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xiaoh105
2025-06-07 15:23:11 +08:00
parent e7bc194ec7
commit 1873d949ce
8 changed files with 448 additions and 175 deletions
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126
projects/int_array.strategies Normal file
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@ -0,0 +1,126 @@
//test curent rules
//max rule id:30
#include "int_array_def.h"
#include "verification_list.h"
#include "verification_stdlib.h"
id : 1
priority : core(1)
left : store_int_array(?p, ?n, ?l) at 0
right : data_at(?p + (?i * sizeof(I32)), I32, ?v) at 1
check : infer(0 <= i);
infer(i < n);
action : right_erase(1);
left_erase(0);
left_add(store_int_array_missing_i_rec(p, i, 0, n, l));
right_add(v == l[i]);
id : 2
priority : post(1)
left : store_int_array_missing_i_rec(?p, ?i, 0, ?n, ?l) at 0
data_at(p + i * sizeof(I32), I32, l[i]) at 1
check : infer(0 <= i);
infer(i < n);
action : left_erase(1);
left_erase(0);
left_add(store_int_array(p, n, l));
id : 3
priority : post(3)
left : store_int_array_missing_i_rec(?p, ?i, 0, ?n, ?l) at 0
data_at(p + i * sizeof(I32), I32, ?v) at 1
check : infer(0 <= i);
infer(i < n);
action : left_erase(1);
left_erase(0);
left_add(store_int_array(p, n, replace_Znth{Z}(i, v, l)));
id : 4
priority : core(1)
left : store_int_array(?p, ?n, ?l1) at 0
right : store_int_array(p, n, ?l2) at 1
action : right_erase(1);
left_erase(0);
right_add(l1 == l2);
id : 5
priority : core(1)
left : store_int_array_missing_i_rec(?p, ?i, ?v, ?n, ?l) at 0
right : store_int_array_missing_i_rec(p, i, v, n, l) at 1
action : left_erase(0);
right_erase(1);
id : 6
priority : core(1)
left : store_int_array_rec(?p, ?x, ?y, ?l1) at 0
right : store_int_array_rec(?p, ?x, ?y, ?l2) at 1
action : right_erase(1);
left_erase(0);
right_add(l1 == l2);
id : 7
priority : core(1)
left : store_int_array_rec(?p, ?x, ?y, ?l) at 0
right : data_at(?p + (?i * sizeof(I32)), I32, ?v) at 1
check : infer(x <= i);
infer(i < y);
action : right_erase(1);
left_erase(0);
left_add(store_int_array_missing_i_rec(p, i, x, y, l));
right_add(v == l[i - x]);
id : 8
priority : core(1)
left : store_int_array_rec(?p, ?x, ?y, ?l1) at 0
store_int_array_rec(?p, ?y, ?z, ?l2) at 1
right : store_int_array_rec(?p, ?x, ?z, ?l3) at 2
check : infer(y <= z);
infer(x <= y);
action : right_erase(2);
left_erase(0);
left_erase(1);
right_add(l3 == app{Z}(l1, l2));
id : 9
priority : core(1)
left : store_int_array_rec(?p, ?x, ?z, ?l3) at 2
right : store_int_array_rec(?p, ?x, ?y, ?l1) at 0
store_int_array_rec(?p, ?y, ?z, ?l2) at 1
check : infer(y <= z);
infer(x <= y);
action : left_erase(2);
right_erase(0);
right_erase(1);
right_add(l3 == app{Z}(l1, l2));
right_add(Zlength{Z}(l1) == y - x);
id : 10
priority : core(1)
right : store_int_array_rec(?p, ?x, ?x, ?l) at 0
action : right_erase(0);
right_add(l == nil{Z});
id : 11
priority : post(1)
left : store_int_array_missing_i_rec(?p, ?i, ?x, ?y, ?l) at 0
data_at(p + ?i * sizeof(I32), I32, l[?i - ?x]) at 1
check : infer(x <= i);
infer(i < y);
action : left_erase(1);
left_erase(0);
left_add(store_int_array_rec(p, x, y, l));
id : 12
