Source file MemVar.ml
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open Cil_types
open Cil_datatype
open Ctypes
open MemoryContext
open Lang
open Lang.F
open Sigs
module type VarUsage =
sig
val datatype : string
val param : varinfo -> MemoryContext.param
val iter: ?kf:kernel_function -> init:bool -> (varinfo -> unit) -> unit
end
module Raw : VarUsage =
struct
let datatype = "Raw"
let param _x = MemoryContext.ByValue
let iter ?kf ~init f =
begin
ignore init ;
Globals.Vars.iter (fun x _initinfo -> f x) ;
match kf with
| None -> ()
| Some kf -> List.iter f (Kernel_function.get_formals kf) ;
end
end
module Static : VarUsage =
struct
let datatype = "Static"
let param x =
let open Cil_types in
if x.vaddrof || Cil.isArrayType x.vtype || Cil.isPointerType x.vtype
then MemoryContext.ByAddr else MemoryContext.ByValue
let iter = Raw.iter
end
module Make(V : VarUsage)(M : Sigs.Model) =
struct
let datatype = "MemVar." ^ V.datatype ^ M.datatype
let configure = M.configure
let no_binder = { bind = fun _ f v -> f v }
let configure_ia _ = no_binder
let hypotheses p =
let kf,init = match WpContext.get_scope () with
| WpContext.Global -> None,false
| WpContext.Kf f ->
Some f, CfgInfos.is_entry_point f in
let w = ref p in
V.iter ?kf ~init (fun vi -> w := MemoryContext.set vi (V.param vi) !w) ;
M.hypotheses !w
type chunk =
| Var of varinfo
| Alloc of varinfo
| Init of varinfo
| Mem of M.Chunk.t
let is_framed_var x = not x.vglob && not x.vaddrof
module VAR =
struct
type t = varinfo
let self = "var"
let hash = Varinfo.hash
let equal = Varinfo.equal
let compare = Varinfo.compare
let pretty = Varinfo.pretty
let typ_of_chunk x =
match V.param x with
| ByRef -> Cil.typeOf_pointed x.vtype
| _ -> x.vtype
let tau_of_chunk x = Lang.tau_of_ctype (typ_of_chunk x)
let is_framed = is_framed_var
let basename_of_chunk = LogicUsage.basename
end
module VALLOC =
struct
type t = varinfo
let self = "alloc"
let hash = Varinfo.hash
let compare = Varinfo.compare
let equal = Varinfo.equal
let pretty = Varinfo.pretty
let tau_of_chunk _x = Qed.Logic.Bool
let basename_of_chunk x =
match V.param x with
| ByRef ->
"ra_" ^ LogicUsage.basename x
| NotUsed | ByValue | ByShift | ByAddr | InContext _ | InArray _ ->
"ta_" ^ LogicUsage.basename x
let is_framed = is_framed_var
end
module VINIT =
struct
type t = varinfo
let self = "init"
let hash = Varinfo.hash
let compare = Varinfo.compare
let equal = Varinfo.equal
let pretty = Varinfo.pretty
let typ_of_chunk x =
match V.param x with
| ByRef -> Cil.typeOf_pointed x.vtype
| _ -> x.vtype
let tau_of_chunk x = Lang.init_of_ctype (typ_of_chunk x)
let is_framed = is_framed_var
let basename_of_chunk x = "Init_" ^ (LogicUsage.basename x)
end
module Chunk =
struct
type t = chunk
let self = "varmem"
let hash = function
| Var x -> 3 * Varinfo.hash x
| Alloc x -> 5 * Varinfo.hash x
| Mem m -> 7 * M.Chunk.hash m
| Init x -> 11 * Varinfo.hash x
let compare c1 c2 =
if c1 == c2 then 0 else
match c1 , c2 with
| Var x , Var y
| Alloc x , Alloc y
| Init x, Init y -> Varinfo.compare x y
| Mem p , Mem q -> M.Chunk.compare p q
| Var _ , _ -> (-1)
| _ , Var _ -> 1
| Init _, _ -> (-1)
| _, Init _ -> 1
| Alloc _ , _ -> (-1)
| _ , Alloc _ -> 1
let equal c1 c2 = (compare c1 c2 = 0)
let pretty fmt = function
| Var x -> Varinfo.pretty fmt x
| Alloc x -> Format.fprintf fmt "alloc(%a)" Varinfo.pretty x
| Init x -> Format.fprintf fmt "init(%a)" Varinfo.pretty x
| Mem m -> M.Chunk.pretty fmt m
let tau_of_chunk = function
| Var x -> VAR.tau_of_chunk x
| Alloc x -> VALLOC.tau_of_chunk x
| Init x -> VINIT.tau_of_chunk x
| Mem m -> M.Chunk.tau_of_chunk m
let basename_of_chunk = function
| Var x -> VAR.basename_of_chunk x
| Alloc x -> VALLOC.basename_of_chunk x
| Init x -> VINIT.basename_of_chunk x
| Mem m -> M.Chunk.basename_of_chunk m
let is_framed = function
| Var x -> VAR.is_framed x
| Alloc x -> VALLOC.is_framed x
| Init x -> VINIT.is_framed x
| Mem m -> M.Chunk.is_framed m
end
module HEAP = Qed.Collection.Make(VAR)
module TALLOC = Qed.Collection.Make(VALLOC)
module TINIT = Qed.Collection.Make(VINIT)
module SIGMA = Sigma.Make(VAR)(HEAP)
module ALLOC = Sigma.Make(VALLOC)(TALLOC)
module INIT = Sigma.Make(VINIT)(TINIT)
module Heap = Qed.Collection.Make(Chunk)
type sigma = {
mem : M.Sigma.t ;
vars : SIGMA.t ;
init : INIT.t ;
alloc : ALLOC.t ;
}
module Sigma =
struct
type t = sigma
type chunk = Chunk.t
module Chunk = Heap
type domain = Heap.set
let empty = Heap.Set.empty
let union = Heap.Set.union
let create () = {
vars = SIGMA.create () ;
init = INIT.create () ;
alloc = ALLOC.create () ;
mem = M.Sigma.create () ;
}
let copy s = {
vars = SIGMA.copy s.vars ;
init = INIT.copy s.init ;
alloc = ALLOC.copy s.alloc ;
mem = M.Sigma.copy s.mem ;
}
let choose s1 s2 =
let s = SIGMA.choose s1.vars s2.vars in
let i = INIT.choose s1.init s2.init in
let a = ALLOC.choose s1.alloc s2.alloc in
let m = M.Sigma.choose s1.mem s2.mem in
{ vars = s ; alloc = a ; mem = m ; init = i }
let merge s1 s2 =
let s,pa1,pa2 = SIGMA.merge s1.vars s2.vars in
