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feat(mpz_sgn): Proved correctness of function mpz_sgn.

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xiaoh105
2025-06-22 19:10:35 +08:00
parent f4db688a30
commit 3a102d0d65
6 changed files with 382 additions and 5 deletions
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221
projects/lib/gmp_goal.v
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@ -3679,6 +3679,215 @@ forall (size_pre: Z) (r_pre: Z) (n: Z) (cap: Z) (old: Z) (retval: Z) (retval_2:
Definition mpz_realloc_partial_solve_wit_10 := mpz_realloc_partial_solve_wit_10_pure -> mpz_realloc_partial_solve_wit_10_aux.
(*----- Function mpz_sgn -----*)
Definition mpz_sgn_safety_wit_1 :=
forall (u_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) ,
[| (size >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr n size cap )
** ((( &( "u" ) )) # Ptr |-> u_pre)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|--
[| (0 <= INT_MAX) |]
&& [| ((INT_MIN) <= 0) |]
.
Definition mpz_sgn_safety_wit_2 :=
forall (u_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) (retval: Z) ,
[| (size < 0) |]
&& [| (retval = (-1)) |]
&& [| (size >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr n size cap )
** ((( &( "u" ) )) # Ptr |-> u_pre)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|--
[| False |]
.
Definition mpz_sgn_safety_wit_3 :=
forall (u_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) ,
[| (size < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr (-n) (-size) cap )
** ((( &( "u" ) )) # Ptr |-> u_pre)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|--
[| (0 <= INT_MAX) |]
&& [| ((INT_MIN) <= 0) |]
.
Definition mpz_sgn_safety_wit_4 :=
forall (u_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) (retval: Z) ,
[| (size = 0) |]
&& [| (retval = 0) |]
&& [| (size < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr (-n) (-size) cap )
** ((( &( "u" ) )) # Ptr |-> u_pre)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|--
[| False |]
.
Definition mpz_sgn_safety_wit_5 :=
forall (u_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) (retval: Z) ,
[| (size > 0) |]
&& [| (retval = 1) |]
&& [| (size < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr (-n) (-size) cap )
** ((( &( "u" ) )) # Ptr |-> u_pre)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|--
[| False |]
.
Definition mpz_sgn_return_wit_1_1 :=
forall (u_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) (retval: Z) ,
[| (size < 0) |]
&& [| (retval = (-1)) |]
&& [| (size < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr (-n) (-size) cap )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|--
([| (n < 0) |]
&& [| (retval = (-1)) |]
&& (store_Z u_pre n ))
||
([| (n = 0) |]
&& [| (retval = 0) |]
&& (store_Z u_pre n ))
||
([| (n > 0) |]
&& [| (retval = 1) |]
&& (store_Z u_pre n ))
.
Definition mpz_sgn_return_wit_1_2 :=
forall (u_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) (retval: Z) ,
[| (size > 0) |]
&& [| (retval = 1) |]
&& [| (size >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr n size cap )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|--
([| (n < 0) |]
&& [| (retval = (-1)) |]
&& (store_Z u_pre n ))
||
([| (n = 0) |]
&& [| (retval = 0) |]
&& (store_Z u_pre n ))
||
([| (n > 0) |]
&& [| (retval = 1) |]
&& (store_Z u_pre n ))
.
Definition mpz_sgn_return_wit_1_3 :=
forall (u_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) (retval: Z) ,
[| (size = 0) |]
&& [| (retval = 0) |]
&& [| (size >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr n size cap )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|--
([| (n < 0) |]
&& [| (retval = (-1)) |]
&& (store_Z u_pre n ))
||
([| (n = 0) |]
&& [| (retval = 0) |]
&& (store_Z u_pre n ))
||
([| (n > 0) |]
&& [| (retval = 1) |]
&& (store_Z u_pre n ))
.
Definition mpz_sgn_partial_solve_wit_1 :=
forall (u_pre: Z) (n: Z) ,
(store_Z u_pre n )
|--
(store_Z u_pre n )
.
Definition mpz_sgn_partial_solve_wit_2 :=
forall (u_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) ,
[| (size >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr n size cap )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|--
[| (size >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr n size cap )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
.
Definition mpz_sgn_partial_solve_wit_3 :=
forall (u_pre: Z) (n: Z) (ptr: Z) (cap: Z) (size: Z) ,
[| (size < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr (-n) (-size) cap )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
|--
[| (size < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr (-n) (-size) cap )
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u_pre) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr)
.
Definition mpz_sgn_which_implies_wit_1 :=
forall (n: Z) (u: Z) ,
(store_Z u n )
|--
(EX (ptr: Z) (cap: Z) (size: Z) ,
[| (size >= 0) |]
&& [| (n >= 0) |]
&& (mpd_store_Z_compact ptr n size cap )
** ((&((u) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr))
||
(EX (ptr: Z) (cap: Z) (size: Z) ,
[| (size < 0) |]
&& [| (n < 0) |]
&& (mpd_store_Z_compact ptr (-n) (-size) cap )
** ((&((u) # "__mpz_struct" ->ₛ "_mp_size")) # Int |-> size)
** ((&((u) # "__mpz_struct" ->ₛ "_mp_alloc")) # Int |-> cap)
** ((&((u) # "__mpz_struct" ->ₛ "_mp_d")) # Ptr |-> ptr))
.
Module Type VC_Correct.
Axiom proof_of_gmp_abs_safety_wit_1 : gmp_abs_safety_wit_1.
@ -3810,5 +4019,17 @@ Axiom proof_of_mpz_realloc_partial_solve_wit_9_pure : mpz_realloc_partial_solve_
Axiom proof_of_mpz_realloc_partial_solve_wit_9 : mpz_realloc_partial_solve_wit_9.
Axiom proof_of_mpz_realloc_partial_solve_wit_10_pure : mpz_realloc_partial_solve_wit_10_pure.
Axiom proof_of_mpz_realloc_partial_solve_wit_10 : mpz_realloc_partial_solve_wit_10.
Axiom proof_of_mpz_sgn_safety_wit_1 : mpz_sgn_safety_wit_1.
Axiom proof_of_mpz_sgn_safety_wit_2 : mpz_sgn_safety_wit_2.
Axiom proof_of_mpz_sgn_safety_wit_3 : mpz_sgn_safety_wit_3.
Axiom proof_of_mpz_sgn_safety_wit_4 : mpz_sgn_safety_wit_4.
Axiom proof_of_mpz_sgn_safety_wit_5 : mpz_sgn_safety_wit_5.
Axiom proof_of_mpz_sgn_return_wit_1_1 : mpz_sgn_return_wit_1_1.
Axiom proof_of_mpz_sgn_return_wit_1_2 : mpz_sgn_return_wit_1_2.
Axiom proof_of_mpz_sgn_return_wit_1_3 : mpz_sgn_return_wit_1_3.
Axiom proof_of_mpz_sgn_partial_solve_wit_1 : mpz_sgn_partial_solve_wit_1.
Axiom proof_of_mpz_sgn_partial_solve_wit_2 : mpz_sgn_partial_solve_wit_2.
Axiom proof_of_mpz_sgn_partial_solve_wit_3 : mpz_sgn_partial_solve_wit_3.
Axiom proof_of_mpz_sgn_which_implies_wit_1 : mpz_sgn_which_implies_wit_1.
End VC_Correct.