Source file MemVal.ml
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open Cil_types
open Cil_datatype
open Ctypes
open Lang
open Lang.F
open Sigs
open Definitions
module Logic = Qed.Logic
module type State =
sig
type t
val bottom : t
val join : t -> t -> t
val of_kinstr : Cil_types.kinstr -> t
val of_stmt : Cil_types.stmt -> t
val of_kf : Cil_types.kernel_function -> t
val pretty : Format.formatter -> t -> unit
end
module type Value =
sig
val configure : unit -> WpContext.rollback
val datatype : string
module State : State
type t
type state = State.t
val null : t
val literal: eid:int -> Cstring.cst -> int * t
val cvar : varinfo -> t
val field : t -> Cil_types.fieldinfo -> t
val shift : t -> Ctypes.c_object -> term -> t
val base_addr : t -> t
val load : state -> t -> Ctypes.c_object -> t
val domain : t -> Base.t list
val offset : t -> (term -> pred)
val pretty : Format.formatter -> t -> unit
end
module type Base =
sig
end
let dkey = Wp_parameters.register_category "memval"
let dkey_val = Wp_parameters.register_category "memval:val"
let debug fmt = Wp_parameters.debug ~dkey fmt
let debug_val = Wp_parameters.debug ~dkey:dkey_val
let library = "memory"
let a_addr = Lang.datatype ~library "addr"
let t_addr = Logic.Data(a_addr,[])
let f_base = Lang.extern_f ~library ~result:Logic.Int
~link:(Qed.Engine.F_subst ("base", "%1.base")) "base"
let f_offset = Lang.extern_f ~library ~result:Logic.Int
~link:(Qed.Engine.F_subst ("offset", "%1.offset")) "offset"
let f_shift = Lang.extern_f ~library ~result:t_addr "shift"
let f_global = Lang.extern_f ~library ~result:t_addr "global"
let f_null = Lang.extern_f ~library ~result:t_addr "null"
let a_null = F.constant (e_fun f_null [])
let a_base p = e_fun f_base [p]
let a_offset p = e_fun f_offset [p]
let a_global b = e_fun f_global [b]
let a_shift l k = e_fun f_shift [l;k]
let a_addr b k = a_shift (a_global b) k
let a_iabs i = e_fun ~result:Logic.Int Cmath.f_iabs [i]
let t_words = Logic.Array (Logic.Int, Logic.Int)
let phi_base t = match F.repr t with
| Logic.Fun (f, [p; _]) when f == f_shift -> a_base p
| Logic.Fun (f, [b]) when f == f_global -> b
| _ -> raise Not_found
let phi_offset t = match F.repr t with
| Logic.Fun (f, [p; k]) when f == f_shift -> e_add (a_offset p) k
| Logic.Fun (f, _) when f == f_global -> F.e_zero
| _ -> raise Not_found
let phi_shift p i =
if F.is_zero i then p
else match F.repr p with
| Logic.Fun (f, [q; j]) when f == f_shift -> F.e_fun f [q; F.e_add i j]
| _ -> raise Not_found
let _phi_read ~obj ~read ~write mem off = match F.repr mem with
| Logic.Fun (f, [_; o; v]) when f == write && off == o -> v
| Logic.Fun (f, [m; o; _]) when f == write ->
let offset = a_iabs (F.e_sub off o) in
if F.eval_leq (F.e_int (Ctypes.sizeof_object obj)) offset then
F.e_fun read [m; off]
else raise Not_found
| _ -> raise Not_found
let () = Context.register
begin fun () ->
F.set_builtin_1 f_base phi_base;
F.set_builtin_1 f_offset phi_offset;
F.set_builtin_2 f_shift phi_shift;
end
module Cstring =
struct
include Cstring
let str_cil ~eid cstr =
let enode = match cstr with
| C_str str -> Const (CStr str)
| W_str wstr -> Const (CWStr wstr)
in {
eid = eid;
enode = enode;
eloc = Location.unknown;
}
end
