mirror of
https://github.com/FreeRTOS/FreeRTOS-Kernel.git
synced 2025-12-11 14:15:12 -05:00
Adapted proof of prvSelectHighestPriorityTask to use new DLS representation and opening & closing lemmas.
This commit is contained in:
Tobias Reinhard
parent
bb00bee690
commit
c0df2a2894
1 changed files with 35 additions and 128 deletions
163
tasks.c
163
tasks.c
|
|
@ -932,7 +932,6 @@ static void prvYieldForTask( TCB_t * pxTCB,
|
||||||
prvTCB_p(gCurrentTCB, ulFreeBytesOnStack);
|
prvTCB_p(gCurrentTCB, ulFreeBytesOnStack);
|
||||||
@*/
|
@*/
|
||||||
{
|
{
|
||||||
//@ assume(false);
|
|
||||||
//@ open taskISRLockInv();
|
//@ open taskISRLockInv();
|
||||||
//@ assert( integer_((void*) &uxTopReadyPriority, sizeof(UBaseType_t), false, ?gTopReadyPriority) );
|
//@ assert( integer_((void*) &uxTopReadyPriority, sizeof(UBaseType_t), false, ?gTopReadyPriority) );
|
||||||
//@ assert( gTopReadyPriority == uxTopReadyPriority);
|
//@ assert( gTopReadyPriority == uxTopReadyPriority);
|
||||||
|
|
@ -990,76 +989,45 @@ static void prvYieldForTask( TCB_t * pxTCB,
|
||||||
//@ open readyLists_p();
|
//@ open readyLists_p();
|
||||||
//@ List_array_p_index_within_limits(&pxReadyTasksLists, uxCurrentPriority);
|
//@ List_array_p_index_within_limits(&pxReadyTasksLists, uxCurrentPriority);
|
||||||
//@ List_array_get_l(pxReadyTasksLists, uxCurrentPriority);
|
//@ List_array_get_l(pxReadyTasksLists, uxCurrentPriority);
|
||||||
/*@ assert( xLIST(&pxReadyTasksLists[ uxCurrentPriority ],
|
//@ List_t* gReadyList = &pxReadyTasksLists[uxCurrentPriority];
|
||||||
?gNumberOfItems,
|
/*@ assert( xLIST(gReadyList, ?gNumberOfItems, ?gIndex, ?gListEnd,
|
||||||
?gIndex,
|
?gCells, ?gVals) );
|
||||||
?gListEnd,
|
|
||||||
?gCells,
|
|
||||||
?gVals) );
|
|
||||||
@*/
|
@*/
|
||||||
//@ open xLIST(&pxReadyTasksLists[uxCurrentPriority], _, _, _, _, _);
|
//@ open xLIST(gReadyList, _, _, _, _, _);
|
||||||
if( listLIST_IS_EMPTY( &( pxReadyTasksLists[ uxCurrentPriority ] ) ) == pdFALSE )
|
if( listLIST_IS_EMPTY( &( pxReadyTasksLists[ uxCurrentPriority ] ) ) == pdFALSE )
|
||||||
{
|
{
|
||||||
List_t * const pxReadyList = &( pxReadyTasksLists[ uxCurrentPriority ] );
|
List_t * const pxReadyList = &( pxReadyTasksLists[ uxCurrentPriority ] );
|
||||||
//@ assert( pxReadyList->pxIndex |-> gIndex );
|
//@ assert( pxReadyList->pxIndex |-> gIndex );
|
||||||
//@ assert( DLS(gListEnd, ?gEndPrev, gListEnd, gEndPrev, gCells, gVals, &pxReadyTasksLists[uxCurrentPriority]) );
|
/*@ assert( DLS(gListEnd, ?gEndPrev, gListEnd, gEndPrev,
|
||||||
///@ open DLS(gListEnd, gEndPrev, gListEnd, gEndPrev, gCells, gVals, &pxReadyTasksLists[uxCurrentPriority]);
|
gCells, gVals, gReadyList) );
|
||||||
//@ assert( mem(pxReadyList->pxIndex, gCells) == true );
|
@*/
|
||||||
/*@
|
|
||||||
if( pxReadyList->pxIndex == gListEnd ) {
|
|
||||||
open DLS(gListEnd, gEndPrev, gListEnd, gEndPrev, gCells, gVals, &pxReadyTasksLists[uxCurrentPriority]);
|
|
||||||
assert( gVals == cons(?gV, ?gRest) );
|
|
||||||
assert( xLIST_ITEM(gIndex, gV, ?gO, gEndPrev, &pxReadyTasksLists[uxCurrentPriority]) );
|
|
||||||
} else {
|
|
||||||
int gCellIndex = index_of(gIndex, gCells);
