Added adaptation of Aalok's and Nathan's single-core proof for uxListRemove

This commit is contained in:
Tobias Reinhard 2022-12-01 11:47:52 -05:00
parent 6f782b494a
commit cd3fa4e577
4 changed files with 484 additions and 7 deletions

477
list.c
View file

@ -186,10 +186,154 @@ void vListInsert( List_t * const pxList,
/*-----------------------------------------------------------*/ /*-----------------------------------------------------------*/
UBaseType_t uxListRemove( ListItem_t * const pxItemToRemove ) UBaseType_t uxListRemove( ListItem_t * const pxItemToRemove )
{ #ifndef VERIFAST_SINGLE_CORE
/* Reason for rewrite:
* Predicates `xLIST_ITEM`, `DLS` and `xLIST` have been extended to expose
* node owners. Proofs using these predicates must be adapted as well.
*/
/*@requires
exists<struct xLIST * >(?l) &*&
xLIST(l, ?len, ?idx, ?end, ?cells, ?vals, ?owners) &*&
end != pxItemToRemove &*&
mem(pxItemToRemove, cells) == true;@*/
/*@ensures
result == len-1 &*&
xLIST_ITEM(pxItemToRemove, nth(index_of(pxItemToRemove, cells), vals), _, ?pxItemToRemovePrevious, nth(index_of(pxItemToRemove, cells), owners), NULL) &*&
pxItemToRemovePrevious == nth(index_of(pxItemToRemove, cells)-1, cells) &*&
xLIST(l, result, idx == pxItemToRemove ? pxItemToRemovePrevious : idx, end, remove(pxItemToRemove, cells), remove_nth(index_of(pxItemToRemove, cells), vals), remove_nth(index_of(pxItemToRemove, cells), owners));
@*/
{
/* For brevity we alias x to pxItemToRemove */
/*@struct xLIST_ITEM *x = pxItemToRemove;@*/
/* Start by establishing that the list must be non-empty since x != end */
/*@open xLIST(l, len, idx, end, cells, vals, owners);@*/
/*@assert DLS(end, ?endprev, end, _, cells, vals, owners, l);@*/
/*@assert vals == cons(portMAX_DELAY, _);@*/
/*@dls_not_empty(end, endprev, cells, x);@*/
/* We know the xLIST is a DLS: end...endprev
Split this into DLS1:end...xprev and DLS2:x...endprev */
/*@int i = index_of(x, cells);@*/
/*@split(end, endprev, end, endprev, cells, vals, x, i);@*/
/*@list<struct xLIST_ITEM *> ys = take(i, cells);@*/
/*@list<struct xLIST_ITEM *> zs = drop(i, cells);@*/
/*@list<TickType_t> vs = take(i, vals);@*/
/*@list<TickType_t> ws = drop(i, vals);@*/
/*@list<void*> ts = take(i, owners);@*/
/*@list<void*> us = drop(i, owners);@*/
/*@assert length(ys) == length(vs);@*/
/*@assert length(zs) == length(ws);@*/
/*@assert length(ts) == length(vs);@*/
/*@assert length(us) == length(ws);@*/
/*@assert DLS(end, endprev, x, ?xprev, ys, vs, ts, l);@*/ /*< DLS1 (ys, vs) */
/*@assert DLS(x, xprev, end, endprev, zs, ws, us, l);@*/ /*< DLS2 (zs, ws) */
/* Now case split to open DLS1 and DLS2 appropriately */
/*@
if (end == xprev)
{
if (x == endprev)
{
//Case A
//DLS1: extract end=prev=next
open DLS(end, endprev, x, xprev, ys, vs, ts, l);
assert owners == cons(_, _);
open xLIST_ITEM(end, portMAX_DELAY, x, endprev, head(owners), l);
//DLS2: extract x
open DLS(x, xprev, end, endprev, zs, ws, us, l);
//Lengths
assert length(ys) == 1;
assert length(zs) == 1;
assert length(us) == 1;
}
else
{
//Case B
//DLS1: extract end=prev
open DLS(end, endprev, x, xprev, ys, vs, ts, l);
