[修改] 增加freeRTOS

1. 版本FreeRTOSv202212.01,命名为kernel;
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2023-05-06 16:43:01 +00:00
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# FreeRTOS list proofs
The list predicates and proofs are inspired by and based on the work from
Ferreira et al. (STTT'14).
The main shape predicate is a doubly-linked list segment (DLS), as defined
by Ferreira et al. in Fig 15. A DLS is defined by two `xLIST_ITEM` struct
pointers `n` and `m` (possibly pointing to the same item) which are the start
and end of the segment. We track the item pointers and values within the DLS in
the lists `cells` and `vals`, respectively. Therefore `n` and `m` are the first
and last items of `cells`.
```
+--+ +--+
-----n-> |*n| ... |*m| -mnext->
<-nprev- | | | | <-m-----
+--+ +--+
^-----------^
DLS(n, nprev, mnext, m)
```
With base case: `n == m` (single item case)
```
+--+
-----n-> |*n| -mnext->
<-nprev- | | <-n-----
+--+
^--^
xLIST_ITEM
DLS(n, nprev, mnext, n)
```
Cons case:
```
+--+ +--+ +--+
-----n-> |*n| -o-> |*o| ... |*m| -mnext->
<-nprev- | | <-n- | | | | <-m-----
+--+ +--+ +--+
^--^ ^-----------^
xLIST_ITEM DLS(o, n, mnext, m)
^---------------------^
DLS(n, nprev, mnext, m)
```
A DLS can be made into a well-formed list by joining `n` and `m` into a cycle.
Note that unlike Ferreira et al.'s list shape predicate, we always start with
the sentinel end item to avoid a top-level case-split. So in the following
diagram the start and end of the DLS are `end` and the item-before-end
`endprev`.
```
.-----------------------------------.
| +--------+ +--------+ |
`--> |*end | ... |*endprev| ----'
.---- | | | | <---.
| +--------+ +--------+ |
`----------------------------------'
^-----------------------^
DLS(end, endprev, end, endprev)
```
## References
- Automated Verification of the FreeRTOS Scheduler in HIP/SLEEK\
João F. Ferreira, Cristian Gherghina, Guanhua He, Shengchao Qin, Wei-Ngan Chin\
https://joaoff.com/publication/2014/sttt/

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/*
* FreeRTOS V202212.01
* Copyright (C) 2020 Amazon.com, Inc. or its affiliates. All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
* https://www.FreeRTOS.org
* https://github.com/FreeRTOS
*
*/
/* *INDENT-OFF* */
#include "proof/list.h"
/* Wrap the macro in a function call so we can give a function contract */
#define listLIST_IS_EMPTY( pxList ) ( ( ( pxList )->uxNumberOfItems == ( UBaseType_t ) 0 ) ? pdTRUE : pdFALSE )
BaseType_t wrapper_listLIST_IS_EMPTY( List_t * pxList )
/*@requires xLIST(pxList, ?len, ?idx, ?end, ?cells, ?vals);@*/
/*@ensures xLIST(pxList, len, idx, end, cells, vals) &*&
result == ((len == 0) ? pdTRUE : pdFALSE); @*/
{
/*@open xLIST(pxList, len, _, _, _, _);@*/
return listLIST_IS_EMPTY( pxList );
/*@close xLIST(pxList, len, _, _, cells, vals);@*/
}
/* *INDENT-ON* */

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/*
* FreeRTOS V202212.01
* Copyright (C) 2020 Amazon.com, Inc. or its affiliates. All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
* https://www.FreeRTOS.org
* https://github.com/FreeRTOS
*
*/
/* *INDENT-OFF* */
#include "proof/list.h"
UBaseType_t uxListRemove( ListItem_t * const pxItemToRemove )
/*@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);@*/
}
ListItem_t * client_example( List_t * l )
/*@requires
xLIST(l, ?len, ?idx, ?end, ?cells, ?vals) &*&
idx != end &*&
cells == cons(end, cons(idx, ?cells_tl)) &*&
vals == cons(portMAX_DELAY, cons(42, ?vals_tl));@*/
/*@ensures
xLIST(l, len - 1, _, end, cons(end, cells_tl), cons(portMAX_DELAY, vals_tl)) &*&
xLIST_ITEM(result, 42, _, _, NULL);@*/
{
/*@open xLIST(l, len, idx, end, cells, vals);@*/
ListItem_t *index = l->pxIndex;
/*@close xLIST(l, len, idx, end, cells, vals);@*/
/*@close exists(l);@*/
uxListRemove( index );
return index;
}
void client_example2( List_t * l )
/*@requires
xLIST(l, ?len, ?idx, ?end, ?cells, ?vals) &*&
cells == cons(end, cons(?x1, cons(?x2, ?cells_tl))) &*&
idx == x2 &*&
vals == cons(portMAX_DELAY, cons(1, cons(2, ?vals_tl)));@*/
