Source file Cvalues.ml
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open Cil_types
open Ctypes
open Qed
open Lang
open Lang.F
open Sigs
open Definitions
let ainf = Some e_zero
let asup n = Some (e_int (n-1))
let arange k n = p_and (p_leq e_zero k) (p_lt k (e_int n))
let equation = function
| Set(a,b) -> p_equal a b
| Assert p -> p
let rec constant = function
| CInt64(z,_,_) -> e_bigint z
| CChr c -> e_int64 (Ctypes.char c)
| CReal(f,fk,s) -> Cfloat.code_lit (Ctypes.c_float fk) f s
| CEnum e -> constant_exp e.eival
| CStr _ | CWStr _ -> Warning.error "String constants not yet implemented"
and logic_constant = function
| Integer(z,_) -> e_bigint z
| LChr c -> e_int64 (Ctypes.char c)
| LReal r -> Cfloat.acsl_lit r
| LEnum e -> constant_exp e.eival
| LStr _ | LWStr _ -> Warning.error "String constants not yet implemented"
and constant_exp e =
let e = Cil.constFold true e in
match e.enode with
| Const c -> constant c
| _ -> Warning.error "constant(%a)" Printer.pp_exp e
and constant_term t =
let e = Cil.constFoldTerm t in
match e.term_node with
| TConst c -> logic_constant c
| _ -> Warning.error "constant(%a)" Printer.pp_term t
module OPAQUE_COMP_INIT = struct
type initialization_funs = {
init: lfun ;
uninit: lfun ;
}
include WpContext.Generator(Cil_datatype.Compinfo)
(struct
let name = "Cvalues.EmptyCompInit"
type key = compinfo
type data = initialization_funs
let compile c =
if c.cfields <> None then
Wp_parameters.fatal
"Asking for opaque struct init on non opaque struct" ;
let result = Lang.t_init c in
let generate_init name =
Lang.generated_f ~params:[] ~result "%s" name
in
let init = generate_init ("Initialized" ^ Lang.comp_id c) in
let uninit = generate_init ("Uninitialized" ^ Lang.comp_id c) in
Definitions.define_symbol {
d_cluster = Definitions.compinfo c ;
d_lfun = init ; d_types = 0 ; d_params = [] ;
d_definition = Logic result ;
} ;
Definitions.define_symbol {
d_cluster = Definitions.compinfo c ;
d_lfun = uninit ; d_types = 0 ; d_params = [] ;
d_definition = Logic result ;
} ;
{ init ; uninit }
end)
end
let initialized_value_opaque_comp value comp =
let pick_fun r =
if value = e_true then r.OPAQUE_COMP_INIT.init
else r.uninit
in
Lang.F.e_fun (pick_fun (OPAQUE_COMP_INIT.get comp)) []
let rec init_value value obj =
match obj with
| C_int _ | C_float _ | C_pointer _ -> value
| C_comp ci -> init_comp_value value ci
| C_array _ as arr ->
Lang.F.e_const Lang.t_int
(init_value value (object_of_array_elem arr))
and init_comp_value value ci =
match ci.cfields with
| None -> initialized_value_opaque_comp value ci
| Some fields ->
let make f = cfield ~kind:KInit f, init_value value (object_of f.ftype) in
Lang.F.e_record (List.map make fields)
let initialized_obj = init_value e_true
let uninitialized_obj = init_value e_false
let always_initialized x =
(x.vformal || x.vglob) && not @@ Cil.isStructOrUnionType x.vtype
module OPAQUE_COMP_BYTES_LENGTH = WpContext.Generator(Cil_datatype.Compinfo)
(struct
let name = "Cvalues.EmptyCompBytesLength"