open xLIST_ITEM(end, portMAX_DELAY, x, endprev, head(owners), l);
//DLS2: extract next and x
open DLS(x, end, end, endprev, zs, ws, us, l);
assert DLS(?xnext, x, end, endprev, tail(zs), tail(ws), tail(us), l);
open DLS(xnext, x, end, endprev, tail(zs), tail(ws), tail(us), l);
open xLIST_ITEM(xnext, _, _, x, _, l);
//Lengths
assert length(ys) == 1;
}
}
else
{
if (x == endprev)
{
//Case C
//DLS1: extract end=next and prev
dls_last_mem(end, endprev, x, xprev, ys);
assert mem(xprev, ys) == true;
open DLS(end, endprev, x, xprev, ys, vs, ts, l);
open xLIST_ITEM(end, portMAX_DELAY, ?endnext, endprev, head(ts), l);
if (endnext == xprev)
{
open DLS(endnext, end, x, xprev, tail(ys), tail(vs), tail(ts), l);
open xLIST_ITEM(xprev, _, x, _, _, l);
}
else
{
assert DLS(endnext, end, x, xprev, tail(ys), tail(vs), tail(ts), l);
int k = index_of(xprev, tail(ys));
dls_last_mem(endnext, end, x, xprev, tail(ys));
split(endnext, end, x, xprev, tail(ys), tail(vs), xprev, k);
open DLS(xprev, _, x, xprev, _, _, _, l);
open xLIST_ITEM(xprev, _, x, _, _, l);
}
//DLS2: extract x
open DLS(x, xprev, end, endprev, zs, ws, us, l);
//Lengths
assert length(zs) == 1;
}
else
{
//Case D
//DLS1: extract prev
dls_last_mem(end, endprev, x, xprev, ys);
int j = index_of(xprev, ys);
open DLS(end, endprev, x, xprev, ys, vs, ts, l);
open xLIST_ITEM(end, portMAX_DELAY, ?endnext, endprev, head(ts), l);
if (endnext == xprev)
{
open DLS(endnext, end, x, xprev, tail(ys), tail(vs), tail(ts), l);
assert tail(ys) == singleton(xprev);
open xLIST_ITEM(xprev, _, x, _, _, l);
}
else
{
assert DLS(endnext, end, x, xprev, tail(ys), tail(vs), tail(ts), l);
int k = index_of(xprev, tail(ys));
dls_last_mem(endnext, end, x, xprev, tail(ys));
split(endnext, end, x, xprev, tail(ys), tail(vs), xprev, k);
open DLS(xprev, _, x, xprev, _, _, _, l);
open xLIST_ITEM(xprev, _, x, _, _, l);
}
//DLS2: extract next and x
open DLS(x, xprev, end, endprev, zs, ws, us, l);
assert xLIST_ITEM(x, _, ?xnext, _, _, l);
open DLS(xnext, x, end, endprev, tail(zs), tail(ws), tail(us), l);
open xLIST_ITEM(xnext, _, _, x, _, l);
}
}
@*/
/*@drop_nth_index_of(vals, i);@*/
/*@drop_nth_index_of(owners, i);@*/
/*@open xLIST_ITEM(x, nth(i, vals), ?xnext, xprev, nth(i, owners), l);@*/
/* The list item knows which list it is in. Obtain the list from the list /* The list item knows which list it is in. Obtain the list from the list
* item. */ * item. */
#ifdef VERIFAST /*< const pointer declaration */
List_t * pxList = pxItemToRemove->pxContainer;
#else
List_t * const pxList = pxItemToRemove->pxContainer; List_t * const pxList = pxItemToRemove->pxContainer;
#endif
pxItemToRemove->pxNext->pxPrevious = pxItemToRemove->pxPrevious; pxItemToRemove->pxNext->pxPrevious = pxItemToRemove->pxPrevious;
pxItemToRemove->pxPrevious->pxNext = pxItemToRemove->pxNext; pxItemToRemove->pxPrevious->pxNext = pxItemToRemove->pxNext;
@ -211,5 +355,336 @@ UBaseType_t uxListRemove( ListItem_t * const pxItemToRemove )
( pxList->uxNumberOfItems )--; ( pxList->uxNumberOfItems )--;
return pxList->uxNumberOfItems; return pxList->uxNumberOfItems;
/*@
// Reassemble DLS1 and a modified DLS2, which no longer includes x