/*@ensures
xLIST(l, len-2, end, end, cons(end, cells_tl), cons(portMAX_DELAY, vals_tl)) &*&
xLIST_ITEM(_, 1, _, _, NULL) &*&
xLIST_ITEM(_, 2, _, _, NULL);@*/
{
/*@xLIST_distinct_cells(l);@*/
/*@open xLIST(l, len, idx, end, cells, vals);@*/
ListItem_t *index = l->pxIndex;
/*@close xLIST(l, len, idx, end, cells, vals);@*/
/*@close exists(l);@*/
uxListRemove( index );
/*@open xLIST(l, len-1, x1, end, cons(end, cons(x1, cells_tl)), cons(portMAX_DELAY, cons(1, vals_tl)));@*/
index = l->pxIndex;
/*@close xLIST(l, len-1, x1, end, cons(end, cons(x1, cells_tl)), cons(portMAX_DELAY, cons(1, vals_tl)));@*/
/*@close exists(l);@*/
uxListRemove( index );
}
/* *INDENT-ON* */

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/*
* FreeRTOS V202212.01
* Copyright (C) 2020 Amazon.com, Inc. or its affiliates. All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
* https://www.FreeRTOS.org
* https://github.com/FreeRTOS
*
*/
/* *INDENT-OFF* */
#include "proof/list.h"
/*@
predicate xLIST_uninitialised(struct xLIST *l) =
l->uxNumberOfItems |-> _ &*&
l->pxIndex |-> _ &*&
l->xListEnd.xItemValue |-> _ &*&
l->xListEnd.pxNext |-> _ &*&
l->xListEnd.pxPrevious |-> _ &*&
l->xListEnd.pvOwner |-> _ &*&
l->xListEnd.pxContainer |-> _ &*&
struct_xLIST_ITEM_padding(&l->xListEnd);
@*/
void vListInitialise( List_t * const pxList )
/*@requires xLIST_uninitialised(pxList);@*/
/*@ensures xLIST(pxList, 0, ?end, end, singleton(end), singleton(portMAX_DELAY));@*/
{
/*@open xLIST_uninitialised(pxList);@*/
/* The list structure contains a list item which is used to mark the
* end of the list. To initialise the list the list end is inserted
* as the only list entry. */
pxList->pxIndex = ( ListItem_t * ) &( pxList->xListEnd ); /*lint !e826 !e740 !e9087 The mini list structure is used as the list end to save RAM. This is checked and valid. */
listSET_FIRST_LIST_ITEM_INTEGRITY_CHECK_VALUE( &( pxList->xListEnd ) );
/* The list end value is the highest possible value in the list to
* ensure it remains at the end of the list. */
pxList->xListEnd.xItemValue = portMAX_DELAY;
/* The list end next and previous pointers point to itself so we know
* when the list is empty. */
pxList->xListEnd.pxNext = ( ListItem_t * ) &( pxList->xListEnd ); /*lint !e826 !e740 !e9087 The mini list structure is used as the list end to save RAM. This is checked and valid. */
pxList->xListEnd.pxPrevious = ( ListItem_t * ) &( pxList->xListEnd ); /*lint !e826 !e740 !e9087 The mini list structure is used as the list end to save RAM. This is checked and valid. */
/* Initialize the remaining fields of xListEnd when it is a proper ListItem_t */
#if ( configUSE_MINI_LIST_ITEM == 0 )
{
pxList->xListEnd.pvOwner = NULL;
pxList->xListEnd.pxContainer = NULL;
listSET_SECOND_LIST_ITEM_INTEGRITY_CHECK_VALUE( &( pxList->xListEnd ) );
}
#endif
pxList->uxNumberOfItems = ( UBaseType_t ) 0U;
/* Write known values into the list if
* configUSE_LIST_DATA_INTEGRITY_CHECK_BYTES is set to 1. */
listSET_LIST_INTEGRITY_CHECK_1_VALUE( pxList );
listSET_LIST_INTEGRITY_CHECK_2_VALUE( pxList );
#ifdef VERIFAST /*< ***change MiniList_t to ListItem_t*** */
pxList->xListEnd.pxContainer = pxList;
#endif
/*@ListItem_t *end = &(pxList->xListEnd);@*/
/*@close xLIST_ITEM(end, portMAX_DELAY, _, _, pxList);@*/
/*@close DLS(end, end, end, end, singleton(end), singleton(portMAX_DELAY), pxList);@*/
/*@close xLIST(pxList, 0, end, end, singleton(end), singleton(portMAX_DELAY));@*/
}
/* *INDENT-ON* */

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/*
* FreeRTOS V202212.01
* Copyright (C) 2020 Amazon.com, Inc. or its affiliates. All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
* https://www.FreeRTOS.org
* https://github.com/FreeRTOS
*
*/
/* *INDENT-OFF* */
#include "proof/list.h"
void vListInitialiseItem( ListItem_t * const pxItem )
/*@requires xLIST_ITEM(pxItem, _, _, _, _);@*/
/*@ensures xLIST_ITEM(pxItem, _, _, _, NULL);@*/
{
/* Make sure the list item is not recorded as being on a list. */
pxItem->pxContainer = NULL;
