mlw_wp.ml 23.4 KB
Newer Older
Andrei Paskevich's avatar
Andrei Paskevich committed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
(**************************************************************************)
(*                                                                        *)
(*  Copyright (C) 2010-2012                                               *)
(*    François Bobot                                                      *)
(*    Jean-Christophe Filliâtre                                           *)
(*    Claude Marché                                                       *)
(*    Guillaume Melquiond                                                 *)
(*    Andrei Paskevich                                                    *)
(*                                                                        *)
(*  This software is free software; you can redistribute it and/or        *)
(*  modify it under the terms of the GNU Library General Public           *)
(*  License version 2.1, with the special exception on linking            *)
(*  described in file LICENSE.                                            *)
(*                                                                        *)
(*  This software is distributed in the hope that it will be useful,      *)
(*  but WITHOUT ANY WARRANTY; without even the implied warranty of        *)
(*  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.                  *)
(*                                                                        *)
(**************************************************************************)

open Why3
open Ident
open Ty
open Term
25
open Decl
Andrei Paskevich's avatar
Andrei Paskevich committed
26 27 28 29 30
open Theory
open Mlw_ty
open Mlw_ty.T
open Mlw_expr

31 32
let debug = Debug.register_flag "whyml_wp"

33
(** Marks *)
Andrei Paskevich's avatar
Andrei Paskevich committed
34 35 36 37

let ts_mark = create_tysymbol (id_fresh "'mark") [] None
let ty_mark = ty_app ts_mark []

38 39
let fresh_mark () = create_vsymbol (id_fresh "mark") ty_mark

Andrei Paskevich's avatar
Andrei Paskevich committed
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61
let fs_at =
  let ty = ty_var (create_tvsymbol (id_fresh "a")) in
  create_lsymbol (id_fresh "at") [ty; ty_mark] (Some ty)

let fs_old =
  let ty = ty_var (create_tvsymbol (id_fresh "a")) in
  create_lsymbol (id_fresh "old") [ty] (Some ty)

let th_mark =
  let uc = create_theory (id_fresh "WP builtins") in
  let uc = add_ty_decl uc ts_mark in
  let uc = add_param_decl uc fs_at in
  let uc = add_param_decl uc fs_old in
  close_theory uc

let fs_setmark =
  create_lsymbol (id_fresh "set_mark") [] (Some ty_mark)

let e_setmark = e_lapp fs_setmark [] (ity_pur ts_mark [])

let vs_old = create_vsymbol (id_fresh "'old") ty_mark
let vs_now = create_vsymbol (id_fresh "'now") ty_mark
62

63 64
let ls_absurd = create_lsymbol (id_fresh "absurd") [] None
let t_absurd  = ps_app ls_absurd []
65

66
let mk_t_if f = t_if f t_bool_true t_bool_false
67
let to_term t = if t.t_ty = None then mk_t_if t else t
68 69 70 71 72 73 74

(* replace [at(t,'old)] with [at(t,lab)] everywhere in formula [f] *)
let old_mark lab t = t_subst_single vs_old (t_var lab) t

(* replace [at(t,lab)] with [at(t,'now)] everywhere in formula [f] *)
let erase_mark lab t = t_subst_single lab (t_var vs_now) t

75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93
(* replace [at(t,now)] with [t] modulo variable renaming *)
let rec drop_at now m t = match t.t_node with
  | Tvar vs when now ->
      begin try t_var (Mvs.find vs m) with Not_found -> t end
  | Tapp (ls, _) when ls_equal ls fs_old ->
      assert false
  | Tapp (ls, [e;{t_node = Tvar lab}]) when ls_equal ls fs_at ->
      if vs_equal lab vs_old then assert false else
      if vs_equal lab vs_now then drop_at true m e else
      (* no longer assume that unmarked variables are at mark 'now *)
      t_map (drop_at false m) t
  | Tlet _ | Tcase _ | Teps _ | Tquant _ ->
      (* do not open unless necessary *)
      let m = Mvs.set_inter m t.t_vars in
      if Mvs.is_empty m then t else
      t_map (drop_at now m) t
  | _ ->
      t_map (drop_at now m) t

