(** Truth values.  Non-zero integers are treated as [True]. The integer 0 (also used to represent the null pointer) is [False]. Other values are neither true nor false. *)
Inductive bool_of_val: val -> bool -> Prop :=
| bool_of_val_int:
forall n, bool_of_val (Vint n) (negb (Int.eq n Int.zero)).
(** Arithmetic operations *)
Definition neg (v: val) : val :=
match v with
| Vint n => Vint (Int.neg n)
| _ => Vundef
end.
Definition negf (v: val) : val :=
match v with
| Vfloat f => Vfloat (Float.neg f)
| _ => Vundef
end.
Definition absf (v: val) : val :=
match v with
| Vfloat f => Vfloat (Float.abs f)
| _ => Vundef
end.
Definition negfs (v: val) : val :=
match v with
| Vsingle f => Vsingle (Float32.neg f)
| _ => Vundef
end.
Definition absfs (v: val) : val :=
match v with
| Vsingle f => Vsingle (Float32.abs f)
| _ => Vundef
end.
Definition maketotal (ov: option val) : val :=
match ov with Some v => v | None => Vundef end.
Definition intoffloat (v: val) : option val :=
match v with
| Vfloat f => option_map Vint (Float.to_int f)
| _ => None
end.
Definition intuoffloat (v: val) : option val :=
match v with
| Vfloat f => option_map Vint (Float.to_intu f)
| _ => None
end.
Definition floatofint (v: val) : option val :=
match v with
| Vint n => Some (Vfloat (Float.of_int n))
| _ => None
end.
Definition floatofintu (v: val) : option val :=
match v with
| Vint n => Some (Vfloat (Float.of_intu n))
| _ => None
end.
Definition intofsingle (v: val) : option val :=
match v with
| Vsingle f => option_map Vint (Float32.to_int f)
| _ => None
end.
Definition intuofsingle (v: val) : option val :=
match v with
| Vsingle f => option_map Vint (Float32.to_intu f)
| _ => None
end.
Definition singleofint (v: val) : option val :=
match v with
| Vint n => Some (Vsingle (Float32.of_int n))
| _ => None
end.
Definition singleofintu (v: val) : option val :=
match v with
| Vint n => Some (Vsingle (Float32.of_intu n))
| _ => None
end.
Definition negint (v: val) : val :=
match v with
| Vint n => Vint (Int.neg n)
| _ => Vundef
end.
Definition notint (v: val) : val :=
match v with
| Vint n => Vint (Int.not n)
| _ => Vundef
end.
Definition of_bool (b: bool): val := if b then Vtrue else Vfalse.
Definition boolval (v: val) : val :=
match v with
| Vint n => of_bool (negb (Int.eq n Int.zero))
| Vptr b ofs => Vtrue
| _ => Vundef
end.
Definition notbool (v: val) : val :=
match v with
| Vint n => of_bool (Int.eq n Int.zero)
| Vptr b ofs => Vfalse
| _ => Vundef
end.
Definition zero_ext (nbits: Z) (v: val) : val :=
match v with
| Vint n => Vint(Int.zero_ext nbits n)
| _ => Vundef
end.
Definition sign_ext (nbits: Z) (v: val) : val :=
match v with
| Vint n => Vint(Int.sign_ext nbits n)
| _ => Vundef
end.
Definition singleoffloat (v: val) : val :=
match v with
| Vfloat f => Vsingle (Float.to_single f)
| _ => Vundef
end.
Definition floatofsingle (v: val) : val :=
match v with
| Vsingle f => Vfloat (Float.of_single f)
| _ => Vundef
end.
Definition add (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.add n1 n2)
| Vptr b1 ofs1, Vint n2 => if Archi.ptr64 then Vundef else Vptr b1 (Ptrofs.add ofs1 (Ptrofs.of_int n2))
| Vint n1, Vptr b2 ofs2 => if Archi.ptr64 then Vundef else Vptr b2 (Ptrofs.add ofs2 (Ptrofs.of_int n1))
| _, _ => Vundef
end.