let i,ia1,ia2 = INIT.merge s1.init s2.init in
let a,ta1,ta2 = ALLOC.merge s1.alloc s2.alloc in
let m,qa1,qa2 = M.Sigma.merge s1.mem s2.mem in
{ vars = s ; alloc = a ; mem = m ; init = i } ,
Passive.union (Passive.union (Passive.union pa1 ta1) qa1) ia1 ,
Passive.union (Passive.union (Passive.union pa2 ta2) qa2) ia2
let merge_list l =
let s,pa = SIGMA.merge_list (List.map (fun s -> s.vars) l) in
let i,ia = INIT.merge_list (List.map (fun s -> s.init) l) in
let a,ta = ALLOC.merge_list (List.map (fun s -> s.alloc) l) in
let m,qa = M.Sigma.merge_list (List.map (fun s -> s.mem) l) in
{ vars = s ; alloc = a ; mem = m ; init = i } ,
let union = List.map2 Passive.union in
union (union (union pa ta) qa) ia
let join s1 s2 =
Passive.union
(Passive.union
(Passive.union
(SIGMA.join s1.vars s2.vars)
(ALLOC.join s1.alloc s2.alloc))
(M.Sigma.join s1.mem s2.mem))
(INIT.join s1.init s2.init)
let get s = function
| Var x -> SIGMA.get s.vars x
| Init x -> INIT.get s.init x
| Alloc x -> ALLOC.get s.alloc x
| Mem m -> M.Sigma.get s.mem m
let mem s = function
| Var x -> SIGMA.mem s.vars x
| Init x -> INIT.mem s.init x
| Alloc x -> ALLOC.mem s.alloc x
| Mem m -> M.Sigma.mem s.mem m
let value s c = e_var (get s c)
let iter f s =
begin
SIGMA.iter (fun x -> f (Var x)) s.vars ;
INIT.iter (fun x -> f (Init x)) s.init ;
ALLOC.iter (fun x -> f (Alloc x)) s.alloc ;
M.Sigma.iter (fun m -> f (Mem m)) s.mem ;
end
let iter2 f s t =
begin
SIGMA.iter2 (fun x a b -> f (Var x) a b) s.vars t.vars ;
INIT.iter2 (fun x a b -> f (Init x) a b) s.init t.init ;
ALLOC.iter2 (fun x a b -> f (Alloc x) a b) s.alloc t.alloc ;
M.Sigma.iter2 (fun m p q -> f (Mem m) p q) s.mem t.mem ;
end
let domain_partition r =
begin
let xs = ref HEAP.Set.empty in
let is = ref TINIT.Set.empty in
let ts = ref TALLOC.Set.empty in
let ms = ref M.Heap.Set.empty in
Heap.Set.iter
(function
| Var x -> xs := HEAP.Set.add x !xs
| Init x -> is := TINIT.Set.add x !is
| Alloc x -> ts := TALLOC.Set.add x !ts
| Mem c -> ms := M.Heap.Set.add c !ms
) r ;
!xs , !is, !ts , !ms
end
let domain_var xs =
HEAP.Set.fold (fun x s -> Heap.Set.add (Var x) s) xs Heap.Set.empty
let domain_init xs =
TINIT.Set.fold (fun x s -> Heap.Set.add (Init x) s) xs Heap.Set.empty
let domain_alloc ts =
TALLOC.Set.fold (fun x s -> Heap.Set.add (Alloc x) s) ts Heap.Set.empty
let domain_mem ms =
M.Heap.Set.fold (fun m s -> Heap.Set.add (Mem m) s) ms Heap.Set.empty
let assigned ~pre ~post w =
let w_vars , w_init, w_alloc , w_mem = domain_partition w in
let h_vars = SIGMA.assigned ~pre:pre.vars ~post:post.vars w_vars in
let h_init = INIT.assigned ~pre:pre.init ~post:post.init w_init in
let h_alloc = ALLOC.assigned ~pre:pre.alloc ~post:post.alloc w_alloc in
let h_mem = M.Sigma.assigned ~pre:pre.mem ~post:post.mem w_mem in
Bag.ulist [h_vars;h_init;h_alloc;h_mem]
let havoc s r =
let rvar , rinit, ralloc , rmem = domain_partition r
in {
vars = SIGMA.havoc s.vars rvar ;
init = INIT.havoc s.init rinit ;
alloc = ALLOC.havoc s.alloc ralloc ;
mem = M.Sigma.havoc s.mem rmem ;
}
let havoc_chunk s = function
| Var x -> { s with vars = SIGMA.havoc_chunk s.vars x }
| Init x -> { s with init = INIT.havoc_chunk s.init x }
| Alloc x -> { s with alloc = ALLOC.havoc_chunk s.alloc x }
| Mem m -> { s with mem = M.Sigma.havoc_chunk s.mem m }
let havoc_any ~call s = {
alloc = s.alloc ;
vars = SIGMA.havoc_any ~call s.vars ;
init = INIT.havoc_any ~call s.init ;
mem = M.Sigma.havoc_any ~call s.mem ;
}
let remove_chunks s r =
let rvar , rinit, ralloc , rmem = domain_partition r
in {
vars = SIGMA.remove_chunks s.vars rvar ;
init = INIT.remove_chunks s.init rinit ;
alloc = ALLOC.remove_chunks s.alloc ralloc ;
mem = M.Sigma.remove_chunks s.mem rmem ;
}
let domain s =
Heap.Set.union
(Heap.Set.union
(Heap.Set.union
(domain_var (SIGMA.domain s.vars))
(domain_alloc (ALLOC.domain s.alloc)))
(domain_mem (M.Sigma.domain s.mem)))
(domain_init (INIT.domain s.init))
let writes s =
Heap.Set.union
(Heap.Set.union
(Heap.Set.union
(domain_var (SIGMA.writes {pre=s.pre.vars;post=s.post.vars}))
(domain_alloc (ALLOC.writes {pre=s.pre.alloc;post=s.post.alloc})))
(domain_mem (M.Sigma.writes {pre=s.pre.mem;post=s.post.mem})))
(domain_init (INIT.writes {pre=s.pre.init;post=s.post.init}))
let pretty fmt s =
Format.fprintf fmt "@[<hov 2>{X:@[%a@]@ I:@[%a@]@ T:@[%a@]@ M:@[%a@]}@]"
SIGMA.pretty s.vars
INIT.pretty s.init
ALLOC.pretty s.alloc
M.Sigma.pretty s.mem
end
type domain = Sigma.domain
let get_var s x = SIGMA.get s.vars x
let get_term s x = e_var (get_var s x)
let get_init s x = INIT.get s.init x
let get_init_term s x = e_var (get_init s x)
type ichunk = Iref of varinfo | Ivar of varinfo | Iinit of varinfo
type state = {
svar : ichunk Tmap.t ;
smem : M.state ;
}
module IChunk =
struct
let compare_var x y =
let rank x =
if x.vformal then 0 else
if x.vglob then 1 else
if x.vtemp then 3 else 2 in
let cmp = rank x - rank y in
if cmp <> 0 then cmp else Varinfo.compare x y
type t = ichunk
let hash = function
| Iref x | Ivar x -> Varinfo.hash x
| Iinit x -> 13 * Varinfo.hash x