type key = compinfo
type data = lfun
let compile c =
if c.cfields <> None then
Wp_parameters.fatal
"Asking for opaque struct length on non opaque struct" ;
let result = Lang.t_int in
let f_name = "BytesLength_of_" ^ (comp_id c) in
let l_name = "Positive_" ^ f_name in
let size = Lang.generated_f ~params:[] ~result "%s" f_name in
Definitions.define_symbol {
d_cluster = Definitions.compinfo c ;
d_lfun = size ; d_types = 0 ; d_params = [] ;
d_definition = Logic result ;
} ;
let min_size = if Cil.acceptEmptyCompinfo () then e_zero else e_one in
Definitions.define_lemma {
l_kind = Admit ; l_name ;
l_triggers = [] ; l_forall = [] ;
l_cluster = Definitions.compinfo c ;
l_lemma = Lang.F.(p_leq min_size (e_fun size []))
} ;
size
end)
let bytes_length_of_opaque_comp c =
Lang.F.e_fun (OPAQUE_COMP_BYTES_LENGTH.get c) []
let rec is_constrained typ =
is_constrained_obj (Ctypes.object_of typ)
and is_constrained_obj = function
| C_int _ -> true
| C_float _ -> false
| C_pointer _ -> false
| C_array a -> is_constrained a.arr_element
| C_comp c -> is_constrained_comp c
and is_constrained_comp { cfields } =
match cfields with
| None -> false
| Some l -> List.exists (fun f -> is_constrained f.ftype) l
module type CASES =
sig
val prefix : string
val natural : bool
val is_int : c_int -> term -> pred
val is_float : c_float -> term -> pred
val is_pointer : term -> pred
end
module STRUCTURAL(C : CASES) =
struct
let constrained_elt ty = C.natural || is_constrained ty
let constrained_comp c = C.natural || is_constrained_comp c
let model_int fmt i =
if C.natural
then Format.pp_print_string fmt "int"
else Ctypes.pp_int fmt i
let array_name te ds =
let dim = List.length ds in
let pp_dim fmt d = if d > 1 then Format.fprintf fmt "_d%d" d in
match te with
| C_int i ->
Format.asprintf "%sArray%a_%a" C.prefix pp_dim dim model_int i
| C_comp c ->
Format.asprintf "%sArray%a_%s" C.prefix pp_dim dim (Lang.comp_id c)
| C_float _ | C_pointer _ | C_array _ ->
assert false
let rec is_obj obj t =
match obj with
| C_int i -> C.is_int i t
| C_float f -> C.is_float f t
| C_pointer _ty -> C.is_pointer t
| C_comp c ->
if constrained_comp c then is_record c t else p_true
| C_array a ->
if constrained_elt a.arr_element
then
let te,ds = Ctypes.array_dimensions a in
is_array te ds t
else p_true
and is_typ typ t = is_obj (Ctypes.object_of typ) t
and is_record c s =
Definitions.call_pred
(Lang.generated_p ~coloring:true (C.prefix ^ Lang.comp_id c))
(fun lfun ->
let basename = if c.cstruct then "S" else "U" in
let s = Lang.freshvar ~basename (Lang.t_comp c) in
let dfun =
match c.cfields with
| None -> Logic Lang.t_prop
| Some fields ->
let value f = e_getfield (e_var s) (Lang.cfield f) in
let def = p_all (fun f -> is_typ f.ftype (value f)) fields in
Predicate(Def,def)
in {
d_lfun = lfun ; d_types = 0 ; d_params = [s] ;
d_cluster = Definitions.compinfo c ;
d_definition = dfun ;
})
[s]
and is_array elt ds t =
Definitions.call_pred
(Lang.generated_p ~coloring:true (array_name elt ds))
(fun lfun ->
let cluster =
