src/Pure/goals.ML
 author wenzelm Wed Oct 31 21:59:07 2001 +0100 (2001-10-31) changeset 12004 1703de633aaf parent 11963 a6608d44a46b child 12012 1d534baa2827 permissions -rw-r--r--
IsarThy.theorem_i: no locale;
```     1 (*  Title: 	Pure/goals.ML
```
```     2     ID:         \$Id\$
```
```     3     Author: 	Lawrence C Paulson, Cambridge University Computer Laboratory
```
```     4     Copyright   1993  University of Cambridge
```
```     5
```
```     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 *)
```
```    11
```
```    12 signature GOALS =
```
```    13 sig
```
```    14   type proof
```
```    15   val reset_goals       : unit -> unit
```
```    16   val atomic_goal	: theory -> string -> thm list
```
```    17   val atomic_goalw	: theory -> thm list -> string -> thm list
```
```    18   val Goal		: string -> thm list
```
```    19   val Goalw		: thm list -> string -> thm list
```
```    20   val ba		: int -> unit
```
```    21   val back		: unit -> unit
```
```    22   val bd		: thm -> int -> unit
```
```    23   val bds		: thm list -> int -> unit
```
```    24   val be		: thm -> int -> unit
```
```    25   val bes		: thm list -> int -> unit
```
```    26   val br		: thm -> int -> unit
```
```    27   val brs		: thm list -> int -> unit
```
```    28   val bw		: thm -> unit
```
```    29   val bws		: thm list -> unit
```
```    30   val by		: tactic -> unit
```
```    31   val byev		: tactic list -> unit
```
```    32   val chop		: unit -> unit
```
```    33   val choplev		: int -> unit
```
```    34   val export_thy        : theory -> thm -> thm
```
```    35   val export            : thm -> thm
```
```    36   val Export		: thm -> thm
```
```    37   val fa		: unit -> unit
```
```    38   val fd		: thm -> unit
```
```    39   val fds		: thm list -> unit
```
```    40   val fe		: thm -> unit
```
```    41   val fes		: thm list -> unit
```
```    42   val filter_goal	: (term*term->bool) -> thm list -> int -> thm list
```
```    43   val fr		: thm -> unit
```
```    44   val frs		: thm list -> unit
```
```    45   val getgoal		: int -> term
```
```    46   val gethyps		: int -> thm list
```
```    47   val goal		: theory -> string -> thm list
```
```    48   val goalw		: theory -> thm list -> string -> thm list
```
```    49   val goalw_cterm	: thm list -> cterm -> thm list
```
```    50   val pop_proof		: unit -> thm list
```
```    51   val pr		: unit -> unit
```
```    52   val disable_pr        : unit -> unit
```
```    53   val enable_pr         : unit -> unit
```
```    54   val prlev		: int -> unit
```
```    55   val prlim		: int -> unit
```
```    56   val premises		: unit -> thm list
```
```    57   val prin		: term -> unit
```
```    58   val printyp		: typ -> unit
```
```    59   val pprint_term	: term -> pprint_args -> unit
```
```    60   val pprint_typ	: typ -> pprint_args -> unit
```
```    61   val print_exn		: exn -> 'a
```
```    62   val print_sign_exn	: Sign.sg -> exn -> 'a
```
```    63   val prove_goal	: theory -> string -> (thm list -> tactic list) -> thm
```
```    64   val prove_goalw      : theory->thm list->string->(thm list->tactic list)->thm
```
```    65   val prove_goalw_cterm	: thm list->cterm->(thm list->tactic list)->thm
```
```    66   val prove_goalw_cterm_nocheck	: thm list->cterm->(thm list->tactic list)->thm
```
```    67   val quick_and_dirty_prove_goalw_cterm: theory -> thm list -> cterm
```
```    68     -> (thm list -> tactic list) -> thm
```
```    69   val push_proof	: unit -> unit
```
```    70   val read		: string -> term
```
```    71   val ren		: string -> int -> unit
```
```    72   val restore_proof	: proof -> thm list
```
```    73   val result		: unit -> thm
```
```    74   val result_error_fn   : (thm -> string -> thm) ref
```
```    75   val rotate_proof	: unit -> thm list
```
```    76   val uresult		: unit -> thm
```
```    77   val save_proof	: unit -> proof
```
```    78   val topthm		: unit -> thm
```
```    79   val undo		: unit -> unit
```
```    80   val bind_thm          : string * thm -> unit
```
```    81   val bind_thms         : string * thm list -> unit
```
```    82   val qed               : string -> unit
```
```    83   val qed_goal          : string -> theory -> string -> (thm list -> tactic list) -> unit
```
```    84   val qed_goalw         : string -> theory -> thm list -> string
```
```    85     -> (thm list -> tactic list) -> unit
```
```    86   val qed_spec_mp       : string -> unit
```
```    87   val qed_goal_spec_mp  : string -> theory -> string -> (thm list -> tactic list) -> unit
```
```    88   val qed_goalw_spec_mp : string -> theory -> thm list -> string
```
```    89     -> (thm list -> tactic list) -> unit
```
```    90   val no_qed: unit -> unit
```
```    91   val thms_containing   : xstring list -> (string * thm) list
```
```    92   val findI             : int -> (string * thm) list
```
```    93   val findEs            : int -> (string * thm) list
```
```    94   val findE             : int -> int -> (string * thm) list
```
```    95 end;
```
```    96
```
```    97 structure Goals : GOALS =
```
```    98 struct
```
```    99
```
```   100 (*Each level of goal stack includes a proof state and alternative states,
```
```   101   the output of the tactic applied to the preceeding level.  *)
```
```   102 type gstack = (thm * thm Seq.seq) list;
```
```   103
```
```   104 datatype proof = Proof of gstack list * thm list * (bool*thm->thm);
```
```   105
```
```   106
```
```   107 (*** References ***)
```
```   108
```
```   109 (*Current assumption list -- set by "goal".*)
```
```   110 val curr_prems = ref([] : thm list);
```
```   111
```
```   112 (*Return assumption list -- useful if you didn't save "goal"'s result. *)
```
```   113 fun premises() = !curr_prems;
```
```   114
```
```   115 (*Current result maker -- set by "goal", used by "result".  *)
```
```   116 fun init_mkresult _ = error "No goal has been supplied in subgoal module";
```
```   117 val curr_mkresult = ref (init_mkresult: bool*thm->thm);
```
```   118
```
```   119 val dummy = trivial(read_cterm (Theory.sign_of ProtoPure.thy)
```
```   120     ("PROP No_goal_has_been_supplied",propT));
```
```   121
```
```   122 (*List of previous goal stacks, for the undo operation.  Set by setstate.
