(** * Abstracting values *)

Inductive aval : Type :=
  | Vbot                     (**r bottom (empty set of values) *)
  | I (n: int)               (**r exactly [Vint n] *)
  | Uns (p: aptr) (n: Z)     (**r a [n]-bit unsigned integer, or [Vundef] *)
  | Sgn (p: aptr) (n: Z)     (**r a [n]-bit signed integer, or [Vundef] *)
  | L (n: int64)             (**r exactly [Vlong n] *)
  | F (f: float)             (**r exactly [Vfloat f] *)
  | FS (f: float32)          (**r exactly [Vsingle f] *)
  | Ptr (p: aptr)            (**r a pointer from the set [p], or [Vundef] *)
  | Ifptr (p: aptr).(** * Abstracting values *)

Inductive aval : Type :=
  | Vbot                     (**r bottom (empty set of values) *)
  | I (n: int)               (**r exactly [Vint n] *)
  | Uns (p: aptr) (n: Z)     (**r a [n]-bit unsigned integer, or [Vundef] *)
  | Sgn (p: aptr) (n: Z)     (**r a [n]-bit signed integer, or [Vundef] *)
  | L (n: int64)             (**r exactly [Vlong n] *)
  | F (f: float)             (**r exactly [Vfloat f] *)
  | FS (f: float32)          (**r exactly [Vsingle f] *)
  | Ptr (p: aptr)            (**r a pointer from the set [p], or [Vundef] *)
  | Ifptr (p: aptr).(** * Abstracting values *)

Inductive aval : Type :=
  | Vbot                     (**r bottom (empty set of values) *)
  | I (n: int)               (**r exactly [Vint n] *)
  | Uns (p: aptr) (n: Z)     (**r a [n]-bit unsigned integer, or [Vundef] *)
  | Sgn (p: aptr) (n: Z)     (**r a [n]-bit signed integer, or [Vundef] *)
  | L (n: int64)             (**r exactly [Vlong n] *)
  | F (f: float)             (**r exactly [Vfloat f] *)
  | FS (f: float32)          (**r exactly [Vsingle f] *)
  | Ptr (p: aptr)            (**r a pointer from the set [p], or [Vundef] *)
  | Ifptr (p: aptr).(** * Abstracting values *)

Inductive aval : Type :=
  | Vbot                     (**r bottom (empty set of values) *)
  | I (n: int)               (**r exactly [Vint n] *)
  | Uns (p: aptr) (n: Z)     (**r a [n]-bit unsigned integer, or [Vundef] *)
  | Sgn (p: aptr) (n: Z)     (**r a [n]-bit signed integer, or [Vundef] *)
  | L (n: int64)             (**r exactly [Vlong n] *)
  | F (f: float)             (**r exactly [Vfloat f] *)
  | FS (f: float32)          (**r exactly [Vsingle f] *)
  | Ptr (p: aptr)            (**r a pointer from the set [p], or [Vundef] *)
  | Ifptr (p: aptr).(** * Abstracting values *)

Inductive aval : Type :=
  | Vbot                     (**r bottom (empty set of values) *)
  | I (n: int)               (**r exactly [Vint n] *)
  | Uns (p: aptr) (n: Z)     (**r a [n]-bit unsigned integer, or [Vundef] *)
  | Sgn (p: aptr) (n: Z)     (**r a [n]-bit signed integer, or [Vundef] *)
  | L (n: int64)             (**r exactly [Vlong n] *)
  | F (f: float)             (**r exactly [Vfloat f] *)
  | FS (f: float32)          (**r exactly [Vsingle f] *)
  | Ptr (p: aptr)            (**r a pointer from the set [p], or [Vundef] *)
  | Ifptr (p: aptr).(** * Abstracting values *)

Inductive aval : Type :=
  | Vbot                     (**r bottom (empty set of values) *)
  | I (n: int)               (**r exactly [Vint n] *)
  | Uns (p: aptr) (n: Z)     (**r a [n]-bit unsigned integer, or [Vundef] *)
  | Sgn (p: aptr) (n: Z)     (**r a [n]-bit signed integer, or [Vundef] *)
  | L (n: int64)             (**r exactly [Vlong n] *)
  | F (f: float)             (**r exactly [Vfloat f] *)
  | FS (f: float32)          (**r exactly [Vsingle f] *)
  | Ptr (p: aptr)            (**r a pointer from the set [p], or [Vundef] *)
  | Ifptr (p: aptr).(** * Abstracting values *)

Inductive aval : Type :=
  | Vbot                     (**r bottom (empty set of values) *)
  | I (n: int)               (**r exactly [Vint n] *)
  | Uns (p: aptr) (n: Z)     (**r a [n]-bit unsigned integer, or [Vundef] *)
  | Sgn (p: aptr) (n: Z)     (**r a [n]-bit signed integer, or [Vundef] *)
  | L (n: int64)             (**r exactly [Vlong n] *)
  | F (f: float)             (**r exactly [Vfloat f] *)
  | FS (f: float32)          (**r exactly [Vsingle f] *)
  | Ptr (p: aptr)            (**r a pointer from the set [p], or [Vundef] *)
  | Ifptr (p: aptr).(** * Abstracting values *)

