You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
356 lines
13 KiB
356 lines
13 KiB
(*
|
|
* Copyright (c) Facebook, Inc. and its affiliates.
|
|
*
|
|
* This source code is licensed under the MIT license found in the
|
|
* LICENSE file in the root directory of this source tree.
|
|
*)
|
|
|
|
(** Abstract domain *)
|
|
|
|
type t = Sh.t [@@deriving equal, sexp]
|
|
|
|
let pp fs q = Format.fprintf fs "@[{ %a@ }@]" Sh.pp q
|
|
let report_fmt_thunk = Fn.flip pp
|
|
|
|
(* set by cli *)
|
|
let simplify_states = ref true
|
|
let simplify q = if !simplify_states then Sh.simplify q else q
|
|
|
|
let init globals =
|
|
IArray.fold globals ~init:Sh.emp ~f:(fun q -> function
|
|
| {Global.reg; init= Some arr} ->
|
|
let loc = Term.var (Reg.var reg) in
|
|
let len = Term.size_of (Exp.typ arr) in
|
|
let arr = arr.term in
|
|
Sh.star q (Sh.seg {loc; bas= loc; len; siz= len; arr})
|
|
| _ -> q )
|
|
|
|
let join p q =
|
|
[%Trace.call fun {pf} -> pf "%a@ %a" pp p pp q]
|
|
;
|
|
Some (Sh.or_ p q) |> Option.map ~f:simplify
|
|
|>
|
|
[%Trace.retn fun {pf} -> pf "%a" (Option.pp "%a" pp)]
|
|
|
|
let is_false = Sh.is_false
|
|
let dnf = Sh.dnf
|
|
let exec_assume q b = Exec.assume q (Exp.term b) |> Option.map ~f:simplify
|
|
let exec_kill q r = Exec.kill q (Reg.var r) |> simplify
|
|
|
|
let exec_move q res =
|
|
Exec.move q (IArray.map res ~f:(fun (r, e) -> (Reg.var r, Exp.term e)))
|
|
|> simplify
|
|
|
|
let exec_inst pre inst =
|
|
( match (inst : Llair.inst) with
|
|
| Move {reg_exps; _} ->
|
|
Some
|
|
(Exec.move pre
|
|
(IArray.map reg_exps ~f:(fun (r, e) -> (Reg.var r, Exp.term e))))
|
|
| Load {reg; ptr; len; _} ->
|
|
Exec.load pre ~reg:(Reg.var reg) ~ptr:(Exp.term ptr)
|
|
~len:(Exp.term len)
|
|
| Store {ptr; exp; len; _} ->
|
|
Exec.store pre ~ptr:(Exp.term ptr) ~exp:(Exp.term exp)
|
|
~len:(Exp.term len)
|
|
| Memset {dst; byt; len; _} ->
|
|
Exec.memset pre ~dst:(Exp.term dst) ~byt:(Exp.term byt)
|
|
~len:(Exp.term len)
|
|
| Memcpy {dst; src; len; _} ->
|
|
Exec.memcpy pre ~dst:(Exp.term dst) ~src:(Exp.term src)
|
|
~len:(Exp.term len)
|
|
| Memmov {dst; src; len; _} ->
|
|
Exec.memmov pre ~dst:(Exp.term dst) ~src:(Exp.term src)
|
|
~len:(Exp.term len)
|
|
| Alloc {reg; num; len; _} ->
|
|
Exec.alloc pre ~reg:(Reg.var reg) ~num:(Exp.term num)
|
|
~len:(Exp.term len)
|
|
| Free {ptr; _} -> Exec.free pre ~ptr:(Exp.term ptr)
|
|
| Nondet {reg; _} -> Some (Exec.nondet pre (Option.map ~f:Reg.var reg))
|
|
| Abort _ -> Exec.abort pre )
|
|
|> Option.map ~f:simplify
|
|
|
|
let exec_intrinsic ~skip_throw q r i es =
|
|
Exec.intrinsic ~skip_throw q (Option.map ~f:Reg.var r) (Reg.var i)
|
|
(List.map ~f:Exp.term es)
|
|
|> Option.map ~f:(Option.map ~f:simplify)
|
|
|
|
let term_eq_class_has_only_vars_in fvs cong term =
|
|
[%Trace.call fun {pf} ->
|
|
pf "@[<v> fvs: @[%a@] @,cong: @[%a@] @,term: @[%a@]@]" Var.Set.pp fvs
|
|
Equality.pp cong Term.pp term]
|
|
;
|
|
let term_has_only_vars_in fvs term =
|
|
Var.Set.is_subset (Term.fv term) ~of_:fvs
|
|
in
|
|
let term_eq_class = Equality.class_of cong term in
|
|
List.exists ~f:(term_has_only_vars_in fvs) term_eq_class
|
|
|>
|
|
[%Trace.retn fun {pf} -> pf "%b"]
|
|
|
|
let garbage_collect (q : t) ~wrt =
|
|
[%Trace.call fun {pf} -> pf "%a" pp q]
|
|
;
|
|
(* only support DNF for now *)
|
|
assert (List.is_empty q.djns) ;
|
|
let rec all_reachable_vars previous current (q : t) =
|
|
if Var.Set.equal previous current then current
|
|
else
|
|
let new_set =
|
|
List.fold ~init:current q.heap ~f:(fun current seg ->
|
|
if term_eq_class_has_only_vars_in current q.cong seg.loc then
|
|
List.fold (Equality.class_of q.cong seg.arr) ~init:current
|
|
~f:(fun c e -> Var.Set.union c (Term.fv e))
|
|
else current )
|
|
in
|
|
all_reachable_vars current new_set q
|
|
in
|
|
let r_vars = all_reachable_vars Var.Set.empty wrt q in
|
|
Sh.filter_heap q ~f:(fun seg ->
|
|
term_eq_class_has_only_vars_in r_vars q.cong seg.loc )
|
|
|>
|
|
[%Trace.retn fun {pf} -> pf "%a" pp]
|
|
|
|
let and_eqs sub formals actuals q =
|
|
let and_eq q formal actual =
|
|
let actual' = Term.rename sub actual in
|
|
Sh.and_ (Term.eq (Term.var formal) actual') q
|
|
in
|
|
List.fold2_exn ~f:and_eq formals actuals ~init:q
|
|
|
|
let localize_entry globals actuals formals freturn locals subst pre entry =
|
|
(* Add the formals here to do garbage collection and then get rid of them *)
|
|
let formals_set = Var.Set.of_list formals in
|
|
let freturn_locals = Reg.Set.vars (Reg.Set.add_option freturn locals) in
|
|
let function_summary_pre =
|
|
garbage_collect entry
|
|
~wrt:(Var.Set.union formals_set (Reg.Set.vars globals))
|
|
in
|
|
[%Trace.info "function summary pre %a" pp function_summary_pre] ;
|
|
let foot = Sh.exists formals_set function_summary_pre in
|
|
let xs, foot = Sh.bind_exists ~wrt:pre.Sh.us foot in
|
|
let frame =
|
|
Option.value_exn
|
|
(Solver.infer_frame pre xs foot)
|
|
~message:"Solver couldn't infer frame of a garbage-collected pre"
|
|
in
|
|
let q'' =
|
|
Sh.extend_us freturn_locals (and_eqs subst formals actuals foot)
|
|
in
|
|
(q'', frame)
|
|
|
|
type from_call = {areturn: Var.t option; subst: Var.Subst.t; frame: Sh.t}
|
|
[@@deriving compare, equal, sexp]
|
|
|
|
(** Express formula in terms of formals instead of actuals, and enter scope
|
|
of locals: rename formals to fresh vars in formula and actuals, add
|
|
equations between each formal and actual, and quantify fresh vars. *)
|
|
let call ~summaries ~globals ~actuals ~areturn ~formals ~freturn ~locals q =
|
|
[%Trace.call fun {pf} ->
|
|
pf
|
|
"@[<hv>actuals: (@[%a@])@ formals: (@[%a@])@ locals: {@[%a@]}@ \
|
|
globals: {@[%a@]}@ q: %a@]"
|
|
(List.pp ",@ " Exp.pp) (List.rev actuals) (List.pp ",@ " Reg.pp)
|
|
(List.rev formals) Reg.Set.pp locals Reg.Set.pp globals pp q]
|
|
;
|
|
let actuals = List.map ~f:Exp.term actuals in
|
|
let areturn = Option.map ~f:Reg.var areturn in
|
|
let formals = List.map ~f:Reg.var formals in
|
|
let freturn_locals = Reg.Set.vars (Reg.Set.add_option freturn locals) in
|
|
let modifs = Var.Set.of_option areturn in
|
|
(* quantify modifs, their current value will be overwritten and so does
|
|
not need to be saved in the freshening renaming *)
|
|
let q = Sh.exists modifs q in
|
|
(* save current values of shadowed formals and locals with a renaming *)
|
|
let q', subst =
|
|
Sh.freshen q ~wrt:(Var.Set.add_list formals freturn_locals)
|
|
in
|
|
assert (Var.Set.disjoint modifs (Var.Subst.domain subst)) ;
|
|
(* pass arguments by conjoining equations between formals and actuals *)
|
|
let entry = and_eqs subst formals actuals q' in
|
|
(* note: locals and formals are in scope *)