/* Write known values into the list item if
* configUSE_LIST_DATA_INTEGRITY_CHECK_BYTES is set to 1. */
listSET_FIRST_LIST_ITEM_INTEGRITY_CHECK_VALUE( pxItem );
listSET_SECOND_LIST_ITEM_INTEGRITY_CHECK_VALUE( pxItem );
/*@close xLIST_ITEM(pxItem, _, _, _, NULL);@*/
}
/* *INDENT-ON* */

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/*
* FreeRTOS V202212.01
* Copyright (C) 2020 Amazon.com, Inc. or its affiliates. All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
* https://www.FreeRTOS.org
* https://github.com/FreeRTOS
*
*/
/* *INDENT-OFF* */
#include "proof/list.h"
ListItem_t * choose(List_t * list);
/*@ requires DLS(&(list->xListEnd), ?endprev, &(list->xListEnd), endprev, ?cells, ?vals, ?container);@*/
/*@ ensures DLS(&(list->xListEnd), endprev, &(list->xListEnd), endprev, cells, vals, container) &*&
mem(result, cells) == true;@*/
void vListInsert( List_t * const pxList,
ListItem_t * const pxNewListItem )
/*@requires xLIST(pxList, ?len, ?idx, ?end, ?cells, ?vals) &*&
xLIST_ITEM(pxNewListItem, ?val, _, _, _);@*/
/*@ensures xLIST(pxList, len+1, idx, end, ?new_cells, ?new_vals) &*&
remove(pxNewListItem, new_cells) == cells
;@*/
{
/*@xLIST_star_item(pxList, pxNewListItem);@*/
/*@open xLIST_ITEM(pxNewListItem, _, _, _, _);@*/
/*@open xLIST(pxList, len, idx, end, cells, vals);@*/
/*@assert DLS(end, ?endprev, end, endprev, cells, vals, pxList);@*/
ListItem_t * pxIterator;
const TickType_t xValueOfInsertion = pxNewListItem->xItemValue;
/* Only effective when configASSERT() is also defined, these tests may catch
* the list data structures being overwritten in memory. They will not catch
* data errors caused by incorrect configuration or use of FreeRTOS. */
listTEST_LIST_INTEGRITY( pxList );
listTEST_LIST_ITEM_INTEGRITY( pxNewListItem );
/* Insert the new list item into the list, sorted in xItemValue order.
*
* If the list already contains a list item with the same item value then the
* new list item should be placed after it. This ensures that TCBs which are
* stored in ready lists (all of which have the same xItemValue value) get a
* share of the CPU. However, if the xItemValue is the same as the back marker
* the iteration loop below will not end. Therefore the value is checked
* first, and the algorithm slightly modified if necessary. */
if( xValueOfInsertion == portMAX_DELAY )
{
/*@open DLS(end, endprev, end, endprev, cells, vals, pxList);@*/
/*@open xLIST_ITEM(end, portMAX_DELAY, ?endnext, endprev, pxList);@*/
/*@
if (end != endprev)
{
assert DLS(endnext, end, end, endprev, tail(cells), tail(vals), pxList);
if (endnext == endprev)
{
// done
}
else
{
dls_last_mem(endnext, end, end, endprev, tail(cells));
split(endnext, end, end, endprev, tail(cells), tail(vals), endprev, index_of(endprev, tail(cells)));
}
open DLS(endprev, _, _, _, _, _, _);
open xLIST_ITEM(endprev, _, _, _, _);
}
@*/
pxIterator = pxList->xListEnd.pxPrevious;
}
else
{
/* *** NOTE ***********************************************************
* If you find your application is crashing here then likely causes are
* listed below. In addition see https://www.FreeRTOS.org/FAQHelp.html for
* more tips, and ensure configASSERT() is defined!
* https://www.FreeRTOS.org/a00110.html#configASSERT
*
* 1) Stack overflow -
* see https://www.FreeRTOS.org/Stacks-and-stack-overflow-checking.html
* 2) Incorrect interrupt priority assignment, especially on Cortex-M
* parts where numerically high priority values denote low actual
* interrupt priorities, which can seem counter intuitive. See
* https://www.FreeRTOS.org/RTOS-Cortex-M3-M4.html and the definition
* of configMAX_SYSCALL_INTERRUPT_PRIORITY on
* https://www.FreeRTOS.org/a00110.html
* 3) Calling an API function from within a critical section or when
* the scheduler is suspended, or calling an API function that does
* not end in "FromISR" from an interrupt.
* 4) Using a queue or semaphore before it has been initialised or
* before the scheduler has been started (are interrupts firing
* before vTaskStartScheduler() has been called?).