if (end == xprev)
{
if (x == endprev)
{
//Case A
close xLIST_ITEM(end, portMAX_DELAY, _, _, _, _);
close DLS(end, end, end, end, singleton(end), singleton(portMAX_DELAY), singleton(head(owners)), l);
}
else
{
//Case B
close xLIST_ITEM(xprev, _, xnext, endprev, head(owners), l);
close DLS(end, endprev, xnext, xprev, singleton(end), singleton(portMAX_DELAY), singleton(head(owners)), l);
close xLIST_ITEM(xnext, _, _, xprev, _, l);
close DLS(xnext, xprev, end, endprev, tail(zs), tail(ws), tail(us), l);
join(end, endprev, xnext, xprev, singleton(end), singleton(portMAX_DELAY),
xnext, xprev, end, endprev, tail(zs), tail(ws));
}
}
else
{
if (x == endprev)
{
//Case C
close xLIST_ITEM(end, _, ?endnext, xprev, head(ts), l);
close xLIST_ITEM(xprev, ?xprev_val, end, _, ?xprev_owner, l);
if (endnext == xprev)
{
close DLS(xprev, end, end, xprev, singleton(xprev), singleton(xprev_val), singleton(xprev_owner), l);
close DLS(end, xprev, end, xprev, cons(end, singleton(xprev)), cons(portMAX_DELAY, singleton(xprev_val)), cons(head(ts), singleton(xprev_owner)), l);
}
else
{
close DLS(xprev, ?xprevprev, xnext, xprev, singleton(xprev), singleton(xprev_val), singleton(xprev_owner), l);
assert DLS(endnext, end, xprev, xprevprev, ?cells_endnext_to_xprevprev, ?vals_endnext_to_xprevprev, _, l);
join(endnext, end, xprev, xprevprev, cells_endnext_to_xprevprev, vals_endnext_to_xprevprev,
xprev, xprevprev, xnext, xprev, singleton(xprev), singleton(xprev_val));
close DLS(end, xprev, end, xprev, ys, vs, ts, l);
}
}
else
{
//Case D
close xLIST_ITEM(xnext, _, ?xnextnext, xprev, ?xnext_owner, l);
close DLS(xnext, xprev, end, endprev, tail(zs), tail(ws), tail(us), l);
close xLIST_ITEM(end, _, ?endnext, endprev, head(ts), l);
close xLIST_ITEM(xprev, ?xprev_val, xnext, _, ?xprev_owner, l);
if (endnext == xprev)
{
close DLS(xprev, _, xnext, xprev, singleton(xprev), singleton(xprev_val), singleton(xprev_owner), l);
close DLS(end, endprev, xnext, xprev, ys, vs, ts, l);
join(end, endprev, xnext, xprev, ys, vs,
xnext, xprev, end, endprev, tail(zs), tail(ws));
}
else
{
close DLS(xprev, ?xprevprev, xnext, xprev, singleton(xprev), singleton(xprev_val), singleton(xprev_owner), l);
assert DLS(endnext, end, xprev, xprevprev, ?cells_endnext_to_xprevprev, ?vals_endnext_to_xprevprev, _, l);
join(endnext, end, xprev, xprevprev, cells_endnext_to_xprevprev, vals_endnext_to_xprevprev,
xprev, xprevprev, xnext, xprev, singleton(xprev), singleton(xprev_val));
close DLS(end, endprev, xnext, xprev, ys, vs, ts, l);
join(end, endprev, xnext, xprev, ys, vs,
xnext, xprev, end, endprev, tail(zs), tail(ws));
}
}
}
@*/
/*@remove_remove_nth(cells, x);@*/
/*@
if (idx == x)
{
close xLIST(l, len-1, xprev, end, append(ys, tail(zs)), append(vs, tail(ws)), append(ts, tail(us)));
}
else
{
idx_remains_in_list(cells, idx, x, i);
close xLIST(l, len-1, idx, end, append(ys, tail(zs)), append(vs, tail(ws)), append(ts, tail(us)));
}
@*/
/*@close xLIST_ITEM(x, nth(i, vals), xnext, xprev, nth(i, owners), NULL);@*/
} }
#else
// Contract and proof written by Aalok Thakkar and Nathan Chong for the
// single-core setup in 2020.