priority : post(4)
left : store_int_array_missing_i_rec(?p, ?i, ?x, ?y, ?l) at 0
data_at(p + ?i * sizeof(I32), I32, ?v) at 1
check : infer(x <= i);
infer(i < y);
action : left_erase(1);
left_erase(0);
left_add(store_int_array_rec(p, x, y, replace_Znth{Z}(i - x, v, l)));

18
projects/int_array_def.h Normal file
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@ -0,0 +1,18 @@
/*@ Extern Coq (sum : list Z -> Z)
(sublist : {A} -> Z -> Z -> list A -> list A)
(store_int_array : Z -> Z -> list Z -> Assertion)
(store_uint_array : Z -> Z -> list Z -> Assertion)(store_uint_array : Z -> Z -> list Z -> Assertion)
(store_int_array_missing_i_rec: Z -> Z -> Z -> Z -> list Z -> Assertion)
(store_uint_array_missing_i_rec: Z -> Z -> Z -> Z -> list Z -> Assertion)
(store_array_box: Z -> Z -> list Z -> Assertion)
(store_array_box_array: Z -> list Z -> Assertion)
(store_int_array_rec: Z -> Z -> Z -> list Z -> Assertion)
(store_uint_array_rec: Z -> Z -> Z -> list Z -> Assertion)
(Znth: {A} -> Z -> list A -> A -> A)
(replace_Znth: {A} -> Z -> A -> list A -> list A)
(zeros: Z -> list Z)
*/
/*@ include strategies "int_array.strategies" */
/*@ include strategies "uint_array.strategies" */

45
projects/lib/gmp_aux.v → projects/lib/GmpAux.v
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@ -21,6 +21,10 @@ Local Open Scope sac.
Module Aux.
Lemma Z_of_nat_succ: forall (n: nat),
Z.of_nat (S n) = Z.of_nat n + 1.
Proof. lia. Qed.
Lemma Zpow_add_1: forall (a b: Z),
a >= 0 -> b >= 0 ->
a ^ (b + 1) = a ^ b * a.
@ -29,8 +33,29 @@ Proof.
rewrite (Z.pow_add_r a b 1); lia.
Qed.
Lemma Z_of_nat_succ: forall (n: nat),
Z.of_nat (S n) = Z.of_nat n + 1.
Lemma Zmul_mod_cancel: forall (n a b: Z),
n >= 0 -> a > 0 -> b >= 0 ->
(n * a) mod (a ^ (b + 1)) = a * (n mod (a ^ b)).
Proof.
intros.
pose proof (Z_div_mod_eq_full n (a ^ b)).
pose proof (Z.mod_bound_pos n (a ^ b) ltac:(lia) ltac:(nia)).
remember (n / a ^ b) as q eqn:Hq.
remember (n mod a ^ b) as rem eqn:Hrem.
rewrite H2.
rewrite Z.mul_add_distr_r.
rewrite (Z.mul_comm (a ^ b) q); rewrite <-Z.mul_assoc.
rewrite <-Zpow_add_1; try lia.
assert (0 <= rem * a < a ^ (b + 1)). {
rewrite Zpow_add_1; try lia.
nia.
}
rewrite <-(Zmod_unique_full (q * a ^ (b + 1) + rem * a) (a ^ (b + 1)) q (rem * a)).
+ lia.
+ unfold Remainder.
lia.
+ lia.
Qed.
Lemma Zdiv_mod_pow: forall (n a b: Z),
a > 0 -> b >= 0 -> n >= 0 ->
@ -59,5 +84,21 @@ Proof.
exists q.
lia.
Qed.
Lemma list_app_cons: forall (l1 l2: list Z) (a: Z),
app l1 (a :: l2) = app (app l1 (a :: nil)) l2.
Proof.
intros.
revert a l2.
induction l1.
+ intros.
rewrite app_nil_l.
reflexivity.
+ intros.
simpl in *.
specialize (IHl1 a0 l2).
rewrite IHl1.
reflexivity.
Qed.
End Aux.

89
projects/lib/gmp_number.v → projects/lib/GmpNumber.v
View File

@ -9,6 +9,7 @@ Require Import String.
From AUXLib Require Import int_auto Axioms Feq Idents List_lemma VMap.
Require Import SetsClass.SetsClass. Import SetsNotation.
From SimpleC.SL Require Import CommonAssertion Mem SeparationLogic IntLib.
Require Import GmpLib.GmpAux.
Require Import Logic.LogicGenerator.demo932.Interface.
Local Open Scope Z_scope.
Local Open Scope sets.
