typing.ml 32 KB
Newer Older
1 2
(**************************************************************************)
(*                                                                        *)
Jean-Christophe Filliâtre's avatar
headers  
Jean-Christophe Filliâtre committed
3 4 5 6 7
(*  Copyright (C) 2010-                                                   *)
(*    Francois Bobot                                                      *)
(*    Jean-Christophe Filliatre                                           *)
(*    Johannes Kanig                                                      *)
(*    Andrei Paskevich                                                    *)
8 9 10 11 12 13 14 15 16 17 18
(*                                                                        *)
(*  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.                  *)
(*                                                                        *)
(**************************************************************************)
19

20 21
open Util
open Format
22
open Pp
Andrei Paskevich's avatar
Andrei Paskevich committed
23
open Ptree
24
open Ident
25
open Ty
26
open Term
Andrei Paskevich's avatar
Andrei Paskevich committed
27
open Decl
28
open Theory
Andrei Paskevich's avatar
Andrei Paskevich committed
29
open Env
30
open Denv
Andrei Paskevich's avatar
Andrei Paskevich committed
31

32 33
(** errors *)

34 35 36 37 38 39 40 41 42 43 44 45 46
exception Message of string
exception DuplicateTypeVar of string
exception TypeArity of qualid * int * int
exception Clash of string
exception PredicateExpected
exception TermExpected
exception BadNumberOfArguments of Ident.ident * int * int
exception ClashTheory of string
exception UnboundTheory of qualid
exception CyclicTypeDef
exception UnboundTypeVar of string
exception UnboundType of string list
exception UnboundSymbol of string list
47 48

let error ?loc e = match loc with
49 50
  | None -> raise e
  | Some loc -> raise (Loc.Located (loc,e))
51

Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
52 53 54
let errorm ?loc f =
  let buf = Buffer.create 512 in
  let fmt = Format.formatter_of_buffer buf in
55 56
  Format.kfprintf
    (fun _ ->
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
57 58 59
       Format.pp_print_flush fmt ();
       let s = Buffer.contents buf in
       Buffer.clear buf;
60
       error ?loc (Message s))
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
61 62
    fmt f

63
let rec print_qualid fmt = function
64
  | Qident s -> fprintf fmt "%s" s.id
65
  | Qdot (m, s) -> fprintf fmt "%a.%s" print_qualid m s.id
66

67
let () = Exn_printer.register (fun fmt e -> match e with
68 69
  | Message s ->
      fprintf fmt "%s" s
70
  | DuplicateTypeVar s ->
71
      fprintf fmt "duplicate type parameter %s" s
72
  | TypeArity (id, a, n) ->
73
      fprintf fmt "@[The type %a expects %d argument(s),@ " print_qualid id a;
74 75
      fprintf fmt "but is applied to %d argument(s)@]" n
  | Clash id ->
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
76
      fprintf fmt "Clash with previous symbol %s" id
77 78 79 80
  | PredicateExpected ->
      fprintf fmt "syntax error: predicate expected"
  | TermExpected ->
      fprintf fmt "syntax error: term expected"
81
  | BadNumberOfArguments (s, n, m) ->
82
      fprintf fmt "@[Symbol `%s' is applied to %d terms,@ " s.id_string n;
83
      fprintf fmt "but is expecting %d arguments@]" m
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
84 85
  | ClashTheory s ->
      fprintf fmt "clash with previous theory %s" s
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
86 87
  | UnboundTheory q ->
      fprintf fmt "unbound theory %a" print_qualid q
88 89 90 91
  | CyclicTypeDef ->
      fprintf fmt "cyclic type definition"
  | UnboundTypeVar s ->
      fprintf fmt "unbound type variable '%s" s
92 93 94 95
  | UnboundType sl ->
       fprintf fmt "Unbound type '%a'" (print_list dot pp_print_string) sl
  | UnboundSymbol sl ->
       fprintf fmt "Unbound symbol '%a'" (print_list dot pp_print_string) sl
96
  | _ -> raise e)
97

98 99 100
let debug_parse_only = Debug.register_flag "parse_only"
let debug_type_only  = Debug.register_flag "type_only"

101 102
(** Environments *)

103
(** typing using destructive type variables
104

105 106 107 108 109 110
    parsed trees        intermediate trees       typed trees
      (Ptree)               (D below)               (Term)
   -----------------------------------------------------------
     ppure_type  ---dty--->   dty       ---ty--->    ty
      lexpr      --dterm-->   dterm     --term-->    term
      lexpr      --dfmla-->   dfmla     --fmla-->    fmla
111

112 113
*)

Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
114 115 116 117 118
let term_expected_type ~loc ty1 ty2 =
  errorm ~loc
    "@[This term has type %a@ but is expected to have type@ %a@]"
    print_dty ty1 print_dty ty2

119 120 121 122
(** Destructive typing environment, that is
    environment + local variables.
    It is only local to this module and created with [create_denv] below. *)

123
type denv = {
124 125 126 127 128
  uc : theory_uc; (* the theory under construction *)
  utyvars : (string, type_var) Hashtbl.t; (* user type variables *)
  dvars : dty Mstr.t; (* local variables, to be bound later *)
}

129 130 131
let create_denv uc = {
  uc = uc;
  utyvars = Hashtbl.create 17;
132 133 134 135 136 137 138 139 140 141 142 143
  dvars = Mstr.empty;
}

let find_user_type_var x env =
  try
    Hashtbl.find env.utyvars x
  with Not_found ->
    (* TODO: shouldn't we localize this ident? *)
    let v = create_tvsymbol (id_fresh x) in
    let v = create_ty_decl_var ~user:true v in
    Hashtbl.add env.utyvars x v;
    v
144

145 146 147 148
let mem_var x denv = Mstr.mem x denv.dvars
let find_var x denv = Mstr.find x denv.dvars
let add_var x ty denv = { denv with dvars = Mstr.add x ty denv.dvars }

149 150 151 152 153 154 155 156 157 158 159 160
(* parsed types -> intermediate types *)

let rec qloc = function
  | Qident x -> x.id_loc
  | Qdot (m, x) -> Loc.join (qloc m) x.id_loc

let rec string_list_of_qualid acc = function
  | Qident id -> id.id :: acc
  | Qdot (p, id) -> string_list_of_qualid (id.id :: acc) p

let specialize_tysymbol loc p uc =
  let sl = string_list_of_qualid [] p in
161
  let ts =
162 163 164
    try ns_find_ts (get_namespace uc) sl
    with Not_found -> error ~loc (UnboundType sl)
  in
165 166 167 168 169 170 171 172 173 174
  ts, List.length ts.ts_args

(* lazy declaration of tuples *)

let tuples_needed = Hashtbl.create 17

let ts_tuple n = Hashtbl.replace tuples_needed n (); ts_tuple n
let fs_tuple n = Hashtbl.replace tuples_needed n (); fs_tuple n

let add_tuple_decls uc =
175
  Hashtbl.fold (fun n _ uc -> Theory.use_export uc (tuple_theory n))
176 177 178 179 180 181 182 183
    tuples_needed uc

let with_tuples ?(reset=false) f uc x =
  let uc = f (add_tuple_decls uc) x in
  if reset then Hashtbl.clear tuples_needed;
  uc

let add_ty_decl  = with_tuples add_ty_decl
184
let add_ty_decls = with_tuples ~reset:true add_ty_decl
185 186

let add_logic_decl  = with_tuples add_logic_decl
187
let add_logic_decls = with_tuples ~reset:true add_logic_decl
188 189

let add_ind_decl  = with_tuples add_ind_decl
190
let add_ind_decls = with_tuples ~reset:true add_ind_decl
191

192 193
let add_prop_decl = with_tuples ~reset:true add_prop_decl

194 195 196 197 198
let rec type_inst s ty = match ty.ty_node with
  | Ty.Tyvar n -> Mtv.find n s
  | Ty.Tyapp (ts, tyl) -> Tyapp (ts, List.map (type_inst s) tyl)

let rec dty env = function
199
  | PPTtyvar {id=x} ->
200 201 202
      Tyvar (find_user_type_var x env)
  | PPTtyapp (p, x) ->
      let loc = qloc x in
203
      let ts, a = specialize_tysymbol loc x env.uc in
204 205 206
      let np = List.length p in
      if np <> a then error ~loc (TypeArity (x, a, np));
      let tyl = List.map (dty env) p in
207
      begin match ts.ts_def with
208
	| None ->
209
	    Tyapp (ts, tyl)
210
	| Some ty ->
211 212 213
	    let add m v t = Mtv.add v t m in
            let s = List.fold_left2 add Mtv.empty ts.ts_args tyl in
	    type_inst s ty
214 215 216 217
      end
  | PPTtuple tyl ->
      let ts = ts_tuple (List.length tyl) in
      Tyapp (ts, List.map (dty env) tyl)
218 219 220 221

let find_ns find p ns =
  let loc = qloc p in
  let sl = string_list_of_qualid [] p in
222
  try find ns sl
223 224
  with Not_found -> error ~loc (UnboundSymbol sl)

225
let find_prop_ns = find_ns ns_find_pr
226 227 228 229 230 231 232 233 234 235
let find_prop p uc = find_prop_ns p (get_namespace uc)

let find_tysymbol_ns = find_ns ns_find_ts
let find_tysymbol q uc = find_tysymbol_ns q (get_namespace uc)

let find_lsymbol_ns = find_ns ns_find_ls
let find_lsymbol q uc = find_lsymbol_ns q (get_namespace uc)

let specialize_lsymbol p uc =
  let s = find_lsymbol p uc in
236 237
  let tl,ty = specialize_lsymbol ~loc:(qloc p) s in
  s,tl,ty
238

239
let specialize_fsymbol p uc =
240
  let s,tl,ty = specialize_lsymbol p uc in
241
  match ty with
242
    | None -> let loc = qloc p in error ~loc TermExpected
243
    | Some ty -> s, tl, ty
244

245
let specialize_psymbol p uc =
246
  let s,tl,ty = specialize_lsymbol p uc in
247 248
  match ty with
    | None -> s, tl
249 250
    | Some _ -> let loc = qloc p in error ~loc PredicateExpected

251
let is_psymbol p uc =
252 253
  let s = find_lsymbol p uc in
  s.ls_value = None
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
254

255

256 257
(** Typing types *)

Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
258 259 260 261
let split_qualid = function
  | Qident id -> [], id.id
  | Qdot (p, id) -> string_list_of_qualid [] p, id.id

262
(** Typing terms and formulas *)
263 264 265 266 267 268 269

let binop = function
  | PPand -> Fand
  | PPor -> For
  | PPimplies -> Fimplies
  | PPiff -> Fiff

Andrei Paskevich's avatar
Andrei Paskevich committed
270
let check_pat_linearity p =
Andrei Paskevich's avatar
Andrei Paskevich committed
271
  let s = ref Sstr.empty in
272
  let add id =
273
    if Sstr.mem id.id !s then
274
      errorm ~loc:id.id_loc "duplicate variable %s" id.id;
Andrei Paskevich's avatar
Andrei Paskevich committed
275
    s := Sstr.add id.id !s
276 277 278 279
  in
  let rec check p = match p.pat_desc with
    | PPpwild -> ()
    | PPpvar id -> add id
280
    | PPpapp (_, pl) | PPptuple pl -> List.iter check pl
281
    | PPpas (p, id) -> check p; add id
Andrei Paskevich's avatar
Andrei Paskevich committed
282
    | PPpor (p, _) -> check p
283
  in
Andrei Paskevich's avatar
Andrei Paskevich committed
284
  check p
285

286 287 288 289
let fresh_type_var loc =
  let tv = create_tvsymbol (id_user "a" loc) in
  Tyvar (create_ty_decl_var ~loc ~user:false tv)

Andrei Paskevich's avatar
Andrei Paskevich committed
290 291 292 293 294
let rec dpat env pat =
  let env, n, ty = dpat_node pat.pat_loc env pat.pat_desc in
  env, { dp_node = n; dp_ty = ty }

and dpat_node loc env = function
295
  | PPpwild ->
296
      let ty = fresh_type_var loc in
Andrei Paskevich's avatar
Andrei Paskevich committed
297
      env, Pwild, ty
Andrei Paskevich's avatar
Andrei Paskevich committed
298
  | PPpvar x ->
299
      let ty = fresh_type_var loc in
Andrei Paskevich's avatar
Andrei Paskevich committed
300
      let env = { env with dvars = Mstr.add x.id ty env.dvars } in
Andrei Paskevich's avatar
Andrei Paskevich committed
301 302
      env, Pvar x, ty
  | PPpapp (x, pl) ->
303
      let s, tyl, ty = specialize_fsymbol x env.uc in
Andrei Paskevich's avatar
Andrei Paskevich committed
304 305
      let env, pl = dpat_args s.ls_name loc env tyl pl in
      env, Papp (s, pl), ty
306 307 308 309 310 311 312
  | PPptuple pl ->
      let n = List.length pl in
      let s = fs_tuple n in
      let tyl = List.map (fun _ -> fresh_type_var loc) pl in
      let env, pl = dpat_args s.ls_name loc env tyl pl in
      let ty = Tyapp (ts_tuple n, tyl) in
      env, Papp (s, pl), ty
Andrei Paskevich's avatar
Andrei Paskevich committed
313
  | PPpas (p, x) ->
Andrei Paskevich's avatar
Andrei Paskevich committed
314
      let env, p = dpat env p in
Andrei Paskevich's avatar
Andrei Paskevich committed
315
      let env = { env with dvars = Mstr.add x.id p.dp_ty env.dvars } in
Andrei Paskevich's avatar
Andrei Paskevich committed
316
      env, Pas (p,x), p.dp_ty
Andrei Paskevich's avatar
Andrei Paskevich committed
317 318 319 320 321 322
  | PPpor (p, q) ->
      let env, p = dpat env p in
      let env, q = dpat env q in
      if not (unify p.dp_ty q.dp_ty)
        then term_expected_type ~loc p.dp_ty q.dp_ty;
      env, Por (p,q), p.dp_ty
Andrei Paskevich's avatar
Andrei Paskevich committed
323

324
and dpat_args s loc env el pl =
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
325
  let n = List.length el and m = List.length pl in
Andrei Paskevich's avatar
Andrei Paskevich committed
326
  if n <> m then error ~loc (BadNumberOfArguments (s, m, n));
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
327
  let rec check_arg env = function
328
    | [], [] ->
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
329 330 331 332 333 334 335
	env, []
    | a :: al, p :: pl ->
	let loc = p.pat_loc in
	let env, p = dpat env p in
	if not (unify a p.dp_ty) then term_expected_type ~loc p.dp_ty a;
	let env, pl = check_arg env (al, pl) in
	env, p :: pl
Andrei Paskevich's avatar
Andrei Paskevich committed
336 337 338
    | _ ->
	assert false
  in
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
339
  check_arg env (el, pl)
Andrei Paskevich's avatar
Andrei Paskevich committed
340

Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
341
let rec trigger_not_a_term_exn = function
342
  | TermExpected -> true
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
343 344 345
  | Loc.Located (_, exn) -> trigger_not_a_term_exn exn
  | _ -> false

346
let check_quant_linearity uqu =
Andrei Paskevich's avatar
Andrei Paskevich committed
347
  let s = ref Sstr.empty in
348
  let check id =
Andrei Paskevich's avatar
Andrei Paskevich committed
349 350
    if Sstr.mem id.id !s then errorm ~loc:id.id_loc "duplicate variable %s" id.id;
    s := Sstr.add id.id !s
351
  in
352
  List.iter (fun (idl, _) -> Util.option_iter check idl) uqu
353

Andrei Paskevich's avatar
Andrei Paskevich committed
354 355 356 357 358 359 360 361 362
let check_highord env x tl = match x with
  | Qident { id = x } when Mstr.mem x env.dvars -> true
  | _ -> List.length tl > List.length ((find_lsymbol x env.uc).ls_args)

let apply_highord loc x tl = match List.rev tl with
  | a::[] -> [{pp_loc = loc; pp_desc = PPvar x}; a]
  | a::tl -> [{pp_loc = loc; pp_desc = PPapp (x, List.rev tl)}; a]
  | [] -> assert false

363
let rec dterm env t =
364 365 366 367
  let n, ty = dterm_node t.pp_loc env t.pp_desc in
  { dt_node = n; dt_ty = ty }

and dterm_node loc env = function
Andrei Paskevich's avatar
Andrei Paskevich committed
368
  | PPvar (Qident {id=x}) when Mstr.mem x env.dvars ->
369
      (* local variable *)
Andrei Paskevich's avatar
Andrei Paskevich committed
370
      let ty = Mstr.find x env.dvars in
371
      Tvar x, ty
372
  | PPvar x ->
373
      (* 0-arity symbol (constant) *)
374
      let s, tyl, ty = specialize_fsymbol x env.uc in
375
      let n = List.length tyl in
376
      if n > 0 then error ~loc (BadNumberOfArguments (s.ls_name, 0, n));
377
      Tapp (s, []), ty
Andrei Paskevich's avatar
Andrei Paskevich committed
378 379 380 381 382
  | PPapp (x, tl) when check_highord env x tl ->
      let tl = apply_highord loc x tl in
      let atyl, aty = Denv.specialize_lsymbol ~loc fs_func_app in
      let tl = dtype_args fs_func_app.ls_name loc env atyl tl in
      Tapp (fs_func_app, tl), Util.of_option aty
383
  | PPapp (x, tl) ->
384
      let s, tyl, ty = specialize_fsymbol x env.uc in
385
      let tl = dtype_args s.ls_name loc env tyl tl in
386
      Tapp (s, tl), ty
387 388 389 390 391 392 393
  | PPtuple tl ->
      let n = List.length tl in
      let s = fs_tuple n in
      let tyl = List.map (fun _ -> fresh_type_var loc) tl in
      let tl = dtype_args s.ls_name loc env tyl tl in
      let ty = Tyapp (ts_tuple n, tyl) in
      Tapp (s, tl), ty
394 395 396 397
  | PPinfix (e1, x, e2) ->
      let s, tyl, ty = specialize_fsymbol (Qident x) env.uc in
      let tl = dtype_args s.ls_name loc env tyl [e1; e2] in
      Tapp (s, tl), ty
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
398
  | PPconst (ConstInt _ as c) ->
399
      Tconst c, Tyapp (Ty.ts_int, [])
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
400
  | PPconst (ConstReal _ as c) ->
401
      Tconst c, Tyapp (Ty.ts_real, [])
Andrei Paskevich's avatar
Andrei Paskevich committed
402
  | PPlet (x, e1, e2) ->
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
403 404
      let e1 = dterm env e1 in
      let ty = e1.dt_ty in
Andrei Paskevich's avatar
Andrei Paskevich committed
405
      let env = { env with dvars = Mstr.add x.id ty env.dvars } in
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
406 407
      let e2 = dterm env e2 in
      Tlet (e1, x, e2), e2.dt_ty
Andrei Paskevich's avatar
Andrei Paskevich committed
408 409 410
  | PPmatch (e1, bl) ->
      let t1 = dterm env e1 in
      let ty1 = t1.dt_ty in
411
      let tb = fresh_type_var loc in (* the type of all branches *)
Andrei Paskevich's avatar
Andrei Paskevich committed
412 413
      let branch (p, e) =
        let env, p = dpat_list env ty1 p in
414
        let loc = e.pp_loc in
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
415 416
	let e = dterm env e in
	if not (unify e.dt_ty tb) then term_expected_type ~loc e.dt_ty tb;
Andrei Paskevich's avatar
Andrei Paskevich committed
417
        p, e
Andrei Paskevich's avatar
Andrei Paskevich committed
418 419 420
      in
      let bl = List.map branch bl in
      let ty = (snd (List.hd bl)).dt_ty in
Andrei Paskevich's avatar
Andrei Paskevich committed
421
      Tmatch (t1, bl), ty
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
422 423 424
  | PPnamed (x, e1) ->
      let e1 = dterm env e1 in
      Tnamed (x, e1), e1.dt_ty
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
425 426 427 428 429 430
  | PPcast (e1, ty) ->
      let loc = e1.pp_loc in
      let e1 = dterm env e1 in
      let ty = dty env ty in
      if not (unify e1.dt_ty ty) then term_expected_type ~loc e1.dt_ty ty;
      e1.dt_node, ty
431 432 433 434 435 436 437
  | PPif (e1, e2, e3) ->
      let loc = e3.pp_loc in
      let e2 = dterm env e2 in
      let e3 = dterm env e3 in
      if not (unify e2.dt_ty e3.dt_ty) then
        term_expected_type ~loc e3.dt_ty e2.dt_ty;
      Tif (dfmla env e1, e2, e3), e2.dt_ty
Andrei Paskevich's avatar
Andrei Paskevich committed
438
  | PPeps (x, ty, e1) ->
Andrei Paskevich's avatar
Andrei Paskevich committed
439
      let ty = dty env ty in
Andrei Paskevich's avatar
Andrei Paskevich committed
440
      let env = { env with dvars = Mstr.add x.id ty env.dvars } in
Andrei Paskevich's avatar
Andrei Paskevich committed
441 442
      let e1 = dfmla env e1 in
      Teps (x, ty, e1), ty
443
  | PPquant ((PPlambda|PPfunc|PPpred) as q, uqu, trl, a) ->
Andrei Paskevich's avatar
Andrei Paskevich committed
444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460
      check_quant_linearity uqu;
      let uquant env (idl,ty) =
        let ty = dty env ty in
        let id = match idl with
          | Some id -> id
          | None -> assert false
        in
        { env with dvars = Mstr.add id.id ty env.dvars }, (id,ty)
      in
      let env, uqu = map_fold_left uquant env uqu in
      let trigger e =
	try
	  TRterm (dterm env e)
	with exn when trigger_not_a_term_exn exn ->
	  TRfmla (dfmla env e)
      in
      let trl = List.map (List.map trigger) trl in
461 462 463 464 465 466 467
      let e = match q with
        | PPfunc -> TRterm (dterm env a)
        | PPpred -> TRfmla (dfmla env a)
        | PPlambda -> trigger a
        | _ -> assert false
      in
      let id, ty, f = match e with
Andrei Paskevich's avatar
Andrei Paskevich committed
468
        | TRterm t ->
469
            let id = { id = "fc"; id_lab = []; id_loc = loc } in
Andrei Paskevich's avatar
Andrei Paskevich committed
470 471 472 473 474 475 476 477 478 479 480
            let tyl,ty = List.fold_right (fun (_,uty) (tyl,ty) ->
              let nty = Tyapp (ts_func, [uty;ty]) in ty :: tyl, nty)
              uqu ([],t.dt_ty)
            in
            let h = { dt_node = Tvar id.id ; dt_ty = ty } in
            let h = List.fold_left2 (fun h (uid,uty) ty ->
              let u = { dt_node = Tvar uid.id ; dt_ty = uty } in
              { dt_node = Tapp (fs_func_app, [h;u]) ; dt_ty = ty })
              h uqu tyl
            in
            id, ty, Fapp (ps_equ, [h;t])
Andrei Paskevich's avatar
Andrei Paskevich committed
481
        | TRfmla f ->
482
            let id = { id = "pc"; id_lab = []; id_loc = loc } in
Andrei Paskevich's avatar
Andrei Paskevich committed
483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500
            let (uid,uty),uqu = match List.rev uqu with
              | uq :: uqu -> uq, List.rev uqu
              | [] -> assert false
            in
            let tyl,ty = List.fold_right (fun (_,uty) (tyl,ty) ->
              let nty = Tyapp (ts_func, [uty;ty]) in ty :: tyl, nty)
              uqu ([],Tyapp (ts_pred, [uty]))
            in
            let h = { dt_node = Tvar id.id ; dt_ty = ty } in
            let h = List.fold_left2 (fun h (uid,uty) ty ->
              let u = { dt_node = Tvar uid.id ; dt_ty = uty } in
              { dt_node = Tapp (fs_func_app, [h;u]) ; dt_ty = ty })
              h uqu tyl
            in
            let u = { dt_node = Tvar uid.id ; dt_ty = uty } in
            id, ty, Fbinop (Fiff, Fapp (ps_pred_app, [h;u]), f)
      in
      Teps (id, ty, Fquant (Fforall, uqu, trl, f)), ty
Andrei Paskevich's avatar
Andrei Paskevich committed
501
  | PPquant _ | PPbinop _ | PPunop _ | PPfalse | PPtrue ->
502
      error ~loc TermExpected
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
503

504 505 506 507 508
and dfmla env e = match e.pp_desc with
  | PPtrue ->
      Ftrue
  | PPfalse ->
      Ffalse
509
  | PPunop (PPnot, a) ->
510
      Fnot (dfmla env a)
511
  | PPbinop (a, (PPand | PPor | PPimplies | PPiff as op), b) ->
512 513
      Fbinop (binop op, dfmla env a, dfmla env b)
  | PPif (a, b, c) ->
514
      Fif (dfmla env a, dfmla env b, dfmla env c)
515
  | PPquant (q, uqu, trl, a) ->
516
      check_quant_linearity uqu;
517 518
      let uquant env (idl,ty) =
        let ty = dty env ty in
519
        let id = match idl with
Andrei Paskevich's avatar
Andrei Paskevich committed
520
          | Some id -> id
521
          | None -> assert false
522
        in
Andrei Paskevich's avatar
Andrei Paskevich committed
523
        { env with dvars = Mstr.add id.id ty env.dvars }, (id,ty)
524
      in
525
      let env, uqu = map_fold_left uquant env uqu in
526
      let trigger e =
527 528
	try
	  TRterm (dterm env e)
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
529
	with exn when trigger_not_a_term_exn exn ->
530
	  TRfmla (dfmla env e)
531 532
      in
      let trl = List.map (List.map trigger) trl in
533 534
      let q = match q with
        | PPforall -> Fforall
535
        | PPexists -> Fexists
Andrei Paskevich's avatar
Andrei Paskevich committed
536
        | _ -> error ~loc:e.pp_loc PredicateExpected
537 538
      in
      Fquant (q, uqu, trl, dfmla env a)
Andrei Paskevich's avatar
Andrei Paskevich committed
539 540 541 542 543
  | PPapp (x, tl) when check_highord env x tl ->
      let tl = apply_highord e.pp_loc x tl in
      let atyl, _ = Denv.specialize_lsymbol ~loc:(e.pp_loc) ps_pred_app in
      let tl = dtype_args ps_pred_app.ls_name e.pp_loc env atyl tl in
      Fapp (ps_pred_app, tl)
544
  | PPapp (x, tl) ->
545
      let s, tyl = specialize_psymbol x env.uc in
546
      let tl = dtype_args s.ls_name e.pp_loc env tyl tl in
547
      Fapp (s, tl)
548 549 550 551 552 553 554 555 556 557
  | PPinfix (e12, op2, e3) ->
      begin match e12.pp_desc with
	| PPinfix (_, op1, e2) when is_psymbol (Qident op1) env.uc ->
	    let e23 = { e with pp_desc = PPinfix (e2, op2, e3) } in
	    Fbinop (Fand, dfmla env e12, dfmla env e23)
	| _ ->
	    let s, tyl = specialize_psymbol (Qident op2) env.uc in
	    let tl = dtype_args s.ls_name e.pp_loc env tyl [e12; e3] in
	    Fapp (s, tl)
      end
Andrei Paskevich's avatar
Andrei Paskevich committed
558
  | PPlet (x, e1, e2) ->
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
559 560
      let e1 = dterm env e1 in
      let ty = e1.dt_ty in
Andrei Paskevich's avatar
Andrei Paskevich committed
561
      let env = { env with dvars = Mstr.add x.id ty env.dvars } in
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
562 563
      let e2 = dfmla env e2 in
      Flet (e1, x, e2)
Andrei Paskevich's avatar
Andrei Paskevich committed
564 565 566 567 568
  | PPmatch (e1, bl) ->
      let t1 = dterm env e1 in
      let ty1 = t1.dt_ty in
      let branch (p, e) =
        let env, p = dpat_list env ty1 p in p, dfmla env e
Andrei Paskevich's avatar
Andrei Paskevich committed
569
      in
Andrei Paskevich's avatar
Andrei Paskevich committed
570
      Fmatch (t1, List.map branch bl)
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
571 572 573
  | PPnamed (x, f1) ->
      let f1 = dfmla env f1 in
      Fnamed (x, f1)
574
  | PPvar x ->
575 576
      let pr = find_prop x env.uc in
      Fvar (Decl.find_prop (Theory.get_known env.uc) pr)
577
  | PPeps _ | PPconst _ | PPcast _ | PPtuple _ ->
578
      error ~loc:e.pp_loc PredicateExpected
579

Andrei Paskevich's avatar
Andrei Paskevich committed
580 581 582 583 584 585 586
and dpat_list env ty p =
  check_pat_linearity p;
  let loc = p.pat_loc in
  let env, p = dpat env p in
  if not (unify p.dp_ty ty)
    then term_expected_type ~loc p.dp_ty ty;
  env, p
587

588 589 590 591
and dtype_args s loc env el tl =
  let n = List.length el and m = List.length tl in
  if n <> m then error ~loc (BadNumberOfArguments (s, m, n));
  let rec check_arg = function
592
    | [], [] ->
593 594 595 596
	[]
    | a :: al, t :: bl ->
	let loc = t.pp_loc in
	let t = dterm env t in
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
597
	if not (unify a t.dt_ty) then term_expected_type ~loc t.dt_ty a;
598 599 600 601 602 603
	t :: check_arg (al, bl)
    | _ ->
	assert false
  in
  check_arg (el, tl)

604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619
(** Add projection functions for the algebraic types *)

let add_projection cl p (fs,tyarg,tyval) th =
  let vs = create_vsymbol (id_fresh p) tyval in
  let per_cs (_,id,pl) =
    let cs = find_lsymbol (Qident id) th in
    let tc = match cs.ls_value with
      | None -> assert false
      | Some t -> t
    in
    let m = ty_match Mtv.empty tc tyarg in
    let per_param ty (n,_) = match n with
      | Some id when id.id = p -> pat_var vs
      | _ -> pat_wild (ty_inst m ty)
    in
    let al = List.map2 per_param cs.ls_args pl in
620
    t_close_branch (pat_app cs al tyarg) (t_var vs)
621 622
  in
  let vs = create_vsymbol (id_fresh "u") tyarg in
623
  let t = t_case (t_var vs) (List.map per_cs cl) in
624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648
  let d = make_fs_defn fs [vs] t in
  add_logic_decl th [d]

let add_projections th d = match d.td_def with
  | TDabstract | TDalias _ -> th
  | TDalgebraic cl ->
      let per_cs acc (_,id,pl) =
        let cs = find_lsymbol (Qident id) th in
        let tc = match cs.ls_value with
          | None -> assert false
          | Some t -> t
        in
        let per_param acc ty (n,_) = match n with
          | Some id when not (Mstr.mem id.id acc) ->
              let fn = id_user id.id id.id_loc in
              let fs = create_fsymbol fn [tc] ty in
              Mstr.add id.id (fs,tc,ty) acc
          | _ -> acc
        in
        List.fold_left2 per_param acc cs.ls_args pl
      in
      let ps = List.fold_left per_cs Mstr.empty cl in
      try Mstr.fold (add_projection cl) ps th
      with e -> raise (Loc.Located (d.td_loc, e))

649
(** Typing declarations, that is building environments. *)
650 651 652

open Ptree

653
let add_types dl th =
654
  let def = List.fold_left
655
    (fun def d ->
656
      let id = d.td_ident.id in
657
      if Mstr.mem id def then error ~loc:d.td_loc (Clash id);
658 659
      Mstr.add id d def)
    Mstr.empty dl
660
  in
661
  let tysymbols = Hashtbl.create 17 in
662
  let rec visit x =
663 664 665 666 667 668
    try
      match Hashtbl.find tysymbols x with
	| None -> error CyclicTypeDef
	| Some ts -> ts
    with Not_found ->
      Hashtbl.add tysymbols x None;
Andrei Paskevich's avatar
Andrei Paskevich committed
669
      let d = Mstr.find x def in
670 671
      let id = d.td_ident.id in
      let vars = Hashtbl.create 17 in
672 673 674 675
      let vl =
	List.map
	  (fun v ->
	     if Hashtbl.mem vars v.id then
676
	       error ~loc:v.id_loc (DuplicateTypeVar v.id);
677
	     let i = create_tvsymbol (id_user v.id v.id_loc) in
678 679
	     Hashtbl.add vars v.id i;
	     i)
680
	  d.td_params
681
      in
Andrei Paskevich's avatar
Andrei Paskevich committed
682
      let id = id_user id d.td_loc in
683
      let ts = match d.td_def with
684
	| TDalias ty ->
685
	    let rec apply = function
686 687
	      | PPTtyvar v ->
		  begin
688 689 690 691 692
		    try ty_var (Hashtbl.find vars v.id)
		    with Not_found -> error ~loc:v.id_loc (UnboundTypeVar v.id)
		  end
	      | PPTtyapp (tyl, q) ->
		  let ts = match q with
Andrei Paskevich's avatar
Andrei Paskevich committed
693
		    | Qident x when Mstr.mem x.id def ->
694 695 696 697
			visit x.id
		    | Qident _ | Qdot _ ->
			find_tysymbol q th
		  in
698
		  begin try
699
		    ty_app ts (List.map apply tyl)
700
		  with Ty.BadTypeArity (_, tsal, tyll) ->
701
		    error ~loc:(qloc q) (TypeArity (q, tsal, tyll))
702 703 704 705
		  end
	      | PPTtuple tyl ->
		  let ts = ts_tuple (List.length tyl) in
		  ty_app ts (List.map apply tyl)
706 707
	    in
	    create_tysymbol id vl (Some (apply ty))
708
	| TDabstract | TDalgebraic _ ->
709 710 711 712 713
	    create_tysymbol id vl None
      in
      Hashtbl.add tysymbols x (Some ts);
      ts
  in
714
  let tsl = List.rev_map (fun d -> visit d.td_ident.id, Tabstract) dl in
715
  let th' = try add_ty_decl th tsl
716
    with ClashSymbol s -> error ~loc:(Mstr.find s def).td_loc (Clash s)
717
  in
718
  let csymbols = Hashtbl.create 17 in
719
  let decl d =
720
    let ts, th' = match Hashtbl.find tysymbols d.td_ident.id with
721
      | None ->
722
	  assert false
723
      | Some ts ->
724 725
	  let th' = create_denv th' in
	  let vars = th'.utyvars in
726 727
	  List.iter
	    (fun v ->
728
	       Hashtbl.add vars v.tv_name.id_string
729
                  (create_ty_decl_var ~user:true v))
730 731 732 733
	    ts.ts_args;
	  ts, th'
    in
    let d = match d.td_def with
734
      | TDabstract | TDalias _ ->
735
	  Tabstract
736
      | TDalgebraic cl ->
737
	  let ty = ty_app ts (List.map ty_var ts.ts_args) in
738
	  let constructor (loc, id, pl) =
739
	    let param (_,t) = ty_of_dty (dty th' t) in
740
	    let tyl = List.map param pl in
741
	    Hashtbl.replace csymbols id.id loc;
742
	    create_fsymbol (id_user id.id loc) tyl ty
743 744 745 746
	  in
	  Talgebraic (List.map constructor cl)
    in
    ts, d
747
  in
748 749 750 751
  let th = try add_ty_decls th (List.map decl dl)
    with ClashSymbol s -> error ~loc:(Hashtbl.find csymbols s) (Clash s)
  in
  List.fold_left add_projections th dl
752

Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
753
let env_of_vsymbol_list vl =
754
  List.fold_left (fun env v -> Mstr.add v.vs_name.id_string v env) Mstr.empty vl
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
755

756
let add_logics dl th =
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
757 758
  let fsymbols = Hashtbl.create 17 in
  let psymbols = Hashtbl.create 17 in
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
759
  let denvs = Hashtbl.create 17 in
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
760
  (* 1. create all symbols and make an environment with these symbols *)
761
  let create_symbol th d =
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
762
    let id = d.ld_ident.id in
Andrei Paskevich's avatar
Andrei Paskevich committed
763
    let v = id_user id d.ld_loc in
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
764
    let denv = create_denv th in
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
765
    Hashtbl.add denvs id denv;
766
    let type_ty (_,t) = ty_of_dty (dty denv t) in
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
767
    let pl = List.map type_ty d.ld_params in
768
    try match d.ld_type with
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
769 770 771
      | None -> (* predicate *)
	  let ps = create_psymbol v pl in
	  Hashtbl.add psymbols id ps;
772
	  add_logic_decl th [ps, None]
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
773 774
      | Some t -> (* function *)
	  let t = type_ty (None, t) in
775
	  let fs = create_fsymbol v pl t in
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
776
	  Hashtbl.add fsymbols id fs;
777
	  add_logic_decl th [fs, None]
778
    with ClashSymbol s -> error ~loc:d.ld_loc (Clash s)
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
779 780 781
  in
  let th' = List.fold_left create_symbol th dl in
  (* 2. then type-check all definitions *)
782
  let type_decl d =
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
783 784 785
    let id = d.ld_ident.id in
    let dadd_var denv (x, ty) = match x with
      | None -> denv
Andrei Paskevich's avatar
Andrei Paskevich committed
786
      | Some id -> { denv with dvars = Mstr.add id.id (dty denv ty) denv.dvars }
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
787
    in
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
788
    let denv = Hashtbl.find denvs id in
789
    let denv = { denv with uc = th' } in
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
790
    let denv = List.fold_left dadd_var denv d.ld_params in
791 792
    let create_var (x, _) ty =
      let id = match x with
793 794
	| None -> id_fresh "%x"
	| Some id -> id_user id.id id.id_loc
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
795 796 797
      in
      create_vsymbol id ty
    in
798
    let mk_vlist = List.map2 create_var d.ld_params in
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
799 800 801
    match d.ld_type with
    | None -> (* predicate *)
	let ps = Hashtbl.find psymbols id in
802 803
        begin match d.ld_def with
	  | None -> ps,None
804
	  | Some f ->
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
805
	      let f = dfmla denv f in
806 807 808 809
              let vl = match ps.ls_value with
                | None -> mk_vlist ps.ls_args
                | _ -> assert false
              in
Jean-Christophe Filliâtre's avatar
logic  
Jean-Christophe Filliâtre committed
810
	      let env = env_of_vsymbol_list vl in
811 812
              make_ps_defn ps vl (fmla env f)
        end
Jean-Christophe Filliâtre's avatar
Jean-Christophe Filliâtre committed
813
    | Some ty -> (* function *)
Jean-Christophe Filliâtre's avatar