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376 lines
11 KiB
C
376 lines
11 KiB
C
/*
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* FreeRTOS V202212.00
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* Copyright (C) 2020 Amazon.com, Inc. or its affiliates. All Rights Reserved.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy of
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* this software and associated documentation files (the "Software"), to deal in
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* the Software without restriction, including without limitation the rights to
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* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
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* the Software, and to permit persons to whom the Software is furnished to do so,
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* subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in all
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* copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
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* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
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* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
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* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*
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* https://www.FreeRTOS.org
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* https://github.com/FreeRTOS
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*
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*/
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/* *INDENT-OFF* */
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#ifndef LIST_H
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#define LIST_H
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#define VERIFAST
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#include <stdlib.h>
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#include <stdint.h>
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//@#include "common.gh"
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typedef size_t TickType_t;
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typedef size_t UBaseType_t;
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typedef ssize_t BaseType_t;
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#define pdTRUE 1
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#define pdFALSE 0
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/* Empty/no-op macros */
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#define mtCOVERAGE_TEST_MARKER()
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#define mtCOVERAGE_TEST_DELAY()
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#define listSET_LIST_INTEGRITY_CHECK_1_VALUE( pxList )
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#define listSET_LIST_INTEGRITY_CHECK_2_VALUE( pxList )
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#define listTEST_LIST_INTEGRITY( pxList )
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#define listTEST_LIST_ITEM_INTEGRITY( pxListItem )
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#define listSET_FIRST_LIST_ITEM_INTEGRITY_CHECK_VALUE( pxListItem )
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#define listSET_SECOND_LIST_ITEM_INTEGRITY_CHECK_VALUE( pxListItem )
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/* Max value stored in sentinel xListEnd element */
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#define portMAX_DELAY UINT_MAX
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struct xLIST;
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struct xLIST_ITEM {
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TickType_t xItemValue;
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struct xLIST_ITEM * pxNext;
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struct xLIST_ITEM * pxPrevious;
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void * pvOwner;
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struct xLIST *pxContainer;
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};
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typedef struct xLIST_ITEM ListItem_t;
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typedef struct xLIST {
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UBaseType_t uxNumberOfItems;
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struct xLIST_ITEM *pxIndex;
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#ifdef VERIFAST /*< ***change MiniList_t to ListItem_t*** */
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struct xLIST_ITEM xListEnd;
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#else
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MiniListItem_t xListEnd;
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#endif
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} List_t;
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/*@
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predicate xLIST_ITEM(
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struct xLIST_ITEM *n,
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TickType_t xItemValue,
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struct xLIST_ITEM *pxNext,
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struct xLIST_ITEM *pxPrevious,
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struct xLIST *pxContainer;) =
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n->xItemValue |-> xItemValue &*&
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n->pxNext |-> pxNext &*&
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n->pxPrevious |-> pxPrevious &*&
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n->pvOwner |-> _ &*&
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n->pxContainer |-> pxContainer;
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@*/
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/* Ferreira et al. (STTT'14) doubly-linked list segment (DLS). */
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/*@
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predicate DLS(
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struct xLIST_ITEM *n,
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struct xLIST_ITEM *nprev,
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struct xLIST_ITEM *mnext,
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struct xLIST_ITEM *m,
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list<struct xLIST_ITEM * > cells,
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list<TickType_t > vals,
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struct xLIST *pxContainer) =
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n == m
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? cells == cons(n, nil) &*&
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vals == cons(?v, nil) &*&
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xLIST_ITEM(n, v, mnext, nprev, pxContainer)
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: cells == cons(n, ?cells0) &*&
