Source file MemBytes.ml
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open Lang.F
open Memory
open Ctypes
module Logic = Qed.Logic
module WBytes =
struct
let library = "membytes"
let t_vblock = Qed.Logic.Array (Qed.Logic.Int, Qed.Logic.Int)
let t_memory = Qed.Logic.Array (Qed.Logic.Int,t_vblock)
let t_iblock = Qed.Logic.Array (Qed.Logic.Int, Qed.Logic.Bool)
let t_init = Qed.Logic.Array (Qed.Logic.Int,t_iblock)
let ty_fst_arg = function
| Some l :: _ -> l
| _ -> raise Not_found
let f_eqmem = Lang.extern_fp ~library "eqmem"
let f_memcpy = Lang.extern_f ~library ~typecheck:ty_fst_arg "memcpy"
let p_sconst = Lang.extern_fp ~coloring:true ~library "sconst"
let sconst m = p_call p_sconst [m]
let p_scinit = Lang.extern_fp ~coloring:true ~library "scinit"
let scinit m = p_call p_scinit [m]
let p_bytes = Lang.extern_fp ~library "bytes"
let bytes m = p_call p_bytes [ m ]
let f_read_uint8 = Lang.extern_f ~result:Qed.Logic.Int ~library "read_uint8"
let read_uint8 m a = e_fun f_read_uint8 [ m ; a ]
let f_read_uint16 = Lang.extern_f ~result:Qed.Logic.Int ~library "read_uint16"
let read_uint16 m a = e_fun f_read_uint16 [ m ; a ]
let f_read_uint32 = Lang.extern_f ~result:Qed.Logic.Int ~library "read_uint32"
let read_uint32 m a = e_fun f_read_uint32 [ m ; a ]
let f_read_uint64 = Lang.extern_f ~result:Qed.Logic.Int ~library "read_uint64"
let read_uint64 m a = e_fun f_read_uint64 [ m ; a ]
let f_read_sint8 = Lang.extern_f ~result:Qed.Logic.Int ~library "read_sint8"
let read_sint8 m a = e_fun f_read_sint8 [ m ; a ]
let f_read_sint16 = Lang.extern_f ~result:Qed.Logic.Int ~library "read_sint16"
let read_sint16 m a = e_fun f_read_sint16 [ m ; a ]
let f_read_sint32 = Lang.extern_f ~result:Qed.Logic.Int ~library "read_sint32"
let read_sint32 m a = e_fun f_read_sint32 [ m ; a ]
let f_read_sint64 = Lang.extern_f ~result:Qed.Logic.Int ~library "read_sint64"
let read_sint64 m a = e_fun f_read_sint64 [ m ; a ]
let f_write_uint8 = Lang.extern_f ~result:t_memory ~library "write_uint8"
let write_uint8 m a v = e_fun f_write_uint8 [ m ; a ; v ]
let f_write_uint16 = Lang.extern_f ~result:t_memory ~library "write_uint16"
let write_uint16 m a v = e_fun f_write_uint16 [ m ; a ; v ]
let f_write_uint32 = Lang.extern_f ~result:t_memory ~library "write_uint32"
let write_uint32 m a v = e_fun f_write_uint32 [ m ; a ; v ]
let f_write_uint64 = Lang.extern_f ~result:t_memory ~library "write_uint64"
let write_uint64 m a v = e_fun f_write_uint64 [ m ; a ; v ]
let f_write_sint8 = Lang.extern_f ~result:t_memory ~library "write_sint8"
let write_sint8 m a v = e_fun f_write_sint8 [ m ; a ; v ]
let f_write_sint16 = Lang.extern_f ~result:t_memory ~library "write_sint16"
let write_sint16 m a v = e_fun f_write_sint16 [ m ; a ; v ]
let f_write_sint32 = Lang.extern_f ~result:t_memory ~library "write_sint32"
let write_sint32 m a v = e_fun f_write_sint32 [ m ; a ; v ]
let f_write_sint64 = Lang.extern_f ~result:t_memory ~library "write_sint64"
let write_sint64 m a v = e_fun f_write_sint64 [ m ; a ; v ]
let f_read_init8 = Lang.extern_f ~result:Qed.Logic.Bool ~library "read_init8"
let read_init8 m a = e_fun f_read_init8 [ m ; a ]
let f_read_init16 = Lang.extern_f ~result:Qed.Logic.Bool ~library "read_init16"
let read_init16 m a = e_fun f_read_init16 [ m ; a ]
let f_read_init32 = Lang.extern_f ~result:Qed.Logic.Bool ~library "read_init32"
let read_init32 m a = e_fun f_read_init32 [ m ; a ]
let f_read_init64 = Lang.extern_f ~result:Qed.Logic.Bool ~library "read_init64"
let read_init64 m a = e_fun f_read_init64 [ m ; a ]
let f_write_init8 = Lang.extern_f ~result:t_init ~library "write_init8"
let write_init8 m a v = e_fun f_write_init8 [ m ; a ; v ]
let f_write_init16 = Lang.extern_f ~result:t_init ~library "write_init16"
let write_init16 m a v = e_fun f_write_init16 [ m ; a ; v ]
let f_write_init32 = Lang.extern_f ~result:t_init ~library "write_init32"
let write_init32 m a v = e_fun f_write_init32 [ m ; a ; v ]
let f_write_init64 = Lang.extern_f ~result:t_init ~library "write_init64"
let write_init64 m a v = e_fun f_write_init64 [ m ; a ; v ]
end
let datatype = "MemBytes"
let lc_name = String.lowercase_ascii datatype
let dkey_model = Wp_parameters.register_category (lc_name ^ ":model")
let configure () =
begin
let orig_pointer = Context.push Lang.pointer MemAddr.t_addr in
let orig_null = Context.push Cvalues.null (p_equal MemAddr.null) in
let rollback () =
Context.pop Lang.pointer orig_pointer ;
Context.pop Cvalues.null orig_null ;
in
rollback
end
let no_binder = { bind = fun _ f v -> f v }
let configure_ia _ = no_binder
let hypotheses p = p
module Chunk =
struct
type t = Mem | Init | Alloc
let self = "Chunk" ^ datatype
let hash = Hashtbl.hash
let equal = (=)
let compare c1 c2 =
match c1, c2 with
| Mem, Mem | Init, Init | Alloc, Alloc -> 0
| Mem, _ -> 1
| _, Mem -> -1
| Init, _ -> 1
| _, Init -> -1
let pretty fmt = function
| Mem -> Format.fprintf fmt "Mem"
| Init -> Format.fprintf fmt "Init"
| Alloc -> Format.fprintf fmt "Alloc"
let tau_of_memory = WBytes.t_memory
let tau_of_init = WBytes.t_init
let tau_of_chunk = function
| Mem -> tau_of_memory
| Init -> tau_of_init
| Alloc -> Logic.Array (Logic.Int, Logic.Int)
let basename_of_chunk = function
| Mem -> "mem"
| Init -> "init"
| Alloc -> "alloc"
let is_init = function Init -> true | Mem | Alloc -> false
let is_primary _ = false
let is_framed _ = false
end
module State = Sigma.Make(Chunk)
let m_alloc = State.chunk Alloc
let m_init = State.chunk Init
let m_mem = State.chunk Mem
type loc = term
let vars = vars
let occurs = occurs
type segment = loc rloc
let shift_cluster () =
Definitions.cluster ~id:"Shifts" ~title:"Shifts Definitions" ()
module OPAQUE_COMP_LENGTH = WpContext.Generator(Cil_datatype.Compinfo)
(struct
let name = "MemBytes.EmptyCompLength"
type key = Cil_types.compinfo
type data = Lang.lfun
let compile c =
if c.Cil_types.cfields <> None then
Wp_parameters.fatal
"Asking for opaque struct length on non opaque struct" ;
let result = Lang.t_int in
let size =
Lang.generated_f ~params:[] ~result "Length_of_%s" (Lang.comp_id c)
in
Definitions.define_symbol {
d_cluster = Definitions.compinfo c ;
d_lfun = size ; d_types = 0 ; d_params = [] ;
d_definition = Logic result ;
} ;
Definitions.define_lemma {
l_kind = Admit ;
l_name = "Positive_Length_of_" ^ Lang.comp_id c ;
l_triggers = [] ; l_forall = [] ;
l_cluster = Definitions.compinfo c ;
l_lemma = Lang.F.(p_lt e_zero (e_fun size []))
} ;
size
end)
let protected_sizeof_object = function
| C_comp ({ cfields = None } as c) ->
e_fun (OPAQUE_COMP_LENGTH.get c) []
| obj -> e_int @@ Ctypes.sizeof_object obj
type shift =
| RS_Field of Cil_types.fieldinfo * term
| RS_Index of term
let phi_base = function
| p::_ -> MemAddr.base p
| _ -> raise Not_found
let phi_field offset = function
| [p] -> e_add (MemAddr.offset p) offset
| _ -> raise Not_found
let phi_index size = function
| [p;k] -> e_add (MemAddr.offset p) (e_mul size k)
| _ -> raise Not_found