match elt with
| C_comp c -> Definitions.compinfo c
| _ -> Definitions.matrix () in
let te = Lang.tau_of_object elt in
let d = List.length ds in
let x = Lang.freshvar ~basename:"T" (Lang.t_matrix te d) in
let fk _d = Lang.freshvar ~basename:"k" Logic.Int in
let ks = List.map fk ds in
let e = List.fold_left (fun a k -> e_get a (e_var k)) (e_var x) ks in
let def = p_forall ks (is_obj elt e) in
{
d_lfun = lfun ; d_types = 0 ; d_params = [x] ;
d_cluster = cluster ;
d_definition = Predicate(Def,def) ;
}
) [t]
end
let null = Context.create "Lang.null"
module NULL = STRUCTURAL
(struct
let prefix = "Null"
let natural = true
let is_int _i = p_equal e_zero
let is_float _f = p_equal e_zero_real
let is_pointer p = Context.get null p
end)
let is_null = NULL.is_obj
module TYPE = STRUCTURAL
(struct
let prefix = "Is"
let natural = false
let is_int = Cint.range
let is_float _ _ = p_true
let is_pointer _ = p_true
end)
let has_ctype = TYPE.is_typ
let is_object obj = function
| Loc _ -> p_true
| Val e -> TYPE.is_obj obj e
let cdomain obj =
if is_constrained_obj obj then Some(TYPE.is_obj obj) else None
let ldomain ltype =
match Logic_utils.unroll_type ~unroll_typedef:false ltype with
| Ctype typ -> cdomain (Ctypes.object_of typ)
| Ltype _ | Lvar _ | Linteger | Lreal | Larrow _ -> None
let volatile ?warn () =
Wp_parameters.Volatile.get () ||
( Option.iter
(fun w -> Warning.emit ~severe:false
~effect:"ignore volatile attribute" "%s" w)
warn ; false )
let equal_rec = ref (fun _ _ _ -> assert false)
let rec reduce_eqcomp = function
| [a;b] when Lang.F.equal a b -> F.e_true
| _::ws -> reduce_eqcomp ws
| [] -> raise Not_found
module AKEY =
struct
type t = base * Matrix.t
and base = I | F of c_float | P | C of compinfo
let make elt ds =
let base = match elt with
| C_int _ -> I
| C_float f -> F f
| C_pointer _ -> P
| C_comp c -> C c
| C_array _ -> assert false
in base , ds
let key = function
| I -> "int"
| P -> "ptr"
| F f -> Ctypes.f_name f
| C c -> Lang.comp_id c
let cluster = function
| I | P | F _ -> Definitions.matrix ()
| C c -> Definitions.compinfo c
let tau = function
| I -> Lang.t_int
| F f -> Lang.t_float f
| P -> Lang.t_addr ()
| C c -> Lang.t_comp c
let equal = function
| I | F _ | P -> F.p_equal
| C c -> !equal_rec (C_comp c)
let compare (a,p) (b,q) =
let cmp = String.compare (key a) (key b) in
if cmp <> 0 then cmp else Matrix.compare p q
let pretty fmt (a,ds) =
Format.fprintf fmt "%s%a" (key a) Matrix.pp_suffix_id ds
end
module EQARRAY = WpContext.Generator(AKEY)
(struct
let name = "Cvalues.EqArray"
type key = AKEY.t
type data = lfun
let compile (a,ds) =
let lfun = Lang.generated_f
~context:true
~sort:Logic.Sprop
"EqArray_%s%a" (AKEY.key a) Matrix.pp_suffix_id ds in
Lang.F.set_builtin lfun reduce_eqcomp ;
let denv = Matrix.cc_env ds in
let tau = Matrix.cc_tau (AKEY.tau a) ds in
let xa = Lang.freshvar ~basename:"T" tau in
let xb = Lang.freshvar ~basename:"T" tau in
let ta = e_var xa in
let tb = e_var xb in
let ta_xs = List.fold_left e_get ta denv.index_val in