module Base =
struct
include Base
let bitsize_from_validity = function
| Invalid -> Integer.zero
| Empty -> Integer.zero
| Known (_, m)
| Unknown (_, _, m) -> Integer.succ m
| Variable { max_allocable } -> Integer.succ max_allocable
let size_from_validity b =
Integer.(e_div (bitsize_from_validity b) eight)
end
module Make(V : Value) =
struct
let datatype = "MemVal." ^ V.datatype
let configure () =
let rollback = V.configure () in
let orig_pointer = Context.push Lang.pointer t_addr in
let rollback () =
rollback ();
Context.pop Lang.pointer orig_pointer;
in
rollback
module StateRef =
struct
let model : V.State.t Context.value = Context.create "Memval.model"
let get () = Context.get model
let update () =
try
(match WpContext.get_scope () with
| WpContext.Global -> assert false
| WpContext.Kf kf -> Context.set model (V.State.of_kf kf))
with | Invalid_argument _ -> Context.set model (V.State.of_kinstr Kglobal)
| Kernel_function.No_Definition -> assert false
end
type chunk =
| M_base of Base.t
module Chunk =
struct
type t = chunk
let self = "MemVal.Chunk"
let hash = function
| M_base b -> 5 * Base.hash b
let equal c1 c2 = match c1, c2 with
| M_base b1, M_base b2 -> Base.equal b1 b2
let compare c1 c2 = match c1, c2 with
| M_base b1, M_base b2 -> Base.compare b1 b2
let pretty fmt = function
| M_base b -> Base.pretty fmt b
let tau_of_chunk = function
| M_base _ -> t_words
let basename_of_base = function
| Base.Var (vi, _) -> Format.sprintf "MVar_%s" (LogicUsage.basename vi)
| Base.CLogic_Var (_, _, _) -> assert false
| Base.Null -> "MNull"
| Base.String (eid, _) -> Format.sprintf "MStr_%d" eid
| Base.Allocated (vi, _dealloc, _) ->
Format.sprintf "MAlloc_%s" (LogicUsage.basename vi)
let basename_of_chunk = function
| M_base b -> basename_of_base b
let is_framed = function
| M_base b ->
try
(match WpContext.get_scope () with
| WpContext.Global -> assert false
| WpContext.Kf kf -> Base.is_formal_or_local b (Kernel_function.get_definition kf))
with Invalid_argument _ | Kernel_function.No_Definition ->
assert false
end
let cluster () = Definitions.cluster ~id:"MemVal" ()
module Heap = Qed.Collection.Make(Chunk)
module Sigma = Sigma.Make(Chunk)(Heap)
type loc = {
loc_v : V.t;
loc_t : term
}
type sigma = Sigma.t
type segment = loc rloc
type state = unit
let state _ = ()
let iter _ _ = ()
let lookup _ _ = Mterm
let updates _ _ = Bag.empty
let apply _ _ = ()
let pretty fmt l =
Format.fprintf fmt "([@ t:%a,@ v:%a @])"
F.pp_term l.loc_t
V.pretty l.loc_v
let vars _l = Vars.empty
let occurs _x _l = false
let null = {
loc_v = V.null;
loc_t = a_null;
}
let literal ~eid cstr =
let bid, v = V.literal ~eid cstr in
{
loc_v = v;
loc_t = a_global (F.e_int bid)
}
let cvar x = {
loc_v = V.cvar x;
loc_t = a_addr (F.e_int (Base.id (Base.of_varinfo x))) (F.e_zero);
}
module Obj =
struct
include C_object
let compare a b =
if a==b then 0 else
match a, b with
| C_pointer _, C_pointer _ -> 0
| _ -> compare a b
end
module Access = WpContext.Generator(Obj)
(struct
let name = "MemVal.Access"
type key = c_object
type data = lfun * lfun
let read suffix t_mem t_data =
let result = t_data in
let lfun = Lang.generated_f ~result "read_%s" suffix in
let xw = Lang.freshvar ~basename:"w" t_mem in
let xo = Lang.freshvar ~basename:"o" Logic.Int in
let dfun = Definitions.Logic result in
let cluster = cluster () in
Definitions.define_symbol {
d_lfun = lfun; d_types = 0;
d_params = [xw; xo];
d_definition = dfun;
d_cluster = cluster;
};
lfun
let write suffix t_mem t_data =
let result = t_mem in
let lfun = Lang.generated_f ~result "write_%s" suffix in
let xw = Lang.freshvar ~basename:"w" t_mem in
let xo = Lang.freshvar ~basename:"o" Logic.Int in
let xv = Lang.freshvar ~basename:"v" t_data in
let dfun = Definitions.Logic result in
let cluster = cluster () in
Definitions.define_symbol {
d_lfun = lfun; d_types = 0;
d_params = [xw; xo; xv];
d_definition = dfun;
d_cluster = cluster;
};
lfun
let axiomatize ~obj:_ suffix t_mem t_data f_rd f_wr =
let name = "axiom_" ^ suffix in
let xw = Lang.freshvar ~basename:"w" t_mem in
let w = e_var xw in
let xo = Lang.freshvar ~basename:"o" Logic.Int in
let o = e_var xo in
let xv = Lang.freshvar ~basename:"v" t_data in
let v = e_var xv in
let p_write = e_fun f_wr [w; o; v] ~result:t_mem in
let p_read = e_fun f_rd [p_write; o] ~result:t_data in
let lemma = p_equal p_read v in
let cluster = cluster () in
Definitions.define_lemma {
l_kind = Cil_types.Admit;
l_name = name;
l_triggers = [];
l_forall = [xw; xo; xv];
l_lemma = lemma;
l_cluster = cluster;
}
let axiomatize2 ~obj suffix t_mem t_data f_rd f_wr =
let name = "axiom_" ^ suffix ^ "_2" in
let xw = Lang.freshvar ~basename:"w" t_mem in
let w = e_var xw in
let xwo = Lang.freshvar ~basename:"xwo" Logic.Int in
let wo = e_var xwo in
let xro = Lang.freshvar ~basename:"xro" Logic.Int in
let ro = e_var xro in
let xv = Lang.freshvar ~basename:"v" t_data in
let v = e_var xv in
let p_write = e_fun f_wr [w; wo; v] ~result:t_mem in
let p_read = e_fun f_rd [p_write; ro] ~result:t_data in
let sizeof = (F.e_int (Ctypes.sizeof_object obj)) in
let offset = a_iabs (F.e_sub ro wo) in
let lemma =
F.p_imply
(F.p_leq sizeof offset)
(F.p_equal p_read (e_fun f_rd [w; ro] ~result:t_data))
in
let cluster = cluster () in
Definitions.define_lemma {
l_kind = Cil_types.Admit;
l_name = name;
l_triggers = [];
l_forall = [xw; xwo; xro; xv];
l_lemma = lemma;
l_cluster = cluster;
}
let generate obj =
let suffix = Ctypes.basename obj in
let t_mem = t_words in
let t_data = Lang.tau_of_object obj in
let d_read = read suffix t_mem t_data in
let d_write = write suffix t_mem t_data in
axiomatize ~obj suffix t_mem t_data d_read d_write;
axiomatize2 ~obj suffix t_mem t_data d_read d_write;
d_read, d_write
let compile = Lang.local generate
end)
let read obj ~mem ~offset =
F.e_fun (fst (Access.get obj)) [mem; offset] ~result:(Lang.tau_of_object obj)
let write obj ~mem ~offset ~value =
F.e_fun (snd (Access.get obj)) [mem; offset; value] ~result:t_words
let fold_ite f l =
let rec aux = function
| [] -> assert false
| [x] -> f x
| x :: xs ->
F.e_if
(F.e_eq (a_base l.loc_t) (F.e_int (Base.id x)))
(f x)
(aux xs)
in
aux (V.domain l.loc_v)
let fold_ite_pred f l =
let rec aux = function
| [] -> assert false
| [x] -> f x
| x :: xs ->
F.p_if
(F.p_equal (a_base l.loc_t) (F.e_int (Base.id x)))
(f x)
(aux xs)
in
aux (V.domain l.loc_v)
let pointer_loc _ = Warning.error ~source:"MemVal" "Cannot build top from EVA"