* 5) If the FreeRTOS port supports interrupt nesting then ensure that
* the priority of the tick interrupt is at or below
* configMAX_SYSCALL_INTERRUPT_PRIORITY.
**********************************************************************/
#ifdef VERIFAST /*< ***over-approximate list insert loop*** */
pxIterator = choose(pxList);
#else
for( pxIterator = ( ListItem_t * ) &( pxList->xListEnd ); pxIterator->pxNext->xItemValue <= xValueOfInsertion; pxIterator = pxIterator->pxNext ) /*lint !e826 !e740 !e9087 The mini list structure is used as the list end to save RAM. This is checked and valid. *//*lint !e440 The iterator moves to a different value, not xValueOfInsertion. */
{
/* There is nothing to do here, just iterating to the wanted
* insertion position. */
}
#endif
/*@int i = index_of(pxIterator, cells);@*/
/*@
if (pxIterator == end)
{
open DLS(end, endprev, end, endprev, cells, vals, pxList);
open xLIST_ITEM(end, portMAX_DELAY, ?endnext, endprev, pxList);
if (end != endprev)
{
assert DLS(endnext, end, end, endprev, tail(cells), tail(vals), pxList);
open DLS(endnext, _, _, _, _, _, _);
open xLIST_ITEM(endnext, _, _, _, _);
}
}
else
{
assert DLS(end, endprev, end, endprev, cells, vals, pxList);
dls_first_mem(end, endprev, end, endprev, cells);
assert pxIterator != end;
assert index_of(end, cells) == 0;
split(end, endprev, end, endprev, cells, vals, pxIterator, i);
assert DLS(end, endprev, pxIterator, ?iterprev, take(i, cells), take(i, vals), pxList);
assert DLS(pxIterator, iterprev, end, endprev, drop(i, cells), drop(i, vals), pxList);
open DLS(pxIterator, iterprev, end, endprev, drop(i, cells), drop(i, vals), pxList);
open xLIST_ITEM(pxIterator, _, ?iternext, iterprev, pxList);
if (pxIterator == endprev)
{
open DLS(end, endprev, pxIterator, iterprev, take(i, cells), take(i, vals), pxList);
take_take(1, i, vals);
assert xLIST_ITEM(end, portMAX_DELAY, _, _, _);
open xLIST_ITEM(iternext, _, _, pxIterator, _);
}
else
{
open DLS(iternext, pxIterator, end, endprev, _, _, _);
open xLIST_ITEM(iternext, _, _, pxIterator, _);
}
}@*/
}
pxNewListItem->pxNext = pxIterator->pxNext;
pxNewListItem->pxNext->pxPrevious = pxNewListItem;
pxNewListItem->pxPrevious = pxIterator;
pxIterator->pxNext = pxNewListItem;
/* Remember which list the item is in. This allows fast removal of the
* item later. */
pxNewListItem->pxContainer = pxList;
( pxList->uxNumberOfItems )++;
/*@close xLIST_ITEM(pxNewListItem, val, ?iternext, pxIterator, pxList);@*/
/*@close xLIST_ITEM(pxIterator, ?iterval, pxNewListItem, ?iterprev, pxList);@*/
/*@
if( xValueOfInsertion == portMAX_DELAY )
{
assert iternext == end;
assert pxIterator == endprev;
if (end == endprev)
{
close DLS(end, pxNewListItem, pxNewListItem, end, cells, vals, pxList);
close DLS(pxNewListItem, end, end, pxNewListItem, singleton(pxNewListItem), singleton(val), pxList);
join(end, pxNewListItem, pxNewListItem, end, cells, vals,
pxNewListItem, end, end, pxNewListItem, singleton(pxNewListItem), singleton(val));
close xLIST(pxList, len+1, idx, end, append(cells, singleton(pxNewListItem)), append(vals, singleton(val)));
}
else
{
close xLIST_ITEM(end, portMAX_DELAY, ?endnext, pxNewListItem, pxList);
close DLS(pxNewListItem, endprev, end, pxNewListItem, singleton(pxNewListItem), singleton(val), pxList);
if (endnext == endprev)
{
assert xLIST_ITEM(endnext, ?endnextval, pxNewListItem, end, pxList);
close DLS(end, pxNewListItem, endnext, end, singleton(end), singleton(portMAX_DELAY), pxList);
close DLS(endnext, end, pxNewListItem, endnext, singleton(endnext), singleton(endnextval), pxList);
join(end, pxNewListItem, endnext, end, singleton(end), singleton(portMAX_DELAY),
endnext, end, pxNewListItem, endnext, singleton(endnext), singleton(endnextval));
assert DLS(end, pxNewListItem, pxNewListItem, endnext, cells, vals, pxList);
}
else
{
assert DLS(endnext, end, endprev, ?endprevprev, ?cells_endnext_to_endprevprev, ?vals_endnext_to_endprevprev, pxList);