let tb_xs = List.fold_left e_get tb denv.index_val in
let property = p_hyps (denv.index_range) (AKEY.equal a ta_xs tb_xs) in
let definition = p_forall denv.index_var property in
Definitions.define_symbol {
d_cluster = AKEY.cluster a ;
d_lfun = lfun ; d_types = 0 ;
d_params = denv.size_var @ [xa ; xb ] ;
d_definition = Predicate(Def,definition) ;
} ; lfun
end)
module EQCOMP = WpContext.Generator(Cil_datatype.Compinfo)
(struct
let name = "Cvalues.EqComp"
type key = compinfo
type data = lfun
let compile c =
let lfun = Lang.generated_p ~context:true ("Eq" ^ Lang.comp_id c) in
Lang.F.set_builtin lfun reduce_eqcomp ;
let basename = if c.cstruct then "S" else "U" in
let tc = Lang.t_comp c in
let xa = Lang.freshvar ~basename tc in
let xb = Lang.freshvar ~basename tc in
let ra = e_var xa in
let rb = e_var xb in
let d_definition =
match c.cfields with
| None -> Logic Lang.t_prop
| Some fields ->
let def = p_all
(fun f ->
let fd = cfield f in
!equal_rec (Ctypes.object_of f.ftype)
(e_getfield ra fd) (e_getfield rb fd))
fields
in Predicate(Def, def)
in
Definitions.define_symbol {
d_cluster = Definitions.compinfo c ;
d_lfun = lfun ; d_types = 0 ; d_params = [xa;xb] ;
d_definition ;
} ; lfun
end)
type matrixinfo = c_object * int option list
let equal_comp c a b = p_call (EQCOMP.get c) [a;b]
let equal_array m a b =
let elt,ns = m in
let ds = Matrix.of_dims ns in
let ms = Matrix.cc_dims ns in
p_call (EQARRAY.get @@ AKEY.make elt ds) (ms @ [a;b])
let equal_object obj a b =
match obj with
| C_int _ | C_float _ | C_pointer _ -> p_equal a b
| C_comp c -> equal_comp c a b
| C_array m -> equal_array (Ctypes.array_dimensions m) a b
let () = equal_rec := equal_object
let map_value f = function
| Val t -> Val t
| Loc l -> Loc (f l)
let map_sloc f = function
| Sloc l -> Sloc (f l)
| Sarray(l,obj,n) -> Sarray(f l,obj,n)
| Srange(l,obj,a,b) -> Srange(f l,obj,a,b)
| Sdescr(xs,l,p) -> Sdescr(xs,f l,p)
let map_logic f = function
| Vexp t -> Vexp t
| Vloc l -> Vloc (f l)
| Vset s -> Vset s
| Lset ls -> Lset (List.map (map_sloc f) ls)
let plain lt e =
if Logic_typing.is_set_type lt then
let te = Logic_typing.type_of_set_elem lt in
Vset [Vset.Set(tau_of_ltype te,e)]
else
Vexp e
type 'a printer = Format.formatter -> 'a -> unit
let pp_acs fmt = function
| RW -> Format.pp_print_string fmt "RW"
| RD -> Format.pp_print_string fmt "RD"
| OBJ -> Format.pp_print_string fmt "OBJ"
let pp_bound fmt = function None -> () | Some p -> F.pp_term fmt p
let pp_value pp fmt = function
| Loc l -> pp fmt l
| Val v -> F.pp_term fmt v
let pp_logic pp fmt = function
| Vexp e -> F.pp_term fmt e
| Vloc l -> pp fmt l
| Lset _ | Vset _ -> Format.pp_print_string fmt "<set>"
let pp_rloc pp fmt = function
| Rloc(obj,l) ->
Format.fprintf fmt "@[<hov 2>%a:@,%a@]" pp l Ctypes.pretty obj
| Rrange(l,obj,a,b) ->
Format.fprintf fmt "@[<hov2>%a@,.(%a@,..%a):@,%a@]"
pp l pp_bound a pp_bound b Ctypes.pretty obj
let pp_sloc pp fmt = function
| Sloc l -> pp fmt l
| Sarray(l,_,n) ->
Format.fprintf fmt "@[<hov2>%a@,.(..%d)@]" pp l (n-1)