let compare x y =
match x,y with
| Iref x , Iref y -> Varinfo.compare x y
| Ivar x , Ivar y -> compare_var x y
| Iinit x, Iinit y -> compare_var x y
| Iref _ , _ -> (-1)
| Iinit _, _ -> (-1)
| _ , Iref _ -> 1
| _ , Iinit _ -> 1
let equal x y =
match x,y with
| Iref x, Iref y | Ivar x, Ivar y | Iinit x, Iinit y -> Varinfo.equal x y
| _, _ -> false
end
module Icmap = Qed.Mergemap.Make(IChunk)
let set_chunk v c m =
let c =
try
let c0 = Tmap.find v m in
if IChunk.compare c c0 < 0 then c else c0
with Not_found -> c in
Tmap.add v c m
let state s =
let m = ref Tmap.empty in
SIGMA.iter (fun x v ->
let c = match V.param x with ByRef -> Iref x | _ -> Ivar x in
m := set_chunk (e_var v) c !m
) s.vars ;
INIT.iter (fun x v ->
match V.param x with
| ByRef -> ()
| _ -> m := set_chunk (e_var v) (Iinit x) !m
) s.init ;
{ svar = !m ; smem = M.state s.mem }
let ilval = function
| Iref x -> (Mvar x,[Mindex e_zero])
| Ivar x | Iinit x -> (Mvar x,[])
let imval c = match c with
| Iref _ | Ivar _ -> Sigs.Mlval (ilval c, KValue)
| Iinit _ -> Sigs.Mlval (ilval c, KInit)
let lookup s e =
try imval (Tmap.find e s.svar)
with Not_found -> M.lookup s.smem e
let apply f s =
let m = ref Tmap.empty in
Tmap.iter (fun e c ->
let e = f e in
m := set_chunk e c !m ;
) s.svar ;
{ svar = !m ; smem = M.apply f s.smem }
let iter f s =
Tmap.iter (fun v c -> f (imval c) v) s.svar ;
M.iter f s.smem
let icmap domain istate =
Tmap.fold (fun m c w ->
if Vars.intersect (F.vars m) domain
then Icmap.add c m w else w
) istate Icmap.empty
let rec diff lv v1 v2 =
if v1 == v2 then Bag.empty else
match F.repr v2 with
| Qed.Logic.Aset(m , k , vk) ->
let upd = diff (Mstate.index lv k) (F.e_get m k) vk in
Bag.concat (diff lv v1 m) upd
| Qed.Logic.Rdef fvs ->
rdiff lv v1 v2 fvs
| _ ->
Bag.elt (Mstore(lv,v2))
and rdiff lv v1 v2 = function
| (Lang.Cfield (fi, _k) as fd ,f2) :: fvs ->
let f1 = F.e_getfield v1 fd in
if f1 == f2 then rdiff lv v1 v2 fvs else
let upd = diff (Mstate.field lv fi) f1 f2 in
let m = F.e_setfield v2 fd f1 in
Bag.concat upd (diff lv v1 m)
| (Lang.Mfield _,_)::_ -> Bag.elt (Mstore(lv,v2))
| [] -> Bag.empty
let updates seq domain =
let pre = icmap domain seq.pre.svar in
let post = icmap domain seq.post.svar in
let pool = ref Bag.empty in
Icmap.iter2
(fun c v1 v2 ->
match v1 , v2 with
| _ , None -> ()
| None , Some v -> pool := Bag.add (Mstore(ilval c,v)) !pool
| Some v1 , Some v2 -> pool := Bag.concat (diff (ilval c) v1 v2) !pool
) pre post ;
let seq_mem = { pre = seq.pre.smem ; post = seq.post.smem } in
Bag.concat !pool (M.updates seq_mem domain)
type mem =
| CVAL
| CREF
| CTXT of MemoryContext.validity
| CARR of MemoryContext.validity
| HEAP
let is_heap_allocated = function
| CREF | CVAL -> false | HEAP | CTXT _ | CARR _ -> true
type loc =
| Ref of varinfo
| Val of mem * varinfo * ofs list
| Loc of M.loc
and ofs =
| Field of fieldinfo
| Shift of c_object * term
type segment = loc rloc
let rec ofs_vars xs = function
| [] -> xs
| Field _ :: ofs -> ofs_vars xs ofs
| Shift(_,k) :: ofs -> ofs_vars (Vars.union xs (F.vars k)) ofs
let vars = function
| Ref _ -> Vars.empty
| Loc l -> M.vars l
| Val(_,_,ofs) -> ofs_vars Vars.empty ofs
let rec ofs_occurs x = function
| [] -> false
| Field _ :: ofs -> ofs_occurs x ofs
| Shift(_,k) :: ofs -> Vars.mem x (F.vars k) || ofs_occurs x ofs
let occurs x = function
| Ref _ -> false
| Loc l -> M.occurs x l
| Val(_,_,ofs) -> ofs_occurs x ofs
let byte_offset n = function
| Field fd -> F.e_add n (F.e_int (Ctypes.field_offset fd))
| Shift(obj,k) -> F.e_add n (F.e_fact (Ctypes.sizeof_object obj) k)
let vtype m x =
match m with
| CVAL | HEAP -> x.vtype
| CTXT _ | CREF -> Cil.typeOf_pointed x.vtype
| CARR _ -> Ast_info.array_type (Cil.typeOf_pointed x.vtype)
let vobject m x = Ctypes.object_of (vtype m x)
let vbase m x =
match m with
| CVAL | HEAP -> x
| _ -> { x with vglob = true ; vtype = vtype m x }
let rec pp_offset ~obj fmt = function
| [] -> ()
| Field f :: ofs ->
Format.fprintf fmt ".%s" f.fname ;
pp_offset ~obj:(object_of f.ftype) fmt ofs
| Shift(elt,k) :: ofs ->
if Ctypes.is_array obj ~elt then
( Format.fprintf fmt ".(%a)" F.pp_term k ;
pp_offset ~obj:elt fmt ofs )
else
( Format.fprintf fmt ".(%a : %a)" F.pp_term k Ctypes.pretty elt ;
pp_offset ~obj:elt fmt ofs )
let pp_mem fmt = function
| CVAL -> Format.pp_print_string fmt "var"
| CREF -> Format.pp_print_string fmt "ref"
| CTXT _ -> Format.pp_print_string fmt "ptr"
| CARR _ -> Format.pp_print_string fmt "arr"
| HEAP -> Format.pp_print_string fmt "mem"
let pp_var_model fmt = function
| ByValue | ByShift | NotUsed -> Format.pp_print_string fmt "non-aliased"
| ByRef -> Format.pp_print_string fmt "by reference"
| InContext _ | InArray _ -> Format.pp_print_string fmt "in an isolated context"
| ByAddr -> Format.pp_print_string fmt "aliased"
let pretty fmt = function
| Ref x -> VAR.pretty fmt x
| Loc l -> M.pretty fmt l
| Val(m,x,ofs) ->
let obj = vobject m x in
Format.fprintf fmt "@[%a:%a%a@]"
pp_mem m VAR.pretty x
(pp_offset ~obj) ofs
let noref ~op var =