module RegisterShift = WpContext.Static
(struct
type key = Lang.lfun
type data = shift
let name = "MemBytes.RegisterShift"
include Lang.Fun
end)
let field_offset ci field =
let comp = Cil_const.mk_tcomp ci in
let field = Cil_types.Field(field, NoOffset) in
let bits_offset, bits_size = Cil.bitsOffset comp field in
if 0 <> bits_offset mod 8 || 0 <> bits_size mod 8 then
Wp_parameters.error "Bitfields not allowed in Bytes model" ;
bits_offset / 8
module ShiftFieldDef = WpContext.StaticGenerator(Cil_datatype.Fieldinfo)
(struct
let name = "MemBytes.ShiftFieldDef"
type key = Cil_types.fieldinfo
type data = Definitions.dfun
let generate f =
let result = MemAddr.t_addr in
let lfun = Lang.generated_f ~result "shiftfield_%s" (Lang.field_id f) in
let p = Lang.freshvar ~basename:"p" MemAddr.t_addr in
let tp = e_var p in
let position = e_int @@ field_offset f.fcomp f in
let def = MemAddr.shift tp position in
let dfun = Definitions.Function( result , Def , def) in
RegisterShift.define lfun (RS_Field(f,position)) ;
MemAddr.register ~base:phi_base ~offset:(phi_field position) lfun ;
Definitions.{
d_lfun = lfun ; d_types = 0 ;
d_params = [p] ;
d_definition = dfun ;
d_cluster = Definitions.dummy () ;
}
let compile = Lang.local generate
end)
module ShiftField = WpContext.Generator(Cil_datatype.Fieldinfo)
(struct
let name = "MemBytes.ShiftField"
type key = Cil_types.fieldinfo
type data = Lang.lfun
let compile fd =
let dfun = ShiftFieldDef.get fd in
let d_cluster = shift_cluster () in
Definitions.define_symbol { dfun with d_cluster } ;
dfun.d_lfun
end)
module Cobj =
struct
type t = c_object
let pretty = C_object.pretty
let compare = compare_ptr_conflated
end
module ShiftGen = WpContext.StaticGenerator(Cobj)
(struct
let name = "MemBytes.ShiftDef"
type key = Cobj.t
type data = Definitions.dfun
let rec c_object_id fmt = function
| C_int i -> pp_int fmt i
| C_float f -> pp_float fmt f
| C_pointer _ -> Format.fprintf fmt "PTR"
| C_comp c -> Format.pp_print_string fmt (Lang.comp_id c)
| C_array a ->
let te = object_of a.arr_element in
match a.arr_flat with
| None -> Format.fprintf fmt "A_%a" c_object_id te
| Some f -> Format.fprintf fmt "A%d_%a" f.arr_size c_object_id te
let c_object_id c = Format.asprintf "%a@?" c_object_id c
let generate obj =
let result = MemAddr.t_addr in
let shift = Lang.generated_f ~result "shift_%s" (c_object_id obj) in
let size = protected_sizeof_object obj in
let p = Lang.freshvar ~basename:"p" MemAddr.t_addr in
let tp = e_var p in
let k = Lang.freshvar ~basename:"k" Qed.Logic.Int in
let tk = e_var k in
let def = MemAddr.shift tp (e_mul size tk) in
let dfun = Definitions.Function( result , Def , def) in
RegisterShift.define shift (RS_Index size) ;
MemAddr.register ~base:phi_base ~offset:(phi_index size)
~linear:true shift ;
Definitions.{
d_lfun = shift ; d_types = 0 ;
d_params = [p;k] ;
d_definition = dfun ;
d_cluster = Definitions.dummy () ;
}
let compile = Lang.local generate
end)
module Shift = WpContext.Generator(Cobj)
(struct
let name = "MemBytes.Shift"
type key = Cobj.t
type data = Lang.lfun
let compile obj =
let dfun = ShiftGen.get obj in
let d_cluster = shift_cluster () in
Definitions.define_symbol { dfun with d_cluster } ;
dfun.d_lfun
end)
let field loc f = e_fun (ShiftField.get f) [loc]
let shift loc obj k = e_fun (Shift.get obj) [loc;k]
let allocated sigma l =
e_get (Sigma.value sigma m_alloc) (MemAddr.base l)
let s_valid sigma acs p n =
let valid = match acs with