|
|
assert (
|
|
Var.Set.is_subset
|
|
(Var.Set.add_list formals freturn_locals)
|
|
~of_:entry.us ) ;
|
|
(* simplify *)
|
|
let entry = simplify entry in
|
|
( if not summaries then (entry, {areturn; subst; frame= Sh.emp})
|
|
else
|
|
let q'', frame =
|
|
localize_entry globals actuals formals freturn locals subst q' entry
|
|
in
|
|
(q'', {areturn; subst; frame}) )
|
|
|>
|
|
[%Trace.retn fun {pf} (entry, {subst; frame}) ->
|
|
pf "@[<v>subst: %a@ frame: %a@ entry: %a@]" Var.Subst.pp subst pp frame
|
|
pp entry]
|
|
|
|
(** Leave scope of locals: existentially quantify locals. *)
|
|
let post locals _ q =
|
|
[%Trace.call fun {pf} ->
|
|
pf "@[<hv>locals: {@[%a@]}@ q: %a@]" Reg.Set.pp locals Sh.pp q]
|
|
;
|
|
Sh.exists (Reg.Set.vars locals) q |> simplify
|
|
|>
|
|
[%Trace.retn fun {pf} -> pf "%a" Sh.pp]
|
|
|
|
(** Express in terms of actuals instead of formals: existentially quantify
|
|
formals, and apply inverse of fresh variables for formals renaming to
|
|
restore the shadowed variables. *)
|
|
let retn formals freturn {areturn; subst; frame} q =
|
|
[%Trace.call fun {pf} ->
|
|
pf "@[<v>formals: {@[%a@]}%a%a@ subst: %a@ q: %a@ frame: %a@]"
|
|
(List.pp ", " Reg.pp) formals
|
|
(Option.pp "@ freturn: %a" Reg.pp)
|
|
freturn
|
|
(Option.pp "@ areturn: %a" Var.pp)
|
|
areturn Var.Subst.pp (Var.Subst.invert subst) pp q pp frame]
|
|
;
|
|
let formals = List.map ~f:Reg.var formals in
|
|
let freturn = Option.map ~f:Reg.var freturn in
|
|
let inv_subst = Var.Subst.invert subst in
|
|
let q, inv_subst =
|
|
match areturn with
|
|
| Some areturn -> (
|
|
(* reenter scope of areturn just before exiting scope of formals *)
|
|
let q = Sh.extend_us (Var.Set.of_ areturn) q in
|
|
(* pass return value *)
|
|
match freturn with
|
|
| Some freturn ->
|
|
(Exec.move q (IArray.of_ (areturn, Term.var freturn)), inv_subst)
|
|
| None -> (Exec.kill q areturn, inv_subst) )
|
|
| None -> (q, inv_subst)
|
|
in
|
|
(* exit scope of formals *)
|
|
let q =
|
|
Sh.exists (Var.Set.add_list formals (Var.Set.of_option freturn)) q
|
|
in
|
|
(* reinstate shadowed values of locals *)
|
|
let q = Sh.rename inv_subst q in
|
|
(* reconjoin frame *)
|
|
Sh.star frame q
|
|
(* simplify *)
|
|
|> simplify
|
|
|>
|
|
[%Trace.retn fun {pf} -> pf "%a" pp]
|
|
|
|
let resolve_callee lookup ptr q =
|
|
match Reg.of_exp ptr with
|
|
| Some callee -> (lookup (Reg.name callee), q)
|
|
| None -> ([], q)
|
|
|
|
let recursion_beyond_bound = `prune
|
|
|
|
type summary = {xs: Var.Set.t; foot: t; post: t}
|
|
|
|
let pp_summary fs {xs; foot; post} =
|
|
Format.fprintf fs "@[<v>xs: @[%a@]@ foot: %a@ post: %a @]" Var.Set.pp xs
|
|
pp foot pp post
|
|
|
|
let create_summary ~locals ~formals ~entry ~current:(post : Sh.t) =
|
|
[%Trace.call fun {pf} ->
|
|
pf "formals %a@ entry: %a@ current: %a" Reg.Set.pp formals pp entry pp
|
|
post]
|
|
;
|
|
let locals = Reg.Set.vars locals in
|
|
let formals = Reg.Set.vars formals in
|
|
let foot = Sh.exists locals entry in
|
|
let foot, subst = Sh.freshen ~wrt:(Var.Set.union foot.us post.us) foot in
|
|
let restore_formals q =
|
|
Var.Set.fold formals ~init:q ~f:(fun q var ->
|
|
let var = Term.var var in
|
|
let renamed_var = Term.rename subst var in
|
|
Sh.and_ (Term.eq renamed_var var) q )
|
|
in
|
|
(* Add back the original formals name *)
