mirror of
https://github.com/FreeRTOS/FreeRTOS-Kernel.git
synced 2025-12-14 15:45:09 -05:00
96 lines
No EOL
2.5 KiB
C
96 lines
No EOL
2.5 KiB
C
#ifndef VERIFAST_LISTS_EXTENDED_H
|
|
#define VERIFAST_LISTS_EXTENDED_H
|
|
|
|
/* This file contains lemmas that would fit `list.gh` which is part
|
|
* of VeriFast's standard library.
|
|
*/
|
|
|
|
// TODO: prove
|
|
/*@
|
|
lemma void mem_suffix_implies_mem<t>(t x, list<t> xs, int i);
|
|
requires mem(x, drop(i, xs)) == true;
|
|
ensures mem(x, xs) == true;
|
|
@*/
|
|
|
|
|
|
// TODO: prove
|
|
/*@
|
|
lemma void head_drop_n_equals_nths<t>(list<t> xs, int n)
|
|
requires n >= 0;
|
|
ensures head(drop(n, xs)) == nth(n, xs);
|
|
{
|
|
// Will prove later. For now, we only validate with an example.
|
|
|
|
list<int> _xs = cons(1, cons(2, cons(3, cons(4, cons(5, cons(6, cons(7, nil)))))));
|
|
int _n = 4;
|
|
|
|
list<int> dn = drop(_n, _xs);
|
|
int hdn = head(dn);
|
|
int nthn = nth(_n, _xs);
|
|
|
|
assert( hdn == head(drop(_n, _xs)) );
|
|
assert( nthn == nth(_n, _xs ));
|
|
assert( head(drop(_n, _xs)) == nth(_n, _xs) );
|
|
|
|
|
|
// ADMIT LEMMA, PROVE LATER
|
|
assume(false);
|
|
}
|
|
|
|
// TODO: prove
|
|
lemma void drop_index_equals_singleton_implies_last_element<t>(list<t> xs, t x)
|
|
requires drop(index_of(x, xs), xs) == cons(x, nil);
|
|
ensures index_of(x, xs) == length(xs) - 1;
|
|
{
|
|
// Will prove later. For now, we only validate with an example.
|
|
list<int> _xs = cons(1, cons(2, cons(3, cons(4, cons(5, cons(6, cons(7, nil)))))));
|
|
int _x = 7;
|
|
|
|
int i = index_of(_x, _xs);
|
|
list<int> d = drop(index_of(x, xs), _xs);
|
|
|
|
assert( index_of(_x, _xs) == length(_xs) - 1 );
|
|
|
|
// ADMIT LEMMA, PROVE LATER
|
|
assume(false);
|
|
}
|
|
|
|
// TODO: prove
|
|
lemma void drop_cons<t>(list<t> xs, int n)
|
|
requires n < length(xs);
|
|
ensures drop(n, xs) == cons(nth(n, xs), drop(n+1, xs));
|
|
{
|
|
// Will prove later. For now, we only validate with an example.
|
|
list<int> _xs = cons(1, cons(2, cons(3, cons(4, cons(5, cons(6, cons(7, nil)))))));
|
|
int _n = 3;
|
|
|
|
list<int> dn = drop(_n, _xs);
|
|
int nthn = nth(_n, _xs);
|
|
list<int> dnp1 = drop(_n + 1, _xs);
|
|
|
|
assert( drop(_n, _xs) == cons(nth(_n, _xs), drop(_n+1, _xs)) );
|
|
|
|
// ADMIT LEMMA, PROVE LATER
|
|
assume(false);
|
|
}
|
|
|
|
// TODO: prove
|
|
lemma void nth_index<t>(list<t> xs, t x)
|
|
requires mem(x, xs) == true;
|
|
ensures nth(index_of(x, xs), xs) == x;
|
|
{
|
|
// Will prove later. For now, we only validate with an example.
|
|
list<int> _xs = cons(1, cons(2, cons(3, cons(4, cons(5, cons(6, cons(7, nil)))))));
|
|
int _x = 4;
|
|
|
|
int i = index_of(_x, _xs);
|
|
int nthi = nth(index_of(_x, _xs), _xs);
|
|
|
|
assert( nth(index_of(_x, _xs), _xs) == _x );
|
|
|
|
// ADMIT LEMMA, PROVE LATER
|
|
assume(false);
|
|
}
|
|
@*/
|
|
|
|
#endif /* VERIFAST_LISTS_EXTENDED_H */ |