| RW -> MemAddr.valid_rw
| RD -> MemAddr.valid_rd
| OBJ -> (fun m p _ -> MemAddr.valid_obj m p)
in
valid (Sigma.value sigma m_alloc) p n
let s_invalid sigma p n =
MemAddr.invalid (Sigma.value sigma m_alloc) p n
let segment phi = function
| Rloc(obj,l) ->
phi l @@ protected_sizeof_object obj
| Rrange(l,obj,Some a,Some b) ->
let l = shift l obj a in
let n = e_mul (protected_sizeof_object obj) (e_range a b) in
phi l n
| Rrange(l,_,a,b) ->
Wp_parameters.abort ~current:true
"Invalid infinite range @[<hov 2>%a+@,(%a@,..%a)@]"
Lang.F.pp_term l Vset.pp_bound a Vset.pp_bound b
let valid sigma acs =
Wp_parameters.debug ~level:2 ~dkey:dkey_model "%s.valid _ _" datatype ;
segment (s_valid sigma acs)
let invalid sigma =
Wp_parameters.debug ~level:2 ~dkey:dkey_model "%s.invalid _ _" datatype ;
segment (s_invalid sigma)
let included =
Wp_parameters.debug ~level:2 ~dkey:dkey_model "%s.included _ _" datatype ;
let addrof l = l in
let sizeof obj = protected_sizeof_object obj in
MemAddr.included ~shift ~addrof ~sizeof
let separated =
Wp_parameters.debug ~level:2 ~dkey:dkey_model "%s.separated _ _" datatype ;
let addrof l = l in
let sizeof obj = protected_sizeof_object obj in
MemAddr.separated ~shift ~addrof ~sizeof
let float_cluster () =
Definitions.cluster ~id:"MemBytes.Float" ~title:"MemBytes definitions" ()
module Float = struct
type t = Ctypes.c_float
let pretty = Ctypes.pp_float
let compare = Ctypes.compare_c_float
let ikind = function
| Float32 -> UInt32
| Float64 -> UInt64
end
module CODEC_FLOAT = WpContext.Generator(Float)
(struct
let name = "MemBytes.LOAD_FLOAT"
type key = Float.t
type data = Lang.lfun * Lang.lfun
let decode ft =
let result = Cfloat.tau_of_float ft in
let f = Lang.freshvar ~basename:"f" Lang.t_int in
let decode =
Lang.generated_f ~result "int_to_%a" Float.pretty ft in
Definitions.define_symbol {
d_lfun = decode ;
d_cluster = float_cluster () ; d_types = 0 ;
d_params = [ f ] ;
d_definition = Logic result ;
} ;
decode
let encode ft =
let result = Lang.t_int in
let f = Lang.freshvar ~basename:"f" @@ Cfloat.tau_of_float ft in
let encode =
Lang.generated_f ~result "%a_to_int" Float.pretty ft in
Definitions.define_symbol {
d_lfun = encode ;
d_cluster = float_cluster () ; d_types = 0 ;
d_params = [ f ] ;
d_definition = Logic result ;
} ;
encode
let add_decode_encode ft encode decode =
let f = Lang.freshvar ~basename:"f" @@ Cfloat.tau_of_float ft in
let tf = e_var f in
let name = Format.asprintf "decode_encode_%a" Float.pretty ft in
let lemma =
p_equal tf (e_fun decode [e_fun encode [tf]]) in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ;
l_triggers = [] ;
l_forall = [f] ;
l_cluster = float_cluster () ;
l_lemma = lemma
}
let add_encode_decode ft encode decode =
let i = Lang.freshvar ~basename:"i" Lang.t_int in
let ti = e_var i in
let name = Format.asprintf "encode_decode_%a" Float.pretty ft in
let lemma =
p_equal ti (e_fun encode [e_fun decode [ti]]) in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ;
l_triggers = [] ;
l_forall = [i] ;
l_cluster = float_cluster () ;
l_lemma = lemma
}
let add_encode_bounds ft encode =
let f = Lang.freshvar ~basename:"f" @@ Cfloat.tau_of_float ft in
let tf = e_var f in
let name = Format.asprintf "encode_bounds_%a" Float.pretty ft in
let lemma = Cint.range (Float.ikind ft) @@ e_fun encode [ tf ] in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ;
l_triggers = [] ;
l_forall = [f] ;
l_cluster = float_cluster () ;
l_lemma = lemma
}
let compile ft =