@ -21,95 +22,11 @@ Local Open Scope sac.
Notation "'UINT_MOD'" := (4294967296).
Module Aux.
Lemma Z_of_nat_succ: forall (n: nat),
Z.of_nat (S n) = Z.of_nat n + 1.
Proof. lia. Qed.
Lemma Zpow_add_1: forall (a b: Z),
a >= 0 -> b >= 0 ->
a ^ (b + 1) = a ^ b * a.
Proof.
intros.
rewrite (Z.pow_add_r a b 1); lia.
Qed.
Lemma Zmul_mod_cancel: forall (n a b: Z),
n >= 0 -> a > 0 -> b >= 0 ->
(n * a) mod (a ^ (b + 1)) = a * (n mod (a ^ b)).
Proof.
intros.
pose proof (Z_div_mod_eq_full n (a ^ b)).
pose proof (Z.mod_bound_pos n (a ^ b) ltac:(lia) ltac:(nia)).
remember (n / a ^ b) as q eqn:Hq.
remember (n mod a ^ b) as rem eqn:Hrem.
rewrite H2.
rewrite Z.mul_add_distr_r.
rewrite (Z.mul_comm (a ^ b) q); rewrite <-Z.mul_assoc.
rewrite <-Zpow_add_1; try lia.
assert (0 <= rem * a < a ^ (b + 1)). {
rewrite Zpow_add_1; try lia.
nia.
}
rewrite <-(Zmod_unique_full (q * a ^ (b + 1) + rem * a) (a ^ (b + 1)) q (rem * a)).
+ lia.
+ unfold Remainder.
lia.
+ lia.
Qed.
Lemma Zdiv_mod_pow: forall (n a b: Z),
a > 0 -> b >= 0 -> n >= 0 ->
(n / a) mod (a ^ b) = (n mod (a ^ (b + 1))) / a.
Proof.
intros.
pose proof (Z_div_mod_eq_full n (a ^ (b + 1))).
remember (n / (a ^ (b + 1))) as q eqn:Hq.
remember (n mod a ^ (b + 1)) as rem eqn:Hrem.
assert (n / a = a ^ b * q + rem / a). {
rewrite H2.
rewrite Zpow_add_1; try lia.
pose proof (Z_div_plus_full_l (a ^ b * q) a rem ltac:(lia)).
assert (a ^ b * q * a + rem = a ^ b * a * q + rem). { lia. }
rewrite H4 in H3.
tauto.
}
apply Znumtheory.Zdivide_mod_minus.
+ pose proof (Z.mod_bound_pos n (a ^ (b + 1)) ltac:(lia) (Z.pow_pos_nonneg a (b + 1) ltac:(lia) ltac:(lia))).
rewrite <-Hrem in H4.
rewrite Zpow_add_1 in H4; try lia.
pose proof (Z.div_lt_upper_bound rem a (a ^ b) ltac:(lia) ltac:(lia)).
split; try lia.
apply (Z_div_pos rem a ltac:(lia) ltac:(lia)).
+ unfold Z.divide.
exists q.
lia.
Qed.
Lemma list_app_cons: forall (l1 l2: list Z) (a: Z),
app l1 (a :: l2) = app (app l1 (a :: nil)) l2.
Proof.
intros.
revert a l2.
induction l1.
+ intros.
rewrite app_nil_l.
reflexivity.
+ intros.
simpl in *.
specialize (IHl1 a0 l2).
rewrite IHl1.
reflexivity.
Qed.
End Aux.
Module Internal.
Definition mpd_store_list (ptr: addr) (data: list Z) (cap: Z): Assertion :=
[| Zlength data <= cap |] &&
store_uint_array ptr (Zlength data) data &&
store_uint_array ptr (Zlength data) data **
store_undef_uint_array_rec ptr ((Zlength data) + 1) cap.
Fixpoint list_to_Z (data: list Z): Z :=
@ -440,7 +357,7 @@ Record bigint_ent: Type := {
sign: Prop;
}.