```
```   123   A list of lists!*)
```
```   124 val undo_list = ref([[(dummy, Seq.empty)]] : gstack list);
```
```   125
```
```   126 (* Stack of proof attempts *)
```
```   127 val proofstack = ref([]: proof list);
```
```   128
```
```   129 (*reset all refs*)
```
```   130 fun reset_goals () =
```
```   131   (curr_prems := []; curr_mkresult := init_mkresult;
```
```   132     undo_list := [[(dummy, Seq.empty)]]);
```
```   133
```
```   134
```
```   135 (*** Setting up goal-directed proof ***)
```
```   136
```
```   137 (*Generates the list of new theories when the proof state's signature changes*)
```
```   138 fun sign_error (sign,sign') =
```
```   139   let val names = Sign.stamp_names_of sign' \\ Sign.stamp_names_of sign
```
```   140   in  case names of
```
```   141         [name] => "\nNew theory: " ^ name
```
```   142       | _       => "\nNew theories: " ^ space_implode ", " names
```
```   143   end;
```
```   144
```
```   145 (*Default action is to print an error message; could be suppressed for
```
```   146   special applications.*)
```
```   147 fun result_error_default state msg : thm =
```
```   148   Pretty.str "Bad final proof state:" :: Display.pretty_goals (!goals_limit) state @
```
```   149     [Pretty.str msg, Pretty.str "Proof failed!"] |> Pretty.chunks |> Pretty.string_of |> error;
```
```   150
```
```   151 val result_error_fn = ref result_error_default;
```
```   152
```
```   153 (* alternative to standard: this function does not discharge the hypotheses
```
```   154    first. Is used for locales, in the following function prepare_proof *)
```
```   155 fun varify th =
```
```   156   let val {maxidx,...} = rep_thm th
```
```   157   in
```
```   158     th |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
```
```   159        |> Drule.strip_shyps_warning
```
```   160        |> zero_var_indexes |> Thm.varifyT |> Thm.compress
```
```   161   end;
```
```   162
```
```   163 (** exporting a theorem out of a locale means turning all meta-hyps into assumptions
```
```   164     and expand and cancel the locale definitions.
```
```   165     export goes through all levels in case of nested locales, whereas
```
```   166     export_thy just goes one up. **)
```
```   167
```
```   168 fun get_top_scope_thms thy =
```
```   169    let val sc = (Locale.get_scope_sg (Theory.sign_of thy))
```
```   170    in if (null sc) then (warning "No locale in theory"; [])
```
```   171       else map (#prop o rep_thm) (map #2 (#thms(snd(hd sc))))
```
```   172    end;
```
```   173
```
```   174 fun implies_intr_some_hyps thy A_set th =
```
```   175    let
```
```   176        val sign = Theory.sign_of thy;
```
```   177        val used_As = A_set inter #hyps(rep_thm(th));
```
```   178        val ctl = map (cterm_of sign) used_As
```
```   179    in foldl (fn (x, y) => Thm.implies_intr y x) (th, ctl)
```
```   180    end;
```
```   181
```
```   182 fun standard_some thy A_set th =
```
```   183   let val {maxidx,...} = rep_thm th
```
```   184   in
```
```   185     th |> implies_intr_some_hyps thy A_set
```
```   186        |> forall_intr_frees |> forall_elim_vars (maxidx + 1)
```
```   187        |> Drule.strip_shyps_warning
```
```   188        |> zero_var_indexes |> Thm.varifyT |> Thm.compress
```
```   189   end;
```
```   190
```
```   191 fun export_thy thy th =
```
```   192   let val A_set = get_top_scope_thms thy
```
```   193   in
```
```   194      standard_some thy [] (Seq.hd ((REPEAT (FIRSTGOAL (rtac reflexive_thm))) (standard_some thy A_set th)))
```
```   195   end;
```
```   196
```
```   197 val export = standard o Seq.hd o (REPEAT (FIRSTGOAL (rtac reflexive_thm))) o standard;
```
```   198
```
```   199 fun Export th = export_thy (the_context ()) th;
```
```   200
```
```   201
```
```   202 (*Common treatment of "goal" and "prove_goal":
```
```   203   Return assumptions, initial proof state, and function to make result.
```
```   204   "atomic" indicates if the goal should be wrapped up in the function
```
```   205   "Goal::prop=>prop" to avoid assumptions being returned separately.