assert cells_endnext_to_endprevprev == take(index_of(endprev, tail(cells)), tail(cells));
assert index_of(endprev, tail(cells)) == length(tail(cells)) - 1;
assert cells_endnext_to_endprevprev == take(length(tail(cells)) - 1, tail(cells));
assert xLIST_ITEM(endprev, ?endprevval, pxNewListItem, endprevprev, pxList);
close DLS(endprev, endprevprev, pxNewListItem, endprev, singleton(endprev), singleton(endprevval), pxList);
dls_last_mem(endnext, end, endprev, endprevprev, cells_endnext_to_endprevprev);
dls_star_item(endnext, endprevprev, end);
close DLS(end, pxNewListItem, endprev, endprevprev, cons(end, cells_endnext_to_endprevprev), cons(portMAX_DELAY, vals_endnext_to_endprevprev), pxList);
join(end, pxNewListItem, endprev, endprevprev, cons(end, cells_endnext_to_endprevprev), cons(portMAX_DELAY, vals_endnext_to_endprevprev),
endprev, endprevprev, pxNewListItem, endprev, singleton(endprev), singleton(endprevval));
assert DLS(end, pxNewListItem, pxNewListItem, endprev, cells, vals, pxList);
}
join(end, pxNewListItem, pxNewListItem, endprev, cells, vals,
pxNewListItem, endprev, end, pxNewListItem, singleton(pxNewListItem), singleton(val));
remove_append(pxNewListItem, cells, singleton(pxNewListItem));
close xLIST(pxList, len+1, idx, end, append(cells, singleton(pxNewListItem)), append(vals, singleton(val)));
}
}
else
{
if (pxIterator == end)
{
if (iternext == end)
{
close DLS(end, pxNewListItem, pxNewListItem, end, cells, vals, pxList);
close DLS(pxNewListItem, pxIterator, end, pxNewListItem, singleton(pxNewListItem), singleton(val), pxList);
join(end, pxNewListItem, pxNewListItem, end, cells, vals,
pxNewListItem, pxIterator, end, pxNewListItem, singleton(pxNewListItem), singleton(val));
close xLIST(pxList, len+1, idx, end, append(cells, singleton(pxNewListItem)), append(vals, singleton(val)));
}
else
{
close xLIST_ITEM(iternext, ?iternextval, _, pxNewListItem, pxList);
if (iternext == endprev)
{
close DLS(iternext, pxNewListItem, end, endprev, singleton(iternext), singleton(iternextval), pxList);
dls_last_mem(iternext, pxNewListItem, end, endprev, singleton(iternext));
}
else
{
assert DLS(?iternextnext, iternext, end, endprev, ?cells_iternextnext_to_endprev, ?vals_iternextnext_to_endprev, pxList);
close DLS(iternext, pxNewListItem, end, endprev, cons(iternext, cells_iternextnext_to_endprev), cons(iternextval, vals_iternextnext_to_endprev), pxList);
dls_last_mem(iternext, pxNewListItem, end, endprev, cons(iternext, cells_iternextnext_to_endprev));
}
close DLS(end, endprev, pxNewListItem, end, singleton(end), singleton(portMAX_DELAY), pxList);
assert DLS(iternext, pxNewListItem, end, endprev, ?cells_iternext_to_endprev, ?vals_iternext_to_endprev, pxList);
dls_star_item(iternext, endprev, pxNewListItem);
close DLS(pxNewListItem, pxIterator, end, endprev, cons(pxNewListItem, cells_iternext_to_endprev), cons(val, vals_iternext_to_endprev), pxList);
join(end, endprev, pxNewListItem, end, singleton(end), singleton(portMAX_DELAY),
pxNewListItem, pxIterator, end, endprev, cons(pxNewListItem, cells_iternext_to_endprev), cons(val, vals_iternext_to_endprev));
close xLIST(pxList, len+1, idx, end, cons(end, cons(pxNewListItem, cells_iternext_to_endprev)), cons(portMAX_DELAY, cons(val, vals_iternext_to_endprev)));
}
}
else
{
close xLIST_ITEM(iternext, ?iternextval, _, pxNewListItem, pxList);
if (pxIterator == endprev)
{
if (iterprev == end)
{
close DLS(end, pxNewListItem, pxIterator, end, singleton(end), singleton(portMAX_DELAY), pxList);
}
else
{
assert DLS(_, iternext, pxIterator, iterprev, ?cells1, ?vals1, _);
close DLS(end, pxNewListItem, pxIterator, iterprev, cons(end, cells1), cons(portMAX_DELAY, vals1), pxList);
}
int i = index_of(pxIterator, cells);
assert DLS(end, pxNewListItem, pxIterator, iterprev, take(i, cells), take(i, vals), pxList);
close DLS(pxIterator, iterprev, pxNewListItem, pxIterator, drop(i, cells), drop(i, vals), pxList);
close DLS(pxNewListItem, pxIterator, end, pxNewListItem, singleton(pxNewListItem), singleton(val), pxList);