|
|
||||||
split(gListEnd, gEndPrev, gListEnd, gEndPrev, gCells, gVals, gIndex, gCellIndex);
|
|
||||||
assert( DLS( gListEnd, gEndPrev, gIndex, ?gIndexPrev, take(gCellIndex, gCells), take(gCellIndex, gVals), &pxReadyTasksLists[uxCurrentPriority]) );
|
|
||||||
assert( DLS( gIndex, gIndexPrev, gListEnd, gEndPrev, drop(gCellIndex, gCells), drop(gCellIndex, gVals), &pxReadyTasksLists[uxCurrentPriority]) );
|
|
||||||
open DLS( gIndex, gIndexPrev, gListEnd, gEndPrev, drop(gCellIndex, gCells), drop(gCellIndex, gVals), &pxReadyTasksLists[uxCurrentPriority]);
|
|
||||||
}
|
|
||||||
@*/
|
|
||||||
|
|
||||||
|
//@ DLS_open_2(pxReadyList->pxIndex);
|
||||||
|
//@ assert( xLIST_ITEM(gIndex, _, ?gIndexNext, ?gIndexPrev, gReadyList) );
|
||||||
ListItem_t * pxLastTaskItem = pxReadyList->pxIndex->pxPrevious;
|
ListItem_t * pxLastTaskItem = pxReadyList->pxIndex->pxPrevious;
|
||||||
ListItem_t * pxTaskItem = pxLastTaskItem;
|
ListItem_t * pxTaskItem = pxLastTaskItem;
|
||||||
/*@
|
//@ close xLIST_ITEM(gIndex, _, gIndexNext, gIndexPrev, gReadyList);
|
||||||
if( gIndex == gListEnd ) {
|
//@ DLS_close_2(pxReadyList->pxIndex, gCells, gVals);
|
||||||
close xLIST_ITEM(gIndex, _, _, gEndPrev, &pxReadyTasksLists[uxCurrentPriority]);
|
|
||||||
close DLS(gListEnd, gEndPrev, gListEnd, gEndPrev, gCells, gVals, &pxReadyTasksLists[uxCurrentPriority]);
|
|
||||||
|
|
||||||
// Loop invariant for inner search loop below requires us
|
//@ assert( mem(pxTaskItem, gCells) == true);
|
||||||
// to prove that `pxTaskItem` points to a valid list item.
|
|
||||||
dls_last_mem(gListEnd, gEndPrev, gListEnd, gEndPrev, gCells);
|
|
||||||
assert( mem(pxTaskItem, gCells) == true );
|
|
||||||
} else {
|
|
||||||
int gCellIndex = index_of(gIndex, gCells);
|
|
||||||
assert( DLS( gListEnd, gEndPrev, gIndex, ?gIndexPrev, take(gCellIndex, gCells), take(gCellIndex, gVals), &pxReadyTasksLists[uxCurrentPriority]) );
|
|
||||||
close xLIST_ITEM(gIndex, _, _, gIndexPrev, &pxReadyTasksLists[uxCurrentPriority]);
|
|
||||||
close DLS( gIndex, gIndexPrev, gListEnd, gEndPrev, drop(gCellIndex, gCells), drop(gCellIndex, gVals), &pxReadyTasksLists[uxCurrentPriority]);
|
|
||||||
assert( DLS( gIndex, gIndexPrev, gListEnd, gEndPrev, drop(gCellIndex, gCells), drop(gCellIndex, gVals), &pxReadyTasksLists[uxCurrentPriority]) );
|
|
||||||
|
|
||||||
join( gListEnd, gEndPrev, gIndex, gIndexPrev, take(gCellIndex, gCells), take(gCellIndex, gVals),
|
|
||||||
gIndex, gIndexPrev, gListEnd, gEndPrev, drop(gCellIndex, gCells), drop(gCellIndex, gVals) );
|
|
||||||
}
|
|
||||||
@*/
|
|
||||||
// Unified ghost branches
|
|
||||||
//@ assert( DLS(gListEnd, gEndPrev, gListEnd, gEndPrev, gCells, gVals, &pxReadyTasksLists[uxCurrentPriority]) );
|
|
||||||
|
|
||||||
//@ open DLS(gListEnd, gEndPrev, gListEnd, gEndPrev, gCells, gVals, &pxReadyTasksLists[uxCurrentPriority]);
|
//@ open DLS(gListEnd, gEndPrev, gListEnd, gEndPrev, gCells, gVals, gReadyList);
|
||||||
//@ assert( xLIST_ITEM(&pxReadyList->xListEnd, _, _, _, &pxReadyTasksLists[uxCurrentPriority]) );
|
//@ assert( xLIST_ITEM(&pxReadyList->xListEnd, _, _, _, gReadyList) );
