mirror of
https://github.com/FreeRTOS/FreeRTOS-Kernel.git
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100 lines
No EOL
3.2 KiB
C
100 lines
No EOL
3.2 KiB
C
#ifndef READY_LIST_PREDICATES_H
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#define READY_LIST_PREDICATES_H
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#include "single_core_proofs/scp_list_predicates.h"
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/*@
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predicate List_array_p(List_t* array, int size,
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list<list<struct xLIST_ITEM*> > cellLists) =
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size >= 0 &*&
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length(cellLists) == size &*&
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size > 0
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? (
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cellLists == cons(?gCells, ?gTailcellLists) &*&
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pointer_within_limits(array) == true &*&
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xLIST(array, ?gNumberOfItems, ?gIndex, ?gListEnd, gCells, ?gVals)
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&*&
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List_array_p(array + 1, size - 1, gTailcellLists)
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)
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: cellLists == nil;
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lemma void List_array_size_positive(List_t* pxArray)
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requires List_array_p(pxArray, ?gSize, ?gCellLists);
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ensures List_array_p(pxArray, gSize, gCellLists) &*&
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gSize >= 0 &*& gSize == length(gCellLists);
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{
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open List_array_p(pxArray, gSize, gCellLists);
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close List_array_p(pxArray, gSize, gCellLists);
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}
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lemma void List_array_split(List_t* array, int index)
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requires
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List_array_p(array, ?gSize, ?gCellLists) &*&
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0 <= index &*& index < gSize;
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ensures
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List_array_p(array, index, ?gPrefCellLists) &*&
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gPrefCellLists == take(index, gCellLists) &*&
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pointer_within_limits(array) == true &*&
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xLIST(array + index, _, _, _, ?gCells, ?vals) &*&
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gCells == nth(index, gCellLists) &*&
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List_array_p(array + index + 1, gSize-index-1, ?gSufCellLists) &*&
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gSufCellLists == drop(index+1, gCellLists);
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{
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open List_array_p(array, gSize, gCellLists);
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if( index > 0 ) {
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List_array_split(array + 1, index - 1);
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}
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close List_array_p(array, index, take(index, gCellLists));
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}
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lemma void List_array_join(List_t* array)
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requires
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List_array_p(array, ?gPrefSize, ?gPrefCellLists) &*&
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xLIST(array + gPrefSize, _, _, _, ?gCells, _) &*&
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pointer_within_limits(array + gPrefSize) == true &*&
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List_array_p(array + gPrefSize + 1, ?gSufSize, ?gSufCellLists);
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ensures
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List_array_p(array, ?gSize, ?gCellLists) &*&
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gSize == length(gCellLists) &*&
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gSize == gPrefSize + 1 + gSufSize &*&
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gCellLists == append(gPrefCellLists, cons(gCells, gSufCellLists));
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{
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open List_array_p(array, gPrefSize, gPrefCellLists);
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List_array_size_positive(array + gPrefSize + 1);
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if( gPrefSize > 0 ) {
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List_array_join(array + 1);
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}
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close List_array_p(array, gPrefSize + 1 + gSufSize,
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append(gPrefCellLists, cons(gCells, gSufCellLists)));
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}
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@*/
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/*@
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// TODO: We know that the list of priority 0 is never empty.
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// It contains the idle task and nothing else.
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predicate readyLists_p(list<list<struct xLIST_ITEM*> > gCellLists) =
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List_array_p(&pxReadyTasksLists, configMAX_PRIORITIES, gCellLists);
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@*/
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/*@
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lemma void List_array_p_index_within_limits(List_t* array, int index)
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requires List_array_p(array, ?gSize, ?gCellListss) &*&
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0 <= index &*& index < gSize;
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ensures List_array_p(array, gSize, gCellListss) &*&
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pointer_within_limits(&array[index]) == true;
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{
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open List_array_p(array, gSize, gCellListss);
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if( index > 0) {
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List_array_p_index_within_limits(&array[1], index-1);
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}
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close List_array_p(array, gSize, gCellListss);
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}
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@*/
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#endif /* READY_LIST_PREDICATES_H */ |