Warning.error
"forbidden %s variable '%a' considered %a.@\n\
Use model 'Typed' instead or specify '-wp-unalias-vars %a'"
op Varinfo.pretty var
pp_var_model (V.param var)
Varinfo.pretty var
let null = Loc M.null
let literal ~eid cst = Loc (M.literal ~eid cst)
let cvar x = match V.param x with
| NotUsed | ByValue | ByShift -> Val(CVAL,x,[])
| ByAddr -> Val(HEAP,x,[])
| InContext _ | InArray _ | ByRef -> Ref x
module Nullable = WpContext.Generator(Varinfo)
(struct
let name = "MemVar.Nullable"
type key = varinfo
type data = lfun
let compile v =
let result = t_addr () in
let lfun = Lang.generated_f ~result "pointer_%s" v.vname in
let cluster =
Definitions.cluster ~id:"Globals" ~title:"Context pointers" ()
in
Definitions.define_symbol {
d_lfun = lfun ;
d_types = 0 ;
d_params = [] ;
d_definition = Definitions.Logic result ;
d_cluster = cluster
} ;
lfun
end)
let nullable_address v =
Lang.F.e_fun (Nullable.get v) []
let moffset l = function
| Field f -> M.field l f
| Shift(e,k) -> M.shift l e k
let mseq_of_seq seq = { pre = seq.pre.mem ; post = seq.post.mem }
let mloc_of_path m x ofs =
let l = match m with
| CTXT Nullable | CARR Nullable -> M.pointer_loc @@ nullable_address x
| _ -> M.cvar (vbase m x)
in
List.fold_left moffset l ofs
let mloc_of_loc = function
| Loc l -> l
| Ref x -> M.cvar x
| Val(m,x,ofs) -> mloc_of_path m x ofs
let pointer_loc p = Loc (M.pointer_loc p)
let pointer_val l = M.pointer_val (mloc_of_loc l)
let field l f =
match l with
| Loc l -> Loc (M.field l f)
| Ref x -> noref ~op:"field access to" x
| Val(m,x,ofs) ->
if not @@ is_heap_allocated m then MemMemory.unsupported_union f ;
Val(m,x,ofs @ [Field f])
let rec ofs_shift obj k = function
| [] -> [Shift(obj,k)]
| [Shift(elt,i)] when Ctypes.equal obj elt -> [Shift(elt,F.e_add i k)]
| f::ofs -> f :: ofs_shift obj k ofs
let shift l obj k = match l with
| Loc l -> Loc (M.shift l obj k)
| Ref x -> noref ~op:"array access to" x
| Val(m,x,ofs) -> Val(m,x,ofs_shift obj k ofs)
let base_addr = function
| Loc l -> Loc (M.base_addr l)
| Ref x -> noref ~op:"base address of" x
| Val(m,x,_) -> Val(m,x,[])
let base_offset = function
| Loc l -> M.base_offset l
| Ref x -> noref ~op:"offset address of" x
| Val(_,_,ofs) -> List.fold_left byte_offset e_zero ofs
let block_length sigma obj = function
| Loc l -> M.block_length sigma.mem obj l
| Ref x -> noref ~op:"block-length of" x
| Val(m,x,_) ->
begin match Ctypes.object_of (vtype m x) with
| C_comp ({ cfields = None } as c) ->
Cvalues.bytes_length_of_opaque_comp c
| obj ->
let size =
if Ctypes.sizeof_defined obj
then Ctypes.sizeof_object obj
else if Wp_parameters.ExternArrays.get ()
then max_int
else Warning.error ~source:"MemVar" "Unknown array-size"
in F.e_int size
end
let cast obj l = Loc(M.cast obj (mloc_of_loc l))
let loc_of_int e a = Loc(M.loc_of_int e a)
let int_of_loc i l = M.int_of_loc i (mloc_of_loc l)
let rec access_gen kind a = function
| [] -> a
| Field f :: ofs -> access_gen kind (e_getfield a (cfield ~kind f)) ofs
| Shift(_,k) :: ofs -> access_gen kind (e_get a k) ofs
let access = access_gen KValue
let access_init = access_gen KInit
let rec update_gen kind a ofs v = match ofs with
| [] -> v
| Field f :: ofs ->
let phi = cfield ~kind f in
let a_f = F.e_getfield a phi in
let a_f_v = update_gen kind a_f ofs v in
F.e_setfield a phi a_f_v
| Shift(_,k) :: ofs ->
let a_k = F.e_get a k in
let a_k_v = update_gen kind a_k ofs v in
F.e_set a k a_k_v
let update = update_gen KValue
let update_init = update_gen KInit
let load sigma obj = function
| Ref x ->
begin match V.param x with
| ByRef -> Sigs.Loc(Val(CREF,x,[]))
| InContext n -> Sigs.Loc(Val(CTXT n,x,[]))
| InArray n -> Sigs.Loc(Val(CARR n,x,[]))
| NotUsed | ByAddr | ByValue | ByShift -> assert false
end
| Val((CREF|CVAL),x,ofs) ->
Sigs.Val(access (get_term sigma x) ofs)
| Loc l ->
Cvalues.map_value
(fun l -> Loc l)
(M.load sigma.mem obj l)
| Val((CTXT _|CARR _|HEAP) as m,x,ofs) ->
Cvalues.map_value
(fun l -> Loc l)
(M.load sigma.mem obj (mloc_of_path m x ofs))
let load_init sigma obj = function
| Ref _ ->
e_true
| Val((CREF|CVAL),x,_) when Cvalues.always_initialized x ->
Cvalues.initialized_obj obj
| Val((CREF|CVAL),x,ofs) ->
access_init (get_init_term sigma x) ofs
| Loc l ->
M.load_init sigma.mem obj l
| Val((CTXT _|CARR _|HEAP) as m,x,ofs) ->
M.load_init sigma.mem obj (mloc_of_path m x ofs)
let memvar_stored kind seq x ofs v =
let get_term, update = match kind with
| KValue -> get_term, update
| KInit -> get_init_term, update_init
in
let v1 = get_term seq.pre x in
let v2 = get_term seq.post x in
Set( v2 , update v1 ofs v )
let gen_stored kind seq obj l v =
let mstored = match kind with KValue -> M.stored | KInit -> M.stored_init in
match l with
| Ref x -> noref ~op:"write to" x
| Val((CREF|CVAL),x,ofs) ->
[memvar_stored kind seq x ofs v]
| Val((CTXT _|CARR _|HEAP) as m,x,ofs) ->
mstored (mseq_of_seq seq) obj (mloc_of_path m x ofs) v
| Loc l ->
mstored (mseq_of_seq seq) obj l v
let stored = gen_stored KValue
let stored_init = gen_stored KInit