|
||||||
//@ open xLIST_ITEM(&pxReadyList->xListEnd, _, _, _, &pxReadyTasksLists[uxCurrentPriority]);
|
//@ open xLIST_ITEM(&pxReadyList->xListEnd, _, _, _, gReadyList);
|
||||||
// opening required to prove validity of `&( pxReadyList->xListEnd )`
|
// opening required to prove validity of `&( pxReadyList->xListEnd )`
|
||||||
///@ assert( pointer_within_limits( &pxReadyList->xListEnd ) == true );
|
///@ assert( pointer_within_limits( &pxReadyList->xListEnd ) == true );
|
||||||
//@ close xLIST_ITEM(&pxReadyList->xListEnd, _, _, _, &pxReadyTasksLists[uxCurrentPriority]);
|
//@ close xLIST_ITEM(&pxReadyList->xListEnd, _, _, _, gReadyList);
|
||||||
if( ( void * ) pxLastTaskItem == ( void * ) &( pxReadyList->xListEnd ) )
|
if( ( void * ) pxLastTaskItem == ( void * ) &( pxReadyList->xListEnd ) )
|
||||||
{
|
{
|
||||||
//@ assert( gVals == cons(?gV, ?gRest) );
|
//@ assert( gVals == cons(?gV, ?gRest) );
|
||||||
//@ assert( xLIST_ITEM(?gOldLastTaskItem, gV, ?gO, gEndPrev, &pxReadyTasksLists[uxCurrentPriority]) );
|
//@ assert( xLIST_ITEM(?gOldLastTaskItem, gV, ?gO, gEndPrev, gReadyList) );
|
||||||
pxLastTaskItem = pxLastTaskItem->pxPrevious;
|
pxLastTaskItem = pxLastTaskItem->pxPrevious;
|
||||||
//@ close xLIST_ITEM(gOldLastTaskItem, gV, gO, gEndPrev, &pxReadyTasksLists[uxCurrentPriority]);
|
//@ close xLIST_ITEM(gOldLastTaskItem, gV, gO, gEndPrev, gReadyList);
|
||||||
}
|
}
|
||||||
//@ close DLS(gListEnd, gEndPrev, gListEnd, gEndPrev, gCells, gVals, &pxReadyTasksLists[uxCurrentPriority]);
|
//@ close DLS(gListEnd, gEndPrev, gListEnd, gEndPrev, gCells, gVals, gReadyList);
|
||||||
/*@ close xLIST(&pxReadyTasksLists[ uxCurrentPriority ],
|
/*@ close xLIST(gReadyList, gNumberOfItems, gIndex, gListEnd,
|
||||||
gNumberOfItems, gIndex, gListEnd, gCells, gVals);
|
gCells, gVals);
|
||||||
@*/
|
@*/
|
||||||
|
|
||||||
/* The ready task list for uxCurrentPriority is not empty, so uxTopReadyPriority
|
/* The ready task list for uxCurrentPriority is not empty, so uxTopReadyPriority
|
||||||
|
|
@ -1068,107 +1036,46 @@ static void prvYieldForTask( TCB_t * pxTCB,
|
||||||
|
|
||||||
do
|
do
|
||||||
/*@ invariant
|
/*@ invariant
|
||||||
xLIST(&pxReadyTasksLists[ uxCurrentPriority ],
|
xLIST(gReadyList, gNumberOfItems, gIndex, gListEnd,
|
||||||
gNumberOfItems, gIndex, gListEnd, gCells, gVals) &*&
|
gCells, gVals)
|
||||||
|
&*&
|
||||||
mem(pxTaskItem, gCells) == true;
|
mem(pxTaskItem, gCells) == true;
|
||||||
@*/
|
@*/
|
||||||
{
|
{
|
||||||
TCB_t * pxTCB;
|
TCB_t * pxTCB;
|
||||||
|
|
||||||
//@ List_t* gReadyList = &pxReadyTasksLists[ uxCurrentPriority ];
|
|
||||||
//@ open xLIST(gReadyList, gNumberOfItems, gIndex, gListEnd, gCells, gVals);
|
//@ open xLIST(gReadyList, gNumberOfItems, gIndex, gListEnd, gCells, gVals);
|
||||||
//@ assert( DLS(gListEnd, ?gEndPrev2, gListEnd, gEndPrev2, gCells, gVals, gReadyList) );
|
//@ assert( DLS(gListEnd, ?gEndPrev2, gListEnd, gEndPrev2, gCells, gVals, gReadyList) );
|
||||||
|
|
||||||
//@ int gTaskItemIndex_0 = index_of(pxTaskItem, gCells);
|
// Building an SSA for important variables helps us to
|
||||||
|
// refer to the right instances.