Definition sub (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.sub n1 n2)
| Vptr b1 ofs1, Vint n2 => if Archi.ptr64 then Vundef else Vptr b1 (Ptrofs.sub ofs1 (Ptrofs.of_int n2))
| Vptr b1 ofs1, Vptr b2 ofs2 =>
if Archi.ptr64 then Vundef else
if eq_block b1 b2 then Vint(Ptrofs.to_int (Ptrofs.sub ofs1 ofs2)) else Vundef
| _, _ => Vundef
end.
Definition mul (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.mul n1 n2)
| _, _ => Vundef
end.
Definition mulhs (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.mulhs n1 n2)
| _, _ => Vundef
end.
Definition mulhu (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.mulhu n1 n2)
| _, _ => Vundef
end.
Definition divs (v1 v2: val): option val :=
match v1, v2 with
| Vint n1, Vint n2 =>
if Int.eq n2 Int.zero
|| Int.eq n1 (Int.repr Int.min_signed) && Int.eq n2 Int.mone
then None
else Some(Vint(Int.divs n1 n2))
| _, _ => None
end.
Definition mods (v1 v2: val): option val :=
match v1, v2 with
| Vint n1, Vint n2 =>
if Int.eq n2 Int.zero
|| Int.eq n1 (Int.repr Int.min_signed) && Int.eq n2 Int.mone
then None
else Some(Vint(Int.mods n1 n2))
| _, _ => None
end.
Definition divu (v1 v2: val): option val :=
match v1, v2 with
| Vint n1, Vint n2 =>
if Int.eq n2 Int.zero then None else Some(Vint(Int.divu n1 n2))
| _, _ => None
end.
Definition modu (v1 v2: val): option val :=
match v1, v2 with
| Vint n1, Vint n2 =>
if Int.eq n2 Int.zero then None else Some(Vint(Int.modu n1 n2))
| _, _ => None
end.
Definition add_carry (v1 v2 cin: val): val :=
match v1, v2, cin with
| Vint n1, Vint n2, Vint c => Vint(Int.add_carry n1 n2 c)
| _, _, _ => Vundef
end.
Definition sub_overflow (v1 v2: val) : val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.sub_overflow n1 n2 Int.zero)
| _, _ => Vundef
end.
Definition negative (v: val) : val :=
match v with
| Vint n => Vint (Int.negative n)
| _ => Vundef
end.
Definition and (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.and n1 n2)
| _, _ => Vundef
end.
Definition or (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.or n1 n2)
| _, _ => Vundef
end.
Definition xor (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.xor n1 n2)
| _, _ => Vundef
end.
Definition shl (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 =>
if Int.ltu n2 Int.iwordsize
then Vint(Int.shl n1 n2)
else Vundef
| _, _ => Vundef
end.
Definition shr (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 =>
if Int.ltu n2 Int.iwordsize
then Vint(Int.shr n1 n2)
else Vundef
| _, _ => Vundef
end.
Definition shr_carry (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 =>
if Int.ltu n2 Int.iwordsize
then Vint(Int.shr_carry n1 n2)
else Vundef
| _, _ => Vundef
end.
Definition shrx (v1 v2: val): option val :=
match v1, v2 with
| Vint n1, Vint n2 =>
if Int.ltu n2 (Int.repr 31)
then Some(Vint(Int.shrx n1 n2))
else None
| _, _ => None
end.
Definition shru (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 =>
if Int.ltu n2 Int.iwordsize
then Vint(Int.shru n1 n2)
else Vundef
| _, _ => Vundef
end.
Definition rol (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.rol n1 n2)
| _, _ => Vundef
end.
Definition rolm (v: val) (amount mask: int): val :=
match v with
| Vint n => Vint(Int.rolm n amount mask)
| _ => Vundef
end.
Definition ror (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vint(Int.ror n1 n2)
| _, _ => Vundef
end.
Definition addf (v1 v2: val): val :=
match v1, v2 with
| Vfloat f1, Vfloat f2 => Vfloat(Float.add f1 f2)
| _, _ => Vundef
end.
Definition subf (v1 v2: val): val :=
match v1, v2 with
| Vfloat f1, Vfloat f2 => Vfloat(Float.sub f1 f2)
| _, _ => Vundef
end.
Definition mulf (v1 v2: val): val :=
match v1, v2 with
| Vfloat f1, Vfloat f2 => Vfloat(Float.mul f1 f2)
| _, _ => Vundef
end.
Definition divf (v1 v2: val): val :=
match v1, v2 with
| Vfloat f1, Vfloat f2 => Vfloat(Float.div f1 f2)
| _, _ => Vundef
end.
Definition floatofwords (v1 v2: val) : val :=
match v1, v2 with
| Vint n1, Vint n2 => Vfloat (Float.from_words n1 n2)
| _, _ => Vundef
end.
Definition addfs (v1 v2: val): val :=
match v1, v2 with
| Vsingle f1, Vsingle f2 => Vsingle(Float32.add f1 f2)
| _, _ => Vundef
end.
Definition subfs (v1 v2: val): val :=
match v1, v2 with
| Vsingle f1, Vsingle f2 => Vsingle(Float32.sub f1 f2)
| _, _ => Vundef
end.
Definition mulfs (v1 v2: val): val :=
match v1, v2 with
| Vsingle f1, Vsingle f2 => Vsingle(Float32.mul f1 f2)
| _, _ => Vundef
end.
Definition divfs (v1 v2: val): val :=
match v1, v2 with
| Vsingle f1, Vsingle f2 => Vsingle(Float32.div f1 f2)
| _, _ => Vundef
end.
(** Operations on 64-bit integers *)
Definition longofwords (v1 v2: val) : val :=
match v1, v2 with
| Vint n1, Vint n2 => Vlong (Int64.ofwords n1 n2)
| _, _ => Vundef
end.
Definition loword (v: val) : val :=
match v with
| Vlong n  => Vint (Int64.loword n)
| _ => Vundef
end.
Definition hiword (v: val) : val :=
match v with
| Vlong n  => Vint (Int64.hiword n)
| _ => Vundef
end.
Definition negl (v: val) : val :=
match v with
| Vlong n => Vlong (Int64.neg n)
| _ => Vundef
end.
Definition notl (v: val) : val :=
match v with
| Vlong n => Vlong (Int64.not n)
| _ => Vundef
end.
Definition longofint (v: val) : val :=
match v with
| Vint n => Vlong (Int64.repr (Int.signed n))
| _ => Vundef
end.
Definition longofintu (v: val) : val :=
match v with
| Vint n => Vlong (Int64.repr (Int.unsigned n))
| _ => Vundef
end.
Definition longoffloat (v: val) : option val :=
match v with
| Vfloat f => option_map Vlong (Float.to_long f)
| _ => None
end.
Definition longuoffloat (v: val) : option val :=
match v with
| Vfloat f => option_map Vlong (Float.to_longu f)
| _ => None
end.
Definition longofsingle (v: val) : option val :=
match v with
| Vsingle f => option_map Vlong (Float32.to_long f)
| _ => None
end.
Definition longuofsingle (v: val) : option val :=
match v with
| Vsingle f => option_map Vlong (Float32.to_longu f)
| _ => None
end.
Definition floatoflong (v: val) : option val :=
match v with
| Vlong n => Some (Vfloat (Float.of_long n))
| _ => None
end.
Definition floatoflongu (v: val) : option val :=
match v with
| Vlong n => Some (Vfloat (Float.of_longu n))
| _ => None
end.
Definition singleoflong (v: val) : option val :=
match v with
| Vlong n => Some (Vsingle (Float32.of_long n))
| _ => None
end.
Definition singleoflongu (v: val) : option val :=
match v with
| Vlong n => Some (Vsingle (Float32.of_longu n))
| _ => None
end.
Definition addl (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vlong n2 => Vlong(Int64.add n1 n2)
| Vptr b1 ofs1, Vlong n2 => if Archi.ptr64 then Vptr b1 (Ptrofs.add ofs1 (Ptrofs.of_int64 n2)) else Vundef
| Vlong n1, Vptr b2 ofs2 => if Archi.ptr64 then Vptr b2 (Ptrofs.add ofs2 (Ptrofs.of_int64 n1)) else Vundef
| _, _ => Vundef
end.
Definition subl (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vlong n2 => Vlong(Int64.sub n1 n2)
| Vptr b1 ofs1, Vlong n2 =>
if Archi.ptr64 then Vptr b1 (Ptrofs.sub ofs1 (Ptrofs.of_int64 n2)) else Vundef
| Vptr b1 ofs1, Vptr b2 ofs2 =>
if negb Archi.ptr64 then Vundef else
if eq_block b1 b2 then Vlong(Ptrofs.to_int64 (Ptrofs.sub ofs1 ofs2)) else Vundef
| _, _ => Vundef
end.
Definition mull (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vlong n2 => Vlong(Int64.mul n1 n2)
| _, _ => Vundef
end.
Definition mull' (v1 v2: val): val :=
match v1, v2 with
| Vint n1, Vint n2 => Vlong(Int64.mul' n1 n2)
| _, _ => Vundef
end.
Definition mullhs (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vlong n2 => Vlong(Int64.mulhs n1 n2)
| _, _ => Vundef
end.
Definition mullhu (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vlong n2 => Vlong(Int64.mulhu n1 n2)
| _, _ => Vundef
end.
Definition divls (v1 v2: val): option val :=
match v1, v2 with
| Vlong n1, Vlong n2 =>
if Int64.eq n2 Int64.zero
|| Int64.eq n1 (Int64.repr Int64.min_signed) && Int64.eq n2 Int64.mone
then None
else Some(Vlong(Int64.divs n1 n2))
| _, _ => None
end.
Definition modls (v1 v2: val): option val :=
match v1, v2 with
| Vlong n1, Vlong n2 =>
if Int64.eq n2 Int64.zero
|| Int64.eq n1 (Int64.repr Int64.min_signed) && Int64.eq n2 Int64.mone
then None
else Some(Vlong(Int64.mods n1 n2))
| _, _ => None
end.
Definition divlu (v1 v2: val): option val :=
match v1, v2 with
| Vlong n1, Vlong n2 =>
if Int64.eq n2 Int64.zero then None else Some(Vlong(Int64.divu n1 n2))
| _, _ => None
end.
Definition modlu (v1 v2: val): option val :=
match v1, v2 with
| Vlong n1, Vlong n2 =>
if Int64.eq n2 Int64.zero then None else Some(Vlong(Int64.modu n1 n2))
| _, _ => None
end.
Definition addl_carry (v1 v2 cin: val): val :=
match v1, v2, cin with
| Vlong n1, Vlong n2, Vlong c => Vlong(Int64.add_carry n1 n2 c)
| _, _, _ => Vundef
end.
Definition subl_overflow (v1 v2: val) : val :=
match v1, v2 with
| Vlong n1, Vlong n2 => Vint (Int.repr (Int64.unsigned (Int64.sub_overflow n1 n2 Int64.zero)))
| _, _ => Vundef
end.
Definition negativel (v: val) : val :=
match v with
| Vlong n => Vint (Int.repr (Int64.unsigned (Int64.negative n)))
| _ => Vundef
end.
Definition andl (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vlong n2 => Vlong(Int64.and n1 n2)
| _, _ => Vundef
end.
Definition orl (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vlong n2 => Vlong(Int64.or n1 n2)
| _, _ => Vundef
end.
Definition xorl (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vlong n2 => Vlong(Int64.xor n1 n2)
| _, _ => Vundef
end.
Definition shll (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vint n2 =>
if Int.ltu n2 Int64.iwordsize'
then Vlong(Int64.shl' n1 n2)
else Vundef
| _, _ => Vundef
end.
Definition shrl (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vint n2 =>
if Int.ltu n2 Int64.iwordsize'
then Vlong(Int64.shr' n1 n2)
else Vundef
| _, _ => Vundef
end.
Definition shrlu (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vint n2 =>
if Int.ltu n2 Int64.iwordsize'
then Vlong(Int64.shru' n1 n2)
else Vundef
| _, _ => Vundef
end.
Definition shrxl (v1 v2: val): option val :=
match v1, v2 with
| Vlong n1, Vint n2 =>
if Int.ltu n2 (Int.repr 63)
then Some(Vlong(Int64.shrx' n1 n2))
else None
| _, _ => None
end.
Definition shrl_carry (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vint n2 =>
if Int.ltu n2 Int64.iwordsize'
then Vlong(Int64.shr_carry' n1 n2)
else Vundef
| _, _ => Vundef
end.
Definition roll (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vint n2 => Vlong(Int64.rol n1 (Int64.repr (Int.unsigned n2)))
| _, _ => Vundef
end.
Definition rorl (v1 v2: val): val :=
match v1, v2 with
| Vlong n1, Vint n2 => Vlong(Int64.ror n1 (Int64.repr (Int.unsigned n2)))
| _, _ => Vundef
end.
Definition rolml (v: val) (amount: int) (mask: int64): val :=
match v with
| Vlong n => Vlong(Int64.rolm n (Int64.repr (Int.unsigned amount)) mask)
| _ => Vundef
end.
(** Comparisons *)
Section COMPARISONS.
Variable valid_ptr: block -> Z -> bool.
Let weak_valid_ptr (b: block) (ofs: Z) := valid_ptr b ofs || valid_ptr b (ofs - 1).
Definition cmp_bool (c: comparison) (v1 v2: val): option bool :=
match v1, v2 with
| Vint n1, Vint n2 => Some (Int.cmp c n1 n2)
| _, _ => None
end.
Definition cmp_different_blocks (c: comparison): option bool :=
match c with
| Ceq => Some false
| Cne => Some true
| _   => None
end.
Definition cmpu_bool (c: comparison) (v1 v2: val): option bool :=
match v1, v2 with
| Vint n1, Vint n2 =>
Some (Int.cmpu c n1 n2)
| Vint n1, Vptr b2 ofs2 =>
if Archi.ptr64 then None else
if Int.eq n1 Int.zero && weak_valid_ptr b2 (Ptrofs.unsigned ofs2)
then cmp_different_blocks c
else None
| Vptr b1 ofs1, Vptr b2 ofs2 =>
if Archi.ptr64 then None else
if eq_block b1 b2 then
if weak_valid_ptr b1 (Ptrofs.unsigned ofs1)
&& weak_valid_ptr b2 (Ptrofs.unsigned ofs2)
then Some (Ptrofs.cmpu c ofs1 ofs2)
else None
else
if valid_ptr b1 (Ptrofs.unsigned ofs1)
&& valid_ptr b2 (Ptrofs.unsigned ofs2)
then cmp_different_blocks c
else None
| Vptr b1 ofs1, Vint n2 =>
if Archi.ptr64 then None else
if Int.eq n2 Int.zero && weak_valid_ptr b1 (Ptrofs.unsigned ofs1)
then cmp_different_blocks c
else None
| _, _ => None
end.
Definition cmpf_bool (c: comparison) (v1 v2: val): option bool :=
match v1, v2 with
| Vfloat f1, Vfloat f2 => Some (Float.cmp c f1 f2)
| _, _ => None
end.
Definition cmpfs_bool (c: comparison) (v1 v2: val): option bool :=
match v1, v2 with
| Vsingle f1, Vsingle f2 => Some (Float32.cmp c f1 f2)
| _, _ => None
end.
Definition cmpl_bool (c: comparison) (v1 v2: val): option bool :=
match v1, v2 with
| Vlong n1, Vlong n2 => Some (Int64.cmp c n1 n2)
| _, _ => None
end.
Definition cmplu_bool (c: comparison) (v1 v2: val): option bool :=
match v1, v2 with
| Vlong n1, Vlong n2 => Some (Int64.cmpu c n1 n2)
| Vlong n1, Vptr b2 ofs2 =>
if negb Archi.ptr64 then None else
if Int64.eq n1 Int64.zero && weak_valid_ptr b2 (Ptrofs.unsigned ofs2)
then cmp_different_blocks c
else None
| Vptr b1 ofs1, Vptr b2 ofs2 =>
if negb Archi.ptr64 then None else
if eq_block b1 b2 then
if weak_valid_ptr b1 (Ptrofs.unsigned ofs1)
&& weak_valid_ptr b2 (Ptrofs.unsigned ofs2)
then Some (Ptrofs.cmpu c ofs1 ofs2)
else None
else
if valid_ptr b1 (Ptrofs.unsigned ofs1)
&& valid_ptr b2 (Ptrofs.unsigned ofs2)
then cmp_different_blocks c
else None
| Vptr b1 ofs1, Vlong n2 =>
if negb Archi.ptr64 then None else
if Int64.eq n2 Int64.zero && weak_valid_ptr b1 (Ptrofs.unsigned ofs1)
then cmp_different_blocks c
else None
| _, _ => None
end.
Definition of_optbool (ob: option bool): val :=
match ob with Some true => Vtrue | Some false => Vfalse | None => Vundef end.
Definition cmp (c: comparison) (v1 v2: val): val :=
of_optbool (cmp_bool c v1 v2).
Definition cmpu (c: comparison) (v1 v2: val): val :=
of_optbool (cmpu_bool c v1 v2).
Definition cmpf (c: comparison) (v1 v2: val): val :=
of_optbool (cmpf_bool c v1 v2).
Definition cmpfs (c: comparison) (v1 v2: val): val :=
of_optbool (cmpfs_bool c v1 v2).
Definition cmpl (c: comparison) (v1 v2: val): option val :=
option_map of_bool (cmpl_bool c v1 v2).
Definition cmplu (c: comparison) (v1 v2: val): option val :=
option_map of_bool (cmplu_bool c v1 v2).
Definition maskzero_bool (v: val) (mask: int): option bool :=
match v with
| Vint n => Some (Int.eq (Int.and n mask) Int.zero)
| _ => None
end.
End COMPARISONS.
(** Add the given offset to the given pointer. *)
Definition offset_ptr (v: val) (delta: ptrofs) : val :=
match v with
| Vptr b ofs => Vptr b (Ptrofs.add ofs delta)
| _ => Vundef
end.
(** [load_result] reflects the effect of storing a value with a given memory chunk, then reading it back with the same chunk.  Depending on the chunk and the type of the value, some normalization occurs. For instance, consider storing the integer value [0xFFF] on 1 byte at a given address, and reading it back.  If it is read back with chunk [Mint8unsigned], zero-extension must be performed, resulting in [0xFF].  If it is read back as a [Mint8signed], sign-extension is performed and [0xFFFFFFFF] is returned. *)
Definition load_result (chunk: memory_chunk) (v: val) :=
match chunk, v with
| Mint8signed, Vint n => Vint (Int.sign_ext 8 n)
| Mint8unsigned, Vint n => Vint (Int.zero_ext 8 n)
| Mint16signed, Vint n => Vint (Int.sign_ext 16 n)
| Mint16unsigned, Vint n => Vint (Int.zero_ext 16 n)
| Mint32, Vint n => Vint n
| Mint32, Vptr b ofs => if Archi.ptr64 then Vundef else Vptr b ofs
| Mint64, Vlong n => Vlong n
| Mint64, Vptr b ofs => if Archi.ptr64 then Vptr b ofs else Vundef
| Mfloat32, Vsingle f => Vsingle f
| Mfloat64, Vfloat f => Vfloat f
| Many32, (Vint _ | Vsingle _) => v
| Many32, Vptr _ _ => if Archi.ptr64 then Vundef else v
| Many64, _ => v
| _, _ => Vundef
end.

Lemma load_result_type:
forall chunk v, has_type (load_result chunk v) (type_of_chunk chunk).