let copied seq obj l1 l2 =
let v = match load seq.pre obj l2 with
| Sigs.Val r -> r
| Sigs.Loc l -> pointer_val l
in stored seq obj l1 v
let copied_init seq obj l1 l2 =
stored_init seq obj l1 (load_init seq.pre obj l2)
let is_null = function
| Loc l -> M.is_null l
| Val ((CTXT Nullable|CARR Nullable)as m,x,ofs) ->
M.is_null (mloc_of_path m x ofs)
| Ref _ | Val _ -> F.p_false
let rec offset = function
| [] -> e_zero
| Field f :: ofs ->
e_add (e_int (Ctypes.field_offset f)) (offset ofs)
| Shift(obj,k)::ofs ->
e_add (e_fact (Ctypes.sizeof_object obj) k) (offset ofs)
let loc_diff obj a b =
match a , b with
| Loc l1 , Loc l2 -> M.loc_diff obj l1 l2
| Ref x , Ref y when Varinfo.equal x y -> e_zero
| Val(_,x,p) , Val(_,y,q) when Varinfo.equal x y ->
e_div (e_sub (offset p) (offset q)) (e_int (Ctypes.sizeof_object obj))
| _ ->
Warning.error ~source:"Reference Variable Model"
"Uncomparable locations %a and %a" pretty a pretty b
let loc_compare lcmp icmp same a b =
match a , b with
| Loc l1 , Loc l2 -> lcmp l1 l2
| Ref x , Ref y ->
if Varinfo.equal x y then same else p_not same
| Val(_,x,p) , Val(_,y,q) ->
if Varinfo.equal x y then icmp (offset p) (offset q) else p_not same
| (Val _ | Loc _) , (Val _ | Loc _) -> lcmp (mloc_of_loc a) (mloc_of_loc b)
| Ref _ , (Val _ | Loc _) | (Val _ | Loc _) , Ref _ -> p_not same
let loc_eq = loc_compare M.loc_eq F.p_equal F.p_true
let loc_lt = loc_compare M.loc_lt F.p_lt F.p_false
let loc_leq = loc_compare M.loc_leq F.p_leq F.p_true
let loc_neq = loc_compare M.loc_neq F.p_neq F.p_false
exception ShiftMismatch
let shift_mismatch l =
Wp_parameters.fatal "Invalid shift : %a" pretty l
let unsized_array () = Warning.error ~severe:false
"Validity of unsized-array not implemented yet"
let fits_inside cond a b n =
p_leq e_zero a :: p_lt b (e_int n) :: cond
let fits_off_by_one cond a b n =
p_leq e_zero a :: p_leq b (e_int n) :: cond
let stay_outside cond a b n =
p_lt b e_zero :: p_leq (e_int n) a :: cond
let rec block_check fitting cond (block,size) ((elt,a,b) as range) =
if Ctypes.equal block elt then
fitting cond a b size
else
match Ctypes.get_array block with
| Some( e , Some n ) -> block_check fitting cond (e , n * size) range
| Some( _ , None ) -> unsized_array ()
| None -> raise ShiftMismatch
let array_check fitting cond te k obj =
match Ctypes.get_array obj with
| Some( e , Some n ) when Ctypes.equal e te -> fitting cond k k n
| Some( _ , None ) -> unsized_array ()
| _ -> block_check fitting cond (obj,1) (te,k,k)
let rec offset_fits cond obj offset =
match offset with
| [] -> cond
| Field fd :: ofs ->
offset_fits cond (Ctypes.object_of fd.ftype) ofs
| Shift(te,k) :: ofs ->
let cond = array_check fits_inside cond te k obj in
offset_fits cond te ofs
let rec range_check fitting cond alloc offset ((elt,a,b) as range) =
match offset with
| [] -> block_check fitting cond alloc range
| Field fd :: ofs ->
range_check fitting cond (Ctypes.object_of fd.ftype,1) ofs range
| Shift(te,k) :: ofs ->
if Ctypes.equal te elt then
range_check fitting cond alloc ofs (elt,e_add a k,e_add b k)
else
match Ctypes.get_array (fst alloc) with
| Some( e , Some n ) when Ctypes.equal e te ->
let cond = fitting cond k k n in
range_check fitting cond (e,n) ofs range
| Some( _ , None ) ->
unsized_array ()
| _ ->
let cond = block_check fitting cond alloc (te,k,k) in
range_check fitting cond (te,1) ofs range
let rec last_field_shift acs obj ofs =
match acs , obj , ofs with
| OBJ , _ , [Shift(te,k)] -> Some(te,k,obj)
| OBJ , C_comp c , (Field fd :: ofs) ->
begin
match Option.map List.rev c.cfields with
| Some (fd0::_) when Fieldinfo.equal fd fd0 ->
last_field_shift acs (Ctypes.object_of fd.ftype) ofs
| _ -> None
end
| _ -> None
let valid_offset acs obj ofs =
match last_field_shift acs obj ofs with
| Some(te,k,obj) ->
F.p_conj (array_check fits_off_by_one [] te k obj)
| None ->
F.p_conj (offset_fits [] obj ofs)
let valid_range acs obj ofs range =
match last_field_shift acs obj ofs with
| Some _ ->
F.p_conj (range_check fits_off_by_one [] (obj,1) ofs range)
| _ ->
F.p_conj (range_check fits_inside [] (obj,1) ofs range)
let valid_base sigma acs mem x =
if x.vglob then
match acs with
| RW -> if Cil.typeHasQualifier "const" x.vtype then p_false else p_true
| RD | OBJ -> p_true
else
match mem with
| CVAL | HEAP -> p_bool (ALLOC.value sigma.alloc x)
| CREF | CTXT Valid | CARR Valid -> p_true
| CTXT Nullable | CARR Nullable ->
p_not @@ M.is_null (mloc_of_path mem x [])
let valid_offset_path sigma acs mem x ofs =
p_and
(valid_base sigma acs mem x)
(valid_offset acs (vobject mem x) ofs)
let valid_range_path sigma acs mem x ofs rg =
p_and
(valid_base sigma acs mem x)
(valid_range acs (vobject mem x) ofs rg)
let valid sigma acs = function
| Rloc(obj,l) ->
begin match l with
| Ref _ -> p_true
| Loc l -> M.valid sigma.mem acs (Rloc(obj,l))
| Val(m,x,p) ->
try valid_offset_path sigma acs m x p
with ShiftMismatch ->
if is_heap_allocated m then
M.valid sigma.mem acs (Rloc(obj,mloc_of_loc l))
else
shift_mismatch l
end
| Rrange(l,elt,a,b) ->