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vals == cons(?v, ?vals0) &*&
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xLIST_ITEM(n, v, ?o, nprev, pxContainer) &*& DLS(o, n, mnext, m, cells0, vals0, pxContainer);
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lemma void dls_star_item(
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struct xLIST_ITEM *n,
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struct xLIST_ITEM *m,
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struct xLIST_ITEM *o)
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requires DLS(n, ?nprev, ?mnext, m, ?cells, ?vals, ?l) &*& xLIST_ITEM(o, ?v, ?onext, ?oprev, ?l2);
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ensures DLS(n, nprev, mnext, m, cells, vals, l) &*& xLIST_ITEM(o, v, onext, oprev, l2) &*& mem(o, cells) == false;
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{
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open DLS(n, nprev, mnext, m, cells, vals, l);
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if (n == m) {
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assert xLIST_ITEM(n, _, _, _, _);
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open xLIST_ITEM(n, _, _, _, _);
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open xLIST_ITEM(o, _, _, _, _);
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assert n != o;
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close xLIST_ITEM(o, _, _, _, _);
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close xLIST_ITEM(n, _, _, _, _);
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close DLS(n, nprev, mnext, m, cells, vals, l);
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}
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else {
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assert DLS(?nnext, n, mnext, m, tail(cells), tail(vals), l);
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dls_star_item(nnext, m, o);
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open xLIST_ITEM(n, _, _, _, _);
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open xLIST_ITEM(o, _, _, _, _);
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assert n != o;
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close xLIST_ITEM(o, _, _, _, _);
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close xLIST_ITEM(n, _, _, _, _);
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close DLS(n, nprev, mnext, m, cells, vals, l);
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}
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}
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lemma void dls_distinct(
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struct xLIST_ITEM *n,
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struct xLIST_ITEM *nprev,
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struct xLIST_ITEM *mnext,
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struct xLIST_ITEM *m,
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list<struct xLIST_ITEM * > cells)
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requires DLS(n, nprev, mnext, m, cells, ?vals, ?l);
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ensures DLS(n, nprev, mnext, m, cells, vals, l) &*& distinct(cells) == true;
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{
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if (n == m) {
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open DLS(n, nprev, mnext, m, cells, vals, l);
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close DLS(n, nprev, mnext, m, cells, vals, l);
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} else {
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open DLS(n, nprev, mnext, m, cells, vals, l);
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assert DLS(?nnext, n, mnext, m, tail(cells), tail(vals), l);
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dls_distinct(nnext, n, mnext, m, tail(cells));
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dls_star_item(nnext, m, n);
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close DLS(n, nprev, mnext, m, cells, vals, l);
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}
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}
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predicate xLIST(
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struct xLIST *l,
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int uxNumberOfItems,
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struct xLIST_ITEM *pxIndex,
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struct xLIST_ITEM *xListEnd,
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list<struct xLIST_ITEM *>cells,
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list<TickType_t >vals) =
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l->uxNumberOfItems |-> uxNumberOfItems &*&
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l->pxIndex |-> pxIndex &*&
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mem(pxIndex, cells) == true &*&
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xListEnd == &(l->xListEnd) &*&
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xListEnd == head(cells) &*&
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portMAX_DELAY == head(vals) &*&
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struct_xLIST_ITEM_padding(&l->xListEnd) &*&
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length(cells) == length(vals) &*&
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uxNumberOfItems + 1 == length(cells) &*&
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DLS(xListEnd, ?endprev, xListEnd, endprev, cells, vals, l);
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lemma void xLIST_distinct_cells(struct xLIST *l)
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requires xLIST(l, ?n, ?idx, ?end, ?cells, ?vals);
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ensures xLIST(l, n, idx, end, cells, vals) &*& distinct(cells) == true;
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{
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open xLIST(l, n, idx, end, cells, vals);
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assert DLS(end, ?endprev, end, _, cells, vals, l);
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dls_distinct(end, endprev, end, endprev, cells);
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close xLIST(l, n, idx, end, cells, vals);
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}
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lemma void xLIST_star_item(struct xLIST *l, struct xLIST_ITEM *x)
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requires xLIST(l, ?n, ?idx, ?end, ?cells, ?vals) &*& xLIST_ITEM(x, ?v, ?xnext, ?xprev, ?l2);
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ensures xLIST(l, n, idx, end, cells, vals) &*& xLIST_ITEM(x, v, xnext, xprev, l2) &*& mem(x, cells) == false;
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{
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open xLIST(l, n, idx, end, cells, vals);
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assert DLS(end, ?endprev, end, _, cells, vals, l);