let pointer_val l = l.loc_t
let field l fd =
let offs = Integer.of_int (Ctypes.field_offset fd) in
{
loc_v = V.field l.loc_v fd;
loc_t = a_shift l.loc_t (F.e_bigint offs);
}
let shift l obj k =
let size = Integer.of_int (Ctypes.sizeof_object obj) in
let offs = F.e_times size k in
{
loc_v = V.shift l.loc_v obj k;
loc_t = a_shift l.loc_t offs;
}
let base_addr l =
{
loc_v = V.base_addr l.loc_v;
loc_t = a_addr (a_base l.loc_t) F.e_zero;
}
let block_length _s _obj l =
let size_from_base base =
F.e_bigint Base.(size_from_validity (validity base))
in
fold_ite size_from_base l
let cast _ l = l
let loc_of_int _ v =
if F.is_zero v then null
else
Warning.error ~source:"MemVal Model"
"Forbidden cast of int to pointer"
let int_of_loc _ l = pointer_val l
let domain _ l =
let d = V.domain l.loc_v in
assert (d <> []);
List.fold_left
(fun acc b -> Heap.Set.add (M_base b) acc)
Heap.Set.empty d
let load_value sigma obj l =
let load_base base =
let mem = Sigma.value sigma (M_base base) in
let offset = a_offset l.loc_t in
read obj ~mem ~offset
in
let t = fold_ite load_base l in
begin if Wp_parameters.has_dkey dkey_val then
let v = V.load (StateRef.get ()) l.loc_v obj in
debug_val "load: %a -> %a" V.pretty l.loc_v V.pretty v
end;
Val t
let load_loc ~assume sigma obj l =
let load_base v' base =
let mem = Sigma.value sigma (M_base base) in
let offset = a_offset l.loc_t in
let rd = read obj ~mem ~offset in
if assume then begin
let pred = V.offset v' (a_offset rd) in
Lang.assume pred
end;
rd
in
let v' = V.load (StateRef.get ()) l.loc_v obj in
let t = fold_ite (load_base v') l in
Loc {
loc_v = V.load (StateRef.get ()) l.loc_v obj;
loc_t = t;
}
let load : sigma -> c_object -> loc -> loc value = fun sigma obj l ->
StateRef.update ();
begin match obj with
| C_int _ | C_float _ -> load_value sigma obj l
| C_pointer _ -> load_loc ~assume:true sigma obj l
| _ -> load_loc ~assume:false sigma obj l
end
let load_init _sigma obj _loc =
e_var @@ Lang.freshvar ~basename:"i" @@ Lang.init_of_object obj
let stored : sigma sequence -> c_object -> loc -> term -> equation list = fun seq obj l v ->
let mk_write cond base =
let wpre = Sigma.value seq.pre (M_base base) in
let wpost = Sigma.value seq.post (M_base base) in
let write = write obj ~mem:wpre ~offset:(a_offset l.loc_t) ~value:v in
F.p_equal wpost (F.e_if cond write wpre)
in
let rec store acc = function
| [] -> assert false
| [c] ->
let cond = F.e_and ((List.map (F.e_neq (a_base l.loc_t))) acc) in
[ Assert (mk_write cond c) ]
| c :: cs ->
let bid = (F.e_int (Base.id c)) in
let cond = F.e_eq (a_base l.loc_t) bid in
[ Assert (mk_write cond c) ]
@ store (bid :: acc) cs
in
store [ ] (V.domain l.loc_v)
let stored_init _seq _obj _loc _t = []
let copied seq obj ll lr =
let v = match load seq.pre obj lr with
| Sigs.Val v -> v
| Sigs.Loc l -> l.loc_t
in
stored seq obj ll v
let copied_init _seq _obj _ll _lr = []
let assigned _s _obj _sloc = [ Assert F.p_true ]
let is_null l = p_equal l.loc_t a_null
let loc_delta l1 l2 =
match F.is_equal (a_base l1.loc_t) (a_base l2.loc_t) with
| Logic.Yes -> F.e_sub (a_offset l1.loc_t) (a_offset l2.loc_t)
| Logic.Maybe | Logic.No ->
Warning.error "Can only compare pointers with same base."
let base_eq l1 l2 = F.p_equal (a_base l1.loc_t) (a_base l2.loc_t)
let offset_cmp cmpop l1 l2 = cmpop (a_offset l1.loc_t) (a_offset l2.loc_t)
let loc_diff _obj l1 l2 = loc_delta l1 l2
let loc_eq l1 l2 = F.p_and (base_eq l1 l2) (offset_cmp F.p_equal l1 l2)
let loc_lt l1 l2 = F.p_lt (loc_delta l1 l2) F.e_zero
let loc_leq l1 l2 = F.p_leq (loc_delta l1 l2) F.e_zero
let loc_neq l1 l2 = F.p_neq (loc_delta l1 l2) F.e_zero
type range =
| LOC of loc * term
| RANGE of loc * Vset.set
let range_of_rloc = function
| Rloc (obj, l) ->
LOC (l, F.e_int (Ctypes.sizeof_object obj))
| Rrange (l, obj, Some a, Some b) ->
let la = shift l obj a in
let n = e_fact (Ctypes.sizeof_object obj) (F.e_range a b) in
LOC (la, n)
| Rrange (l, obj, a_opt, b_opt) ->
let f = F.e_fact (Ctypes.sizeof_object obj) in
RANGE (l, Vset.range (Option.map f a_opt) (Option.map f b_opt))
(** [vset_from_validity base] returns the logical set of all valid bytes of
[base]. **)
let vset_from_validity = function
| Base.Empty -> Vset.empty
| Base.Invalid -> Vset.singleton F.e_zero
| Base.Known (min_valid, max_valid)
| Base.Unknown (min_valid, Some max_valid, _) ->
let mn = F.e_bigint Integer.(e_div min_valid eight) in
let mx = F.e_bigint Integer.(e_div max_valid eight) in
Vset.range (Some mn) (Some mx)
| Base.Variable { Base.min_alloc = min_valid } ->
let mn_valid = F.e_bigint Integer.(e_div min_valid eight) in
Vset.range (Some F.e_zero) (Some mn_valid)
| Base.Unknown (_, None, _) -> Vset.empty
let valid_range : sigma -> acs -> range -> pred = fun _ acs r ->
let for_writing = match acs with RW -> true | RD -> false
| OBJ -> true in
let l, base_offset = match r with
| LOC (l, n) ->
let a = a_offset l.loc_t in
let b = F.e_add a (F.e_sub n F.e_one) in
l, Vset.range (Some a) (Some b)
| RANGE (l, r) -> l, Vset.lift_add (Vset.singleton l.loc_t) r
in
let valid_base set base =
if for_writing && (Base.is_read_only base) then
F.p_false
else
let base_vset = vset_from_validity (Base.validity base) in
Vset.subset set base_vset
in
fold_ite_pred (valid_base base_offset) l
(** [valid sigma acs seg] returns the formula that tests if a given memory
segment [seg] (in bytes) is valid (according to [acs]) at memory state
[sigma]. **)
let valid : sigma -> acs -> segment -> pred = fun s acs seg ->
valid_range s acs (range_of_rloc seg)
let invalid = fun _ _ -> F.p_true
let alloc_sigma : sigma -> varinfo list -> sigma = fun sigma xs ->
let alloc sigma x =
let havoc s c = Sigma.havoc_chunk s (M_base c) in
let v = V.cvar x in
List.fold_left havoc sigma (V.domain v)
in
List.fold_left alloc sigma xs
let alloc_pred _ _ _ = []
let alloc sigma xs =
if xs = [] then sigma else alloc_sigma sigma xs
let scope : sigma sequence -> scope -> varinfo list -> pred list = fun seq scope xs ->
match scope with
| Enter -> []
| Leave ->
alloc_pred seq xs ()
let scope seq sc xs =
let preds = scope seq sc xs in
debug "[scope pre:%a post:%a xs:%a] -> preds:%a"
Sigma.pretty seq.pre
Sigma.pretty seq.post
(Pretty_utils.pp_iter ~sep:" " List.iter Varinfo.pretty) xs
(Pretty_utils.pp_iter ~sep:" " List.iter pp_pred) preds;
preds
let global : sigma -> term -> pred = fun _ _ ->
F.p_true
let range_to_base_offset = function