Definition store_bigint_ent (x: addr) (n: bigint_ent): Asrtion :=
Definition store_bigint_ent (x: addr) (n: bigint_ent): Assertion :=
EX size,
&(x # "__mpz_struct" ->ₛ "_mp_size") # Int |-> size &&
([| size < 0 |] && [| sign n |] && [| size = -Zlength (data n) |] ||

151
projects/mini-gmp.c
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@ -1,14 +1,35 @@
#include "mini-gmp.h"
#include "verification_stdlib.h"
#include "verification_list.h"
#include "int_array_def.h"
mp_size_t gmp_abs(mp_size_t x) {
int gmp_abs(int x)
/*@
Require emp
Ensure __return == Zabs(x)
*/
{
return x >= 0 ? x : -x;
}
mp_size_t gmp_max(mp_size_t a, mp_size_t b) {
int gmp_max(int a, int b)
/*@
Require emp
Ensure __return == Zmax(a, b)
*/
{
return a > b ? a : b;
}
int gmp_cmp(mp_size_t a, mp_size_t b) {
int gmp_cmp(int a, int b)
/*@
Require emp
Ensure
a > b && __return == 1 ||
a == b && __return == 0 ||
a < b && __return == -1
*/
{
return (a > b) - (a < b);
}
@ -16,16 +37,42 @@ int gmp_cmp(mp_size_t a, mp_size_t b) {
/* 从 低地址向高地址 顺序复制 */
void
mpn_copyi (mp_ptr d, mp_srcptr s, mp_size_t n)
mpn_copyi (unsigned int *d, unsigned int *s, int n)
/*@
With val data cap1 cap2
Require
mpd_store_Z(s, val, n, cap1) *
store_uint_array(d, cap2, data)
Ensure
mpd_store_Z(s, val, n, cap1) *
mpd_store_Z(d, val, n, cap2)
*/
{
mp_size_t i;
/*
mpd_store_Z(s, val, n, cap1)
which implies
exists l,
store_uint_array(s, n, l) **
store_undef
*/
int i;
for (i = 0; i < n; i++)
d[i] = s[i];
}
/* 大于返回1，小于返回-1，等于返回0 */
int
mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
mpn_cmp (unsigned int *ap, unsigned int *bp, int n)
/*@
With cap1 cap2 val1 val2
Require
mpd_store_Z(ap, val1, n, cap1) **
mpd_store_Z(bp, val2, n, cap2)
Ensure
val1 > val2 && __return == 1 ||
val1 == val2 && __return == 0 ||
val1 < val2 && __return == -1
*/
{
while (--n >= 0)
{
@ -37,7 +84,7 @@ mpn_cmp (mp_srcptr ap, mp_srcptr bp, mp_size_t n)
/*处理位数不同的情况*/
static int
mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
mpn_cmp4 (unsigned int *ap, int an, unsigned int *bp, int bn)
{
if (an != bn)
return an < bn ? -1 : 1;
@ -46,8 +93,8 @@ mpn_cmp4 (mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
}
/*返回非0的位数*/
static mp_size_t
mpn_normalized_size (mp_srcptr xp, mp_size_t n)
static int
mpn_normalized_size (unsigned int *xp, int n)
{
while (n > 0 && xp[n-1] == 0)
--n;
@ -55,15 +102,15 @@ mpn_normalized_size (mp_srcptr xp, mp_size_t n)
}
/* 多精度数ap 加上单精度数b，返回最后产生的进位 */
mp_limb_t
mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
unsigned int
mpn_add_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
{
mp_size_t i;
int i;
//assert (n > 0);
i = 0;
do
{
mp_limb_t r = ap[i] + b;
unsigned int r = ap[i] + b;
/* Carry out */
b = (r < b);
rp[i] = r;
@ -74,15 +121,15 @@ mpn_add_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
}
/* 位数相同的多精度数ap 加上多精度数bp，返回最后产生的进位 */
mp_limb_t
mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
unsigned int
mpn_add_n (unsigned int *rp, unsigned int *ap, unsigned int *bp, int n)
{
mp_size_t i;
mp_limb_t cy;
int i;
unsigned int cy;
for (i = 0, cy = 0; i < n; i++)
{
mp_limb_t a, b, r;
unsigned int a, b, r;
a = ap[i]; b = bp[i];
r = a + cy;
cy = (r < cy);