Inductive aval : Type :=
  | Vbot                     (**r bottom (empty set of values) *)
  | I (n: int)               (**r exactly [Vint n] *)
  | Uns (p: aptr) (n: Z)     (**r a [n]-bit unsigned integer, or [Vundef] *)
  | Sgn (p: aptr) (n: Z)     (**r a [n]-bit signed integer, or [Vundef] *)
  | L (n: int64)             (**r exactly [Vlong n] *)
  | F (f: float)             (**r exactly [Vfloat f] *)
  | FS (f: float32)          (**r exactly [Vsingle f] *)
  | Ptr (p: aptr)            (**r a pointer from the set [p], or [Vundef] *)
  | Ifptr (p: aptr).(** * Abstracting values *)

Inductive aval : Type :=
  | Vbot                     (**r bottom (empty set of values) *)
  | I (n: int)               (**r exactly [Vint n] *)
  | Uns (p: aptr) (n: Z)     (**r a [n]-bit unsigned integer, or [Vundef] *)
  | Sgn (p: aptr) (n: Z)     (**r a [n]-bit signed integer, or [Vundef] *)
  | L (n: int64)             (**r exactly [Vlong n] *)
  | F (f: float)             (**r exactly [Vfloat f] *)
  | FS (f: float32)          (**r exactly [Vsingle f] *)
  | Ptr (p: aptr)            (**r a pointer from the set [p], or [Vundef] *)
  | Ifptr (p: aptr).(** * Abstracting values *)

Inductive aval : Type :=
  | Vbot                     (**r bottom (empty set of values) *)
  | I (n: int)               (**r exactly [Vint n] *)
  | Uns (p: aptr) (n: Z)     (**r a [n]-bit unsigned integer, or [Vundef] *)
  | Sgn (p: aptr) (n: Z)     (**r a [n]-bit signed integer, or [Vundef] *)
  | L (n: int64)             (**r exactly [Vlong n] *)
  | F (f: float)             (**r exactly [Vfloat f] *)
  | FS (f: float32)          (**r exactly [Vsingle f] *)
  | Ptr (p: aptr)            (**r a pointer from the set [p], or [Vundef] *)
  | Ifptr (p: aptr).(**r a pointer from the set [p], or a number, or [Vundef] *)

(** The "top" of the value domain is defined as any pointer, or any
    number, or [Vundef]. *)

Definition Vtop := Ifptr Ptop.(** The [p] parameter (an abstract pointer) to [Uns] and [Sgn] helps keeping
  track of pointers that leak through arithmetic operations such as shifts.
  See the section "Tracking leakage of pointers" below.
  In strict analysis mode, [p] is always [Pbot]. *)

Definition eq_aval: forall (v1 v2: aval), {v1=v2} + {v1<>v2}.Definition is_uns (n: Z) (i: int) : Prop :=
  forall m, 0 <= m < Int.zwordsize -> m >= n -> Int.testbit i m = false.Definition is_sgn (n: Z) (i: int) : Prop :=
  forall m, 0 <= m < Int.zwordsize -> m >= n - 1 -> Int.testbit i m = Int.testbit i (Int.zwordsize - 1).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).Inductive vmatch : val -> aval -> Prop :=
  | vmatch_i: forall i, vmatch (Vint i) (I i)
  | vmatch_Uns: forall p i n, 0 <= n -> is_uns n i -> vmatch (Vint i) (Uns p n)
  | vmatch_Uns_undef: forall p n, vmatch Vundef (Uns p n)
  | vmatch_Sgn: forall p i n, 0 < n -> is_sgn n i -> vmatch (Vint i) (Sgn p n)
  | vmatch_Sgn_undef: forall p n, vmatch Vundef (Sgn p n)
  | vmatch_l: forall i, vmatch (Vlong i) (L i)
  | vmatch_f: forall f, vmatch (Vfloat f) (F f)
  | vmatch_s: forall f, vmatch (Vsingle f) (FS f)
  | vmatch_ptr: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ptr p)
  | vmatch_ptr_undef: forall p, vmatch Vundef (Ptr p)
  | vmatch_ifptr_undef: forall p, vmatch Vundef (Ifptr p)
  | vmatch_ifptr_i: forall i p, vmatch (Vint i) (Ifptr p)
  | vmatch_ifptr_l: forall i p, vmatch (Vlong i) (Ifptr p)
  | vmatch_ifptr_f: forall f p, vmatch (Vfloat f) (Ifptr p)
  | vmatch_ifptr_s: forall f p, vmatch (Vsingle f) (Ifptr p)
  | vmatch_ifptr_p: forall b ofs p, pmatch b ofs p -> vmatch (Vptr b ofs) (Ifptr p).

Lemma is_sgn_mon: forall n1 n2 i, is_sgn n1 i -> n1 <= n2 -> is_sgn n2 i.