/*@requires
exists<struct xLIST * >(?l) &*&
xLIST(l, ?len, ?idx, ?end, ?cells, ?vals) &*&
end != pxItemToRemove &*&
mem(pxItemToRemove, cells) == true;@*/
/*@ensures
result == len-1 &*&
xLIST_ITEM(pxItemToRemove, nth(index_of(pxItemToRemove, cells), vals), _, ?pxItemToRemovePrevious, NULL) &*&
pxItemToRemovePrevious == nth(index_of(pxItemToRemove, cells)-1, cells) &*&
xLIST(l, result, idx == pxItemToRemove ? pxItemToRemovePrevious : idx, end, remove(pxItemToRemove, cells), remove_nth(index_of(pxItemToRemove, cells), vals));@*/
{
/* For brevity we alias x to pxItemToRemove */
/*@struct xLIST_ITEM *x = pxItemToRemove;@*/
/* Start by establishing that the list must be non-empty since x != end */
/*@open xLIST(l, len, idx, end, cells, vals);@*/
/*@assert DLS(end, ?endprev, end, _, cells, vals, l);@*/
/*@assert vals == cons(portMAX_DELAY, _);@*/
/*@dls_not_empty(end, endprev, cells, x);@*/
/* We know the xLIST is a DLS: end...endprev
Split this into DLS1:end...xprev and DLS2:x...endprev */
/*@int i = index_of(x, cells);@*/
/*@split(end, endprev, end, endprev, cells, vals, x, i);@*/
/*@list<struct xLIST_ITEM *> ys = take(i, cells);@*/
/*@list<struct xLIST_ITEM *> zs = drop(i, cells);@*/
/*@list<TickType_t> vs = take(i, vals);@*/
/*@list<TickType_t> ws = drop(i, vals);@*/
/*@assert length(ys) == length(vs);@*/
/*@assert length(zs) == length(ws);@*/
/*@assert DLS(end, endprev, x, ?xprev, ys, vs, l);@*/ /*< DLS1 (ys, vs) */
/*@assert DLS(x, xprev, end, endprev, zs, ws, l);@*/ /*< DLS2 (zs, ws) */
/* Now case split to open DLS1 and DLS2 appropriately */
/*@
if (end == xprev)
{
if (x == endprev)
{
//Case A
//DLS1: extract end=prev=next
open DLS(end, endprev, x, xprev, ys, vs, l);
open xLIST_ITEM(end, portMAX_DELAY, x, endprev, l);
//DLS2: extract x
open DLS(x, xprev, end, endprev, zs, ws, l);
//Lengths
assert length(ys) == 1;
assert length(zs) == 1;
}
else
{
//Case B
//DLS1: extract end=prev
open DLS(end, endprev, x, xprev, ys, vs, l);
open xLIST_ITEM(end, portMAX_DELAY, x, endprev, l);
//DLS2: extract next and x
open DLS(x, end, end, endprev, zs, ws, l);
assert DLS(?xnext, x, end, endprev, tail(zs), tail(ws), l);
open DLS(xnext, x, end, endprev, tail(zs), tail(ws), l);
open xLIST_ITEM(xnext, _, _, x, l);
//Lengths
assert length(ys) == 1;
}
}
else
{
if (x == endprev)
{
//Case C
//DLS1: extract end=next and prev
dls_last_mem(end, endprev, x, xprev, ys);
assert mem(xprev, ys) == true;
open DLS(end, endprev, x, xprev, ys, vs, l);
open xLIST_ITEM(end, portMAX_DELAY, ?endnext, endprev, l);
if (endnext == xprev)
{
open DLS(endnext, end, x, xprev, tail(ys), tail(vs), l);
open xLIST_ITEM(xprev, _, x, _, l);
}
else
{
assert DLS(endnext, end, x, xprev, tail(ys), tail(vs), l);
int k = index_of(xprev, tail(ys));
dls_last_mem(endnext, end, x, xprev, tail(ys));
split(endnext, end, x, xprev, tail(ys), tail(vs), xprev, k);
open DLS(xprev, _, x, xprev, _, _, l);
open xLIST_ITEM(xprev, _, x, _, l);
}
//DLS2: extract x
open DLS(x, xprev, end, endprev, zs, ws, l);
//Lengths
assert length(zs) == 1;
}
else
{
//Case D
//DLS1: extract prev
dls_last_mem(end, endprev, x, xprev, ys);
int j = index_of(xprev, ys);
open DLS(end, endprev, x, xprev, ys, vs, l);