@ -94,10 +141,10 @@ mpn_add_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
}
/*不同位数的多精度数相加，返回最后的进位*/
mp_limb_t
mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
unsigned int
mpn_add (unsigned int *rp, unsigned int *ap, int an, unsigned int *bp, int bn)
{
mp_limb_t cy;
unsigned int cy;
//assert (an >= bn);
cy = mpn_add_n (rp, ap, bp, bn);
if (an > bn)
@ -105,17 +152,17 @@ mpn_add (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
return cy;
}
mp_limb_t
mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
unsigned int
mpn_sub_1 (unsigned int *rp, unsigned int *ap, int n, unsigned int b)
{
mp_size_t i;
int i;
//assert (n > 0);
i = 0;
do
{
mp_limb_t a = ap[i];
unsigned int a = ap[i];
/* Carry out */
mp_limb_t cy = a < b;
unsigned int cy = a < b;
rp[i] = a - b;
b = cy;
}
@ -124,15 +171,15 @@ mpn_sub_1 (mp_ptr rp, mp_srcptr ap, mp_size_t n, mp_limb_t b)
return b;
}
mp_limb_t
mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
unsigned int
mpn_sub_n (unsigned int *rp, unsigned int *ap, unsigned int *bp, int n)
{
mp_size_t i;
mp_limb_t cy;
int i;
unsigned int cy;
for (i = 0, cy = 0; i < n; i++)
{
mp_limb_t a, b;
unsigned int a, b;
a = ap[i]; b = bp[i];
b += cy;
cy = (b < cy);
@ -142,10 +189,10 @@ mpn_sub_n (mp_ptr rp, mp_srcptr ap, mp_srcptr bp, mp_size_t n)
return cy;
}
mp_limb_t
mpn_sub (mp_ptr rp, mp_srcptr ap, mp_size_t an, mp_srcptr bp, mp_size_t bn)
unsigned int
mpn_sub (unsigned int *rp, unsigned int *ap, int an, unsigned int *bp, int bn)
{
mp_limb_t cy;
unsigned int cy;
//assert (an >= bn);
cy = mpn_sub_n (rp, ap, bp, bn);
if (an > bn)
@ -162,8 +209,8 @@ mpz_clear (mpz_t r)
gmp_free_limbs (r->_mp_d, r->_mp_alloc);
}
static mp_ptr
mpz_realloc (mpz_t r, mp_size_t size)
static unsigned int *
mpz_realloc (mpz_t r, int size)
{
size = gmp_max (size, 1);
@ -180,7 +227,7 @@ mpz_realloc (mpz_t r, mp_size_t size)
}
/* Realloc for an mpz_t WHAT if it has less than NEEDED limbs. */
mp_ptr mrz_realloc_if(mpz_t z,mp_size_t n) {
unsigned int *mrz_realloc_if(mpz_t z,int n) {
return n > z->_mp_alloc ? mpz_realloc(z, n) : z->_mp_d;
}
@ -194,25 +241,25 @@ mpz_sgn (const mpz_t u)
void
mpz_swap (mpz_t u, mpz_t v)
{
mp_size_t_swap (u->_mp_alloc, v->_mp_alloc);
mp_ptr_swap(u->_mp_d, v->_mp_d);
mp_size_t_swap (u->_mp_size, v->_mp_size);
int_swap (u->_mp_alloc, v->_mp_alloc);
unsigned int *_swap(u->_mp_d, v->_mp_d);
int_swap (u->_mp_size, v->_mp_size);
}
/* MPZ addition and subtraction */
static mp_size_t
static int
mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
{
mp_size_t an = gmp_abs (a->_mp_size);
mp_size_t bn = gmp_abs (b->_mp_size);
mp_ptr rp;
mp_limb_t cy;
int an = gmp_abs (a->_mp_size);
int bn = gmp_abs (b->_mp_size);
unsigned int *rp;
unsigned int cy;
if (an < bn)
{
mpz_srcptr_swap (a, b);
mp_size_t_swap (an, bn);
int_swap (an, bn);
}
rp = mrz_realloc_if (r, an + 1);
@ -223,13 +270,13 @@ mpz_abs_add (mpz_t r, const mpz_t a, const mpz_t b)
return an + cy;
}
static mp_size_t
static int
mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
{
mp_size_t an = gmp_abs (a->_mp_size);
mp_size_t bn = gmp_abs (b->_mp_size);
int an = gmp_abs (a->_mp_size);
int bn = gmp_abs (b->_mp_size);
int cmp;
mp_ptr rp;
unsigned int *rp;
cmp = mpn_cmp4 (a->_mp_d, an, b->_mp_d, bn);