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dls_distinct(end, endprev, end, endprev, cells);
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dls_star_item(end, endprev, x);
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close xLIST(l, n, idx, end, cells, vals);
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}
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lemma void dls_first_mem(
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struct xLIST_ITEM *n,
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struct xLIST_ITEM *nprev,
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struct xLIST_ITEM *mnext,
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struct xLIST_ITEM *m,
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list<struct xLIST_ITEM * > cells)
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requires DLS(n, nprev, mnext, m, cells, ?vals, ?l);
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ensures DLS(n, nprev, mnext, m, cells, vals, l) &*& mem(n, cells) == true &*& index_of(n, cells) == 0;
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{
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open DLS(n, nprev, mnext, m, cells, vals, l);
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if (n == m) {
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assert cells == cons(n, nil);
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close DLS(n, nprev, mnext, m, cells, vals, l);
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} else {
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assert cells == cons(n, ?tail);
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close DLS(n, nprev, mnext, m, cells, vals, l);
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}
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}
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lemma void dls_not_empty(
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struct xLIST_ITEM *n,
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struct xLIST_ITEM *m,
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list<struct xLIST_ITEM * > cells,
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struct xLIST_ITEM *x)
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requires DLS(n, m, n, m, cells, ?vals, ?l) &*& mem(x, cells) == true &*& x != n;
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ensures DLS(n, m, n, m, cells, vals, l) &*& n != m;
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{
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open DLS(n, m, n, m, cells, vals, l);
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close DLS(n, m, n, m, cells, vals, l);
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}
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lemma void dls_last_mem(
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struct xLIST_ITEM *n,
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struct xLIST_ITEM *nprev,
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struct xLIST_ITEM *mnext,
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struct xLIST_ITEM *m,
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list<struct xLIST_ITEM * > cells)
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requires DLS(n, nprev, mnext, m, cells, ?vals, ?l);
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ensures DLS(n, nprev, mnext, m, cells, vals, l) &*& mem(m, cells) == true &*& index_of(m, cells) == length(cells) - 1;
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{
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open DLS(n, nprev, mnext, m, cells, vals, l);
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if (n == m) {
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// trivial
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} else {
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open xLIST_ITEM(n, _, ?nnext, _, l);
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assert DLS(?o, n, mnext, m, tail(cells), tail(vals), l);
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dls_last_mem(o, n, mnext, m, tail(cells));
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close xLIST_ITEM(n, _, nnext, _, l);
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}
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close DLS(n, nprev, mnext, m, cells, vals, l);
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}
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lemma void split(
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struct xLIST_ITEM *n,
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struct xLIST_ITEM *nprev,
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struct xLIST_ITEM *mnext,
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struct xLIST_ITEM *m,
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list<struct xLIST_ITEM * > cells,
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list<TickType_t > vals,
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struct xLIST_ITEM *x,
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int i)
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requires DLS(n, nprev, mnext, m, cells, vals, ?l) &*& x != n &*& mem(x, cells) == true &*& index_of(x,cells) == i;
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ensures DLS(n, nprev, x, ?xprev, take(i, cells), take(i, vals), l) &*& DLS(x, xprev, mnext, m, drop(i, cells), drop(i, vals), l) &*& xprev == nth(i-1, cells);
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{
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open DLS(n, nprev, mnext, m, cells, vals, l);
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assert n != m;
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assert xLIST_ITEM(n, ?v, ?nnext, _, _);
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assert DLS(nnext, n, mnext, m, tail(cells), tail(vals), l);
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if (nnext == x) {
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close DLS(n, nprev, x, n, singleton(n), singleton(v), l);
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open DLS(x, n, mnext, m, tail(cells), tail(vals), l);
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open xLIST_ITEM(x, _, ?xnext, ?xprev, l);
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close xLIST_ITEM(x, _, xnext, xprev, l);
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close DLS(x, n, mnext, m, tail(cells), tail(vals), l);
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} else {
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assert nnext != x;
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split(nnext, n, mnext, m, tail(cells), tail(vals), x, i - 1);
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assert DLS(nnext, n, x, ?xprev, take(i-1, tail(cells)), take(i-1, tail(vals)), l);
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dls_distinct(nnext, n, x, xprev, take(i-1, tail(cells)));
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dls_star_item(nnext, xprev, n);
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dls_last_mem(nnext, n, x, xprev, take(i-1, tail(cells)));
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assert n != xprev;
