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src/Pure/goals.ML

author | clasohm |

Thu Sep 16 12:20:38 1993 +0200 (1993-09-16) | |

changeset 0 | a5a9c433f639 |

child 39 | deb04a336a99 |

permissions | -rw-r--r-- |

Initial revision

1 (* Title: goals

2 ID: $Id$

3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory

4 Copyright 1993 University of Cambridge

6 Goal stack package. The goal stack initially holds a dummy proof, and can

7 never become empty. Each goal stack consists of a list of levels. The

8 undo list is a list of goal stacks. Finally, there may be a stack of

9 pending proofs.

10 *)

13 signature GOALS =

14 sig

15 structure Tactical: TACTICAL

16 local open Tactical Tactical.Thm in

17 type proof

18 val ba: int -> unit

19 val back: unit -> unit

20 val bd: thm -> int -> unit

21 val bds: thm list -> int -> unit

22 val be: thm -> int -> unit

23 val bes: thm list -> int -> unit

24 val br: thm -> int -> unit

25 val brs: thm list -> int -> unit

26 val bw: thm -> unit

27 val bws: thm list -> unit

28 val by: tactic -> unit

29 val byev: tactic list -> unit

30 val chop: unit -> unit

31 val choplev: int -> unit

32 val fa: unit -> unit

33 val fd: thm -> unit

34 val fds: thm list -> unit

35 val fe: thm -> unit

36 val fes: thm list -> unit

37 val filter_goal: (term*term->bool) -> thm list -> int -> thm list

38 val fr: thm -> unit

39 val frs: thm list -> unit

40 val getgoal: int -> term

41 val gethyps: int -> thm list

42 val goal: theory -> string -> thm list

43 val goalw: theory -> thm list -> string -> thm list

44 val goalw_cterm: thm list -> Sign.cterm -> thm list

45 val pop_proof: unit -> thm list

46 val pr: unit -> unit

47 val premises: unit -> thm list

48 val prin: term -> unit

49 val printyp: typ -> unit

50 val pprint_term: term -> pprint_args -> unit

51 val pprint_typ: typ -> pprint_args -> unit

52 val print_exn: exn -> 'a

53 val prlev: int -> unit

54 val proof_timing: bool ref

55 val prove_goal: theory -> string -> (thm list -> tactic list) -> thm

56 val prove_goalw: theory->thm list->string->(thm list->tactic list)->thm

57 val prove_goalw_cterm: thm list->Sign.cterm->(thm list->tactic list)->thm

58 val push_proof: unit -> unit

59 val read: string -> term

60 val ren: string -> int -> unit

61 val restore_proof: proof -> thm list

62 val result: unit -> thm

63 val rotate_proof: unit -> thm list

64 val uresult: unit -> thm

65 val save_proof: unit -> proof

66 val topthm: unit -> thm

67 val undo: unit -> unit

68 end

69 end;

71 functor GoalsFun (structure Logic: LOGIC and Drule: DRULE and Tactic: TACTIC

72 and Pattern:PATTERN

73 sharing type Pattern.type_sig = Drule.Thm.Sign.Type.type_sig

74 and Drule.Thm = Tactic.Tactical.Thm) : GOALS =

75 struct

76 structure Tactical = Tactic.Tactical

77 local open Tactic Tactic.Tactical Tactic.Tactical.Thm Drule

78 in

80 (*Each level of goal stack includes a proof state and alternative states,

81 the output of the tactic applied to the preceeding level. *)

82 type gstack = (thm * thm Sequence.seq) list;

84 datatype proof = Proof of gstack list * thm list * (bool*thm->thm);

86 (*** References ***)

88 (*Should process time be printed after proof steps?*)

89 val proof_timing = ref false;

91 (*Current assumption list -- set by "goal".*)

92 val curr_prems = ref([] : thm list);

94 (*Return assumption list -- useful if you didn't save "goal"'s result. *)

95 fun premises() = !curr_prems;

97 (*Current result maker -- set by "goal", used by "result". *)

98 val curr_mkresult =

99 ref((fn _=> error"No goal has been supplied in subgoal module")

100 : bool*thm->thm);

102 val dummy = trivial(Sign.read_cterm Sign.pure

103 ("PROP No_goal_has_been_supplied",propT));

105 (*List of previous goal stacks, for the undo operation. Set by setstate.