94 95 96
(** Specifications *)

let psymbol_spec_t : type_v Wps.t = Wps.create 17
97
let e_apply_spec_t : type_c Wexpr.t = Wexpr.create 17
98

99 100 101
let add_pv_varm pv m = Mid.add pv.pv_vs.vs_name pv.pv_vtv.vtv_vars m
let add_pv_vars pv s = vars_union pv.pv_vtv.vtv_vars s

102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117
let rec check_spec vty tyv = match vty, tyv with
  | VTvalue _, SpecV _ -> ()
  | VTarrow vta, SpecA (_::(_::_ as pvl), tyc) ->
      assert (eff_is_empty vta.vta_effect);
      check_spec vta.vta_result (SpecA (pvl, tyc))
  | VTarrow vta, SpecA ([_], tyc) ->
      let eff1 = vta.vta_effect in
      let eff2 = tyc.c_effect in
      assert (Sreg.equal eff1.eff_reads  eff2.eff_reads);
      assert (Sreg.equal eff1.eff_writes eff2.eff_writes);
      assert (Sexn.equal eff1.eff_raises eff2.eff_raises);
      assert (Sreg.equal eff1.eff_ghostr eff2.eff_ghostr);
      assert (Sreg.equal eff1.eff_ghostw eff2.eff_ghostw);
      assert (Sexn.equal eff1.eff_ghostx eff2.eff_ghostx);
      check_spec vta.vta_result tyc.c_result
  | _ -> assert false
118

119
let rec filter_v varm vars = function
120 121 122
  | SpecA (pvl, tyc) ->
      let varm = List.fold_right add_pv_varm pvl varm in
      let vars = List.fold_right add_pv_vars pvl vars in
123
      SpecA (pvl, filter_c varm vars tyc)
124 125
  | tyv -> tyv

126 127 128 129 130 131 132 133
and filter_c varm vars tyc =
  let add _ f s = Mvs.set_union f.t_vars s in
  let vss = add () tyc.c_pre tyc.c_post.t_vars in
  let vss = Mexn.fold add tyc.c_xpost vss in
  let check { vs_name = id } _ = if not (Mid.mem id varm) then
    Loc.errorm "Local variable %s escapes from its scope" id.id_string in
  Mvs.iter check vss;
  let result = filter_v varm vars tyc.c_result in
134 135 136
  let effect = eff_filter vars tyc.c_effect in
  { tyc with c_effect = effect; c_result = result }

137
let add_psymbol_spec varm ps tyv =
138
  let vars = Mid.fold (fun _ -> vars_union) varm vars_empty in
139 140 141 142
  let tyv = filter_v varm vars tyv in
  if Debug.test_flag debug then
    Format.eprintf "@[<hov 2>SPEC %a = %a@]@\n"
      Mlw_pretty.print_psty ps Mlw_pretty.print_type_v tyv;
143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183
  check_spec (VTarrow ps.ps_vta) tyv; (* TODO: prove and remove *)
  Wps.set psymbol_spec_t ps tyv

(* TODO? move spec_inst and subst to Mlw_expr? *)
let vtv_full_inst sbs vtv =
  vty_value ~ghost:vtv.vtv_ghost (ity_full_inst sbs vtv.vtv_ity)

let pv_full_inst sbs pv =
  create_pvsymbol (id_clone pv.pv_vs.vs_name) (vtv_full_inst sbs pv.pv_vtv)

let rec spec_inst_v sbs tvm vsm = function
  | SpecV vtv ->
      SpecV (vtv_full_inst sbs vtv)
  | SpecA (pvl,tyc) ->
      let add m pv =
        let nv = pv_full_inst sbs pv in
        Mvs.add pv.pv_vs (t_var nv.pv_vs) m, nv in
      let vsm, pvl = Util.map_fold_left add vsm pvl in
      SpecA (pvl, spec_inst_c sbs tvm vsm tyc)