| Srange(l,_,a,b) ->
Format.fprintf fmt "@[<hov2>%a@,.(%a@,..%a)@]" pp l pp_bound a pp_bound b
| Sdescr(xs,l,p) ->
Format.fprintf fmt "@[<hov2>{ %a | %a }@]" pp l F.pp_pred (F.p_forall xs p)
let pp_region pp fmt sloc =
List.iter (fun (_,s) -> Format.fprintf fmt "@ %a" (pp_sloc pp) s) sloc
let bool_eq a b = e_if (e_eq a b) e_one e_zero
let bool_lt a b = e_if (e_lt a b) e_one e_zero
let bool_neq a b = e_if (e_eq a b) e_zero e_one
let bool_leq a b = e_if (e_leq a b) e_one e_zero
let bool_and a b = e_and [e_neq a e_zero ; e_neq b e_zero]
let bool_or a b = e_or [e_neq a e_zero ; e_neq b e_zero]
let bool_val e = e_if e e_one e_zero
let is_true p = e_if (e_prop p) e_one e_zero
let is_false p = e_if (e_prop p) e_zero e_one
let startof ~shift loc typ =
if Cil.isArrayType typ then
let t_elt = Cil.typeOf_array_elem typ in
shift loc (Ctypes.object_of t_elt) e_zero
else loc
type polarity = [ `Positive | `Negative | `NoPolarity ]
let negate = function
| `Positive -> `Negative
| `Negative -> `Positive
| `NoPolarity -> `NoPolarity
module Logic(M : Sigs.Model) =
struct
type logic = M.loc Sigs.logic
type segment = c_object * M.loc Sigs.sloc
type region = M.loc Sigs.region
let value = function
| Vexp e -> e
| Vloc l -> M.pointer_val l
| Vset s -> Vset.concretize s
| Lset _ -> Warning.error "T-Set of values not yet implemented"
let loc = function
| Vloc l -> l
| Vexp e -> M.pointer_loc e
| Vset _ -> Warning.error "Set of pointers not yet implemented"
| Lset _ -> Warning.error "T-Set of regions not yet implemented"
let rdescr = function
| Sloc l -> [],l,p_true
| Sdescr(xs,l,p) -> xs,l,p
| Sarray(l,obj,n) ->
let x = Lang.freshvar ~basename:"k" Logic.Int in
let k = e_var x in
[x],M.shift l obj k,arange k n
| Srange(l,obj,a,b) ->
let x = Lang.freshvar ~basename:"k" Logic.Int in
let k = e_var x in
[x],M.shift l obj k,Vset.in_range k a b
let vset_of_sloc sloc =
List.map
(function
| Sloc p -> Vset.Singleton (M.pointer_val p)
| u ->
let xs,l,p = rdescr u in
Vset.Descr( xs , M.pointer_val l , p )
) sloc
let sloc_of_vset phi vset =
List.map
(function
| Vset.Singleton e -> phi (Sloc (M.pointer_loc e))
| w ->
let xs,t,p = Vset.descr w in
phi (Sdescr(xs,M.pointer_loc t,p))
) vset
let vset = function
| Vexp v -> Vset.singleton v
| Vloc l -> Vset.singleton (M.pointer_val l)
| Vset s -> s
| Lset sloc -> vset_of_sloc sloc
let sloc_map phi = function
| Vexp e -> [phi (Sloc (M.pointer_loc e))]
| Vloc l -> [phi (Sloc l)]
| Lset locs -> List.map phi locs
| Vset vset -> sloc_of_vset phi vset
let region obj logic = sloc_map (fun s -> obj , s) logic
let sloc logic = sloc_map (fun s -> s) logic
let is_single = function (Vexp _ | Vloc _) -> true | (Lset _ | Vset _) -> false
let map_lift f1 f2 a =
match a with
| Vexp e -> Vexp (f1 e)
| Vloc l -> Vexp (f1 (M.pointer_val l))
| _ -> Vset(f2 (vset a))
let apply_lift f1 f2 a b =
if is_single a && is_single b then
Vexp (f1 (value a) (value b))
else
Vset (f2 (vset a) (vset b))
let map f = map_lift f (Vset.map f)
let map_opp = map_lift e_opp Vset.map_opp