if (cmp > 0)
@ -251,7 +298,7 @@ mpz_abs_sub (mpz_t r, const mpz_t a, const mpz_t b)
void
mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
{
mp_size_t rn;
int rn;
if ( (a->_mp_size ^ b->_mp_size) >= 0)
rn = mpz_abs_add (r, a, b);
@ -264,7 +311,7 @@ mpz_add (mpz_t r, const mpz_t a, const mpz_t b)
void
mpz_sub (mpz_t r, const mpz_t a, const mpz_t b)
{
mp_size_t rn;
int rn;
if ( (a->_mp_size ^ b->_mp_size) >= 0)
rn = mpz_abs_sub (r, a, b);

45
projects/mini-gmp.h
View File

@ -1,10 +1,3 @@
typedef unsigned long mp_limb_t;
typedef long mp_size_t;
typedef unsigned long mp_bitcnt_t;
typedef mp_limb_t *mp_ptr;
typedef const mp_limb_t *mp_srcptr;
typedef struct
{
int _mp_alloc; /* Number of *limbs* allocated and pointed
@ -12,7 +5,7 @@ typedef struct
int _mp_size; /* abs(_mp_size) is the number of limbs the
last field points to. If _mp_size is
negative this is a negative number. */
mp_limb_t *_mp_d; /* Pointer to the limbs. */
unsigned int *_mp_d; /* Pointer to the limbs. */
} __mpz_struct;
/* mpz_t is an array type that contains a single element of __mpz_struct, acting as a reference. */
@ -23,35 +16,35 @@ typedef const __mpz_struct *mpz_srcptr;
/* BEGIN Given Functions */
/* Swap functions. */
void mp_size_t_swap(mp_size_t x, mp_size_t y);
void int_swap(int x, int y);
void mp_ptr_swap(mp_ptr x, mp_ptr y);
void mp_ptr_swap(unsigned int *x, unsigned int *y);
void mpz_srcptr_swap(mpz_srcptr x, mpz_srcptr y);
/* Memory allocation functions. */
static mp_ptr
gmp_alloc_limbs (mp_size_t size);
static unsigned int *
gmp_alloc_limbs (int size);
static mp_ptr
gmp_realloc_limbs (mp_ptr old, mp_size_t old_size, mp_size_t size);
static unsigned int *
gmp_realloc_limbs (unsigned int *old, int old_size, int size);
static void
gmp_free_limbs (mp_ptr old, mp_size_t size);
gmp_free_limbs (unsigned int *old, int size);
/* END Given Functions */
void mpn_copyi (mp_ptr, mp_srcptr, mp_size_t);
void mpn_copyi (unsigned int *d, unsigned int *s, int n);
int mpn_cmp (mp_srcptr, mp_srcptr, mp_size_t);
int mpn_cmp (unsigned int *, unsigned int *, int);
mp_limb_t mpn_add_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
mp_limb_t mpn_add_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
mp_limb_t mpn_add (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
unsigned int mpn_add_1 (unsigned int *, unsigned int *, int, unsigned int);
unsigned int mpn_add_n (unsigned int *, unsigned int *, unsigned int *, int);
unsigned int mpn_add (unsigned int *, unsigned int *, int, unsigned int *, int);
mp_limb_t mpn_sub_1 (mp_ptr, mp_srcptr, mp_size_t, mp_limb_t);
mp_limb_t mpn_sub_n (mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
mp_limb_t mpn_sub (mp_ptr, mp_srcptr, mp_size_t, mp_srcptr, mp_size_t);
unsigned int mpn_sub_1 (unsigned int *, unsigned int *, int, unsigned int);
unsigned int mpn_sub_n (unsigned int *, unsigned int *, unsigned int *, int);
unsigned int mpn_sub (unsigned int *, unsigned int *, int, unsigned int *, int);
void mpz_clear (mpz_t);
@ -64,3 +57,9 @@ void mpz_add (mpz_t, const mpz_t, const mpz_t);
void mpz_sub (mpz_t, const mpz_t, const mpz_t);
void mpz_set (mpz_t, const mpz_t);
/*@
Extern Coq (Zabs: Z -> Z)