```
```   206 *)
```
```   207 fun prepare_proof atomic rths chorn =
```
```   208   let val {sign, t=horn,...} = rep_cterm chorn;
```
```   209       val _ = Term.no_dummy_patterns horn handle TERM (msg, _) => error msg;
```
```   210       val (_,As,B) = Logic.strip_horn(horn);
```
```   211       val atoms = atomic andalso
```
```   212             forall (fn t => not(Logic.is_implies t orelse Logic.is_all t)) As;
```
```   213       val (As,B) = if atoms then ([],horn) else (As,B);
```
```   214       val cAs = map (cterm_of sign) As;
```
```   215       val prems = map (rewrite_rule rths o forall_elim_vars 0 o Thm.assume) cAs;
```
```   216       val cB = cterm_of sign B;
```
```   217       val st0 = let val st = Drule.impose_hyps cAs (Drule.mk_triv_goal cB)
```
```   218                 in  rewrite_goals_rule rths st end
```
```   219       (*discharges assumptions from state in the order they appear in goal;
```
```   220 	checks (if requested) that resulting theorem is equivalent to goal. *)
```
```   221       fun mkresult (check,state) =
```
```   222         let val state = Seq.hd (flexflex_rule state)
```
```   223 	    		handle THM _ => state   (*smash flexflex pairs*)
```
```   224 	    val ngoals = nprems_of state
```
```   225             val ath = implies_intr_list cAs state
```
```   226             val th = ath RS Drule.rev_triv_goal
```
```   227             val {hyps,prop,sign=sign',...} = rep_thm th
```
```   228             val final_th = if (null(hyps)) then standard th else varify th
```
```   229         in  if not check then final_th
```
```   230 	    else if not (Sign.eq_sg(sign,sign')) then !result_error_fn state
```
```   231 		("Signature of proof state has changed!" ^
```
```   232 		 sign_error (sign,sign'))
```
```   233             else if ngoals>0 then !result_error_fn state
```
```   234 		(string_of_int ngoals ^ " unsolved goals!")
```
```   235             else if (not (null hyps) andalso (not (Locale.in_locale hyps sign)))
```
```   236 		 then !result_error_fn state
```
```   237                   ("Additional hypotheses:\n" ^
```
```   238 		   cat_lines
```
```   239 		    (map (Sign.string_of_term sign)
```
```   240 		     (filter (fn x => (not (Locale.in_locale [x] sign)))
```
```   241 		      hyps)))
```
```   242 	    else if Pattern.matches (#tsig(Sign.rep_sg sign))
```
```   243 			            (Envir.beta_norm (term_of chorn), Envir.beta_norm prop)
```
```   244 		 then final_th
```
```   245 	    else  !result_error_fn state "proved a different theorem"
```
```   246         end
```
```   247   in
```
```   248      if Sign.eq_sg(sign, #sign(rep_thm st0))
```
```   249      then (prems, st0, mkresult)
```
```   250      else error ("Definitions would change the proof state's signature" ^
```
```   251 		 sign_error (sign, #sign(rep_thm st0)))
```
```   252   end
```
```   253   handle THM(s,_,_) => error("prepare_proof: exception THM was raised!\n" ^ s);
```
```   254
```
```   255 (*Prints exceptions readably to users*)
```
```   256 fun print_sign_exn_unit sign e =
```
```   257   case e of
```
```   258      THM (msg,i,thms) =>
```
```   259 	 (writeln ("Exception THM " ^ string_of_int i ^ " raised:\n" ^ msg);
```
```   260 	  seq print_thm thms)
```
```   261    | THEORY (msg,thys) =>
```
```   262 	 (writeln ("Exception THEORY raised:\n" ^ msg);
```
```   263 	  seq (Pretty.writeln o Display.pretty_theory) thys)
```
```   264    | TERM (msg,ts) =>
```
```   265 	 (writeln ("Exception TERM raised:\n" ^ msg);
```
```   266 	  seq (writeln o Sign.string_of_term sign) ts)
```
```   267    | TYPE (msg,Ts,ts) =>
```
```   268 	 (writeln ("Exception TYPE raised:\n" ^ msg);
```
```   269 	  seq (writeln o Sign.string_of_typ sign) Ts;
```
```   270 	  seq (writeln o Sign.string_of_term sign) ts)
```
```   271    | e => raise e;
```
```   272
```
```   273 (*Prints an exception, then fails*)
```
```   274 fun print_sign_exn sign e = (print_sign_exn_unit sign e; raise ERROR);
```
```   275
```
```   276 (** the prove_goal.... commands
```
```   277     Prove theorem using the listed tactics; check it has the specified form.