begin match l with
| Ref x -> noref ~op:"valid sub-range of" x
| Loc l -> M.valid sigma.mem acs (Rrange(l,elt,a,b))
| Val(m,x,p) ->
match a,b with
| Some ka,Some kb ->
begin
try
F.p_imply (F.p_leq ka kb)
(valid_range_path sigma acs m x p (elt,ka,kb))
with ShiftMismatch ->
if is_heap_allocated m then
let l = mloc_of_loc l in
M.valid sigma.mem acs (Rrange(l,elt,a,b))
else shift_mismatch l
end
| _ ->
Warning.error "Validity of infinite range @[%a.(%a..%a)@]"
pretty l Vset.pp_bound a Vset.pp_bound b
end
let invalid_range obj ofs range =
F.p_disj (range_check stay_outside [] (obj,1) ofs range)
let invalid_offset_path sigma m x p =
p_not (valid_offset_path sigma RD m x p)
let invalid_range_path sigma m x p rg =
p_imply
(valid_base sigma RD m x)
(invalid_range (vobject m x) p rg)
let invalid sigma = function
| Rloc(obj,l) ->
begin match l with
| Ref _ -> p_false
| Loc l -> M.invalid sigma.mem (Rloc(obj,l))
| Val(m,x,p) ->
try invalid_offset_path sigma m x p
with ShiftMismatch ->
if is_heap_allocated m then
M.invalid sigma.mem (Rloc(obj,mloc_of_loc l))
else
shift_mismatch l
end
| Rrange(l,elt,a,b) ->
begin match l with
| Ref x -> noref ~op:"invalid sub-range of" x
| Loc l -> M.invalid sigma.mem (Rrange(l,elt,a,b))
| Val(m,x,p) ->
match a,b with
| Some ka,Some kb ->
begin
try
F.p_imply (F.p_leq ka kb)
(invalid_range_path sigma m x p (elt,ka,kb))
with ShiftMismatch ->
if is_heap_allocated m then
let l = mloc_of_loc l in
M.invalid sigma.mem (Rrange(l,elt,a,b))
else shift_mismatch l
end
| _ ->
Warning.error "Invalidity of infinite range @[%a.(%a..%a)@]"
pretty l Vset.pp_bound a Vset.pp_bound b
end
let rec initialized_loc sigma obj x ofs =
match obj with
| C_int _ | C_float _ | C_pointer _ ->
p_bool (access_init (get_init_term sigma x) ofs)
| C_array { arr_flat=flat ; arr_element = te } ->
let size = match flat with
| None -> unsized_array ()
| Some { arr_size } -> arr_size in
let elt = Ctypes.object_of te in
initialized_range sigma elt x ofs (e_int 0) (e_int (size-1))
| C_comp { cfields = None } ->
Lang.F.p_equal
(access_init (get_init_term sigma x) ofs)
(Cvalues.initialized_obj obj)
| C_comp { cfields = Some fields } ->
let init_field fd =
let obj_fd = Ctypes.object_of fd.ftype in
let ofs_fd = ofs @ [Field fd] in
initialized_loc sigma obj_fd x ofs_fd
in
Lang.F.p_conj (List.map init_field fields)
and initialized_range sigma elt x ofs lo up =
let i = Lang.freshvar ~basename:"i" Lang.t_int in
let vi = e_var i in
let ofs = ofs @ [ Shift(elt, vi) ] in
let range_i = p_and (p_leq lo vi) (p_leq vi up) in
let init_i = initialized_loc sigma elt x ofs in
Lang.F.p_forall [i] (p_imply range_i init_i)
let initialized sigma l =
match l with
| Rloc(obj,l) ->
begin match l with
| Ref _ -> p_true
| Loc l -> M.initialized sigma.mem (Rloc(obj,l))
| Val(m,x,p) ->
if is_heap_allocated m then
M.initialized sigma.mem (Rloc(obj,mloc_of_loc l))
else if Cvalues.always_initialized x then
try valid_offset RD (vobject m x) p
with ShiftMismatch -> shift_mismatch l
else
initialized_loc sigma obj x p
end
| Rrange(l,elt, Some a, Some b) ->
begin match l with
| Ref _ -> p_true
| Loc l -> M.initialized sigma.mem (Rrange(l,elt,Some a, Some b))
| Val(m,x,p) ->
try
if is_heap_allocated m then
let l = mloc_of_loc l in
M.initialized sigma.mem (Rrange(l,elt,Some a, Some b))
else
let rec normalize obj = function
| [] -> [], a, b
| [Shift(elt, i)] when Ctypes.equal obj elt ->
[], F.e_add a i, F.e_add b i
| f :: ofs ->
let l, a, b = normalize obj ofs in f :: l, a, b
in
let p, a, b = normalize elt p in
let in_array = valid_range RD (vobject m x) p (elt, a, b) in
let initialized =
if Cvalues.always_initialized x then p_true
else initialized_range sigma elt x p a b
in
F.p_imply (F.p_leq a b) (p_and in_array initialized)
with ShiftMismatch ->
shift_mismatch l
end
| Rrange(l, _,a,b) ->
Warning.error
"Initialization of infinite range @[%a.(%a..%a)@]"
pretty l Vset.pp_bound a Vset.pp_bound b
let rec forall_pointers phi v t =
match Cil.unrollType t with
| TInt _ | TFloat _ | TVoid _ | TEnum _ | TNamed _ | TBuiltin_va_list _
-> F.p_true
| TPtr _ | TFun _ -> phi v
| TComp({ cfields = None },_) ->
F.p_true
| TComp({ cfields = Some fields },_) ->
F.p_all
(fun fd ->
forall_pointers phi (e_getfield v (cfield fd)) fd.ftype)
fields
| TArray(elt,_,_) ->
let k = Lang.freshvar Qed.Logic.Int in
F.p_forall [k] (forall_pointers phi (e_get v (e_var k)) elt)
let frame sigma =
let hs = ref [] in
SIGMA.iter
begin fun x chunk ->
(if (x.vglob || x.vformal) then
let t = VAR.typ_of_chunk x in
let v = e_var chunk in
let h = forall_pointers (M.global sigma.mem) v t in
if not (F.eqp h F.p_true) then hs := h :: !hs ) ;
(if x.vglob then
let v = e_var chunk in
hs := Cvalues.has_ctype x.vtype v :: !hs ) ;
end sigma.vars ;
!hs @ M.frame sigma.mem
let is_mem x = match V.param x with
| ByAddr -> true
| _ -> false
let is_mvar_alloc x =
match V.param x with
| ByRef | InContext _ | InArray _ | NotUsed -> false
| ByValue | ByShift | ByAddr -> true
let alloc sigma xs =