| LOC (l, n) ->
let a = a_offset l.loc_t in
let b = F.e_add a n in
l, Vset.range (Some a) (Some b)
| RANGE (l, r) -> l, Vset.lift_add (Vset.singleton l.loc_t) r
let included : segment -> segment -> pred = fun s1 s2 ->
let l1, vs1 = range_to_base_offset (range_of_rloc s1) in
let l2, vs2 = range_to_base_offset (range_of_rloc s2) in
p_and
(p_equal (a_base l1.loc_t) (a_base l2.loc_t))
(Vset.subset vs1 vs2)
let separated : segment -> segment -> pred = fun s1 s2 ->
let l1, vs1 = range_to_base_offset (range_of_rloc s1) in
let l2, vs2 = range_to_base_offset (range_of_rloc s2) in
p_and
(p_equal (a_base l1.loc_t) (a_base l2.loc_t))
(Vset.disjoint vs1 vs2)
let initialized _sigma _l = F.p_true
let is_well_formed _ = F.p_true
let base_offset _loc = assert false
type domain = Sigma.domain
let no_binder = { bind = fun _ f v -> f v }
let configure_ia _ = no_binder
let hypotheses x = x
let frame _sigma = []
end
module Eva =
struct
open Cvalue
let datatype = "Eva"
let configure () =
if not (Wp_eva.is_computed ()) then
Wp_parameters.abort ~current:true
"Could not use Eva memory model without a previous run of the analysis.";
(fun () -> ())
module State =
struct
type t = Model.t
let bottom = Model.bottom
let join = Model.join
let of_kinstr k = Wp_eva.get_cvalue_state k
let of_stmt s = Wp_eva.get_cvalue_state (Kstmt s)
let of_kf kf =
let state = ref bottom in
let vis = object
inherit Cil.nopCilVisitor
method !vstmt stmt =
state := join (of_stmt stmt) !state;
Cil.DoChildren
end in
ignore (Cil.visitCilFunction vis (Kernel_function.get_definition kf));
!state
let pretty = Model.pretty
end
type t = V.t
type state = Model.t
let null = V.inject Base.null Ival.zero
let literal ~eid cstr =
let b = Base.of_string_exp (Cstring.str_cil ~eid cstr) in
Base.id b, V.inject b Ival.zero
let cvar x = V.inject (Base.of_varinfo x) Ival.zero
let field v fd =
let bsize = Ctypes.field_offset fd |> Integer.of_int in
let offs = Ival.inject_singleton bsize in
Cvalue.V.shift offs v
let shift v obj t =
let bsize = 8 * Ctypes.sizeof_object obj |> Integer.of_int in
let offs = match F.repr t with
| Logic.Kint z -> Ival.inject_singleton (Integer.mul bsize z)
| _ -> Ival.top in
Cvalue.V.shift offs v
let base_addr v =
Cvalue.V.fold_topset_ok
(fun b _ v -> Cvalue.V.add b Ival.zero v)
v (Cvalue.V.bottom)
let load state v obj =
let bsize = 8 * Ctypes.sizeof_object obj in
let bits = Locations.loc_bytes_to_loc_bits v in
let int_base = bsize |> Integer.of_int |> Int_Base.inject in
let vloc = Locations.make_loc bits int_base in
Cvalue.Model.find state vloc
let domain v =
Cvalue.V.fold_topset_ok
(fun b _ acc -> b :: acc)
v []
let logic_ival ival = fun x ->
match Ival.project_small_set ival with
| Some is ->
F.p_any
(fun i -> F.p_equal x (F.e_bigint i))
is
| None -> begin
match Ival.min_and_max ival with
| Some mn, Some mx ->
F.p_and
(F.p_leq (F.e_bigint mn) x)
(F.p_leq x (F.e_bigint mx))
| Some mn, None -> F.p_leq (F.e_bigint mn) x
| None, Some mx -> F.p_leq x (F.e_bigint mx)
| None, None -> F.p_true
end
let offset v = fun x ->
let ivals =
Cvalue.V.fold_topset_ok
(fun _ ival acc -> ival :: acc)
v []
in
F.p_any (fun ival -> logic_ival ival x) ivals
let pretty = Cvalue.V.pretty
end