open xLIST_ITEM(end, portMAX_DELAY, ?endnext, endprev, l);
if (endnext == xprev)
{
open DLS(endnext, end, x, xprev, tail(ys), tail(vs), l);
assert tail(ys) == singleton(xprev);
open xLIST_ITEM(xprev, _, x, _, l);
}
else
{
assert DLS(endnext, end, x, xprev, tail(ys), tail(vs), l);
int k = index_of(xprev, tail(ys));
dls_last_mem(endnext, end, x, xprev, tail(ys));
split(endnext, end, x, xprev, tail(ys), tail(vs), xprev, k);
open DLS(xprev, _, x, xprev, _, _, l);
open xLIST_ITEM(xprev, _, x, _, l);
}
//DLS2: extract next and x
open DLS(x, xprev, end, endprev, zs, ws, l);
assert xLIST_ITEM(x, _, ?xnext, _, l);
open DLS(xnext, x, end, endprev, tail(zs), tail(ws), l);
open xLIST_ITEM(xnext, _, _, x, l);
}
}
@*/
/*@drop_nth_index_of(vals, i);@*/
/*@open xLIST_ITEM(x, nth(i, vals), ?xnext, xprev, l);@*/
/* The list item knows which list it is in. Obtain the list from the list
* item. */
#ifdef VERIFAST /*< const pointer declaration */
List_t * pxList = pxItemToRemove->pxContainer;
#else
List_t * const pxList = pxItemToRemove->pxContainer;
#endif
pxItemToRemove->pxNext->pxPrevious = pxItemToRemove->pxPrevious;
pxItemToRemove->pxPrevious->pxNext = pxItemToRemove->pxNext;
/* Only used during decision coverage testing. */
mtCOVERAGE_TEST_DELAY();
/* Make sure the index is left pointing to a valid item. */
if( pxList->pxIndex == pxItemToRemove )
{
pxList->pxIndex = pxItemToRemove->pxPrevious;
}
else
{
mtCOVERAGE_TEST_MARKER();
}
pxItemToRemove->pxContainer = NULL;
( pxList->uxNumberOfItems )--;
return pxList->uxNumberOfItems;
/*@
// Reassemble DLS1 and a modified DLS2, which no longer includes x
if (end == xprev)
{
if (x == endprev)
{
//Case A
close xLIST_ITEM(end, portMAX_DELAY, _, _, _);
close DLS(end, end, end, end, singleton(end), singleton(portMAX_DELAY), l);
}
else
{
//Case B
close xLIST_ITEM(xprev, _, xnext, endprev, l);
close DLS(end, endprev, xnext, xprev, singleton(end), singleton(portMAX_DELAY), l);
close xLIST_ITEM(xnext, _, _, xprev, l);
close DLS(xnext, xprev, end, endprev, tail(zs), tail(ws), l);
join(end, endprev, xnext, xprev, singleton(end), singleton(portMAX_DELAY),
xnext, xprev, end, endprev, tail(zs), tail(ws));
}
}
else
{
if (x == endprev)
{
//Case C
close xLIST_ITEM(end, _, ?endnext, xprev, l);
close xLIST_ITEM(xprev, ?xprev_val, end, _, l);
if (endnext == xprev)
{
close DLS(xprev, end, end, xprev, singleton(xprev), singleton(xprev_val), l);
close DLS(end, xprev, end, xprev, cons(end, singleton(xprev)), cons(portMAX_DELAY, singleton(xprev_val)), l);
}
else
{
close DLS(xprev, ?xprevprev, xnext, xprev, singleton(xprev), singleton(xprev_val), l);
assert DLS(endnext, end, xprev, xprevprev, ?cells_endnext_to_xprevprev, ?vals_endnext_to_xprevprev, l);
join(endnext, end, xprev, xprevprev, cells_endnext_to_xprevprev, vals_endnext_to_xprevprev,
xprev, xprevprev, xnext, xprev, singleton(xprev), singleton(xprev_val));
close DLS(end, xprev, end, xprev, ys, vs, l);
}
}
else
{
//Case D
close xLIST_ITEM(xnext, _, ?xnextnext, xprev, l);
close DLS(xnext, xprev, end, endprev, tail(zs), tail(ws), l);
close xLIST_ITEM(end, _, ?endnext, endprev, l);
close xLIST_ITEM(xprev, ?xprev_val, xnext, _, l);
if (endnext == xprev)
{
