) = 0; procedure Assign (Target : in out List; Source : List) with Global => null, - Pre => Target.Capacity >= Length (Source); + Pre => Target.Capacity >= Length (Source), + Post => Model (Target) = Model (Source); function Copy (Source : List; Capacity : Count_Type := 0) return List with Global => null, - Pre => Capacity = 0 or else Capacity >= Source.Capacity; + Pre => Capacity = 0 or else Capacity >= Source.Capacity, + Post => Model (Copy'Result) = Model (Source) + and Positions (Copy'Result) = Positions (Source) + and (if Capacity = 0 then Copy'Result.Capacity = Source.Capacity + else Copy'Result.Capacity = Capacity); function Element (Container : List; Position : Cursor) return Element_Type with Global => null, - Pre => Has_Element (Container, Position); + Pre => Has_Element (Container, Position), + Post => + Element'Result = + Element (Model (Container), + P.Get (Positions (Container), Position)); + pragma Annotate (GNATprove, Inline_For_Proof, Element); procedure Replace_Element (Container : in out List; @@ -116,229 +382,1007 @@ New_Item : Element_Type) with Global => null, - Pre => Has_Element (Container, Position); + Pre => Has_Element (Container, Position), + Post => Length (Container) = Length (Container)'Old + -- Cursors are preserved. + and Positions (Container)'Old = Positions (Container) + + -- The element at the position of Position in Container is replaced by + -- New_Item. + and M.Is_Set (Model (Container)'Old, + P.Get (Positions (Container), Position), + New_Item, + Model (Container)); + procedure Move (Target : in out List; Source : in out List) with Global => null, - Pre => Target.Capacity >= Length (Source); + Pre => Target.Capacity >= Length (Source), + Post => Model (Target) = Model (Source'Old) + and Length (Source) = 0; procedure Insert (Container : in out List; Before : Cursor; + New_Item : Element_Type) + with + Global => null, + Pre => + Length (Container) < Container.Capacity + and then (Has_Element (Container, Before) + or else Before = No_Element), + Post => Length (Container) = Length (Container)'Old + 1, + Contract_Cases => + (Before = No_Element => + + -- Positions contains a new mapping from the last cursor of + -- Container to its length. + P.Is_Add + (Positions (Container)'Old, Last (Container), Length (Container), + Result => Positions (Container)) + + -- Model contains a new element New_Item at the end + and M.Is_Add (Model (Container)'Old, New_Item, Model (Container)), + others => + + -- The elements of Container located before Before are preserved. + M_Elements_Equal + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => P.Get (Positions (Container)'Old, Before) - 1) + + -- Other elements are shifted by 1. + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => P.Get (Positions (Container)'Old, Before), + Lst => Length (Container)'Old, + Offset => 1) + + -- New_Item is stored at the previous position of Before in + -- Container + and Element + (Model (Container), P.Get (Positions (Container)'Old, Before)) + = New_Item + + -- A new cursor has been inserted at position Before in Container + and P_Positions_Shifted + (Positions (Container)'Old, + Positions (Container), + Cut => P.Get (Positions (Container)'Old, Before))); + + procedure Insert + (Container : in out List; + Before : Cursor; New_Item : Element_Type; - Count : Count_Type := 1) + Count : Count_Type) with Global => null, - Pre => Length (Container) + Count <= Container.Capacity - and then (Has_Element (Container, Before) - or else Before = No_Element); + Pre => + Length (Container) <= Container.Capacity - Count + and then (Has_Element (Container, Before) + or else Before = No_Element), + Post => Length (Container) = Length (Container)'Old + Count, + Contract_Cases => + (Before = No_Element => + -- The elements of Container are preserved + M_Elements_Equal + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => Length (Container)'Old) + + -- Container contains Count times New_Item at the end + and M_Elements_Cst + (S => Model (Container), + Fst => Length (Container)'Old + 1, + Lst => Length (Container), + E => New_Item) + + -- A Count cursors have been inserted at the end of Container + and P_Positions_Truncated + (Positions (Container)'Old, + Positions (Container), + Cut => Length (Container)'Old + 1, + Count => Count), + others => + + -- The elements of Container located before Before are preserved + M_Elements_Equal + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => P.Get (Positions (Container)'Old, Before) - 1) + + -- Other elements are shifted by Count. + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => P.Get (Positions (Container)'Old, Before), + Lst => Length (Container)'Old, + Offset => Count) + + -- Container contains Count times New_Item after position Before + and M_Elements_Cst + (S => Model (Container), + Fst => P.Get (Positions (Container)'Old, Before), + Lst => P.Get (Positions (Container)'Old, Before) - 1 + Count, + E => New_Item) + + -- Count cursors have been inserted at position Before in Container + and P_Positions_Shifted + (Positions (Container)'Old, + Positions (Container), + Cut => P.Get (Positions (Container)'Old, Before), + Count => Count)); + procedure Insert (Container : in out List; Before : Cursor; New_Item : Element_Type; - Position : out Cursor; - Count : Count_Type := 1) + Position : out Cursor) with Global => null, - Pre => Length (Container) + Count <= Container.Capacity - and then (Has_Element (Container, Before) - or else Before = No_Element); + Pre => + Length (Container) < Container.Capacity + and then (Has_Element (Container, Before) + or else Before = No_Element), + Post => + Length (Container) = Length (Container)'Old + 1 + -- Positions is valid in Container and it is located either before + -- Before if it is valid in Container or at the end if it is + -- No_Element. + and P.Mem (Positions (Container), Position) + and (if Before = No_Element + then P.Get (Positions (Container), Position) + = Length (Container) + else P.Get (Positions (Container), Position) + = P.Get (Positions (Container)'Old, Before)) + + -- The elements of Container located before Position are preserved. + and M_Elements_Equal + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => P.Get (Positions (Container), Position) - 1) + + -- Other elements are shifted by 1. + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => P.Get (Positions (Container), Position), + Lst => Length (Container)'Old, + Offset => 1) + + -- New_Item is stored at Position in Container + and Element + (Model (Container), P.Get (Positions (Container), Position)) + = New_Item + + -- A new cursor has been inserted at position Position in Container + and P_Positions_Shifted + (Positions (Container)'Old, + Positions (Container), + Cut => P.Get (Positions (Container), Position)); + procedure Insert (Container : in out List; Before : Cursor; + New_Item : Element_Type; Position : out Cursor; - Count : Count_Type := 1) + Count : Count_Type) with + Global => null, + Pre => + Length (Container) <= Container.Capacity - Count + and then (Has_Element (Container, Before) + or else Before = No_Element), + Post => Length (Container) = Length (Container)'Old + Count, + Contract_Cases => + (Count = 0 => Position = Before + and Model (Container) = Model (Container)'Old + and Positions (Container) = Positions (Container)'Old, + + others => + -- Positions is valid in Container and it is located either before + -- Before if it is valid in Container or at the end if it is + -- No_Element. + P.Mem (Positions (Container), Position) + and (if Before = No_Element + then P.Get (Positions (Container), Position) + = Length (Container)'Old + 1 + else P.Get (Positions (Container), Position) + = P.Get (Positions (Container)'Old, Before)) + + -- The elements of Container located before Position are preserved. + and M_Elements_Equal + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => P.Get (Positions (Container), Position) - 1) + + -- Other elements are shifted by Count. + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => P.Get (Positions (Container), Position), + Lst => Length (Container)'Old, + Offset => Count) + + -- Container contains Count times New_Item after position Position + and M_Elements_Cst + (S => Model (Container), + Fst => P.Get (Positions (Container), Position), + Lst => P.Get (Positions (Container), Position) - 1 + Count, + E => New_Item) + + -- Count cursor have been inserted at Position in Container + and P_Positions_Shifted + (Positions (Container)'Old, + Positions (Container), + Cut => P.Get (Positions (Container), Position), + Count => Count)); + + procedure Prepend + (Container : in out List; + New_Item : Element_Type) + with Global => null, - Pre => Length (Container) + Count <= Container.Capacity - and then (Has_Element (Container, Before) - or else Before = No_Element); + Pre => Length (Container) < Container.Capacity, + Post => + Length (Container) = Length (Container)'Old + 1 + -- Elements are shifted by 1 + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => Length (Container)'Old, + Offset => 1) + + -- New_Item is the first element of Container + and Element (Model (Container), 1) = New_Item + + -- A new cursor has been inserted at the beginning of Container + and P_Positions_Shifted + (Positions (Container)'Old, + Positions (Container), + Cut => 1); + procedure Prepend (Container : in out List; New_Item : Element_Type; - Count : Count_Type := 1) + Count : Count_Type) with Global => null, - Pre => Length (Container) + Count <= Container.Capacity; + Pre => Length (Container) <= Container.Capacity - Count, + Post => + Length (Container) = Length (Container)'Old + Count + -- Elements are shifted by Count. + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => Length (Container)'Old, + Offset => Count) + + -- Container starts with Count times New_Item + and M_Elements_Cst + (S => Model (Container), + Fst => 1, + Lst => Count, + E => New_Item) + + -- Count cursors have been inserted at the beginning of Container + and P_Positions_Shifted + (Positions (Container)'Old, + Positions (Container), + Cut => 1, + Count => Count); + procedure Append (Container : in out List; + New_Item : Element_Type) + with + Global => null, + Pre => Length (Container) < Container.Capacity, + Post => Length (Container) = Length (Container)'Old + 1 + + -- Positions contains a new mapping from the last cursor of + -- Container to its length. + and P.Is_Add + (Positions (Container)'Old, Last (Container), Length (Container), + Result => Positions (Container)) + + -- Model contains a new element New_Item at the end + and M.Is_Add (Model (Container)'Old, New_Item, Model (Container)); + + procedure Append + (Container : in out List; New_Item : Element_Type; - Count : Count_Type := 1) + Count : Count_Type) with Global => null, - Pre => Length (Container) + Count <= Container.Capacity; + Pre => Length (Container) <= Container.Capacity - Count, + Post => + Length (Container) = Length (Container)'Old + Count + -- The elements of Container are preserved + and Model (Container)'Old <= Model (Container) + + -- Container contains Count times New_Item at the end + and M_Elements_Cst + (S => Model (Container), + Fst => Length (Container)'Old + 1, + Lst => Length (Container), + E => New_Item) + + -- Count cursors have been inserted at the end of Container + and P_Positions_Truncated + (Positions (Container)'Old, + Positions (Container), + Cut => Length (Container)'Old + 1, + Count => Count); + procedure Delete (Container : in out List; + Position : in out Cursor) + with + Global => null, + Pre => Has_Element (Container, Position), + Post => + Length (Container) = Length (Container)'Old - 1 + + -- Position is set to No_Element + and Position = No_Element + + -- The elements of Container located before Position are preserved. + and M_Elements_Equal + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => P.Get (Positions (Container)'Old, Position'Old) - 1) + + -- The elements located after Position are shifted by 1 + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => P.Get (Positions (Container)'Old, Position'Old) + 1, + Lst => Length (Container)'Old, + Offset => -1) + + -- Position has been removed from Container + and P_Positions_Shifted + (Positions (Container), + Positions (Container)'Old, + Cut => P.Get (Positions (Container)'Old, Position'Old)); + + procedure Delete + (Container : in out List; Position : in out Cursor; - Count : Count_Type := 1) + Count : Count_Type) with + Global => null, + Pre => Has_Element (Container, Position), + Post => + Length (Container) in Length (Container)'Old - Count + .. Length (Container)'Old + + -- Position is set to No_Element + and Position = No_Element + + -- The elements of Container located before Position are preserved. + and M_Elements_Equal + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => P.Get (Positions (Container)'Old, Position'Old) - 1), + Contract_Cases => + + -- All the elements after Position have been erased + (Length (Container) - Count < P.Get (Positions (Container), Position) + => + + Length (Container) = + P.Get (Positions (Container)'Old, Position'Old) - 1 + + -- At most Count cursors have been removed at the end of Container + and P_Positions_Truncated + (Positions (Container), + Positions (Container)'Old, + Cut => P.Get (Positions (Container)'Old, Position'Old), + Count => Count), + others => + Length (Container) = Length (Container)'Old - Count + + -- Other elements are shifted by Count + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => + P.Get (Positions (Container)'Old, Position'Old) + Count, + Lst => Length (Container)'Old, + Offset => -Count) + + -- Count cursors have been removed from Container at Position + and P_Positions_Shifted + (Positions (Container), + Positions (Container)'Old, + Cut => P.Get (Positions (Container)'Old, Position'Old), + Count => Count)); + + procedure Delete_First (Container : in out List) + with Global => null, - Pre => Has_Element (Container, Position); + Pre => not Is_Empty (Container), + Post => + Length (Container) = Length (Container)'Old - 1 + -- The elements of Container are shifted by 1 + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 2, + Lst => Length (Container)'Old, + Offset => -1) + + -- The first cursor of Container has been removed + and P_Positions_Shifted + (Positions (Container), + Positions (Container)'Old, + Cut => 1); + procedure Delete_First (Container : in out List; - Count : Count_Type := 1) + Count : Count_Type) with - Global => null; + 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_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => Count + 1, + Lst => Length (Container)'Old, + Offset => -Count) + + -- The first Count cursors have been removed from Container + and P_Positions_Shifted + (Positions (Container), + Positions (Container)'Old, + Cut => 1, + Count => Count)); + + procedure Delete_Last (Container : in out List) + with + Global => null, + Pre => not Is_Empty (Container), + Post => + Length (Container) = Length (Container)'Old - 1 + + -- The elements of Container are preserved. + and Model (Container) <= Model (Container)'Old + + -- The last cursor of Container has been removed + and P.Is_Add (Positions (Container), Last (Container)'Old, + Length (Container)'Old, Positions (Container)'Old); + procedure Delete_Last (Container : in out List; - Count : Count_Type := 1) + Count : Count_Type) with - Global => null; + 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 + + -- The elements of Container are preserved. + and Model (Container) <= Model (Container)'Old + + -- At most Count cursors have been removed at the end of Container + and P_Positions_Truncated + (Positions (Container), + Positions (Container)'Old, + Cut => Length (Container) + 1, + Count => Count)); + procedure Reverse_Elements (Container : in out List) with - Global => null; + Global => null, + Post => M_Elements_Reversed (Model (Container'Old), Model (Container)); procedure Swap (Container : in out List; I, J : Cursor) with Global => null, - Pre => Has_Element (Container, I) and then Has_Element (Container, J); + Pre => Has_Element (Container, I) and then Has_Element (Container, J), + Post => + M_Elements_Swapped + (Model (Container)'Old, Model (Container), + X => P.Get (Positions (Container)'Old, I), + Y => P.Get (Positions (Container)'Old, J)) + and Positions (Container) = Positions (Container)'Old; procedure Swap_Links (Container : in out List; I, J : Cursor) with Global => null, - Pre => Has_Element (Container, I) and then Has_Element (Container, J); + Pre => Has_Element (Container, I) and then Has_Element (Container, J), + Post => + M_Elements_Swapped + (Model (Container'Old), Model (Container), + X => P.Get (Positions (Container)'Old, I), + Y => P.Get (Positions (Container)'Old, J)) + and P_Positions_Swapped + (Positions (Container)'Old, Positions (Container), I, J); procedure Splice (Target : in out List; Before : Cursor; Source : in out List) + -- Target and Source should not be aliased with - Global => null, - Pre => Length (Source) + Length (Target) <= Target.Capacity - and then (Has_Element (Target, Before) - or else Before = No_Element); + Global => null, + Pre => + Length (Source) <= Target.Capacity - Length (Target) + and then (Has_Element (Target, Before) + or else Before = No_Element), + Post => + Length (Source) = 0 + and Length (Target) = Length (Target)'Old + Length (Source)'Old, + Contract_Cases => + (Before = No_Element => + -- The elements of Target are preserved + M_Elements_Equal + (S1 => Model (Target)'Old, + S2 => Model (Target), + Fst => 1, + Lst => Length (Target)'Old) + + -- The elements of Source are appended to target, the order is not + -- specified. + and M_Elements_Shuffle + (S1 => Model (Source)'Old, + S2 => Model (Target), + Fst => 1, + Lst => Length (Source)'Old, + Offset => Length (Target)'Old) + + -- Cursors have been inserted at the end of Target + and P_Positions_Truncated + (Positions (Target)'Old, + Positions (Target), + Cut => Length (Target)'Old + 1, + Count => Length (Source)'Old), + others => + + -- The elements of Target located before Before are preserved + M_Elements_Equal + (S1 => Model (Target)'Old, + S2 => Model (Target), + Fst => 1, + Lst => P.Get (Positions (Target)'Old, Before) - 1) + + -- The elements of Source are inserted before Before, the order is + -- not specified. + and M_Elements_Shuffle + (S1 => Model (Source)'Old, + S2 => Model (Target), + Fst => 1, + Lst => Length (Source)'Old, + Offset => P.Get (Positions (Target)'Old, Before) - 1) + + -- Other elements are shifted by the length of Source + and M_Elements_Shifted + (S1 => Model (Target)'Old, + S2 => Model (Target), + Fst => P.Get (Positions (Target)'Old, Before), + Lst => Length (Target)'Old, + Offset => Length (Source)'Old) + + -- Cursors have been inserted at position Before in Target + and P_Positions_Shifted + (Positions (Target)'Old, + Positions (Target), + Cut => P.Get (Positions (Target)'Old, Before), + Count => Length (Source)'Old)); + procedure Splice (Target : in out List; Before : Cursor; Source : in out List; Position : in out Cursor) + -- Target and Source should not be aliased with Global => null, - Pre => Length (Source) + Length (Target) <= Target.Capacity - and then (Has_Element (Target, Before) - or else Before = No_Element) - and then Has_Element (Source, Position); + Pre => + (Has_Element (Target, Before) + or else Before = No_Element) + and then Has_Element (Source, Position) + and then Length (Target) < Target.Capacity, + Post => + Length (Target) = Length (Target)'Old + 1 + and Length (Source) = Length (Source)'Old - 1 + -- The elements of Source located before Position are preserved. + and M_Elements_Equal + (S1 => Model (Source)'Old, + S2 => Model (Source), + Fst => 1, + Lst => P.Get (Positions (Source)'Old, Position'Old) - 1) + + -- The elements located after Position are shifted by 1 + and M_Elements_Shifted + (S1 => Model (Source)'Old, + S2 => Model (Source), + Fst => P.Get (Positions (Source)'Old, Position'Old) + 1, + Lst => Length (Source)'Old, + Offset => -1) + + -- Position has been removed from Source + and P_Positions_Shifted + (Positions (Source), + Positions (Source)'Old, + Cut => P.Get (Positions (Source)'Old, Position'Old)) + + -- Positions is valid in Target and it is located either before + -- Before if it is valid in Target or at the end if it is + -- No_Element. + and P.Mem (Positions (Target), Position) + and (if Before = No_Element + then P.Get (Positions (Target), Position) + = Length (Target) + else P.Get (Positions (Target), Position) + = P.Get (Positions (Target)'Old, Before)) + + -- The elements of Target located before Position are preserved. + and M_Elements_Equal + (S1 => Model (Target)'Old, + S2 => Model (Target), + Fst => 1, + Lst => P.Get (Positions (Target), Position) - 1) + + -- Other elements are shifted by 1. + and M_Elements_Shifted + (S1 => Model (Target)'Old, + S2 => Model (Target), + Fst => P.Get (Positions (Target), Position), + Lst => Length (Target)'Old, + Offset => 1) + + -- The element located at Position in Source is moved to Target + and Element (Model (Target), P.Get (Positions (Target), Position)) + = Element (Model (Source)'Old, + P.Get (Positions (Source)'Old, Position'Old)) + + -- A new cursor has been inserted at position Position in Target + and P_Positions_Shifted + (Positions (Target)'Old, + Positions (Target), + Cut => P.Get (Positions (Target), Position)); + procedure Splice (Container : in out List; Before : Cursor; Position : Cursor) with - Global => null, - Pre => 2 * Length (Container) <= Container.Capacity - and then (Has_Element (Container, Before) - or else Before = No_Element) - and then Has_Element (Container, Position); + Global => null, + Pre => + (Has_Element (Container, Before) or else Before = No_Element) + and then Has_Element (Container, Position), + Post => Length (Container) = Length (Container)'Old, + Contract_Cases => + (Before = Position => + Model (Container) = Model (Container)'Old + and Positions (Container) = Positions (Container)'Old, + Before = No_Element => + + -- The elements located before Position are preserved + M_Elements_Equal + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => P.Get (Positions (Container)'Old, Position) - 1) + + -- The elements located after Position are shifted by 1 + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => P.Get (Positions (Container)'Old, Position) + 1, + Lst => Length (Container)'Old, + Offset => -1) + + -- The last element of Container is the one that was previously + -- at Position. + and Element (Model (Container), Length (Container)) + = Element (Model (Container)'Old, + P.Get (Positions (Container)'Old, Position)) + + -- Cursors from Container continue designating the same elements + and Mapping_Preserved + (S1 => Model (Container)'Old, + S2 => Model (Container), + M1 => Positions (Container)'Old, + M2 => Positions (Container)), + + others => + + -- The elements located before Position and Before are preserved + M_Elements_Equal + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => 1, + Lst => Count_Type'Min + (P.Get (Positions (Container)'Old, Position) - 1, + P.Get (Positions (Container)'Old, Before) - 1)) + + -- The elements located after Position and Before are preserved + and M_Elements_Equal + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => Count_Type'Max + (P.Get (Positions (Container)'Old, Position) + 1, + P.Get (Positions (Container)'Old, Before) + 1), + Lst => Length (Container)) + + -- The elements located after Before and before Position are shifted + -- by 1 to the right. + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => P.Get (Positions (Container)'Old, Before) + 1, + Lst => P.Get (Positions (Container)'Old, Position) - 1, + Offset => 1) + + -- The elements located after Position and before Before are shifted + -- by 1 to the left. + and M_Elements_Shifted + (S1 => Model (Container)'Old, + S2 => Model (Container), + Fst => P.Get (Positions (Container)'Old, Position) + 1, + Lst => P.Get (Positions (Container)'Old, Before) - 1, + Offset => -1) + + -- The element previously at Position is now before Before + and Element (Model (Container), + P.Get (Positions (Container)'Old, Before)) + = Element (Model (Container)'Old, + P.Get (Positions (Container)'Old, Position)) + + -- Cursors from Container continue designating the same elements + and Mapping_Preserved + (S1 => Model (Container)'Old, + S2 => Model (Container), + M1 => Positions (Container)'Old, + M2 => Positions (Container))); + function First (Container : List) return Cursor with - Global => null; + Global => null, + Contract_Cases => + (Length (Container) = 0 => First'Result = No_Element, + others => Has_Element (Container, First'Result) + and P.Get (Positions (Container), First'Result) = 1); function First_Element (Container : List) return Element_Type with Global => null, - Pre => not Is_Empty (Container); + Pre => not Is_Empty (Container), + Post => First_Element'Result = M.Get (Model (Container), 1); function Last (Container : List) return Cursor with - Global => null; + Global => null, + Contract_Cases => + (Length (Container) = 0 => Last'Result = No_Element, + others => Has_Element (Container, Last'Result) + and P.Get (Positions (Container), Last'Result) = Length (Container)); function Last_Element (Container : List) return Element_Type with Global => null, - Pre => not Is_Empty (Container); + Pre => not Is_Empty (Container), + Post => Last_Element'Result + = M.Get (Model (Container), Length (Container)); function Next (Container : List; Position : Cursor) return Cursor with - Global => null, - Pre => Has_Element (Container, Position) or else Position = No_Element; + Global => null, + Pre => Has_Element (Container, Position) + or else Position = No_Element, + Contract_Cases => + (Position = No_Element + or else P.Get (Positions (Container), Position) = Length (Container) => + Next'Result = No_Element, + others => Has_Element (Container, Next'Result) + and then P.Get (Positions (Container), Next'Result) = + P.Get (Positions (Container), Position) + 1); procedure Next (Container : List; Position : in out Cursor) with - Global => null, - Pre => Has_Element (Container, Position) or else Position = No_Element; + Global => null, + Pre => Has_Element (Container, Position) + or else Position = No_Element, + Contract_Cases => + (Position = No_Element + or else P.Get (Positions (Container), Position) = Length (Container) => + Position = No_Element, + others => Has_Element (Container, Position) + and then P.Get (Positions (Container), Position) = + P.Get (Positions (Container), Position'Old) + 1); function Previous (Container : List; Position : Cursor) return Cursor with - Global => null, - Pre => Has_Element (Container, Position) or else Position = No_Element; + Global => null, + Pre => Has_Element (Container, Position) + or else Position = No_Element, + Contract_Cases => + (Position = No_Element + or else P.Get (Positions (Container), Position) = 1 => + Previous'Result = No_Element, + others => + Has_Element (Container, Previous'Result) + and then P.Get (Positions (Container), Previous'Result) = + P.Get (Positions (Container), Position) - 1); procedure Previous (Container : List; Position : in out Cursor) with - Global => null, - Pre => Has_Element (Container, Position) or else Position = No_Element; + Global => null, + Pre => Has_Element (Container, Position) + or else Position = No_Element, + Contract_Cases => + (Position = No_Element + or else P.Get (Positions (Container), Position) = 1 => + Position = No_Element, + others => + Has_Element (Container, Position) + and then P.Get (Positions (Container), Position) = + P.Get (Positions (Container), Position'Old) - 1); function Find (Container : List; Item : Element_Type; Position : Cursor := No_Element) return Cursor with - Global => null, - Pre => Has_Element (Container, Position) or else Position = No_Element; + Global => null, + Pre => + Has_Element (Container, Position) or else Position = No_Element, + Contract_Cases => + -- If Item is not is not contained in Container after Position, Find + -- returns No_Element. + (not M_Elements_Contains + (S => Model (Container), + Fst => (if Position = No_Element then 1 + else P.Get (Positions (Container), Position)), + Lst => Length (Container), + E => Item) + => + Find'Result = No_Element, + + -- Otherwise, Find returns a valid cusror in Container + others => + P.Mem (Positions (Container), Find'Result) + + -- The element designated by the result of Find is Item + and Element (Model (Container), + P.Get (Positions (Container), Find'Result)) = Item + + -- The result of Find is located after Position + and (if Position /= No_Element + then P.Get (Positions (Container), Find'Result) + >= P.Get (Positions (Container), Position)) + + -- It is the first occurence of Item in this slice + and not M_Elements_Contains + (S => Model (Container), + Fst => (if Position = No_Element then 1 + else P.Get (Positions (Container), Position)), + Lst => P.Get (Positions (Container), Find'Result) - 1, + E => Item)); + function Reverse_Find (Container : List; Item : Element_Type; Position : Cursor := No_Element) return Cursor with - Global => null, - Pre => Has_Element (Container, Position) or else Position = No_Element; + Global => null, + Pre => + Has_Element (Container, Position) or else Position = No_Element, + Contract_Cases => + -- If Item is not is not contained in Container before Position, Find + -- returns No_Element. + (not M_Elements_Contains + (S => Model (Container), + Fst => 1, + Lst => (if Position = No_Element then Length (Container) + else P.Get (Positions (Container), Position)), + E => Item) + => + Reverse_Find'Result = No_Element, + + -- Otherwise, Find returns a valid cusror in Container + others => + P.Mem (Positions (Container), Reverse_Find'Result) + + -- The element designated by the result of Find is Item + and Element (Model (Container), + P.Get (Positions (Container), Reverse_Find'Result)) = Item + + -- The result of Find is located before Position + and (if Position /= No_Element + then P.Get (Positions (Container), Reverse_Find'Result) + <= P.Get (Positions (Container), Position)) + + -- It is the last occurence of Item in this slice + and not M_Elements_Contains + (S => Model (Container), + Fst => P.Get (Positions (Container), Reverse_Find'Result) + 1, + Lst => (if Position = No_Element then Length (Container) + else P.Get (Positions (Container), Position)), + E => Item)); + function Contains (Container : List; Item : Element_Type) return Boolean with - Global => null; + Global => null, + Post => Contains'Result = + M_Elements_Contains + (S => Model (Container), + Fst => 1, + Lst => Length (Container), + E => Item); function Has_Element (Container : List; Position : Cursor) return Boolean with - Global => null; + Global => null, + Post => Has_Element'Result = P.Mem (Positions (Container), Position); + 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 + function M_Elements_Sorted (S : M.Sequence) return Boolean with + Ghost, + Global => null, + Post => M_Elements_Sorted'Result = + (for all I in 1 .. M.Length (S) => + (for all J in I + 1 .. M.Length (S) => + Element (S, I) = Element (S, J) + or Element (S, I) < Element (S, J))); + pragma Annotate (GNATprove, Inline_For_Proof, M_Elements_Sorted); function Is_Sorted (Container : List) return Boolean with - Global => null; + Global => null, + Post => Is_Sorted'Result = M_Elements_Sorted (Model (Container)); procedure Sort (Container : in out List) with - Global => null; + Global => null, + Post => Length (Container) = Length (Container)'Old + and M_Elements_Sorted (Model (Container)); procedure Merge (Target, Source : in out List) with - Global => null; - + -- Target and Source should not be aliased + Global => null, + Pre => Length (Source) <= Target.Capacity - 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))); end Generic_Sorting; - function Strict_Equal (Left, Right : List) 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 : List; Current : Cursor) return List - with - Ghost, - Global => null, - Pre => Has_Element (Container, Current) or else Current = No_Element; - - function Current_To_Last (Container : List; Current : Cursor) return List - 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); @@ -361,12 +1405,6 @@ Nodes : Node_Array (1 .. Capacity) := (others => <>); end record; - type Cursor is record - Node : Count_Type := 0; - end record; - Empty_List : constant List := (0, others => <>); - No_Element : constant Cursor := (Node => 0); - end Ada.Containers.Formal_Doubly_Linked_Lists;