|
||||||
//@ struct xLIST_ITEM* gTaskItem_0 = pxTaskItem;
|
//@ struct xLIST_ITEM* gTaskItem_0 = pxTaskItem;
|
||||||
|
|
||||||
|
//@ DLS_open_2(gTaskItem_0);
|
||||||
/* Proof idea:
|
|
||||||
* - Open DLS predicate to justify access to fields of
|
|
||||||
* `gTaskItem_0`
|
|
||||||
* - Prove `mem(gTaskItem_1, gCells) == true`
|
|
||||||
*
|
|
||||||
* In if-statement:
|
|
||||||
* - Open DLS predicate to justify access to
|
|
||||||
* `gTaskItem_1->next` in if-statement
|
|
||||||
* - Prove `mem(gTaskItem_2, gCells) == true`
|
|
||||||
*
|
|
||||||
* After if-statement:
|
|
||||||
* - Prove `mem(gTaskItem_3, gCells) == true`
|
|
||||||
*/
|
|
||||||
|
|
||||||
|
|
||||||
//@ DLS_next_open(gReadyList, gTaskItem_0);
|
|
||||||
pxTaskItem = pxTaskItem->pxNext;
|
pxTaskItem = pxTaskItem->pxNext;
|
||||||
|
|
||||||
//@ int gTaskItemIndex_1 = index_of(pxTaskItem, gCells);
|
|
||||||
//@ struct xLIST_ITEM* gTaskItem_1 = pxTaskItem;
|
//@ struct xLIST_ITEM* gTaskItem_1 = pxTaskItem;
|
||||||
|
|
||||||
//@ assert( mem(gTaskItem_1, gCells) == true );
|
|
||||||
//@ close xLIST_ITEM(gTaskItem_0, _, _, _, gReadyList);
|
//@ close xLIST_ITEM(gTaskItem_0, _, _, _, gReadyList);
|
||||||
|
//@ DLS_close_2(gTaskItem_0, gCells, gVals);
|
||||||
//@ DLS_next_close(gReadyList, gTaskItem_0, gCells, gVals, gListEnd, gEndPrev2);
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
if( ( void * ) pxTaskItem == ( void * ) &( pxReadyList->xListEnd ) )
|
if( ( void * ) pxTaskItem == ( void * ) &( pxReadyList->xListEnd ) )
|
||||||
{
|
{
|
||||||
//@ assert( pxTaskItem == gTaskItem_1 );
|
//@ DLS_open_2(gTaskItem_1);
|
||||||
//@ DLS_next_open(gReadyList, gTaskItem_1);
|
|
||||||
|
|
||||||
pxTaskItem = pxTaskItem->pxNext;
|
pxTaskItem = pxTaskItem->pxNext;
|
||||||
//@ int gTaskItemIndex_2 = index_of(pxTaskItem, gCells);
|
|
||||||
//@ struct xLIST_ITEM* gTaskItem_2 = pxTaskItem;
|
//@ struct xLIST_ITEM* gTaskItem_2 = pxTaskItem;
|
||||||
|
|
||||||
//@ close xLIST_ITEM(gTaskItem_1, _, _, _, gReadyList);
|
//@ close xLIST_ITEM(gTaskItem_1, _, _, _, gReadyList);
|
||||||
//@ DLS_next_close(gReadyList, gTaskItem_1, gCells, gVals, gListEnd, gEndPrev2);
|
//@ DLS_close_2(gTaskItem_1, gCells, gVals);
|
||||||
}
|
}
|
||||||
|
|
||||||
//@ int gTaskItemIndex_3 = index_of(pxTaskItem, gCells);
|
|
||||||
//@ struct xLIST_ITEM* gTaskItem_3 = pxTaskItem;
|
//@ struct xLIST_ITEM* gTaskItem_3 = pxTaskItem;
|
||||||
|
|
||||||