let apply f = apply_lift f (Vset.lift f)
let apply_add = apply_lift e_add Vset.lift_add
let apply_sub = apply_lift e_sub Vset.lift_sub
let map_loc f lv =
if is_single lv then Vloc (f (loc lv))
else Lset
(List.map
(function
| Sloc l -> Sloc (f l)
| s -> let xs,l,p = rdescr s in Sdescr(xs,f l,p)
) (sloc lv))
let map_l2t f lv =
if is_single lv then Vexp (f (loc lv))
else Vset
(List.map
(function
| Sloc l -> Vset.Singleton (f l)
| s -> let xs,l,p = rdescr s in Vset.Descr(xs,f l,p)
) (sloc lv))
let map_t2l f sv =
if is_single sv then Vloc (f (value sv))
else Lset
(List.map
(function
| Vset.Singleton e -> Sloc (f e)
| s -> let xs,l,p = Vset.descr s in Sdescr(xs,f l,p)
) (vset sv))
let field lv f = map_loc (fun l -> M.field l f) lv
let restrict kset = function
| None -> kset
| Some s ->
if Kernel.SafeArrays.get () then
match kset with
| Vset.Singleton _ | Vset.Set _ -> kset
| Vset.Range(a,b) ->
let cap l = function None -> Some l | u -> u in
Vset.Range(cap e_zero a,cap (e_int (s-1)) b)
| Vset.Descr(xs,k,p) ->
let a = e_zero in
let b = e_int s in
Vset.Descr(xs,k,p_conj [p_leq a k;p_lt k b;p])
else kset
let is_ainf = function
| Some e -> e == e_zero
| None -> false
let is_asup n = function
| Some e -> e == e_int (n-1)
| None -> false
let srange loc obj size a b =
match size with
| None -> Srange(loc,obj,a,b)
| Some n ->
if is_ainf a && is_asup n b then
Sarray(loc,obj,n)
else
Srange(loc,obj,a,b)
let shift_set sloc obj (size : int option) kset =
match sloc , size , kset with
| Sloc l , Some n , Vset.Range(None,None) when Kernel.SafeArrays.get () ->
Sarray(l,obj,n)
| _ ->
match sloc , restrict kset size with
| Sloc l , Vset.Singleton k -> Sloc(M.shift l obj k)
| Sloc l , Vset.Range(a,b) -> srange l obj size a b
| Srange(l,obj0,a0,b0) , Vset.Singleton k
when Ctypes.equal obj0 obj ->
let a = Vset.bound_add a0 (Some k) in
let b = Vset.bound_add b0 (Some k) in
srange l obj0 size a b
| Srange(l,obj0,a0,b0) , Vset.Range(a1,b1)
when Ctypes.equal obj0 obj ->
let a = Vset.bound_add a0 a1 in
let b = Vset.bound_add b0 b1 in
srange l obj0 size a b
| _ ->
let xs,l,p = rdescr sloc in
let ys,k,q = Vset.descr kset in
Sdescr( xs @ ys , M.shift l obj k , p_and p q )
let shift lv obj ?size kv =
if is_single kv then
let k = value kv in map_loc (fun l -> M.shift l obj k) lv
else
let ks = vset kv in
Lset(List.fold_left
(fun s sloc ->
List.fold_left
(fun s kset ->
shift_set sloc obj size kset :: s
) s ks
) [] (sloc lv))
type loader = {
mutable sloc : M.loc sloc list ;
mutable vset : Vset.vset list ;
}
let flush prefer_loc a = match a with
| { vset=[] } -> Lset (List.rev a.sloc)
| { sloc=[] } -> Vset (List.rev a.vset)
| _ ->
if prefer_loc then
Lset (a.sloc @ sloc_of_vset (fun r -> r) a.vset)
else
Vset (vset_of_sloc a.sloc @ a.vset)
let loadsloc a sigma obj = function
| Sloc l ->
begin
match M.load sigma obj l with
| Val t -> a.vset <- Vset.Singleton t :: a.vset
| Loc l -> a.sloc <- Sloc l :: a.sloc
end
| (Sarray _ | Srange _ | Sdescr _) as s ->
let xs , l , p = rdescr s in
begin
match M.load sigma obj l with
| Val t -> a.vset <- Vset.Descr(xs,t,p) :: a.vset
| Loc l -> a.sloc <- Sdescr(xs,l,p) :: a.sloc
end
let load sigma obj lv =
if is_single lv then
let data = M.load sigma obj (loc lv) in
Lang.assume (is_object obj data) ;
match data with
| Val t -> Vexp t
| Loc l -> Vloc l
else
let a = { vset=[] ; sloc=[] } in
List.iter (loadsloc a sigma obj) (sloc_map (fun r -> r) lv) ;
flush (Ctypes.is_pointer obj) a
let union t vs =
let a = { vset=[] ; sloc=[] } in
List.iter
(function
| Vexp e -> a.vset <- Vset.Singleton e::a.vset
| Vloc l -> a.sloc <- Sloc l :: a.sloc
| Vset s -> a.vset <- List.rev_append s a.vset
| Lset s -> a.sloc <- List.rev_append s a.sloc
) vs ;
flush (Logic_typing.is_pointer_type t) a
let inter t vs =
match List.map (fun v -> Vset.concretize (vset v)) vs with
| [] ->
if Logic_typing.is_pointer_type t
then Lset [] else Vset []
| v::vs ->
let s = List.fold_left Vset.inter v vs in
let t = Lang.tau_of_ltype t in
Vset [Vset.Set(t,s)]
let rloc obj = function
| Sloc l -> Rloc(obj,l)
| Sarray(l,t,n) -> Rrange(l,t,ainf,asup n)
| Srange(l,t,a,b) -> Rrange(l,t,a,b)
| Sdescr _ -> raise Exit
let separated_region w (r1 : region) (r2 : region) =
List.fold_left
(fun w (o1,s1) ->
List.fold_left
(fun w (o2,s2) ->
let cond =
try M.separated (rloc o1 s1) (rloc o2 s2)
with Exit ->
let xs,l1,p1 = rdescr s1 in
let ys,l2,p2 = rdescr s2 in
let se1 = Rloc(o1,l1) in
let se2 = Rloc(o2,l2) in
p_forall (xs@ys) (p_hyps [p1;p2] (M.separated se1 se2))
in cond::w
) w r2
) w r1
let rec separated_from w (r1 : region) = function
| r2::rs -> separated_from (separated_region w r1 r2) r1 rs
| [] -> w
let rec separated_regions w = function
| r::rs -> separated_regions (separated_from w r rs) rs
| [] -> w
let separated (regions : region list) =
p_conj (separated_regions [] regions)
let included (obj1,s1) (obj2,s2) =
try M.included (rloc obj1 s1) (rloc obj2 s2)
with Exit ->
let xs,l1,p1 = rdescr s1 in
let ys,l2,p2 = rdescr s2 in
let se1 = Rloc(obj1,l1) in
let se2 = Rloc(obj2,l2) in
p_forall xs (p_imply p1 (p_exists ys (p_and p2 (M.included se1 se2))))
let on_sloc phi (obj,sloc) = match sloc with
| Sloc l -> phi (Rloc(obj,l))
| Sarray(l,t,n) -> phi (Rrange(l,t,ainf,asup n))
| Srange(l,t,a,b) -> phi (Rrange(l,t,a,b))
| Sdescr(xs,l,p) -> p_forall xs (p_imply p (phi (Rloc(obj,l))))
let valid sigma acs sloc = on_sloc (M.valid sigma acs) sloc
let invalid sigma sloc = on_sloc (M.invalid sigma) sloc
let initialized sigma sloc = on_sloc (M.initialized sigma) sloc
let subset ta la tb lb =
match la , lb with
| Vexp x , Vexp y -> F.p_equal x y
| Vexp e , Vset b -> Vset.member e b
| Vset a , Vexp e -> Vset.subset a [Vset.Singleton e]
| Vset a , Vset b -> Vset.subset a b
| Vloc _ , _ | _ , Vloc _
| Lset _ , _ | _ , Lset _ ->
let ta = Ctypes.object_of_logic_pointed ta in
let tb = Ctypes.object_of_logic_pointed tb in
let ra = List.map (fun s -> ta,s) (sloc la) in
let rb = List.map (fun s -> tb,s) (sloc lb) in
p_all (fun s -> p_any (included s) rb) ra
end