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close DLS(n, nprev, x, xprev, take(i, cells), take(i, vals), l);
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}
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}
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lemma void join(
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struct xLIST_ITEM *n1,
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struct xLIST_ITEM *nprev1,
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struct xLIST_ITEM *mnext1,
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struct xLIST_ITEM *m1,
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list<struct xLIST_ITEM * > cells1,
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list<TickType_t > vals1,
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struct xLIST_ITEM *n2,
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struct xLIST_ITEM *nprev2,
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struct xLIST_ITEM *mnext2,
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struct xLIST_ITEM *m2,
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list<struct xLIST_ITEM * > cells2,
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list<TickType_t > vals2)
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requires
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DLS(n1, nprev1, mnext1, m1, cells1, vals1, ?l) &*&
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DLS(n2, nprev2, mnext2, m2, cells2, vals2, l) &*&
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mnext1 == n2 &*& m1 == nprev2;
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ensures DLS(n1, nprev1, mnext2, m2, append(cells1, cells2), append(vals1, vals2), l);
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{
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if (n1 == m1) {
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dls_first_mem(n1, nprev1, mnext1, m1, cells1);
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dls_last_mem(n2, nprev2, mnext2, m2, cells2);
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open DLS(n1, nprev1, mnext1, m1, cells1, vals1, l);
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dls_star_item(n2, m2, n1);
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close DLS(n1, nprev1, mnext2, m2, append(singleton(n1), cells2), append(vals1, vals2), l);
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} else {
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open DLS(n1, nprev1, mnext1, m1, cells1, vals1, l);
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assert DLS(?o, n1, mnext1, m1, ?cells1_tail, ?vals1_tail, l);
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join(o, n1, mnext1, m1, cells1_tail, vals1_tail,
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n2, nprev2, mnext2, m2, cells2, vals2);
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assert DLS(o, n1, mnext2, m2, append(cells1_tail, cells2), append(vals1_tail, vals2), l);
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dls_last_mem(o, n1, mnext2, m2, append(cells1_tail, cells2));
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dls_star_item(o, m2, n1);
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close DLS(n1, nprev1, mnext2, m2, append(cells1, cells2), append(vals1, vals2), l);
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}
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}
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lemma void idx_remains_in_list<t>(
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list<t> cells,
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t idx,
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t x,
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int ix)
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requires
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idx != x &*&
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mem(idx, cells) == true &*&
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mem(x, cells) == true &*&
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index_of(x, cells) == ix;
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ensures mem(idx, remove_nth(ix, cells)) == true;
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{
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neq_mem_remove(idx, x, cells);
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remove_remove_nth(cells, x);
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}
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@*/
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/* Following lemma from `verifast/examples/shared_boxes/concurrentqueue.c`.
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Used in the uxListRemove proof to show that the item to remove `x` must
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have value `nth(i, vals)` where `i == index_of(x, cells)`. */
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/*@
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lemma void drop_nth_index_of<t>(list<t> vs, int i)
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requires
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0 <= i && i < length(vs);
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ensures
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head(drop(i , vs)) == nth(i, vs);
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{
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switch(vs) {
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case nil:
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case cons(h, t):
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if (i == 0) {
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// trivial
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} else {
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drop_nth_index_of(t, i - 1);
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}
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}
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}
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@*/
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/*@
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lemma void remove_append<t>(t x, list<t> l1, list<t> l2)
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requires mem(x, l1) == false;
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ensures remove(x, append(l1, l2)) == append(l1, remove(x, l2));
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{
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switch(l1) {
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case nil:
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case cons(h1, t1):
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remove_append(x, t1, l2);
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}
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}
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@*/
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#endif /* LIST_H */
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/* *INDENT-ON* */
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