//@ assert( DLS(gListEnd, gEndPrev2, gListEnd, gEndPrev2, gCells, gVals, gReadyList) );
|
|
||||||
//@ assert( mem(gTaskItem_3, gCells) == true );
|
|
||||||
|
|
||||||
|
|
||||||
/*@
|
|
||||||
if( gTaskItem_3 == gListEnd ) {
|
|
||||||
open DLS(gListEnd, gEndPrev2, gListEnd, gEndPrev2, gCells, gVals, gReadyList);
|
|
||||||
} else{
|
|
||||||
split(gListEnd, gEndPrev2, gListEnd, gEndPrev2, gCells, gVals, gTaskItem_3, gTaskItemIndex_3);
|
|
||||||
open DLS(gTaskItem_3, _, gListEnd, gEndPrev2, _, _, gReadyList);
|
|
||||||
}
|
|
||||||
@*/
|
|
||||||
|
|
||||||
|
//@ DLS_open_2(gTaskItem_3);
|
||||||
pxTCB = pxTaskItem->pvOwner;
|
pxTCB = pxTaskItem->pvOwner;
|
||||||
|
//@ close xLIST_ITEM(gTaskItem_3, _, _, _, gReadyList);
|
||||||
|
//@ DLS_close_2(gTaskItem_3, gCells, gVals);
|
||||||
|
|
||||||
//@ close xLIST_ITEM(gTaskItem_3, ?gTaskItem_3_val, ?gTaskItem_3_next, _, gReadyList);
|
//@ assume(false);
|
||||||
|
|
||||||
/*@
|
|
||||||
if( gTaskItem_3 == gListEnd ) {
|
|
||||||
close DLS(gListEnd, gEndPrev2, gListEnd, gEndPrev2, gCells, gVals, gReadyList);
|
|
||||||
} else{
|
|
||||||
assert( DLS(gListEnd, gEndPrev2, gTaskItem_3, ?gTaskItem_3_prev, ?gCellsPrefix, ?gValsPrefix, gReadyList) );
|
|
||||||
|
|
||||||
if( gTaskItem_3 == gEndPrev2 ) {
|
|
||||||
close DLS(gTaskItem_3, gTaskItem_3_prev, gListEnd, gEndPrev2,
|
|
||||||
cons(gTaskItem_3, nil), cons(gTaskItem_3_val, nil),
|
|
||||||
gReadyList);
|
|
||||||
} else {
|
|
||||||
assert( DLS(gTaskItem_3_next, gTaskItem_3, gListEnd, gEndPrev2,
|
|
||||||
?gCellsSuffix2, ?gValsSuffix2, gReadyList));
|
|
||||||
close DLS(gTaskItem_3, gTaskItem_3_prev, gListEnd, gEndPrev2,
|
|
||||||
cons(gTaskItem_3, gCellsSuffix2),
|
|
||||||
cons(gTaskItem_3_val, gValsSuffix2),
|
|
||||||
gReadyList);
|
|
||||||
}
|
|
||||||
assert( DLS(gTaskItem_3, gTaskItem_3_prev, gListEnd, gEndPrev2, ?gCellsSuffix, ?gValsSuffix, gReadyList) );
|
|
||||||
join(gListEnd, gEndPrev2, gTaskItem_3, gTaskItem_3_prev, gCellsPrefix, gValsPrefix,
|
|
||||||
gTaskItem_3, gTaskItem_3_prev, gListEnd, gEndPrev2, gCellsSuffix, gValsSuffix);
|
|
||||||
}
|
|
||||||
@*/
|
|
||||||
//@ assert( DLS(gListEnd, gEndPrev2, gListEnd, gEndPrev2, gCells, gVals, gReadyList) );
|
|
||||||
|
|
||||||
// Make sure that we covered all cases so far
|
// Make sure that we covered all cases so far
|
||||||
//@ assume(false);
|
//@ assume(false);
|
||||||
#ifdef IGNORED
|
#ifdef IGNORED
|
||||||
|
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue