FreeRTOS-Kernel/verification/verifast/proof/ready_list_predicates.h

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No EOL
4.4 KiB
C

#ifndef READY_LIST_PREDICATES_H
#define READY_LIST_PREDICATES_H
#include "single_core_proofs/scp_list_predicates.h"
/*@
// TODO: We know that the list of priority 0 is never empty.
// It contains the idle task and nothing else.
predicate readyLists_p(list<list<struct xLIST_ITEM*> > gCellLists,
list<list<void*> > gOwnerLists) =
configMAX_PRIORITIES == length(gCellLists) &*&
List_array_p(&pxReadyTasksLists, configMAX_PRIORITIES,
gCellLists, gOwnerLists);
predicate List_array_p(List_t* array, int size,
list<list<struct xLIST_ITEM*> > cellLists,
list<list<void*> > ownerLists) =
size >= 0 &*&
length(cellLists) == size &*&
length(ownerLists) == length(cellLists) &*&
size > 0
? (
cellLists == cons(?gCells, ?gTailCellLists) &*&
ownerLists == cons(?gOwners, ?gTailOwnerLists) &*&
pointer_within_limits(array) == true &*&
xLIST(array, ?gLen, ?gIndex, ?gListEnd, gCells, ?gVals,
gOwners)
&*&
gLen < INT_MAX &*&
List_array_p(array + 1, size - 1, gTailCellLists, gTailOwnerLists)
)
: (
cellLists == nil &*&
ownerLists == nil
);
lemma void List_array_size_positive(List_t* pxArray)
requires List_array_p(pxArray, ?gSize, ?gCellLists, ?gOwnerLists);
ensures
List_array_p(pxArray, gSize, gCellLists, gOwnerLists) &*&
gSize >= 0 &*&
gSize == length(gCellLists) &*&
length(gCellLists) == length(gOwnerLists);
{
open List_array_p(pxArray, gSize, gCellLists, gOwnerLists);
close List_array_p(pxArray, gSize, gCellLists, gOwnerLists);
}
lemma void List_array_split(List_t* array, int index)
requires
List_array_p(array, ?gSize, ?gCellLists, ?gOwnerLists) &*&
0 <= index &*& index < gSize;
ensures
List_array_p(array, index, ?gPrefCellLists, ?gPrefOwnerLists) &*&
gPrefCellLists == take(index, gCellLists) &*&
gPrefOwnerLists == take(index, gOwnerLists) &*&
pointer_within_limits(array) == true &*&
xLIST(array + index, ?gLen, _, _, ?gCells, ?gVals, ?gOwners) &*&
gLen < INT_MAX &*&
gCells == nth(index, gCellLists) &*&
gOwners == nth(index, gOwnerLists) &*&
mem(gOwners, gOwnerLists) == true &*&
List_array_p(array + index + 1, gSize-index-1, ?gSufCellLists, ?gSufOwnerLists) &*&
gSufCellLists == drop(index+1, gCellLists) &*&
gSufOwnerLists == drop(index+1, gOwnerLists);
{
open List_array_p(array, gSize, gCellLists, gOwnerLists);
if( index > 0 ) {
List_array_split(array + 1, index - 1);
}
close List_array_p(array, index, take(index, gCellLists), take(index, gOwnerLists));
}
lemma void List_array_join(List_t* array)
requires
List_array_p(array, ?gPrefSize, ?gPrefCellLists, ?gPrefOwnerLists) &*&
xLIST(array + gPrefSize, ?gLen, _, _, ?gCells, _, ?gOwners) &*&
gLen < INT_MAX &*&
pointer_within_limits(array + gPrefSize) == true &*&
List_array_p(array + gPrefSize + 1, ?gSufSize, ?gSufCellLists, ?gSufOwnerLists);
ensures
List_array_p(array, ?gSize, ?gCellLists, ?gOwnerLists) &*&
gSize == length(gCellLists) &*&
length(gCellLists) == length(gOwnerLists) &*&
gSize == gPrefSize + 1 + gSufSize &*&
gCellLists == append(gPrefCellLists, cons(gCells, gSufCellLists)) &*&
gOwnerLists == append(gPrefOwnerLists, cons(gOwners, gSufOwnerLists));
{
open List_array_p(array, gPrefSize, gPrefCellLists, gPrefOwnerLists);
List_array_size_positive(array + gPrefSize + 1);
if( gPrefSize > 0 ) {
List_array_join(array + 1);
}
close List_array_p(array, gPrefSize + 1 + gSufSize,
append(gPrefCellLists, cons(gCells, gSufCellLists)),
append(gPrefOwnerLists, cons(gOwners, gSufOwnerLists)));
}
@*/
/*@
lemma void List_array_p_index_within_limits(List_t* array, int index)
requires List_array_p(array, ?gSize, ?gCellLists, ?gOwnerLists) &*&
0 <= index &*& index < gSize;
ensures List_array_p(array, gSize, gCellLists, gOwnerLists) &*&
pointer_within_limits(&array[index]) == true;
{
open List_array_p(array, gSize, gCellLists, gOwnerLists);
if( index > 0) {
List_array_p_index_within_limits(&array[1], index-1);
}
close List_array_p(array, gSize, gCellLists, gOwnerLists);
}
@*/
#endif /* READY_LIST_PREDICATES_H */