join(end, pxNewListItem, pxIterator, iterprev, take(i, cells), take(i, vals),
pxIterator, iterprev, pxNewListItem, pxIterator, drop(i, cells), drop(i, vals));
join(end, pxNewListItem, pxNewListItem, pxIterator, cells, vals,
pxNewListItem, pxIterator, end, pxNewListItem, singleton(pxNewListItem), singleton(val));
close xLIST(pxList, len+1, idx, end, append(cells, singleton(pxNewListItem)), append(vals, singleton(val)));
remove_append(pxNewListItem, cells, singleton(pxNewListItem));
}
else
{
int i = index_of(pxIterator, cells);
if (iternext == endprev)
{
close DLS(iternext, pxNewListItem, end, endprev, singleton(iternext), singleton(iternextval), pxList);
}
else
{
assert DLS(_, iternext, end, endprev, ?cells0, ?vals0, pxList);
dls_star_item(end, iterprev, iternext);
close DLS(iternext, pxNewListItem, end, endprev, tail(drop(i, cells)), tail(drop(i, vals)), pxList);
}
drop_drop(1, i, cells);
drop_drop(1, i, vals);
assert DLS(iternext, pxNewListItem, end, endprev, drop(i+1, cells), drop(i+1, vals), pxList);
assert DLS(end, endprev, pxIterator, iterprev, take(i, cells), take(i, vals), pxList);
dls_star_item(iternext, endprev, pxNewListItem);
dls_last_mem(iternext, pxNewListItem, end, endprev, drop(i+1, cells));
close DLS(pxNewListItem, pxIterator, end, endprev, cons(pxNewListItem, drop(i+1, cells)), cons(val, drop(i+1, vals)), pxList);
close DLS(pxIterator, iterprev, end, endprev, cons(pxIterator, cons(pxNewListItem, drop(i+1, cells))), cons(iterval, cons(val, drop(i+1, vals))), pxList);
join(end, endprev, pxIterator, iterprev, take(i, cells), take(i, vals),
pxIterator, iterprev, end, endprev, cons(pxIterator, cons(pxNewListItem, drop(i+1, cells))), cons(iterval, cons(val, drop(i+1, vals))));
list<struct xLIST_ITEM * >new_cells = append(take(i, cells), cons(pxIterator, cons(pxNewListItem, drop(i+1, cells))));
list<TickType_t >new_vals = append(take(i, vals), cons(iterval, cons(val, drop(i+1, vals))));
head_append(take(i, cells), cons(pxIterator, cons(pxNewListItem, drop(i+1, cells))));
take_head(take(i, cells));
take_take(1, i, cells);
assert( end == head(new_cells) );
head_append(take(i, vals), cons(iterval, cons(val, drop(i+1, vals))));
take_head(take(i, vals));
take_take(1, i, vals);
assert( portMAX_DELAY == head(new_vals) );
append_take_drop_n(cells, index_of(pxIterator, cells));
close xLIST(pxList, len+1, idx, end, append(take(i, cells), cons(pxIterator, cons(pxNewListItem, drop(i+1, cells)))), append(take(i, vals), cons(iterval, cons(val, drop(i+1, vals)))));
mem_take_false(pxNewListItem, i, cells);
remove_append(pxNewListItem, take(i, cells), cons(pxIterator, cons(pxNewListItem, drop(i+1, cells))));
}
}
}@*/
}
/* *INDENT-ON* */

View File

@ -0,0 +1,242 @@
/*
* FreeRTOS V202212.01
* Copyright (C) 2020 Amazon.com, Inc. or its affiliates. All Rights Reserved.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy of
* this software and associated documentation files (the "Software"), to deal in
* the Software without restriction, including without limitation the rights to
* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
* the Software, and to permit persons to whom the Software is furnished to do so,
* subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in all
* copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
* https://www.FreeRTOS.org
* https://github.com/FreeRTOS
*
*/
/* *INDENT-OFF* */
#include "proof/list.h"
void vListInsertEnd( List_t * const pxList,
ListItem_t * const pxNewListItem )
/*@requires xLIST(pxList, ?len, ?idx, ?end, ?cells, ?vals) &*&
xLIST_ITEM(pxNewListItem, ?val, _, _, _);@*/
/*@ensures xLIST(pxList, len+1, idx, end, ?new_cells, ?new_vals) &*&
idx == end
? (new_cells == append(cells, singleton(pxNewListItem)) &*&
new_vals == append(vals, singleton(val)))
: (new_cells == append(take(index_of(idx, cells), cells), append(singleton(pxNewListItem), drop(index_of(idx, cells), cells))) &*&