let encode = encode ft in
let decode = decode ft in
add_encode_decode ft encode decode ;
add_decode_encode ft encode decode ;
add_encode_bounds ft encode ;
encode, decode
end)
let float_to_int fkind f =
e_fun (fst @@ CODEC_FLOAT.get fkind) [ f ]
let int_to_float fkind f =
e_fun (snd @@ CODEC_FLOAT.get fkind) [ f ]
let load_int_raw memory kind addr =
let read = match kind with
| CBool -> WBytes.read_uint8
| UInt8 -> WBytes.read_uint8
| SInt8 -> WBytes.read_sint8
| UInt16 -> WBytes.read_uint16
| SInt16 -> WBytes.read_sint16
| UInt32 -> WBytes.read_uint32
| SInt32 -> WBytes.read_sint32
| UInt64 -> WBytes.read_uint64
| SInt64 -> WBytes.read_sint64
in
read memory addr
let load_int sigma kind addr =
load_int_raw (Sigma.value sigma m_mem) kind addr
let load_float sigma kind addr =
int_to_float kind @@ load_int sigma (Float.ikind kind) addr
let load_pointer_raw memory _ty loc =
MemAddr.addr_of_int @@ load_int_raw memory (Ctypes.c_ptr ()) loc
let load_pointer sigma _ty loc =
MemAddr.addr_of_int @@ load_int sigma (Ctypes.c_ptr ()) loc
let load_init_raw memory size loc =
match size with
| 1 -> WBytes.read_init8 memory loc
| 2 -> WBytes.read_init16 memory loc
| 4 -> WBytes.read_init32 memory loc
| 8 -> WBytes.read_init64 memory loc
| _ -> assert false
let load_init_atom sigma obj loc =
let init_memory = Sigma.value sigma m_init in
let size = sizeof_object obj in
load_init_raw init_memory size loc
let store_int sigma kind addr v =
let write = match kind with
| CBool -> WBytes.write_uint8
| UInt8 -> WBytes.write_uint8
| SInt8 -> WBytes.write_sint8
| UInt16 -> WBytes.write_uint16
| SInt16 -> WBytes.write_sint16
| UInt32 -> WBytes.write_uint32
| SInt32 -> WBytes.write_sint32
| UInt64 -> WBytes.write_uint64
| SInt64 -> WBytes.write_sint64
in
m_mem, write (Sigma.value sigma m_mem) addr v
let store_float sigma kind addr v =
store_int sigma (Float.ikind kind) addr @@ float_to_int kind v
let store_pointer sigma _kind addr v =
store_int sigma (Ctypes.c_ptr ()) addr @@ MemAddr.int_of_addr v
let store_init_raw m size loc v =
let write = match size with
| 1 -> WBytes.write_init8
| 2 -> WBytes.write_init16
| 4 -> WBytes.write_init32
| 8 -> WBytes.write_init64
| _ -> assert false
in
write m loc v
let store_init_atom sigma obj loc v =
let init_memory = Sigma.value sigma m_init in
let size = sizeof_object obj in
m_init, store_init_raw init_memory size loc v
module LOADER =
struct
let name = "MemBytes.LOADER"
type nonrec loc = loc
let pretty = Lang.F.pp_term
let sizeof = protected_sizeof_object
let field = field
let shift = shift
let to_region_pointer l = 0,l
let of_region_pointer _r _obj l = l
let _ _ = Sigma.Domain.singleton m_mem
let _ _ = Sigma.Domain.singleton m_init
let last sigma obj l =
let n = protected_sizeof_object obj in
e_sub (e_div (allocated sigma l) n) e_one
let fresh _l =
let x = Lang.freshvar ~basename:"p" MemAddr.t_addr in
[x] , e_var x
let separated p n p' n' = p_call MemAddr.p_separated [p;n;p';n']
let eqmem _chunk m0 m1 l n = p_call WBytes.f_eqmem [m0;m1;l;n]
let memcpy _chunk m0 l0 m1 l1 n = e_fun WBytes.f_memcpy [m0;l0;m1;l1;n]
let load_int = load_int
let load_float = load_float
let load_pointer = load_pointer
let load_init_atom = load_init_atom
let store_int = store_int
let store_float = store_float
let store_pointer = store_pointer
let store_init_atom = store_init_atom
end
include MemLoader.Make(LOADER)
let cluster_globals () =
Definitions.cluster ~id:"Globals" ~title:"Global Variables" ()