106 A list of lists!*)

107 val undo_list = ref([[(dummy, Sequence.null)]] : gstack list);

109 (* Stack of proof attempts *)

110 val proofstack = ref([]: proof list);

113 (*** Setting up goal-directed proof ***)

115 (*Generates the list of new theories when the proof state's signature changes*)

116 fun sign_error (sign,sign') =

117 let val stamps = #stamps(Sign.rep_sg sign') \\

118 #stamps(Sign.rep_sg sign)

119 in case stamps of

120 [stamp] => "\nNew theory: " ^ !stamp

121 | _ => "\nNew theories: " ^ space_implode ", " (map ! stamps)

122 end;

124 (*Common treatment of "goal" and "prove_goal":

125 Return assumptions, initial proof state, and function to make result. *)

126 fun prepare_proof rths chorn =

127 let val {sign, t=horn,...} = Sign.rep_cterm chorn;

128 val (_,As,B) = Logic.strip_horn(horn);

129 val cAs = map (Sign.cterm_of sign) As;

130 val p_rew = if null rths then I else rewrite_rule rths;

131 val c_rew = if null rths then I else rewrite_goals_rule rths;

132 val prems = map (p_rew o forall_elim_vars(0) o assume) cAs

133 and st0 = c_rew (trivial (Sign.cterm_of sign B))

134 fun result_error state msg =

135 (writeln ("Bad final proof state:");

136 print_goals (!goals_limit) state;

137 error msg)

138 (*discharges assumptions from state in the order they appear in goal;

139 checks (if requested) that resulting theorem is equivalent to goal. *)

140 fun mkresult (check,state) =

141 let val ngoals = nprems_of state

142 val th = implies_intr_list cAs state

143 val {hyps,prop,sign=sign',...} = rep_thm th

144 in if not check then standard th

145 else if not (eq_sg(sign,sign')) then result_error state

146 ("Signature of proof state has changed!" ^

147 sign_error (sign,sign'))

148 else if ngoals>0 then result_error state

149 (string_of_int ngoals ^ " unsolved goals!")

150 else if not (null hyps) then result_error state

151 ("Additional hypotheses:\n" ^

152 cat_lines (map (Sign.string_of_term sign) hyps))

153 else if Pattern.eta_matches (#tsig(Sign.rep_sg sign))

154 (Sign.term_of chorn, prop)

155 then standard th

156 else result_error state "proved a different theorem"

157 end

158 in

159 if eq_sg(sign, #sign(rep_thm st0))

160 then (prems, st0, mkresult)

161 else error ("Definitions would change the proof state's signature" ^

162 sign_error (sign, #sign(rep_thm st0)))

163 end

164 handle THM(s,_,_) => error("prepare_proof: exception THM was raised!\n" ^ s);

166 (*Prints exceptions readably to users*)

167 fun print_sign_exn sign e =

168 case e of

169 THM (msg,i,thms) =>

170 (writeln ("Exception THM " ^ string_of_int i ^ " raised:\n" ^ msg);

171 seq print_thm thms)

172 | THEORY (msg,thys) =>

173 (writeln ("Exception THEORY raised:\n" ^ msg);

174 seq print_theory thys)

175 | TERM (msg,ts) =>

176 (writeln ("Exception TERM raised:\n" ^ msg);

177 seq (writeln o Sign.string_of_term sign) ts)

178 | TYPE (msg,Ts,ts) =>

179 (writeln ("Exception TYPE raised:\n" ^ msg);

180 seq (writeln o Sign.string_of_typ sign) Ts;

181 seq (writeln o Sign.string_of_term sign) ts)

182 | e => raise e;

184 (** the prove_goal.... commands

185 Prove theorem using the listed tactics; check it has the specified form.

186 Augment signature with all type assignments of goal.

187 Syntax is similar to "goal" command for easy keyboard use. **)

189 (*Version taking the goal as a cterm*)

190 fun prove_goalw_cterm rths chorn tacsf =

191 let val (prems, st0, mkresult) = prepare_proof rths chorn

192 val tac = EVERY (tacsf prems)

193 fun statef() =

194 (case Sequence.pull (tapply(tac,st0)) of

195 Some(st,_) => st

196 | _ => error ("prove_goal: tactic failed"))

197 in mkresult (true, cond_timeit (!proof_timing) statef) end;

199 (*Version taking the goal as a string*)

200 fun prove_goalw thy rths agoal tacsf =

201 let val sign = sign_of thy

202 val chorn = Sign.read_cterm sign (agoal,propT)

203 in prove_goalw_cterm rths chorn tacsf

204 handle ERROR => error (*from type_assign, etc via prepare_proof*)

205 ("The error above occurred for " ^ agoal)

206 | e => (print_sign_exn sign e; (*other exceptions*)

207 error ("The exception above was raised for " ^ agoal))

208 end;

210 (*String version with no meta-rewrite-rules*)

211 fun prove_goal thy = prove_goalw thy [];

214 (*** Commands etc ***)

216 (*Return the current goal stack, if any, from undo_list*)

217 fun getstate() : gstack = case !undo_list of

218 [] => error"No current state in subgoal module"

219 | x::_ => x;

221 (*Pops the given goal stack*)

222 fun pop [] = error"Cannot go back past the beginning of the proof!"

223 | pop (pair::pairs) = (pair,pairs);

226 (*Print a level of the goal stack.*)

227 fun print_top ((th,_), pairs) =

228 (prs("Level " ^ string_of_int(length pairs) ^ "\n");

229 print_goals (!goals_limit) th);

231 (*Printing can raise exceptions, so the assignment occurs last.

232 Can do setstate[(st,Sequence.null)] to set st as the state. *)

233 fun setstate newgoals =

234 (print_top (pop newgoals); undo_list := newgoals :: !undo_list);

236 (*Given a proof state transformation, return a command that updates

237 the goal stack*)

238 fun make_command com = setstate (com (pop (getstate())));

240 (*Apply a function on proof states to the current goal stack*)

241 fun apply_fun f = f (pop(getstate()));

243 (*Return the top theorem, representing the proof state*)

244 fun topthm () = apply_fun (fn ((th,_), _) => th);

246 (*Return the final result. *)

247 fun result () = !curr_mkresult (true, topthm());

249 (*Return the result UNCHECKED that it equals the goal -- for synthesis,

250 answer extraction, or other instantiation of Vars *)

251 fun uresult () = !curr_mkresult (false, topthm());

253 (*Get subgoal i from goal stack*)

254 fun getgoal i =

255 (case drop (i-1, prems_of (topthm())) of

256 [] => error"getgoal: Goal number out of range"

257 | Q::_ => Q);

259 (*Return subgoal i's hypotheses as meta-level assumptions.

260 For debugging uses of METAHYPS*)

261 local exception GETHYPS of thm list

262 in

263 fun gethyps i =

264 (tapply(METAHYPS (fn hyps => raise (GETHYPS hyps)) i, topthm()); [])

265 handle GETHYPS hyps => hyps

266 end;

268 (*Which thms could apply to goal i? (debugs tactics involving filter_thms) *)

269 fun filter_goal could ths i = filter_thms could (999, getgoal i, ths);

271 (*For inspecting earlier levels of the backward proof*)

272 fun chop_level n (pair,pairs) =

273 let val level = length pairs

274 in if 0<=n andalso n<= level

275 then drop (level - n, pair::pairs)

276 else error ("Level number must lie between 0 and " ^

277 string_of_int level)

278 end;

280 (*Print the given level of the proof*)

281 fun prlev n = apply_fun (print_top o pop o (chop_level n));

282 fun pr () = apply_fun print_top;

284 (** the goal.... commands

285 Read main goal. Set global variables curr_prems, curr_mkresult.

286 Initial subgoal and premises are rewritten using rths. **)

288 (*Version taking the goal as a cterm; if you have a term t and theory thy, use

289 goalw_cterm rths (Sign.cterm_of (sign_of thy) t); *)

290 fun goalw_cterm rths chorn =

291 let val (prems, st0, mkresult) = prepare_proof rths chorn

292 in undo_list := [];

293 setstate [ (st0, Sequence.null) ];

294 curr_prems := prems;

295 curr_mkresult := mkresult;

296 prems

297 end;

299 (*Version taking the goal as a string*)

300 fun goalw thy rths agoal =

301 goalw_cterm rths (Sign.read_cterm(sign_of thy)(agoal,propT))

302 handle ERROR => error (*from type_assign, etc via prepare_proof*)

303 ("The error above occurred for " ^ agoal);

305 (*String version with no meta-rewrite-rules*)

306 fun goal thy = goalw thy [];

308 (*Proof step "by" the given tactic -- apply tactic to the proof state*)

309 fun by_com tac ((th,ths), pairs) : gstack =

310 (case Sequence.pull(tapply(tac, th)) of

311 None => error"by: tactic failed"

312 | Some(th2,ths2) =>

313 (if eq_thm(th,th2)

314 then writeln"Warning: same as previous level"

315 else if eq_thm_sg(th,th2) then ()

316 else writeln("Warning: signature of proof state has changed" ^

317 sign_error (#sign(rep_thm th), #sign(rep_thm th2)));

318 ((th2,ths2)::(th,ths)::pairs)));

320 fun by tac = cond_timeit (!proof_timing)

321 (fn() => make_command (by_com tac));

323 (* byev[tac1,...,tacn] applies tac1 THEN ... THEN tacn.

