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Going forward, but gently...

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This commit is contained in:
Yorick Barbanneau 2023-05-05 01:48:36 +02:00
parent 4a30965654
commit 97a81f159a
4 changed files with 36 additions and 8 deletions
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10
content/conception_formelle/99-DM_framac/code/abs.h
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@ -6,16 +6,20 @@
/*@ logic integer abs(integer n) = 0<n?n:-n;*/
/*@
requires INT_MIN <= n;
requires INT_MIN < n < INT_MAX;
terminates \true;
ensures \result == abs(n);
assigns \nothing;
*/
int abs(int n);
/*@
requires INT_MIN <= n * (int)((int)n % 2 + ((int)n +1)%2) <= INT_MAX;
requires INT_MIN < n < INT_MAX;
requires INT_MIN <= n * (int)((int)n % 2 + ((int)n + 1)%2) <= INT_MAX;
terminates \true;
ensures \result == abs(n);*/
ensures \result == abs(n);
assigns \nothing;
*/
int abs2(int n);
#endif

12
content/conception_formelle/99-DM_framac/code/max_dist.c
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@ -5,6 +5,16 @@ int max_dist(int *tab, unsigned int n)
int min = tab[0];
int max = tab[0];
unsigned int i = 1;
/*@
loop assigns i, max, min;
loop invariant I1: \at(i, LoopEntry) <= i <= n;
loop invariant I2: min <= max;
loop invariant I3: \forall integer j; (\at(i, LoopEntry) <= j < i ==> max >= tab[j] >= min);
loop invariant I4: \exists integer j; ( 0 < j < i ==> max == tab[j]);
loop invariant I5: \exists integer j; ( 0 < j < i ==> min == tab[j]);
loop variant n - i;
*/
while (i < n)
{
if (tab[i] < min)
@ -14,4 +24,4 @@ int max_dist(int *tab, unsigned int n)
i++;
}
return max - min;
}
}

8
content/conception_formelle/99-DM_framac/code/max_dist.h
View file

@ -1,6 +1,10 @@
#include <limits.h>
#include "abs.h"
/*@ ensures \forall integer a,b; 0 <= a < b < n ==> \result >= abs(tab[a]-tab[b]);
/*@
requires 0 < n < UINT_MAX;
requires \valid_read(tab+(0..n-1));
terminates \true;
ensures \forall integer a,b; 0 <= a < b < n ==> \result >= abs(tab[a]-tab[b]);
*/
int max_dist(int *tab, unsigned int n);
int max_dist(int *tab, unsigned int n);