let globals = 0
let locals = 1
let formals = 2
module RegisterBASE = WpContext.Index
(struct
type key = Lang.lfun
type data = Cil_types.varinfo
let name = "MemBytes.RegisterBASE"
include Lang.Fun
end)
module BASE = WpContext.Generator(Cil_datatype.Varinfo)
(struct
let name = datatype ^ ".BASE"
type key = Cil_types.varinfo
type data = Lang.F.term
open Cil_types
let static_alloc prefix base =
let name = prefix ^ "_static_alloc" in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ; l_triggers = [] ; l_forall = [] ;
l_lemma = MemAddr.static_alloc base ;
l_cluster = cluster_globals () ;
}
let region prefix x base =
let name = prefix ^ "_region" in
let region =
if x.vglob then globals
else if x.vformal then formals
else locals
in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ; l_triggers = [] ; l_forall = [] ;
l_lemma = p_equal (MemAddr.region base) (e_int region) ;
l_cluster = cluster_globals () ;
}
let binit prefix x base =
if Cvalues.always_initialized x then
let name = prefix ^ "_binit" in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ; l_triggers = [] ; l_forall = [] ;
l_lemma = MemAddr.binit base ;
l_cluster = cluster_globals () ;
}
let sizeof x =
Warning.handle
~handler:(fun _ -> None)
~fallback:(Printf.sprintf "No allocation size for variable '%s'" x.vname)
(fun obj -> Some (protected_sizeof_object obj))
(Ctypes.object_of x.vtype)
let alloc prefix x base =
let name = prefix ^ "_linked" in
let size =
if x.vglob then sizeof x else Some e_zero
in
match size with
| None -> ()
| Some size ->
let a = Lang.freshvar ~basename:"alloc" MemAddr.t_malloc in
let m = e_var a in
let base_size = p_equal (Lang.F.e_get m base) size in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ;
l_triggers = [] ; l_forall = [] ;
l_lemma = p_forall [a] (p_imply (MemAddr.linked m) base_size) ;
l_cluster = cluster_globals () ;
}
let pointer_type prefix base =
let name = prefix ^ "_is_pointer" in
let typed =
MemAddr.in_uintptr_range (MemAddr.global base)
in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ;
l_triggers = [] ; l_forall = [] ;
l_lemma = typed ;
l_cluster = cluster_globals () ;
}
let compile vi =
let result = Logic.Int in
let acs_rd = Ast_types.has_qualifier "const" vi.vtype in
let prefix =
if vi.vglob
then if acs_rd then "K" else "G"
else if vi.vformal then "P" else "L" in
let lfun = Lang.generated_f
~category:Logic.Constructor ~result:Logic.Int "%s_%s_%d"
prefix vi.vorig_name vi.vid in
Definitions.define_symbol {
d_lfun = lfun ; d_types = 0 ; d_params = [ ] ;
d_definition = Definitions.Function (result, Def, e_int vi.vid) ;
d_cluster = cluster_globals () ;
} ;
let prefix = Lang.Fun.debug lfun in
let base = e_fun lfun [] in
RegisterBASE.define lfun vi ;
static_alloc prefix base ;
region prefix vi base ;
alloc prefix vi base ;
binit prefix vi base ;
pointer_type prefix base ;
base
end)
module LITERAL =
struct
type t = int * Cstring.cst
let compare (a:t) (b:t) = Stdlib.compare (fst a) (fst b)
let pretty fmt (eid,cst) = Format.fprintf fmt "%a@%d" Cstring.pretty cst eid
end
module EID = State_builder.Ref(Datatype.Int)
(struct
let name = datatype ^ ".EID"
let dependencies = [Ast.self]
let default () = 0
end)
module STRING = WpContext.Generator(LITERAL)
(struct
let name = datatype ^ ".STRING"
type key = LITERAL.t
type data = term
let linked prefix base cst =
let name = prefix ^ "_linked" in
let a = Lang.freshvar ~basename:"alloc" (Chunk.tau_of_chunk Alloc) in
let m = e_var a in
let alloc = Lang.F.e_get m base in
let sized = Cstring.str_len cst (Lang.F.(e_add alloc e_minus_one)) in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ;
l_triggers = [] ; l_forall = [] ;
l_lemma = p_forall [a] (p_imply (MemAddr.linked m) sized) ;
l_cluster = Cstring.cluster () ;
}
let region prefix base cst =
let name = prefix ^ "_region" in
let re = - Cstring.str_id cst in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ; l_triggers = [] ; l_forall = [] ;
l_lemma = p_equal (MemAddr.region base) (e_int re) ;
l_cluster = Cstring.cluster () ;
}
let sconst prefix base cst =
let name = prefix ^ "_literal" in
let i = Lang.freshvar ~basename:"i" Lang.t_int in
let c = Cstring.char_at cst (e_var i) in
let ikind = Ctypes.c_char () in
let m = Lang.freshvar ~basename:"mchar" @@ Chunk.tau_of_chunk Mem in
let addr = shift (MemAddr.global base) (C_int ikind) (e_var i) in
let v = load_int_raw (e_var m) ikind addr in
let read = Lang.F.(p_equal c v) in
Definitions.define_lemma {
l_kind = Admit ;
l_name = name ; l_triggers = [] ;
l_forall = [m;i] ;
l_cluster = Cstring.cluster () ;
l_lemma = Lang.F.p_imply (WBytes.sconst @@ e_var m) read ;
}
let fresh () =
let eid = succ (EID.get ()) in
EID.set eid ; eid
let compile (_,cst) =
let eid = fresh () in
let lfun = Lang.generated_f ~result:Lang.t_int "Str_%d" eid in
let prefix = Lang.Fun.debug lfun in
let base = Lang.F.e_fun lfun [] in
Definitions.define_symbol {
d_lfun = lfun ; d_types = 0 ; d_params = [] ;
d_definition = Logic Lang.t_int ;
d_cluster = Cstring.cluster () ;
} ;
Definitions.define_lemma {
l_name = prefix ^ "_base" ;
l_kind = Admit ;
l_triggers = [] ; l_forall = [] ;
l_lemma = Lang.F.(p_lt base e_zero) ;
l_cluster = Cstring.cluster () ;
} ;
region prefix base cst ;
linked prefix base cst ;
sconst prefix base cst ;
base
end)
let pretty fmt loc =
Format.fprintf fmt "l:(%a)" Lang.F.pp_term loc
let null = MemAddr.null
let literal ~eid cst =
Wp_parameters.debug ~level:3 ~dkey:dkey_model
"%s.literal %d _" datatype eid ;
shift (MemAddr.global (STRING.get (eid,cst))) (C_int (Ctypes.c_char ())) e_zero
let cvar vi =
Wp_parameters.debug ~level:3 ~dkey:dkey_model
"%s.cvar %a" datatype Cil_printer.pp_varinfo vi ;
MemAddr.global (BASE.get vi)
let global _sigma p =
Wp_parameters.debug ~level:2 ~dkey:dkey_model "%s.global _ _" datatype ;
p_leq (MemAddr.region @@ MemAddr.base p) e_zero
let rec lookup_a e =
match repr e with
| Fun( f , [e] ) when MemAddr.is_f_global f -> lookup_a e
| Fun( f , es ) -> lookup_f f es
| _ -> raise Not_found
and lookup_f f es =
try match RegisterShift.find f , es with
| RS_Field(fd,_) , [e] -> Mstate.field (lookup_lv e) fd
| RS_Index _ , [e;k] -> Mstate.index (lookup_lv e) k
| _ -> raise Not_found
with Not_found when es = [] ->
Memory.(Mvar (RegisterBASE.find f),[])
and lookup_lv e = try lookup_a e with Not_found -> Memory.(Mmem e,[])
let lookup s e =
match repr e with
| Fun( f , es ) -> Memory.Maddr (lookup_f f es)
| Aget( m , k ) ->
begin
match Sigma.ckind @@ Tmap.find m s with
| State.Mu Alloc -> raise Not_found
| State.Mu Init -> Memory.Minit (lookup_lv k)
| State.Mu _ -> Memory.Mlval (lookup_lv k)
| _ -> raise Not_found
end
| _ -> raise Not_found
let updates _ _ = Bag.empty
let pointer_loc t = t
let pointer_val t = t
let base_addr loc =
Wp_parameters.debug ~level:3 ~dkey:dkey_model
"%s.base_addr %a" datatype pretty loc ;
MemAddr.mk_addr (MemAddr.base loc) e_zero
let base_offset loc =
Wp_parameters.debug ~level:3 ~dkey:dkey_model