324 Good for debugging proofs involving prove_goal.*)

325 val byev = by o EVERY;

328 (*Backtracking means find an alternative result from a tactic.

329 If none at this level, try earlier levels*)

330 fun backtrack [] = error"back: no alternatives"

331 | backtrack ((th,thstr) :: pairs) =

332 (case Sequence.pull thstr of

333 None => (writeln"Going back a level..."; backtrack pairs)

334 | Some(th2,thstr2) =>

335 (if eq_thm(th,th2)

336 then writeln"Warning: same as previous choice at this level"

337 else if eq_thm_sg(th,th2) then ()

338 else writeln"Warning: signature of proof state has changed";

339 (th2,thstr2)::pairs));

341 fun back() = setstate (backtrack (getstate()));

343 (*Chop back to previous level of the proof*)

344 fun choplev n = make_command (chop_level n);

346 (*Chopping back the goal stack*)

347 fun chop () = make_command (fn (_,pairs) => pairs);

349 (*Restore the previous proof state; discard current state. *)

350 fun undo() = case !undo_list of

351 [] => error"No proof state"

352 | [_] => error"Already at initial state"

353 | _::newundo => (undo_list := newundo; pr()) ;

356 (*** Managing the proof stack ***)

358 fun save_proof() = Proof(!undo_list, !curr_prems, !curr_mkresult);

360 fun restore_proof(Proof(ul,prems,mk)) =

361 (undo_list:= ul; curr_prems:= prems; curr_mkresult := mk; prems);

364 fun top_proof() = case !proofstack of

365 [] => error("Stack of proof attempts is empty!")

366 | p::ps => (p,ps);

368 (* push a copy of the current proof state on to the stack *)

369 fun push_proof() = (proofstack := (save_proof() :: !proofstack));

371 (* discard the top proof state of the stack *)

372 fun pop_proof() =

373 let val (p,ps) = top_proof()

374 val prems = restore_proof p

375 in proofstack := ps; pr(); prems end;

377 (* rotate the stack so that the top element goes to the bottom *)

378 fun rotate_proof() = let val (p,ps) = top_proof()

379 in proofstack := ps@[save_proof()];

380 restore_proof p;

381 pr();

382 !curr_prems

383 end;

386 (** Shortcuts for commonly-used tactics **)

388 fun bws rls = by (rewrite_goals_tac rls);

389 fun bw rl = bws [rl];

391 fun brs rls i = by (resolve_tac rls i);

392 fun br rl = brs [rl];

394 fun bes rls i = by (eresolve_tac rls i);

395 fun be rl = bes [rl];

397 fun bds rls i = by (dresolve_tac rls i);

398 fun bd rl = bds [rl];

400 fun ba i = by (assume_tac i);

402 fun ren str i = by (rename_tac str i);

404 (** Shortcuts to work on the first applicable subgoal **)

406 fun frs rls = by (FIRSTGOAL (trace_goalno_tac (resolve_tac rls)));

407 fun fr rl = frs [rl];

409 fun fes rls = by (FIRSTGOAL (trace_goalno_tac (eresolve_tac rls)));

410 fun fe rl = fes [rl];

412 fun fds rls = by (FIRSTGOAL (trace_goalno_tac (dresolve_tac rls)));

413 fun fd rl = fds [rl];

415 fun fa() = by (FIRSTGOAL (trace_goalno_tac assume_tac));

417 (** Reading and printing terms wrt the current theory **)

419 fun top_sg() = #sign(rep_thm(topthm()));

421 fun read s = Sign.term_of (Sign.read_cterm (top_sg())

422 (s, (TVar(("DUMMY",0),[]))));

424 (*Print a term under the current signature of the proof state*)

425 fun prin t = writeln (Sign.string_of_term (top_sg()) t);

427 fun printyp T = writeln (Sign.string_of_typ (top_sg()) T);

429 fun pprint_term t = Sign.pprint_term (top_sg()) t;

431 fun pprint_typ T = Sign.pprint_typ (top_sg()) T;

433 (*Prints exceptions nicely at top level;

434 raises the exception in order to have a polymorphic type!*)

435 fun print_exn e = (print_sign_exn (top_sg()) e; raise e);

437 end;

438 end;