close DLS(xprev, _, xnext, xprev, singleton(xprev), singleton(xprev_val), l);
close DLS(end, endprev, xnext, xprev, ys, vs, l);
join(end, endprev, xnext, xprev, ys, vs,
xnext, xprev, end, endprev, tail(zs), tail(ws));
}
else
{
close DLS(xprev, ?xprevprev, xnext, xprev, singleton(xprev), singleton(xprev_val), l);
assert DLS(endnext, end, xprev, xprevprev, ?cells_endnext_to_xprevprev, ?vals_endnext_to_xprevprev, l);
join(endnext, end, xprev, xprevprev, cells_endnext_to_xprevprev, vals_endnext_to_xprevprev,
xprev, xprevprev, xnext, xprev, singleton(xprev), singleton(xprev_val));
close DLS(end, endprev, xnext, xprev, ys, vs, l);
join(end, endprev, xnext, xprev, ys, vs,
xnext, xprev, end, endprev, tail(zs), tail(ws));
}
}
}
@*/
/*@remove_remove_nth(cells, x);@*/
/*@
if (idx == x)
{
close xLIST(l, len-1, xprev, end, append(ys, tail(zs)), append(vs, tail(ws)));
}
else
{
idx_remains_in_list(cells, idx, x, i);
close xLIST(l, len-1, idx, end, append(ys, tail(zs)), append(vs, tail(ws)));
}
@*/
/*@close xLIST_ITEM(x, nth(i, vals), xnext, xprev, NULL);@*/
}
#endif /* VERIFAST_SINGLE_CORE */
/*-----------------------------------------------------------*/ /*-----------------------------------------------------------*/

View file

@ -31,13 +31,14 @@
//@ #include <bitops.gh> //@ #include <bitops.gh>
//@ #include "list.gh" //@ #include "list.gh"
//@ #include <listex.gh>
/* The following includes will be visible to VeriFast in the preprocessed /* The following includes will be visible to VeriFast in the preprocessed
* code. VeriFast requires includes to occur befor definitions. Hence, * code. VeriFast requires includes to occur befor definitions. Hence,
* all includes visible to VeriFast must occur before the preprocessed * all includes visible to VeriFast must occur before the preprocessed
* ones. * ones.
*/ */
//VF_include #include "FreeRTOSConfig.h" //VF_macro #include "FreeRTOSConfig.h"
//VF_macro #define NULL 0 //VF_macro #define NULL 0
#endif /* VERIFAST */ #endif /* VERIFAST */
@ -1217,8 +1218,12 @@ static void prvYieldForTask( TCB_t * pxTCB,
} }
} }
//@ close xLIST(gReadyList, gSize, gIndex, gEnd, gCells, gVals, gOwners);
if( xTaskScheduled != pdFALSE ) if( xTaskScheduled != pdFALSE )
{ {
//@ close exists(gReadyList);
/* Once a task has been selected to run on this core, /* Once a task has been selected to run on this core,
* move it to the end of the ready task list. */ * move it to the end of the ready task list. */
uxListRemove( pxTaskItem ); uxListRemove( pxTaskItem );

View file

@ -60,9 +60,6 @@ fixpoint list<t> singleton<t>(t x) {
return cons(x, nil); return cons(x, nil);
} }
@*/
#ifdef VERIFAST_TODO
lemma void note(bool b) lemma void note(bool b)
requires b; requires b;
ensures b; ensures b;
@ -630,6 +627,6 @@ lemma void combine_list_update<t>(list<t>prefix, t x, list<t>suffix, int i, list
} }
@*/ @*/
#endif /* VERIFAST_TODO */
#endif /* SCP_COMMON_H */ #endif /* SCP_COMMON_H */

View file

@ -683,7 +683,7 @@
@*/ @*/
#endif /* VERIFAST_SINGLE_CORE */ #endif /* VERIFAST_SINGLE_CORE */
#ifdef VERIFAST_TODO /*@
lemma void idx_remains_in_list<t>( lemma void idx_remains_in_list<t>(
list<t> cells, list<t> cells,
t idx, t idx,