(Zmax: Z -> Z -> Z)
(mpd_store_Z: Z -> Z -> Z -> Z -> Assertion)
*/

126
projects/uint_array.strategies Normal file
View File

@ -0,0 +1,126 @@
//test curent rules
//max rule id:30
#include "int_array_def.h"
#include "verification_list.h"
#include "verification_stdlib.h"
id : 1
priority : core(1)
left : store_uint_array(?p, ?n, ?l) at 0
right : data_at(?p + (?i * sizeof(I32)), I32, ?v) at 1
check : infer(0 <= i);
infer(i < n);
action : right_erase(1);
left_erase(0);
left_add(store_uint_array_missing_i_rec(p, i, 0, n, l));
right_add(v == l[i]);
id : 2
priority : post(1)
left : store_uint_array_missing_i_rec(?p, ?i, 0, ?n, ?l) at 0
data_at(p + i * sizeof(I32), I32, l[i]) at 1
check : infer(0 <= i);
infer(i < n);
action : left_erase(1);
left_erase(0);
left_add(store_uint_array(p, n, l));
id : 3
priority : post(3)
left : store_uint_array_missing_i_rec(?p, ?i, 0, ?n, ?l) at 0
data_at(p + i * sizeof(I32), I32, ?v) at 1
check : infer(0 <= i);
infer(i < n);
action : left_erase(1);
left_erase(0);
left_add(store_uint_array(p, n, replace_Znth{Z}(i, v, l)));
id : 4
priority : core(1)
left : store_uint_array(?p, ?n, ?l1) at 0
right : store_uint_array(p, n, ?l2) at 1
action : right_erase(1);
left_erase(0);
right_add(l1 == l2);
id : 5
priority : core(1)
left : store_uint_array_missing_i_rec(?p, ?i, ?v, ?n, ?l) at 0
right : store_uint_array_missing_i_rec(p, i, v, n, l) at 1
action : left_erase(0);
right_erase(1);
id : 6
priority : core(1)
left : store_uint_array_rec(?p, ?x, ?y, ?l1) at 0
right : store_uint_array_rec(?p, ?x, ?y, ?l2) at 1
action : right_erase(1);
left_erase(0);
right_add(l1 == l2);
id : 7
priority : core(1)
left : store_uint_array_rec(?p, ?x, ?y, ?l) at 0
right : data_at(?p + (?i * sizeof(I32)), I32, ?v) at 1
check : infer(x <= i);
infer(i < y);
action : right_erase(1);
left_erase(0);
left_add(store_uint_array_missing_i_rec(p, i, x, y, l));
right_add(v == l[i - x]);
id : 8
priority : core(1)
left : store_uint_array_rec(?p, ?x, ?y, ?l1) at 0
store_uint_array_rec(?p, ?y, ?z, ?l2) at 1
right : store_uint_array_rec(?p, ?x, ?z, ?l3) at 2
check : infer(y <= z);
infer(x <= y);
action : right_erase(2);
left_erase(0);
left_erase(1);
right_add(l3 == app{Z}(l1, l2));
id : 9
priority : core(1)
left : store_uint_array_rec(?p, ?x, ?z, ?l3) at 2
right : store_uint_array_rec(?p, ?x, ?y, ?l1) at 0
store_uint_array_rec(?p, ?y, ?z, ?l2) at 1
check : infer(y <= z);
infer(x <= y);
action : left_erase(2);
right_erase(0);
right_erase(1);
right_add(l3 == app{Z}(l1, l2));
right_add(Zlength{Z}(l1) == y - x);
id : 10
priority : core(1)
right : store_uint_array_rec(?p, ?x, ?x, ?l) at 0
action : right_erase(0);
right_add(l == nil{Z});
id : 11
priority : post(1)
left : store_uint_array_missing_i_rec(?p, ?i, ?x, ?y, ?l) at 0
data_at(p + ?i * sizeof(I32), I32, l[?i - ?x]) at 1
check : infer(x <= i);
infer(i < y);
action : left_erase(1);
left_erase(0);
left_add(store_uint_array_rec(p, x, y, l));
id : 12
priority : post(4)
left : store_uint_array_missing_i_rec(?p, ?i, ?x, ?y, ?l) at 0
data_at(p + ?i * sizeof(I32), I32, ?v) at 1
check : infer(x <= i);
infer(i < y);
action : left_erase(1);
left_erase(0);
left_add(store_uint_array_rec(p, x, y, replace_Znth{Z}(i - x, v, l)));