let xm = List.filter is_mem xs in
let mem = M.alloc sigma.mem xm in
let xv = List.filter is_mvar_alloc xs in
let domain = TALLOC.Set.of_list xv in
let alloc = ALLOC.havoc sigma.alloc domain in
{ sigma with alloc ; mem }
let scope_vars seq scope xs =
let xs = List.filter is_mvar_alloc xs in
if xs = [] then []
else
let t_in = seq.pre.alloc in
let t_out = seq.post.alloc in
let v_in = match scope with Enter -> e_false | Leave -> e_true in
let v_out = match scope with Enter -> e_true | Leave -> e_false in
List.map
(fun x ->
F.p_and
(F.p_equal (ALLOC.value t_in x) v_in)
(F.p_equal (ALLOC.value t_out x) v_out)
) xs
let scope_init seq scope xs =
match scope with
| Leave -> []
| Enter ->
let init_status v =
if v.vdefined || Cvalues.always_initialized v || not@@ is_mvar_alloc v
then None
else
let i = Cvalues.uninitialized_obj (Ctypes.object_of v.vtype) in
Some (Lang.F.p_equal (access_init (get_init_term seq.post v) []) i)
in
List.filter_map init_status xs
let is_nullable m v =
let addr = nullable_address v in
p_or
(M.is_null @@ M.pointer_loc addr)
(p_equal (M.pointer_val @@ M.cvar (vbase m v)) addr)
let nullable_scope v =
match V.param v with
| InContext Nullable -> Some (is_nullable (CTXT Nullable) v)
| InArray Nullable -> Some (is_nullable (CARR Nullable) v)
| _ -> None
let scope seq scope xs =
let xm = List.filter is_mem xs in
let smem = { pre = seq.pre.mem ; post = seq.post.mem } in
let hmem = M.scope smem scope xm in
let hvars = scope_vars seq scope xs in
let hinit = scope_init seq scope xs in
let hcontext = List.filter_map nullable_scope xs in
hvars @ hinit @ hmem @ hcontext
let global sigma p = M.global sigma.mem p
let rec assigned_path
kind
(hs : pred list)
(xs : var list)
(ys : var list)
(a : term)
(b : term)
= function
| [] -> hs
| Field f :: ofs ->
let cf = cfield ~kind f in
let af = e_getfield a cf in
let bf = e_getfield b cf in
let hs = assigned_path kind hs xs ys af bf ofs in
List.fold_left
(fun hs g ->
if Fieldinfo.equal f g then hs else
let cg = cfield ~kind g in
let ag = e_getfield a cg in
let bg = e_getfield b cg in
let eqg = p_forall ys (p_equal ag bg) in
eqg :: hs
) hs
(Option.get f.fcomp.cfields)
| Shift(_,e) :: ofs ->
let y = Lang.freshvar ~basename:"k" Qed.Logic.Int in
let k = e_var y in
let ak = e_get a k in
let bk = e_get b k in
if List.exists (fun x -> F.occurs x e) xs then
assigned_path kind hs xs (y::ys) ak bk ofs
else
let ae = e_get a e in
let be = e_get b e in
let ek = p_neq e k in
let eqk = p_forall (y::ys) (p_imply ek (p_equal ak bk)) in
assigned_path kind (eqk :: hs) xs ys ae be ofs
let assigned_genset s xs mem x ofs p =
let valid = valid_offset_path s.post Sigs.RW mem x ofs in
let a = get_term s.pre x in
let b = get_term s.post x in
let a_ofs = access a ofs in
let b_ofs = access b ofs in
let p_sloc = p_forall xs (p_hyps [valid;p_not p] (p_equal a_ofs b_ofs)) in
let conds = assigned_path KValue [p_sloc] xs [] a b ofs in
List.map (fun p -> Assert p) conds
let rec monotonic_initialized seq obj x ofs =
if Cvalues.always_initialized x then p_true
else
match obj with
| C_comp _ -> p_true
| C_array { arr_element=t } when Cil.isStructOrUnionType t -> p_true
| C_int _ | C_float _ | C_pointer _ ->
p_imply
(p_bool (access_init (get_init_term seq.pre x) ofs))
(p_bool (access_init (get_init_term seq.post x) ofs))
| C_array { arr_flat=flat ; arr_element=t } ->
let size = match flat with
| None -> unsized_array ()
| Some { arr_size } -> arr_size
in
let v = Lang.freshvar ~basename:"i" Lang.t_int in
let obj = Ctypes.object_of t in
let ofs = ofs @ [ Shift(obj, e_var v) ] in
let low = Some (e_int 0) in
let up = Some (e_int (size-1)) in
let hyp = Vset.in_range (e_var v) low up in
let in_range = monotonic_initialized seq obj x ofs in
Lang.F.p_forall [v] (p_imply hyp in_range)
let assigned_loc seq obj = function
| Ref x -> noref ~op:"assigns to" x
| Val((CVAL|CREF),x,[]) ->
[ Assert (monotonic_initialized seq obj x []) ]
| Val((CVAL|CREF),x,ofs) ->
let value = Lang.freshvar ~basename:"v" (tau_of_object obj) in
memvar_stored KValue seq x ofs (e_var value) ::
if Cil.isStructOrUnionType x.vtype then []
else begin
let init = Lang.freshvar ~basename:"v" (init_of_object obj) in
Assert(monotonic_initialized seq obj x ofs) ::
[ memvar_stored KInit seq x ofs (e_var init) ]
end
| Val((HEAP|CTXT _|CARR _) as m,x,ofs) ->
M.assigned (mseq_of_seq seq) obj (Sloc (mloc_of_path m x ofs))
| Loc l ->
M.assigned (mseq_of_seq seq) obj (Sloc l)
let assigned_array seq obj l elt n =
match l with
| Ref x -> noref ~op:"assigns to" x
| Val((CVAL|CREF),x,[]) ->
if Ctypes.is_compound elt then []
else
let obj = Ctypes.object_of x.vtype in
[ Assert (monotonic_initialized seq obj x []) ]
| Val((CVAL|CREF),x,ofs) ->
let f_array t =
e_var (Lang.freshvar ~basename:"v" Qed.Logic.(Array(Int, t))) in
[ memvar_stored KValue seq x ofs (f_array @@ Lang.tau_of_object elt) ;
memvar_stored KInit seq x ofs (f_array @@ Lang.init_of_object elt) ]
| Val((HEAP|CTXT _|CARR _) as m,x,ofs) ->
let l = mloc_of_path m x ofs in
M.assigned (mseq_of_seq seq) obj (Sarray(l,elt,n))