|
|
let post = Sh.rename subst post in
|
|
let foot = restore_formals foot in
|
|
let post = restore_formals post in
|
|
[%Trace.info "subst: %a" Var.Subst.pp subst] ;
|
|
let xs = Var.Set.inter (Sh.fv foot) (Sh.fv post) in
|
|
let xs = Var.Set.diff xs formals in
|
|
let xs_and_formals = Var.Set.union xs formals in
|
|
let foot = Sh.exists (Var.Set.diff foot.us xs_and_formals) foot in
|
|
let post = Sh.exists (Var.Set.diff post.us xs_and_formals) post in
|
|
let current = Sh.extend_us xs post in
|
|
({xs; foot; post}, current)
|
|
|>
|
|
[%Trace.retn fun {pf} (fs, _) -> pf "@,%a" pp_summary fs]
|
|
|
|
let apply_summary q ({xs; foot; post} as fs) =
|
|
[%Trace.call fun {pf} -> pf "fs: %a@ q: %a" pp_summary fs pp q]
|
|
;
|
|
let xs_in_q = Var.Set.inter xs q.Sh.us in
|
|
let xs_in_fv_q = Var.Set.inter xs (Sh.fv q) in
|
|
(* Between creation of a summary and its use, the vocabulary of q (q.us)
|
|
might have been extended. That means infer_frame would fail, because q
|
|
and foot have different vocabulary. This might indicate that the
|
|
summary cannot be applied to q, however in the case where
|
|
free-variables of q and foot match it is benign. In the case where free
|
|
variables match, we temporarily reduce the vocabulary of q to match the
|
|
vocabulary of foot. *)
|
|
[%Trace.info "xs inter q.us: %a" Var.Set.pp xs_in_q] ;
|
|
[%Trace.info "xs inter fv.q %a" Var.Set.pp xs_in_fv_q] ;
|
|
let q, add_back =
|
|
if Var.Set.is_empty xs_in_fv_q then (Sh.exists xs_in_q q, xs_in_q)
|
|
else (q, Var.Set.empty)
|
|
in
|
|
let frame =
|
|
if Var.Set.is_empty xs_in_fv_q then Solver.infer_frame q xs foot
|
|
else None
|
|
in
|
|
[%Trace.info "frame %a" (Option.pp "%a" pp) frame] ;
|
|
Option.map ~f:(Sh.extend_us add_back) (Option.map ~f:(Sh.star post) frame)
|
|
|>
|
|
[%Trace.retn fun {pf} r ->
|
|
match r with None -> pf "None" | Some q -> pf "@,%a" pp q]
|
|
|
|
let%test_module _ =
|
|
( module struct
|
|
let pp = Format.printf "@.%a@." Sh.pp
|
|
let wrt = Var.Set.empty
|
|
let main_, wrt = Var.fresh "main" ~wrt
|
|
let a_, wrt = Var.fresh "a" ~wrt
|
|
let n_, wrt = Var.fresh "n" ~wrt
|
|
let b_, wrt = Var.fresh "b" ~wrt
|
|
let end_, _ = Var.fresh "end" ~wrt
|
|
let a = Term.var a_
|
|
let main = Term.var main_
|
|
let b = Term.var b_
|
|
let n = Term.var n_
|
|
let endV = Term.var end_
|
|
let seg_main = Sh.seg {loc= main; bas= b; len= n; siz= n; arr= a}
|
|
let seg_a = Sh.seg {loc= a; bas= b; len= n; siz= n; arr= endV}
|
|
let seg_cycle = Sh.seg {loc= a; bas= b; len= n; siz= n; arr= main}
|
|
|
|
let%expect_test _ =
|
|
pp (garbage_collect seg_main ~wrt:(Var.Set.of_list [])) ;
|
|
[%expect {| emp |}]
|
|
|
|
let%expect_test _ =
|
|
pp
|
|
(garbage_collect (Sh.star seg_a seg_main)
|
|
~wrt:(Var.Set.of_list [a_])) ;
|
|
[%expect {| %a_2 -[ %b_4, %n_3 )-> ⟨%n_3,%end_5⟩ |}]
|
|
|
|
let%expect_test _ =
|
|
pp
|
|
(garbage_collect (Sh.star seg_a seg_main)
|
|
~wrt:(Var.Set.of_list [main_])) ;
|
|
[%expect
|
|
{|
|
|
%main_1 -[ %b_4, %n_3 )-> ⟨%n_3,%a_2⟩
|
|
* %a_2 -[ %b_4, %n_3 )-> ⟨%n_3,%end_5⟩ |}]
|
|
|
|
let%expect_test _ =
|
|
pp
|
|
(garbage_collect
|
|
(Sh.star seg_cycle seg_main)
|
|
~wrt:(Var.Set.of_list [a_])) ;
|
|
[%expect
|
|
{|
|
|
%main_1 -[ %b_4, %n_3 )-> ⟨%n_3,%a_2⟩
|
|
* %a_2 -[ %b_4, %n_3 )-> ⟨%n_3,%main_1⟩ |}]
|
|
end )
|