and spec_inst_c sbs tvm vsm tyc =
  let subst = t_ty_subst tvm vsm in {
    c_pre    = subst tyc.c_pre;
    c_effect = eff_full_inst sbs tyc.c_effect;
    c_result = spec_inst_v sbs tvm vsm tyc.c_result;
    c_post   = subst tyc.c_post;
    c_xpost  = Mexn.map subst tyc.c_xpost; }

let rec subst_v pv t = function
  | SpecA (pvl,tyc) when not (List.exists (pv_equal pv) pvl) ->
      SpecA (pvl, subst_c pv t tyc)
  | tyv -> tyv

and subst_c pv t tyc =
  let subst = t_subst (Mvs.singleton pv.pv_vs t) in {
    c_pre    = subst tyc.c_pre;
    c_effect = tyc.c_effect;
    c_result = subst_v pv t tyc.c_result;
    c_post   = subst tyc.c_post;
    c_xpost  = Mexn.map subst tyc.c_xpost; }

184 185 186 187 188 189 190 191 192
let spec_lambda l tyv =
  let tyc = {
    c_pre    = l.l_pre;
    c_effect = l.l_expr.e_effect;
    c_result = tyv;
    c_post   = l.l_post;
    c_xpost  = l.l_xpost } in
  SpecA (l.l_args, tyc)

193
let spec_val vd = match vd.val_name with
194
  | LetA ps -> add_psymbol_spec vd.val_vars ps vd.val_spec
195 196
  | LetV _  -> ()

197 198 199
let rec spec_let { let_var = lv; let_expr = e } = match lv with
  | LetA ps -> add_psymbol_spec e.e_vars ps (spec_expr e)
  | LetV _  -> ignore (spec_expr e)
200

201
and spec_rec rdl =
202 203 204 205 206
  let add_vars m rd = Mid.set_union m rd.rec_vars in
  let vars = List.fold_left add_vars Mid.empty rdl in
  let add_early_spec rd = match rd.rec_lambda.l_expr.e_vty with
    | VTvalue vtv ->
        let tyv = spec_lambda rd.rec_lambda (SpecV vtv) in
207
        add_psymbol_spec rd.rec_vars rd.rec_ps tyv
208 209 210 211 212 213
    | VTarrow _ when Mid.mem rd.rec_ps.ps_name vars ->
        Loc.errorm ?loc:rd.rec_lambda.l_expr.e_loc
          "The body of a recursive function must be a first-order value"
    | VTarrow _ -> () in
  List.iter add_early_spec rdl;
  let add_late_spec rd =
214
    let tyv = spec_expr rd.rec_lambda.l_expr in
215 216 217
    match rd.rec_lambda.l_expr.e_vty with
    | VTarrow _ ->
        let tyv = spec_lambda rd.rec_lambda tyv in
218
        add_psymbol_spec rd.rec_vars rd.rec_ps tyv
219 220 221
    | VTvalue _ -> () in
  List.iter add_late_spec rdl

222
and spec_expr e = match e.e_node with
223 224 225 226
  | Elogic _
  | Eassert _
  | Eabsurd -> SpecV (vtv_of_expr e)
  | Evalue pv -> SpecV pv.pv_vtv
227 228 229 230
  | Earrow ps ->
    (* TODO: a ps may not be in the table, if it comes from a module
       for which we never computed WPs. Pass the known_map to spec_expr
       and compute it now. *)
231
      let sbs = vta_vars_match ps.ps_subst ps.ps_vta (vta_of_expr e) in
232 233 234 235
      let tvm = Mtv.map ty_of_ity sbs.ity_subst_tv in
      let tyv = Wps.find psymbol_spec_t ps in
      spec_inst_v sbs tvm Mvs.empty tyv
  | Eapp (e1,pv) ->
236 237
      let tyv = spec_expr e1 in
      let t = t_var pv.pv_vs in
238 239 240 241 242 243 244 245 246 247 248 249
      begin match tyv with
        | SpecA ([pv],tyc) ->
            let tyc = subst_c pv t tyc in
            (* we will use this for WP *)
            Wexpr.set e_apply_spec_t e tyc;
            tyc.c_result
        | SpecA (pv::pvl,tyc) ->
            (* pv cannot occur in pvl *)
            SpecA (pvl, subst_c pv t tyc)
        | _ -> assert false
      end
  | Elet (ld,e1) ->
250 251
      spec_let ld;
      spec_expr e1
252
  | Erec (rdl,e1) ->
253 254 255
      spec_rec rdl;
      spec_expr e1
  | Eghost e1 -> spec_expr e1
256 257 258 259 260 261
  | Eany tyc -> tyc.c_result
  | Eassign (e1,_,_)
  | Eloop (_,_,e1)
  | Efor (_,_,_,e1)
  | Eraise (_,e1)
  | Eabstr (e1,_,_) ->
262
      ignore (spec_expr e1);
263 264
      SpecV (vtv_of_expr e)
  | Eif (e1,e2,e3) ->
265 266 267
      ignore (spec_expr e1);
      ignore (spec_expr e2);
      spec_expr e3
268
  | Ecase (e1,bl) ->
269 270
      ignore (spec_expr e1);
      List.iter (fun (_,e) -> ignore (spec_expr e)) bl;
271 272
      SpecV (vtv_of_expr e)
  | Etry (e1,bl) ->
273 274
      ignore (spec_expr e1);
      List.iter (fun (_,_,e) -> ignore (spec_expr e)) bl;
275 276
      SpecV (vtv_of_expr e)

277
(** WP utilities *)
278 279 280 281 282 283 284 285 286 287 288

let ty_of_vty = function
  | VTvalue vtv -> ty_of_ity vtv.vtv_ity
  | VTarrow _   -> ty_unit

let default_exn_post xs _ =
  let vs = create_vsymbol (id_fresh "result") (ty_of_ity xs.xs_ity) in
  create_post vs t_true

let default_post vty ef =
  let vs = create_vsymbol (id_fresh "result") (ty_of_vty vty) in
289
  create_post vs t_true, Mexn.mapi default_exn_post ef.eff_raises
290

291 292 293 294 295
let wp_label e f =
  let loc = if f.t_loc = None then e.e_loc else f.t_loc in
  let lab = Ident.Slab.union e.e_label f.t_label in
  t_label ?loc lab f

296 297 298 299 300
let expl_assert = Ident.create_label "expl:assertion"
let expl_check  = Ident.create_label "expl:check"
let expl_post   = Ident.create_label "expl:normal postcondition"
let expl_xpost  = Ident.create_label "expl:exceptional postcondition"

301 302
let wp_expl l f =
  let lab = Slab.add Split_goal.stop_split f.t_label in
303
  t_label ?loc:f.t_loc (Slab.add l lab) f
304

305
let wp_and ~sym f1 f2 =
306 307
  if sym then t_and_simp f1 f2 else t_and_asym_simp f1 f2

308
let wp_ands ~sym fl =
309 310
  if sym then t_and_simp_l fl else t_and_asym_simp_l fl

311
let wp_implies f1 f2 = t_implies_simp f1 f2
312

313 314 315 316
let wp_forall vl f = t_forall_close_simp vl [] f

let wp_let v t f = t_let_close_simp v t f

317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333
let regs_of_reads  eff = Sreg.union eff.eff_reads eff.eff_ghostr
let regs_of_writes eff = Sreg.union eff.eff_writes eff.eff_ghostw
let regs_of_effect eff = Sreg.union (regs_of_reads eff) (regs_of_writes eff)

let t_void = fs_app (fs_tuple 0) [] ty_unit

let open_unit_post q =
  let v, q = open_post q in
  t_subst_single v t_void q

let create_unit_post =
  let v = create_vsymbol (id_fresh "void") ty_unit in
  fun q -> create_post v q

let vs_result e =
  create_vsymbol (id_fresh ?loc:e.e_loc "result") (ty_of_vty e.e_vty)

334
(* TODO: put this into abstract/opaque wp, it's only relevant there *)
335 336
(*
match f.t_node with
337 338 339 340 341 342 343 344 345 346 347
  | Tbinop (Timplies, {t_node = Tapp (s,[{t_node = Tvar u};r])},h)
    when ls_equal s ps_equ && vs_equal u v && not (Mvs.mem v r.t_vars) ->
      t_let_close_simp v r h
  | Tbinop (Timplies, {t_node = Tbinop (Tand, g,
                      {t_node = Tapp (s,[{t_node = Tvar u};r])})},h)
    when ls_equal s ps_equ && vs_equal u v && not (Mvs.mem v r.t_vars) ->
      t_let_close_simp v r (t_implies_simp g h)
  | _ when Mvs.mem v f.t_vars ->
      t_forall_close_simp [v] [] f
  | _ ->
      f
348
*)
349

350 351 352 353 354 355 356
(** WP state *)

type wp_env = {
  prog_known : Mlw_decl.known_map;
  pure_known : Decl.known_map;
  global_env : Env.env;
}
357

358 359
(** Reconstruct pure values after writes *)

360
let find_constructors env sts ity = match ity.ity_node with
361 362 363
  | Itypur (ts,_) ->
      let base = ity_pur ts (List.map ity_var ts.ts_args) in
      let sbs = ity_match ity_subst_empty base ity in
364
      let csl = Decl.find_constructors env.pure_known ts in
365 366 367 368 369 370 371 372
      if csl = [] || Sts.mem ts sts then Loc.errorm
        "Cannot update values of type %a" Mlw_pretty.print_ity base;
      let subst ty = ity_full_inst sbs (ity_of_ty ty), None in
      let cnstr (cs,_) = cs, List.map subst cs.ls_args in
      Sts.add ts sts, List.map cnstr csl
  | Ityapp (its,_,_) ->
      let base = ity_app its (List.map ity_var its.its_args) its.its_regs in
      let sbs = ity_match ity_subst_empty base ity in
373
      let csl = Mlw_decl.find_constructors env.prog_known its in
374 375 376 377 378 379 380 381 382
      if csl = [] || Sts.mem its.its_pure sts then Loc.errorm
        "Cannot update values of type %a" Mlw_pretty.print_ity base;
      let subst vtv =
        ity_full_inst sbs vtv.vtv_ity,
        Util.option_map (reg_full_inst sbs) vtv.vtv_mut in
      let cnstr (cs,_) = cs.pl_ls, List.map subst cs.pl_args in
      Sts.add its.its_pure sts, List.map cnstr csl
  | Ityvar _ -> assert false

383
let update_var env mreg vs =
384 385 386 387 388 389 390 391 392
  let rec update sts vs ity mut =
    (* are we a mutable variable? *)
    let get_vs r = Mreg.find_def vs r mreg in
    let vs = Util.option_apply vs get_vs mut in
    (* should we update our value further? *)
    let check_reg r _ = reg_occurs r ity.ity_vars in
    if ity_pure ity || not (Mreg.exists check_reg mreg) then
      t_var vs
    else
393
      let sts, csl = find_constructors env sts ity in
394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422
      let branch (cs,ityl) =
        let mk_var (ity,_) = create_vsymbol (id_fresh "y") (ty_of_ity ity) in
        let vars = List.map mk_var ityl in
        let pat = pat_app cs (List.map pat_var vars) vs.vs_ty in
        let mk_arg vs (ity, mut) = update sts vs ity mut in
        let t = fs_app cs (List.map2 mk_arg vars ityl) vs.vs_ty in
        t_close_branch pat t in
      t_case (t_var vs) (List.map branch csl)
  in
  let vtv = (restore_pv vs).pv_vtv in
  update Sts.empty vs vtv.vtv_ity vtv.vtv_mut

(* quantify over all references in eff
   eff : effect
   f   : formula

   let eff = { rho1, ..., rhon }
   we collect in vars all variables involving these regions
   let vars = { v1, ..., vm }

     forall r1:ty(rho1). ... forall rn:ty(rhon).
     let v'1 = update v1 r1...rn in
     ...
     let v'm = update vm r1...rn in
     f[vi <- v'i]
*)

let model1_lab = Slab.singleton (create_label "model:1")
let model2_lab = Slab.singleton (create_label "model:quantify(2)")
423 424
let model3_lab = Slab.singleton (create_label "model:cond")

425 426
let mk_var id label ty = create_vsymbol (id_clone ~label id) ty

427 428
let quantify env regs f =
  (* mreg : updated region -> vs *)
429 430 431 432 433 434 435 436
  let get_var reg () =
    let test vs _ id = match (restore_pv vs).pv_vtv with
      | { vtv_ity = { ity_node = Ityapp (_,_,[r]) }}
      | { vtv_mut = Some r } when reg_equal r reg -> vs.vs_name
      | _ -> id in
    let id = Mvs.fold test f.t_vars reg.reg_name in
    mk_var id model1_lab (ty_of_ity reg.reg_ity)
  in
437
  let mreg = Mreg.mapi get_var regs in
438
  (* update all program variables involving these regions *)
439
  let update_var vs _ = match update_var env mreg vs with
440 441 442 443 444 445 446
    | { t_node = Tvar nv } when vs_equal vs nv -> None
    | t -> Some t in
  let vars = Mvs.mapi_filter update_var f.t_vars in
  (* vv' : old vs -> new vs *)
  let new_var vs _ = mk_var vs.vs_name model2_lab vs.vs_ty in
  let vv' = Mvs.mapi new_var vars in
  (* quantify *)
447
  let update v t f = wp_let (Mvs.find v vv') t f in
448
  let f = Mvs.fold update vars (drop_at true vv' f) in
449
  wp_forall (Mreg.values mreg) f
450 451 452

(** Weakest preconditions *)

453
let rec wp_expr env e q xq =
454 455 456
  let lab = fresh_mark () in
  let q = old_mark lab q in
  let xq = Mexn.map (old_mark lab) xq in
457
  let f = wp_desc env e q xq in
458 459
  let f = erase_mark lab f in
  if Debug.test_flag debug then begin
460
    Format.eprintf "@[--------@\n@[<hov 2>e = %a@]@\n" Mlw_pretty.print_expr e;
461 462 463
    Format.eprintf "@[<hov 2>q = %a@]@\n" Pretty.print_term q;
    Format.eprintf "@[<hov 2>f = %a@]@\n----@]@." Pretty.print_term f;
  end;
464
  f
465

466
and wp_desc env e q xq = match e.e_node with
467 468 469
  | Elogic t ->
      let v, q = open_post q in
      let t = wp_label e t in
470
      t_subst_single v (to_term t) q
Andrei Paskevich's avatar
Andrei Paskevich committed
471 472 473
  | Evalue pv ->
      let v, q = open_post q in
      let t = wp_label e (t_var pv.pv_vs) in
474
      t_subst_single v t q
475 476 477
  | Earrow _ ->
      let q = open_unit_post q in
      (* wp_label e *) q (* FIXME? *)
478 479 480 481 482 483 484 485 486 487
  | Elet ({ let_var = lv; let_expr = e1 }, e2) ->
      (* FIXME? Pgm_wp applies filter_post everywhere, but doesn't
         it suffice to do it only on Etry? The same question about
         saturate_post: why do we supply default exceptional posts
         instead of requiring an explicit xpost for every "raises"? *)
      let w = wp_expr env e2 q xq in
      let q = match lv with
        | LetV v -> create_post v.pv_vs w
        | LetA _ -> create_unit_post w in
      wp_label e (wp_expr env e1 q xq)
Andrei Paskevich's avatar
Andrei Paskevich committed
488
  | Erec (rdl, e) ->
489 490 491
      let fr = wp_rec_defn env rdl in
      let fe = wp_expr env e q xq in
      wp_and ~sym:true (wp_ands ~sym:true fr) fe
492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533
  | Eif (e1, e2, e3) ->
      let res = vs_result e1 in
      let test = t_equ (t_var res) t_bool_true in
      let test = t_label ?loc:e1.e_loc model3_lab test in
      (* if both branches are pure, do not split *)
      let w =
        let get_term e = match e.e_node with
          | Elogic t -> to_term t
          | Evalue v -> t_var v.pv_vs
          | _ -> raise Exit in
        try
          let r2 = get_term e2 in
          let r3 = get_term e3 in
          let v, q = open_post q in
          t_subst_single v (t_if_simp test r2 r3) q
        with Exit ->
          let w2 = wp_expr env e2 q xq in
          let w3 = wp_expr env e3 q xq in
          t_if_simp test w2 w3
      in
      let q = create_post res w in
      wp_label e (wp_expr env e1 q xq)
  | Ecase (e1, bl) ->
      let res = vs_result e1 in
      let branch ({ ppat_pattern = pat }, e) =
        t_close_branch pat (wp_expr env e q xq) in
      let w = t_case (t_var res) (List.map branch bl) in
      let q = create_post res w in
      wp_label e (wp_expr env e1 q xq)
  | Eghost e1 ->
      wp_label e (wp_expr env e1 q xq)
  | Eraise (xs, e1) ->
      let q = try Mexn.find xs xq with
        Not_found -> assert false in
      wp_label e (wp_expr env e1 q xq)
  | Etry (e1, bl) ->
      let branch (xs,v,e) acc =
        let w = wp_expr env e q xq in
        let q = create_post v.pv_vs w in
        Mexn.add xs q acc in
      let xq = List.fold_right branch bl xq in
      wp_label e (wp_expr env e1 q xq)
534 535
  | Eassert (Aassert, f) ->
      let q = open_unit_post q in
536
      let f = wp_expl expl_assert f in
537 538 539
      wp_and ~sym:false (wp_label e f) q
  | Eassert (Acheck, f) ->
      let q = open_unit_post q in
540
      let f = wp_expl expl_check f in
541 542 543 544
      wp_and ~sym:true (wp_label e f) q
  | Eassert (Aassume, f) ->
      let q = open_unit_post q in
      wp_implies (wp_label e f) q
Andrei Paskevich's avatar
Andrei Paskevich committed
545
  | Eabsurd ->
546 547
      wp_label e t_absurd

548 549 550 551 552 553 554
  (* TODO *)
  |Eabstr (_, _, _)-> t_true
  |Efor (_, _, _, _)-> t_true
  |Eloop (_, _, _)-> t_true
  |Eany _-> t_true
  |Eassign (_, _, _)-> t_true
  |Eapp (_, _)-> t_true
555

556
and wp_lambda env l =
557 558
  let q = wp_expl expl_post l.l_post in
  let xq = Mexn.map (wp_expl expl_xpost) l.l_xpost in
559
  let f = wp_expr env l.l_expr q xq in
560
  let f = wp_implies l.l_pre f in
561
  let f = quantify env (regs_of_effect l.l_expr.e_effect) f in
562
  wp_forall (List.map (fun pv -> pv.pv_vs) l.l_args) f
563

564 565
and wp_rec_defn env rdl =
  List.map (fun rd -> wp_lambda env rd.rec_lambda) rdl
566

