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fix(mpz_realloc): fix minor bugs in proof of mpz_realloc.

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This commit is contained in:
xiaoh105
2025-06-21 22:23:37 +08:00
parent 1e627cdb84
commit f4db688a30
5 changed files with 97 additions and 141 deletions
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80
projects/lib/gmp_goal.v
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@ -2826,7 +2826,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z)
[| (retval > retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap = 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -2850,7 +2850,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z)
[| (retval > retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap = 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -2874,7 +2874,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3
[| (retval > retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap <> 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -2897,7 +2897,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3
[| (retval > retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap <> 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -2920,7 +2920,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3
[| (retval <= retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap <> 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -2954,7 +2954,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3
[| (retval <= retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap <> 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -2988,7 +2988,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z)
[| (retval <= retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap = 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3023,7 +3023,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z)
[| (retval <= retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap = 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3058,7 +3058,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z)
[| (retval > retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap = 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3093,7 +3093,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z)
[| (retval > retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap = 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3128,7 +3128,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3
[| (retval > retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap <> 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3162,7 +3162,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval_3
[| (retval > retval_2) |]
&& [| (retval = (Zabs (old))) |]
&& [| (cap <> 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3244,7 +3244,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) ,
Definition mpz_realloc_partial_solve_wit_3_pure :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
[| (cap <> 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3260,13 +3260,13 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|--
[| (cap >= 0) |]
&& [| (retval >= cap) |]
&& [| ((Zmax (size_pre) (1)) >= cap) |]
&& [| ((Z.max (size_pre) (1)) >= cap) |]
.
Definition mpz_realloc_partial_solve_wit_3_aux :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
[| (cap <> 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3280,9 +3280,9 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|--
[| (cap >= 0) |]
&& [| (retval >= cap) |]
&& [| ((Zmax (size_pre) (1)) >= cap) |]
&& [| ((Z.max (size_pre) (1)) >= cap) |]
&& [| (cap <> 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3300,7 +3300,7 @@ Definition mpz_realloc_partial_solve_wit_3 := mpz_realloc_partial_solve_wit_3_pu
Definition mpz_realloc_partial_solve_wit_4_pure :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
[| (cap <> 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3316,13 +3316,13 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|--
[| (cap >= 0) |]
&& [| (retval >= cap) |]
&& [| ((Zmax (size_pre) (1)) >= cap) |]
&& [| ((Z.max (size_pre) (1)) >= cap) |]
.
Definition mpz_realloc_partial_solve_wit_4_aux :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
[| (cap <> 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3336,9 +3336,9 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|--
[| (cap >= 0) |]
&& [| (retval >= cap) |]
&& [| ((Zmax (size_pre) (1)) >= cap) |]
&& [| ((Z.max (size_pre) (1)) >= cap) |]
&& [| (cap <> 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3356,7 +3356,7 @@ Definition mpz_realloc_partial_solve_wit_4 := mpz_realloc_partial_solve_wit_4_pu
Definition mpz_realloc_partial_solve_wit_5_pure :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
[| (cap = 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3376,7 +3376,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
Definition mpz_realloc_partial_solve_wit_5_aux :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
[| (cap = 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3390,7 +3390,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|--
[| (retval >= 0) |]
&& [| (cap = 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3408,7 +3408,7 @@ Definition mpz_realloc_partial_solve_wit_5 := mpz_realloc_partial_solve_wit_5_pu
Definition mpz_realloc_partial_solve_wit_6_pure :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
[| (cap = 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3428,7 +3428,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
Definition mpz_realloc_partial_solve_wit_6_aux :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
[| (cap = 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3442,7 +3442,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) ,
|--
[| (retval >= 0) |]
&& [| (cap = 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3460,7 +3460,7 @@ Definition mpz_realloc_partial_solve_wit_6 := mpz_realloc_partial_solve_wit_6_pu
Definition mpz_realloc_partial_solve_wit_7_pure :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z) (retval: Z) ,
[| (cap = 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3482,7 +3482,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z)
Definition mpz_realloc_partial_solve_wit_7_aux :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) (retval_2: Z) ,
[| (cap = 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3498,7 +3498,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) (r
[| (old <= INT_MAX) |]
&& [| (INT_MIN < old) |]
&& [| (cap = 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3517,7 +3517,7 @@ Definition mpz_realloc_partial_solve_wit_7 := mpz_realloc_partial_solve_wit_7_pu
Definition mpz_realloc_partial_solve_wit_8_pure :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z) (retval: Z) ,
[| (cap = 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3539,7 +3539,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval_2: Z)
Definition mpz_realloc_partial_solve_wit_8_aux :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) (retval_2: Z) ,
[| (cap = 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3555,7 +3555,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (ptr: Z) (retval: Z) (r
[| (INT_MIN < old) |]
&& [| (old <= INT_MAX) |]
&& [| (cap = 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3574,7 +3574,7 @@ Definition mpz_realloc_partial_solve_wit_8 := mpz_realloc_partial_solve_wit_8_pu
Definition mpz_realloc_partial_solve_wit_9_pure :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval: Z) ,
[| (cap <> 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3595,7 +3595,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval:
Definition mpz_realloc_partial_solve_wit_9_aux :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval: Z) (retval_2: Z) ,
[| (cap <> 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3610,7 +3610,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval: Z) (retval_2:
[| (old <= INT_MAX) |]
&& [| (INT_MIN < old) |]
&& [| (cap <> 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3628,7 +3628,7 @@ Definition mpz_realloc_partial_solve_wit_9 := mpz_realloc_partial_solve_wit_9_pu
Definition mpz_realloc_partial_solve_wit_10_pure :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval: Z) ,
[| (cap <> 0) |]
&& [| (retval_2 = (Zmax (size_pre) (1))) |]
&& [| (retval_2 = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3649,7 +3649,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval_2: Z) (retval:
Definition mpz_realloc_partial_solve_wit_10_aux :=
forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval: Z) (retval_2: Z) ,
[| (cap <> 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]
@ -3664,7 +3664,7 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval: Z) (retval_2:
[| (INT_MIN < old) |]
&& [| (old <= INT_MAX) |]
&& [| (cap <> 0) |]
&& [| (retval = (Zmax (size_pre) (1))) |]
&& [| (retval = (Z.max (size_pre) (1))) |]
&& [| (size_pre >= cap) |]
&& [| (size_pre <= 100000000) |]
&& [| (cap >= 0) |]