| Loc l ->
M.assigned (mseq_of_seq seq) obj (Sarray(l,elt,n))
let assigned_range seq obj l elt a b =
match l with
| Ref x -> noref ~op:"assigns to" x
| Loc l ->
M.assigned (mseq_of_seq seq) obj (Srange(l,elt,a,b))
| Val((HEAP|CTXT _|CARR _) as m,x,ofs) ->
M.assigned (mseq_of_seq seq) obj (Srange(mloc_of_path m x ofs,elt,a,b))
| Val((CVAL|CREF) as m,x,ofs) ->
let k = Lang.freshvar ~basename:"k" Qed.Logic.Int in
let p = Vset.in_range (e_var k) a b in
let ofs = ofs_shift elt (e_var k) ofs in
(assigned_genset seq [k] m x ofs p)
let assigned_descr seq obj xs l p =
match l with
| Ref x -> noref ~op:"assigns to" x
| Loc l ->
M.assigned (mseq_of_seq seq) obj (Sdescr(xs,l,p))
| Val((HEAP|CTXT _|CARR _) as m,x,ofs) ->
M.assigned (mseq_of_seq seq) obj (Sdescr(xs,mloc_of_path m x ofs,p))
| Val((CVAL|CREF) as m,x,ofs) ->
(assigned_genset seq xs m x ofs p)
let assigned seq obj = function
| Sloc l -> assigned_loc seq obj l
| Sarray(l,elt,n) -> assigned_array seq obj l elt n
| Srange(l,elt,a,b) -> assigned_range seq obj l elt a b
| Sdescr(xs,l,p) -> assigned_descr seq obj xs l p
type seq =
| Rseg of varinfo
| Fseg of varinfo * delta list
| Mseg of M.loc rloc * varinfo * delta list
| Lseg of M.loc rloc
and delta =
| Dfield of fieldinfo
| Drange of term option * term option
let dofs = function
| Field f -> Dfield f
| Shift(_,k) -> let u = Some k in Drange(u,u)
let tofs = function
| Field d -> Ctypes.object_of d.ftype
| Shift(elt,_) -> elt
let rec dstartof dim = function
| C_array arr ->
let n = match arr.arr_flat with None -> 1 | Some a -> a.arr_dim in
if n > dim then
let u = Some e_zero in
let elt = Ctypes.object_of arr.arr_element in
Drange(u,u) :: dstartof dim elt
else []
| _ -> []
let rec doffset obj host = function
| d::ds -> dofs d :: (doffset obj (tofs d) ds)
| [] -> dstartof (Ctypes.get_array_dim obj) host
let delta obj x ofs = doffset obj (Ctypes.object_of x.vtype) ofs
let rec range ofs obj a b =
match ofs with
| [] -> [ Drange(a,b) ]
| [Shift(elt,k)] when Ctypes.equal elt obj ->
[ Drange( Vset.bound_shift a k , Vset.bound_shift b k ) ]
| d :: ofs -> dofs d :: range ofs obj a b
let locseg = function
| Rloc(_,Ref x) -> Rseg x
| Rrange(Ref x,_,_,_) -> noref ~op:"sub-range of" x
| Rloc(obj,Loc l) -> Lseg (Rloc(obj,l))
| Rloc(obj,Val((CVAL|CREF),x,ofs)) ->
Fseg(x,delta obj x ofs)
| Rrange(Loc l,obj,a,b) -> Lseg (Rrange(l,obj,a,b))
| Rrange(Val((CVAL|CREF),x,ofs),obj,a,b) ->
Fseg(x,range ofs obj a b)
| Rloc(obj,Val((CTXT Nullable|CARR Nullable) as m,x,ofs)) ->
Lseg(Rloc(obj, mloc_of_path m x ofs))
| Rrange(Val((CTXT Nullable|CARR Nullable) as m,x,ofs),obj,a,b) ->
Lseg(Rrange(mloc_of_path m x ofs, obj, a, b))
| Rloc(obj,Val((CTXT Valid|CARR Valid|HEAP) as m,x,ofs)) ->
Mseg(Rloc(obj,mloc_of_path m x ofs),x,delta obj x ofs)
| Rrange(Val((CTXT Valid|CARR Valid|HEAP) as m,x,ofs),obj,a,b) ->
Mseg(Rrange(mloc_of_path m x ofs,obj,a,b),x,range ofs obj a b)
let rec included_delta d1 d2 =
match d1 , d2 with
| _ , [] -> p_true
| [] , _ -> p_false
| u :: d1 , v :: d2 ->
match u , v with
| Dfield f , Dfield g when Fieldinfo.equal f g ->
included_delta d1 d2
| Dfield _ , _ | _ , Dfield _ -> p_false
| Drange(a1,b1) , Drange(a2,b2) ->
p_conj [ Vset.ordered ~strict:false ~limit:true a2 a1 ;
Vset.ordered ~strict:false ~limit:true b1 b2 ;
included_delta d1 d2 ]
let included s1 s2 =
match locseg s1 , locseg s2 with
| Rseg x , Rseg y -> if Varinfo.equal x y then p_true else p_false
| Rseg _ , _ | _ , Rseg _ -> p_false
| Fseg(x1,d1) , Fseg(x2,d2)
| Mseg(_,x1,d1) , Mseg(_,x2,d2) ->
if Varinfo.equal x1 x2 then included_delta d1 d2 else p_false
| Fseg _ , _ | _ , Fseg _ -> p_false
| (Lseg s1|Mseg(s1,_,_)) , (Lseg s2|Mseg(s2,_,_)) -> M.included s1 s2
let rec separated_delta d1 d2 =
match d1 , d2 with
| [] , _ | _ , [] -> p_false
| u :: d1 , v :: d2 ->
match u , v with
| Dfield f , Dfield g when Fieldinfo.equal f g
-> separated_delta d1 d2
| Dfield _ , _ | _ , Dfield _ -> p_true
| Drange(a1,b1) , Drange(a2,b2) ->
p_disj [ Vset.ordered ~strict:true ~limit:false b1 a2 ;
Vset.ordered ~strict:true ~limit:false b2 a1 ;
separated_delta d1 d2 ]
let separated r1 r2 =
match locseg r1 , locseg r2 with
| Rseg x , Rseg y -> if Varinfo.equal x y then p_false else p_true
| Rseg _ , _ | _ , Rseg _ -> p_true
| Fseg(x1,d1) , Fseg(x2,d2)
| Mseg(_,x1,d1) , Mseg(_,x2,d2) ->
if Varinfo.equal x1 x2 then separated_delta d1 d2 else p_true
| Fseg _ , _ | _ , Fseg _ -> p_true
| (Lseg s1|Mseg(s1,_,_)) , (Lseg s2|Mseg(s2,_,_)) -> M.separated s1 s2
let domain obj l =
match l with
| Ref x | Val((CVAL|CREF),x,_) ->
let init =
if not @@ Cvalues.always_initialized x then [ Init x ] else []
in
Heap.Set.of_list ((Var x) :: init)
| Loc _ | Val((CTXT _|CARR _|HEAP),_,_) ->
M.Heap.Set.fold
(fun m s -> Heap.Set.add (Mem m) s)
(M.domain obj (mloc_of_loc l)) Heap.Set.empty
let is_well_formed sigma =
let cstrs = ref [] in
SIGMA.iter
(fun v c -> cstrs := Cvalues.has_ctype v.vtype (e_var c) :: !cstrs)
sigma.vars ;
p_conj ((M.is_well_formed sigma.mem) :: !cstrs)
end