new_vals == append(take(index_of(idx, cells), vals), append(singleton(val), drop(index_of(idx, cells), vals))));@*/
{
/*@xLIST_star_item(pxList, pxNewListItem);@*/
/*@assert mem(pxNewListItem, cells) == false;@*/
/*@open xLIST(pxList, len, idx, end, cells, vals);@*/
#ifdef VERIFAST /*< const pointer declaration */
ListItem_t * pxIndex = pxList->pxIndex;
#else
ListItem_t * const pxIndex = pxList->pxIndex;
/* Only effective when configASSERT() is also defined, these tests may catch
* the list data structures being overwritten in memory. They will not catch
* data errors caused by incorrect configuration or use of FreeRTOS. */
listTEST_LIST_INTEGRITY( pxList );
listTEST_LIST_ITEM_INTEGRITY( pxNewListItem );
#endif
/*@open xLIST_ITEM(pxNewListItem, _, _, _, _);@*/
/*@assert DLS(end, ?endprev, end, _, cells, vals, pxList);@*/
/*@dls_first_mem(end, endprev, end, endprev, cells);@*/
/*@dls_last_mem(end, endprev, end, endprev, cells);@*/
/*@
if (end == idx)
{
open DLS(end, endprev, end, endprev, cells, vals, pxList);
open xLIST_ITEM(end, portMAX_DELAY, ?endnext, endprev, pxList);
if (end == endprev)
{
// Case A (singleton): idx==end==endprev
}
else
{
assert DLS(endnext, end, end, endprev, tail(cells), tail(vals), pxList);
if (endnext == endprev)
{
// Case B (two): idx==end and endnext==endprev
open DLS(endnext, end, end, endnext, _, _, _);
open xLIST_ITEM(endnext, _, _, _, _);
}
else
{
// Case C: idx==end and DLS:endnext...endprev
split(endnext, end, end, endprev, tail(cells), tail(vals), endprev, index_of(endprev, tail(cells)));
open DLS(endprev, _, _, _, _, _, _);
open xLIST_ITEM(endprev, _, _, _, _);
}
}
}
else
{
int i = index_of(idx, cells);
split(end, endprev, end, endprev, cells, vals, idx, i);
assert DLS(end, endprev, idx, ?idxprev, take(i, cells), take(i, vals), pxList);
assert DLS(idx, idxprev, end, endprev, drop(i, cells), drop(i, vals), pxList);
open DLS(idx, idxprev, end, endprev, _, _, _);
open xLIST_ITEM(idx, _, _, _, _);
if (end == idxprev)
{
// Case D: end==idxprev and DLS:idx...endprev
take_take(1, i, vals);
take_head(vals);
open DLS(end, endprev, idx, idxprev, take(i, cells), take(i, vals), pxList);
open xLIST_ITEM(end, portMAX_DELAY, _, _, _);
assert length(take(i, cells)) == 1;
}
else
{
// Case E: DLS:end...idxprev and DLS:idx...endprev
dls_last_mem(end, endprev, idx, idxprev, take(i, cells));
split(end, endprev, idx, idxprev, take(i, cells), take(i, vals), idxprev, index_of(idxprev, take(i, cells)));
open DLS(idxprev, _, _, idxprev, _, _, _);
length_take(i, cells);
drop_take_singleton(i, vals);
open xLIST_ITEM(idxprev, nth(i-1, vals), _, _, _);
}
}
@*/
/* Insert a new list item into pxList, but rather than sort the list,
* makes the new list item the last item to be removed by a call to
* listGET_OWNER_OF_NEXT_ENTRY(). */
pxNewListItem->pxNext = pxIndex;
pxNewListItem->pxPrevious = pxIndex->pxPrevious;
/* Only used during decision coverage testing. */
mtCOVERAGE_TEST_DELAY();
pxIndex->pxPrevious->pxNext = pxNewListItem;
pxIndex->pxPrevious = pxNewListItem;
/* Remember which list the item is in. */
pxNewListItem->pxContainer = pxList;
( pxList->uxNumberOfItems )++;
/*@
if (end == idx)
{
close xLIST_ITEM(pxNewListItem, val, end, endprev, pxList);
close DLS(pxNewListItem, endprev, end, pxNewListItem, singleton(pxNewListItem), singleton(val), pxList);
close xLIST_ITEM(end, portMAX_DELAY, ?endnext, pxNewListItem, pxList);
if (end == endprev)
{
// Case A (singleton): idx==end==endprev
close DLS(end, pxNewListItem, endnext, end, cells, vals, pxList);
join(end, pxNewListItem, endnext, end, cells, vals,
pxNewListItem, endprev, end, pxNewListItem, singleton(pxNewListItem), singleton(val));
close xLIST(pxList, len+1, idx, end, append(cells, singleton(pxNewListItem)), append(vals, singleton(val)));
}
else
{
close xLIST_ITEM(endprev, ?endprevval, pxNewListItem, ?endprevprev, _);
if (endnext == endprev)
{
// Case B (two): idx==end and endnext==endprev