3
projects/lib/gmp_proof_auto.v
View File

@ -15,8 +15,6 @@ Local Open Scope Z_scope.
Local Open Scope sets.
Local Open Scope string.
Local Open Scope list.
Require Import Coq.ZArith.ZArith.
Local Open Scope Z_scope.
Import naive_C_Rules.
Local Open Scope sac.
@ -244,3 +242,4 @@ Proof. Admitted.
Lemma proof_of_mpz_realloc_partial_solve_wit_10 : mpz_realloc_partial_solve_wit_10.
Proof. Admitted.

71
projects/lib/gmp_proof_manual.v
View File

@ -487,7 +487,6 @@ Proof.
assert (b * 4294967296 ^ i + Znth i l_3 0 * 4294967296 ^ i = new_b * 4294967296 ^ i + 1 * 4294967296 ^ (i + 1)).
{
subst new_b.
Search [ Zmult Zplus "distr" ].
rewrite <- Z.mul_add_distr_r.
rewrite (Zpow_add_1 4294967296 i); try lia.
}
@ -604,7 +603,6 @@ Proof.
assert (b * 4294967296 ^ i + Znth i l_3 0 * 4294967296 ^ i = new_b * 4294967296 ^ i + 0 * 4294967296 ^ (i + 1)).
{
subst new_b.
Search [ Zmult Zplus "distr" ].
rewrite <- Z.mul_add_distr_r.
rewrite (Zpow_add_1 4294967296 i); try lia.
}
@ -883,9 +881,6 @@ Proof.
Right.
Exists retval_3 retval_2.
entailer!.
unfold Zmax in *.
pose proof (Z.le_max_l size_pre 1).
lia.
Qed.
Lemma proof_of_mpz_realloc_return_wit_1_2 : mpz_realloc_return_wit_1_2.
@ -894,9 +889,6 @@ Proof.
Left.
Exists retval_3 retval_2.
entailer!.
unfold Zmax in *.
pose proof (Z.le_max_l size_pre 1).
lia.
Qed.
Lemma proof_of_mpz_realloc_return_wit_1_3 : mpz_realloc_return_wit_1_3.
@ -905,33 +897,25 @@ Proof.
Right.
Exists retval_3 retval_2.
entailer!.
+ subst.
subst.
unfold mpd_store_Z_compact.
Intros data.
Exists data.
unfold mpd_store_list, store_undef_uint_array_rec.
entailer!.
- assert (Zlength data = 0). {
assert (Zlength data = 0). {
pose proof (Zlength_nonneg data).
lia.
}
rewrite H8 in *.
rewrite H10 in *.
simpl.
entailer!.
pose proof (Zlength_nil_inv data H8).
pose proof (Zlength_nil_inv data H10).
repeat subst.
unfold store_uint_array, store_array; simpl; entailer!.
unfold store_undef_uint_array, store_undef_array.
rewrite Z.sub_0_r.
reflexivity.
- unfold Zmax in *.
assert (size_pre < 1 \/ size_pre >= 1). { lia. }
destruct H8.
* rewrite (Z.max_r size_pre 1 ltac:(lia)); lia.
* rewrite (Z.max_l size_pre 1 ltac:(lia)); lia.
+ pose proof (Z.le_max_l size_pre 1).
unfold Zmax in *.
lia.
Qed.
Lemma proof_of_mpz_realloc_return_wit_1_4 : mpz_realloc_return_wit_1_4.
@ -940,7 +924,7 @@ Proof.
Left.
Exists retval_3 retval_2.
entailer!.
+ subst.
subst.
unfold mpd_store_Z_compact, mpd_store_list.
Intros data.
Exists data.
@ -948,15 +932,12 @@ Proof.
pose proof (Zlength_nonneg data).
lia.
}
rewrite H8 in *; clear H2.
pose proof (Zlength_nil_inv data H8).
rewrite H2 in *; clear H2 H8.
rewrite H10 in *; clear H2.
pose proof (Zlength_nil_inv data H10).
rewrite H2 in *; clear H2 H10.
unfold store_uint_array, store_array.
simpl.
entailer!.
+ pose proof (Z.le_max_l size_pre 1).
unfold Zmax in *.
lia.
Qed.
Lemma proof_of_mpz_realloc_return_wit_1_5 : mpz_realloc_return_wit_1_5.
@ -965,16 +946,13 @@ Proof.
Left.
Exists retval_3 retval_2.
entailer!.
+ subst.
subst.