567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612
(***
let bool_to_prop env f =
  let ts_bool  = find_ts ~pure:true env "bool" in
  let ls_andb  = find_ls ~pure:true env "andb" in
  let ls_orb   = find_ls ~pure:true env "orb" in
  let ls_notb  = find_ls ~pure:true env "notb" in
  let ls_True  = find_ls ~pure:true env "True" in
  let ls_False = find_ls ~pure:true env "False" in
  let t_True   = fs_app ls_True [] (ty_app ts_bool []) in
  let is_bool ls = ls_equal ls ls_True || ls_equal ls ls_False in
  let rec t_iff_bool f1 f2 = match f1.t_node, f2.t_node with
    | Tnot f1, _ -> t_not_simp (t_iff_bool f1 f2)
    | _, Tnot f2 -> t_not_simp (t_iff_bool f1 f2)
    | Tapp (ps1, [t1; { t_node = Tapp (ls1, []) }]),
      Tapp (ps2, [t2; { t_node = Tapp (ls2, []) }])
      when ls_equal ps1 ps_equ && ls_equal ps2 ps_equ &&
           is_bool ls1 && is_bool ls2 ->
        if ls_equal ls1 ls2 then t_equ t1 t2 else t_neq t1 t2
    | _ ->
        t_iff_simp f1 f2
  in
  let rec t_btop t = t_label ?loc:t.t_loc t.t_label (* t_label_copy? *)
    (match t.t_node with
    | Tif (f,t1,t2) ->
        t_if_simp (f_btop f) (t_btop t1) (t_btop t2)
    | Tapp (ls, [t1;t2]) when ls_equal ls ls_andb ->
        t_and_simp (t_btop t1) (t_btop t2)
    | Tapp (ls, [t1;t2]) when ls_equal ls ls_orb ->
        t_or_simp (t_btop t1) (t_btop t2)
    | Tapp (ls, [t1]) when ls_equal ls ls_notb ->
        t_not_simp (t_btop t1)
    | Tapp (ls, []) when ls_equal ls ls_True ->
        t_true
    | Tapp (ls, []) when ls_equal ls ls_False ->
        t_false
    | _ ->
        t_equ_simp (f_btop t) t_True)
  and f_btop f = match f.t_node with
    | Tapp (ls, [{t_ty = Some {ty_node = Tyapp (ts, [])}} as l; r])
      when ls_equal ls ps_equ && ts_equal ts ts_bool ->
        t_label ?loc:f.t_loc f.t_label (t_iff_bool (t_btop l) (t_btop r))
    | _ ->
        t_map_simp f_btop f
  in
  f_btop f
***)
613

614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647
(* replace every occurrence of [at(t,'now)] with [t] *)
let rec remove_at f = match f.t_node with
  | Tapp (ls, [t;{t_node = Tvar lab}])
    when ls_equal ls fs_at && vs_equal lab vs_now ->
      remove_at t
  | _ ->
      t_map remove_at f

(* replace t_absurd with t_false *)
let rec unabsurd f = match f.t_node with
  | Tapp (ls, []) when ls_equal ls ls_absurd ->
      t_label_copy f t_false
  | _ ->
      t_map unabsurd f

let add_wp_decl name f uc =
  (* prepare a proposition symbol *)
  let s = "WP_" ^ name.id_string in
  let lab = Ident.create_label ("expl:" ^ name.id_string) in
  let label = Slab.add lab name.id_label in
  let id = id_fresh ~label ?loc:name.id_loc s in
  let pr = create_prsymbol id in
  (* prepare the VC formula *)
  let f = remove_at f in
  (* let f = bool_to_prop uc f in *)
  let f = unabsurd f in
  (* get a known map with tuples added *)
  let km = Theory.get_known uc in
  (* simplify f *)
  let f = Eval_match.eval_match ~inline:Eval_match.inline_nonrec_linear km f in
  (* printf "wp: f=%a@." print_term f; *)
  let d = create_prop_decl Pgoal pr f in
  Theory.add_decl uc d

648 649 650 651 652 653
let mk_env env km th = {
  prog_known = km;
  pure_known = Theory.get_known th;
  global_env = env;
}

654
let wp_let env km th ({ let_var = lv; let_expr = e } as ld) =
655
  spec_let ld;
656 657
  let env = mk_env env km th in
  let q, xq = default_post e.e_vty e.e_effect in
658
  let f = wp_expr env e q xq in
659 660 661 662
  let f = wp_forall (Mvs.keys f.t_vars) f in
  let id = match lv with
    | LetV pv -> pv.pv_vs.vs_name
    | LetA ps -> ps.ps_name in
663 664
  add_wp_decl id f th

665
let wp_rec env km th rdl =
666
  spec_rec rdl;
667
  let env = mk_env env km th in
668 669
  let fl = wp_rec_defn env rdl in
  let add_one th d f =
670
    Debug.dprintf debug "wp %s = %a@\n----------------@."
671 672
      d.rec_ps.ps_name.id_string Pretty.print_term f;
    add_wp_decl d.rec_ps.ps_name f th
673 674
  in
  List.fold_left2 add_one th rdl fl
675

676
let wp_val _env _km th vd = spec_val vd; th