"%s.base_offset %a" datatype pretty loc ;
MemAddr.base_offset (MemAddr.base loc) (MemAddr.offset loc)
let block_length sigma _obj loc =
Wp_parameters.debug ~level:3 ~dkey:dkey_model
"%s.block_length _ _ _ " datatype ;
e_get (Sigma.value sigma m_alloc) (MemAddr.base loc)
let cast _ loc =
Wp_parameters.debug ~level:3 ~dkey:dkey_model
"%s.cast _ %a" datatype pretty loc ;
loc
let loc_of_int _ loc =
Wp_parameters.debug ~level:3 ~dkey:dkey_model
"%s.loc_of_int _ %a" datatype pretty loc ;
MemAddr.addr_of_int loc
let int_of_loc _ loc =
Wp_parameters.debug ~level:3 ~dkey:dkey_model
"%s.int_of_loc _ %a" datatype pretty loc ;
MemAddr.int_of_addr loc
let domain _ _ = Sigma.Domain.of_list [ m_init ; m_mem ]
let is_null = p_equal null
let loc_eq = p_equal
let loc_lt = MemAddr.addr_lt
let loc_leq = MemAddr.addr_le
let loc_neq l1 l2 = p_not @@ loc_eq l1 l2
let loc_diff _ l1 l2 =
let byte_size = Ctypes.sizeof_object (C_int (Ctypes.c_char ())) in
e_div (e_sub (MemAddr.offset l1) (MemAddr.offset l2)) (e_int byte_size)
let pointer_cluster () =
Definitions.cluster
~id:"MemBytes.PointersProperties" ~title:"MemBytes definitions" ()
module PointersProperties = WpContext.Generator(Datatype.Unit)
(struct
let name = datatype ^ ".POINTERS"
type key = unit
type data = Lang.lfun
let ranges () =
let a = Lang.freshvar ~basename:"a" MemAddr.t_addr in
let prop = MemAddr.in_uintptr_range (e_var a) in
Definitions.define_lemma {
l_kind = Admit ; l_name = "pointers_int_range" ;
l_triggers = [] ; l_forall = [a] ;
l_cluster = pointer_cluster () ;
l_lemma = prop ;
}
let compile () =
let lfun = Lang.generated_p "framed" in
let m = Lang.freshvar ~basename:"m" WBytes.t_memory in
let a = Lang.freshvar ~basename:"a" MemAddr.t_addr in
let p = load_pointer_raw (e_var m) (Cil_const.voidPtrType) (e_var a) in
let ba = MemAddr.base (e_var a) and bp = MemAddr.base p in
let body =
p_forall [a] @@ p_imply
(p_leq (MemAddr.region ba) e_zero)
(p_leq (MemAddr.region bp) e_zero)
in
Definitions.define_symbol {
d_lfun = lfun ;
d_cluster = pointer_cluster () ; d_types = 0 ;
d_params = [ m ] ; d_definition = Predicate (Def, body)
};
ranges () ;
lfun
end)
let framed m =
p_call (PointersProperties.get ()) [ m ]
let frame sigma =
Wp_parameters.debug ~level:2 ~dkey:dkey_model "%s.frame _" datatype ;
let wellformed_frame phi chunk =
if Sigma.mem sigma chunk
then [ phi (Sigma.value sigma chunk) ]
else []
in
wellformed_frame MemAddr.linked m_alloc @
wellformed_frame WBytes.scinit m_init @
wellformed_frame WBytes.sconst m_mem @
[ framed (Sigma.value sigma m_mem) ]
let is_well_formed s =
Wp_parameters.debug ~level:2 ~dkey:dkey_model "%s.is_well_formed _" datatype ;
WBytes.bytes (Sigma.value s m_mem)
let alloc sigma xs =
Wp_parameters.debug ~level:2 ~dkey:dkey_model
"%s.alloc %a %a"
datatype Sigma.pretty sigma (Pretty_utils.pp_list Cil_printer.pp_varinfo) xs ;
if xs = [] then sigma else Sigma.havoc_chunk sigma m_alloc
let scope seq scope xs =
Wp_parameters.debug ~level:2 ~dkey:dkey_model
"%s.scope { %a ; %a } %s %a"
datatype Sigma.pretty seq.pre Sigma.pretty seq.post
(if scope = Memory.Enter then "Enter" else "Leave")
(Pretty_utils.pp_list Cil_printer.pp_varinfo) xs ;
if xs = [] then [] else
let alloc =
List.fold_left
(fun m x ->
let size = match scope with
| Memory.Leave -> e_zero
| Memory.Enter ->
protected_sizeof_object @@ Ctypes.object_of x.Cil_types.vtype
in e_set m (BASE.get x) size)
(Sigma.value seq.pre m_alloc) xs in
[ p_equal (Sigma.value seq.post m_alloc) alloc ]