close DLS(endprev, end, pxNewListItem, endprev, singleton(endprev), singleton(endprevval), pxList);
close DLS(end, pxNewListItem, pxNewListItem, endprev, cells, vals, pxList);
join(end, pxNewListItem, pxNewListItem, endprev, cells, vals,
pxNewListItem, endprev, end, pxNewListItem, singleton(pxNewListItem), singleton(val));
close xLIST(pxList, len+1, idx, end, append(cells, singleton(pxNewListItem)), append(vals, singleton(val)));
}
else
{
// Case C: idx==end and DLS:endnext...endprev
close DLS(endprev, endprevprev, pxNewListItem, endprev, singleton(endprev), singleton(endprevval), pxList);
assert DLS(endnext, end, endprev, endprevprev, ?cells_endnext_to_endprevprev, ?vals_endnext_to_endprevprev, pxList);
join(endnext, end, endprev, endprevprev, cells_endnext_to_endprevprev, vals_endnext_to_endprevprev,
endprev, endprevprev, pxNewListItem, endprev, singleton(endprev), singleton(endprevval));
close DLS(end, pxNewListItem, pxNewListItem, endprev, cells, vals, pxList);
join(end, pxNewListItem, pxNewListItem, endprev, cells, vals,
pxNewListItem, endprev, end, pxNewListItem, singleton(pxNewListItem), singleton(val));
close xLIST(pxList, len+1, idx, end, append(cells, singleton(pxNewListItem)), append(vals, singleton(val)));
}
}
}
else
{
// Case D: end==idxprev and DLS:idx...endprev
// Case E: DLS:end...idxprev and DLS:idx...endprev
int i = index_of(idx, cells);
close xLIST_ITEM(pxNewListItem, val, idx, ?idxprev, pxList);
close xLIST_ITEM(idx, ?idxval, ?idxnext, pxNewListItem, pxList);
nth_drop2(vals, i);
assert idxval == nth(i, vals);
close xLIST_ITEM(idxprev, ?idxprevval, pxNewListItem, ?idxprevprev, pxList);
if (end == idxprev)
{
close DLS(end, endprev, pxNewListItem, end, singleton(end), singleton(portMAX_DELAY), pxList);
}
else
{
length_take(i, cells);
take_take(i-1, i, vals);
take_singleton(i-1, vals);
take_singleton(i, vals);
assert DLS(end, endprev, idxprev, idxprevprev, ?cells_end_to_idxprevprev, take(i-1, vals), pxList);
close DLS(idxprev, idxprevprev, pxNewListItem, idxprev, singleton(idxprev), singleton(idxprevval), pxList);
join(end, endprev, idxprev, idxprevprev, cells_end_to_idxprevprev, take(i-1, vals),
idxprev, idxprevprev, pxNewListItem, idxprev, singleton(idxprev), singleton(idxprevval));
}
if (idx == endprev)
{
close DLS(idx, pxNewListItem, end, idx, singleton(idx), singleton(idxval), pxList);
}
else
{
assert DLS(end, endprev, pxNewListItem, idxprev, ?cells_end_to_idxprev, ?vals_end_to_idxprev, pxList);
close DLS(idx, pxNewListItem, end, endprev, drop(i, cells), drop(i, vals), pxList);
}
assert DLS(end, endprev, pxNewListItem, idxprev, take(i, cells), take(i, vals), pxList);
assert DLS(idx, pxNewListItem, end, endprev, drop(i, cells), drop(i, vals), pxList);
assert xLIST_ITEM(pxNewListItem, val, idx, idxprev, pxList);
dls_star_item(idx, endprev, pxNewListItem);
close DLS(pxNewListItem, idxprev, end, endprev, cons(pxNewListItem, drop(i, cells)), cons(val, drop(i, vals)), pxList);
join(end, endprev, pxNewListItem, idxprev, take(i, cells), take(i, vals),
pxNewListItem, idxprev, end, endprev, cons(pxNewListItem, drop(i, cells)), cons(val, drop(i, vals)));
assert DLS(end, endprev, end, endprev, ?cells_new, ?vals_new, pxList);
assert cells_new == append(take(i, cells), append(singleton(pxNewListItem), drop(i, cells)));
assert vals_new == append(take(i, vals) , append(singleton(val), drop(i, vals)));
head_append(take(i, cells), append(singleton(pxNewListItem), drop(i, cells)));
take_take(1, i, cells);
head_append(take(i, vals), append(singleton(val), drop(i, vals)));
take_take(1, i, vals);
close xLIST(pxList, len+1, idx, end, cells_new, vals_new);
}
@*/
}
void client_example1( List_t * const l, ListItem_t * const pxNewListItem )
/*@requires
xLIST(l, ?len, ?idx, ?end, ?cells, ?vals) &*&
xLIST_ITEM(pxNewListItem, ?val, _, _, _) &*&
idx == end;@*/
/*@ensures
xLIST(l, len + 1, idx, end, _, append(vals, singleton(val)));@*/
{
vListInsertEnd(l, pxNewListItem);
}
/* *INDENT-ON* */