unfold mpd_store_Z_compact, mpd_store_list.
Intros data.
Exists data.
unfold store_uint_array, store_array.
simpl.
entailer!.
+ pose proof (Z.le_max_l size_pre 1).
unfold Zmax in *.
lia.
Qed.
Lemma proof_of_mpz_realloc_return_wit_1_6 : mpz_realloc_return_wit_1_6.
@ -984,29 +962,20 @@ Proof.
Exists retval_3 retval_2.
subst.
entailer!.
+ unfold mpd_store_Z_compact, mpd_store_list.
unfold mpd_store_Z_compact, mpd_store_list.
Intros data; Exists data.
unfold store_uint_array, store_array.
assert (Zlength data = 0). {
pose proof (Zlength_nonneg data).
lia.
}
rewrite H8 in *; clear H2.
pose proof (Zlength_nil_inv data H8).
rewrite H2 in *; clear H2 H8.
rewrite H10 in *; clear H2.
pose proof (Zlength_nil_inv data H10).
rewrite H2 in *; clear H2 H10.
unfold store_undef_uint_array, store_undef_uint_array_rec, store_undef_array.
subst.
simpl.
entailer!.
- rewrite Z.sub_0_r.
entailer!.
- pose proof (Z.le_max_r size_pre 1).
simpl in H.
unfold Zmax in *.
lia.
+ unfold Zmax in *.
pose proof (Z.le_max_l size_pre 1).
lia.
Qed.
Lemma proof_of_mpz_realloc_return_wit_1_7 : mpz_realloc_return_wit_1_7.
@ -1015,7 +984,6 @@ Proof.
Left.
Exists retval_3 retval_2.
subst.
unfold Zmax in *.
rewrite (Z.abs_neq old ltac:(lia)) in H.
pose proof (Z.le_max_l size_pre 1).
unfold mpd_store_Z_compact.
@ -1030,7 +998,6 @@ Proof.
Right.
Exists retval_3 retval_2.
subst.
unfold Zmax in *.
rewrite (Z.abs_eq old ltac:(lia)) in H.
pose proof (Z.le_max_l size_pre 1).
unfold mpd_store_Z_compact.
@ -1042,33 +1009,21 @@ Qed.
Lemma proof_of_mpz_realloc_partial_solve_wit_3_pure : mpz_realloc_partial_solve_wit_3_pure.
Proof.
pre_process.
unfold Zmax in *.
pose proof (Z.le_max_l size_pre 1).
entailer!.
Qed.
Lemma proof_of_mpz_realloc_partial_solve_wit_4_pure : mpz_realloc_partial_solve_wit_4_pure.
Proof.
pre_process.
unfold Zmax in *.
pose proof (Z.le_max_l size_pre 1).
entailer!.
Qed.
Lemma proof_of_mpz_realloc_partial_solve_wit_5_pure : mpz_realloc_partial_solve_wit_5_pure.
Proof.
pre_process.
unfold Zmax in *.
pose proof (Z.le_max_l size_pre 1).
entailer!.
Qed.
Lemma proof_of_mpz_realloc_partial_solve_wit_6_pure : mpz_realloc_partial_solve_wit_6_pure.
Proof.
pre_process.
unfold Zmax in *.
pose proof (Z.le_max_l size_pre 1).
entailer!.
Qed.
Lemma proof_of_mpz_realloc_partial_solve_wit_7_pure : mpz_realloc_partial_solve_wit_7_pure.

2
projects/mini-gmp.c
View File

@ -15,7 +15,7 @@ int gmp_abs(int x)
int gmp_max(int a, int b)
/*@
Require emp
Ensure __return == Zmax(a, b)
Ensure __return == Z::max(a, b)
*/
{
return a > b ? a : b;

4
projects/mini-gmp.h
View File

@ -1,6 +1,7 @@
/*@
Extern Coq (Zabs : Z -> Z)
(Zmax : Z -> Z -> Z)
(Z::max : Z -> Z -> Z)
(Z::pow : Z -> Z -> Z)
(mpd_store_Z : Z -> Z -> Z -> Z -> Assertion)
(mpd_store_Z_compact: Z -> Z -> Z -> Z -> Assertion)
(mpd_store_list : Z -> list Z -> Z -> Assertion)
@ -8,6 +9,7 @@
(list_store_Z : list Z -> Z -> Prop)
(list_store_Z_compact: list Z -> Z -> Prop)
(last: list Z -> Z -> Z)
(UINT_MOD: Z)
*/
typedef struct __mpz_struct