```
```   278     Augment signature with all type assignments of goal.
```
```   279     Syntax is similar to "goal" command for easy keyboard use. **)
```
```   280
```
```   281 (*Version taking the goal as a cterm*)
```
```   282 fun prove_goalw_cterm_general check rths chorn tacsf =
```
```   283   let val (prems, st0, mkresult) = prepare_proof false rths chorn
```
```   284       val tac = EVERY (tacsf prems)
```
```   285       fun statef() =
```
```   286 	  (case Seq.pull (tac st0) of
```
```   287 	       Some(st,_) => st
```
```   288 	     | _ => error ("prove_goal: tactic failed"))
```
```   289   in  mkresult (check, cond_timeit (!Library.timing) statef)  end
```
```   290   handle e => (print_sign_exn_unit (#sign (rep_cterm chorn)) e;
```
```   291 	       writeln ("The exception above was raised for\n" ^
```
```   292 		      Display.string_of_cterm chorn); raise e);
```
```   293
```
```   294 (*Two variants: one checking the result, one not.
```
```   295   Neither prints runtime messages: they are for internal packages.*)
```
```   296 fun prove_goalw_cterm rths chorn =
```
```   297 	setmp Library.timing false (prove_goalw_cterm_general true rths chorn)
```
```   298 and prove_goalw_cterm_nocheck rths chorn =
```
```   299 	setmp Library.timing false (prove_goalw_cterm_general false rths chorn);
```
```   300
```
```   301
```
```   302 (*Version taking the goal as a string*)
```
```   303 fun prove_goalw thy rths agoal tacsf =
```
```   304   let val sign = Theory.sign_of thy
```
```   305       val chorn = read_cterm sign (agoal,propT)
```
```   306   in  prove_goalw_cterm_general true rths chorn tacsf end
```
```   307   handle ERROR => error (*from read_cterm?*)
```
```   308 		("The error(s) above occurred for " ^ quote agoal);
```
```   309
```
```   310 (*String version with no meta-rewrite-rules*)
```
```   311 fun prove_goal thy = prove_goalw thy [];
```
```   312
```
```   313 (*quick and dirty version (conditional)*)
```
```   314 fun quick_and_dirty_prove_goalw_cterm thy rews ct tacs =
```
```   315   prove_goalw_cterm rews ct
```
```   316     (if ! quick_and_dirty then (K [SkipProof.cheat_tac thy]) else tacs);
```
```   317
```
```   318
```
```   319 (*** Commands etc ***)
```
```   320
```
```   321 (*Return the current goal stack, if any, from undo_list*)
```
```   322 fun getstate() : gstack = case !undo_list of
```
```   323       []   => error"No current state in subgoal module"
```
```   324     | x::_ => x;
```
```   325
```
```   326 (*Pops the given goal stack*)
```
```   327 fun pop [] = error"Cannot go back past the beginning of the proof!"
```
```   328   | pop (pair::pairs) = (pair,pairs);
```
```   329
```
```   330
```
```   331 (* Print a level of the goal stack -- subject to quiet mode *)
```
```   332
```
```   333 val quiet = ref false;
```
```   334 fun disable_pr () = quiet := true;
```
```   335 fun enable_pr () = quiet := false;
```
```   336
```
```   337 fun print_top ((th, _), pairs) =
```
```   338   if ! quiet then ()
```
```   339   else ! Display.print_current_goals_fn (length pairs) (! goals_limit) th;
```
```   340
```
```   341 (*Printing can raise exceptions, so the assignment occurs last.
```
```   342   Can do   setstate[(st,Seq.empty)]  to set st as the state.  *)
```
```   343 fun setstate newgoals =
```
```   344   (print_top (pop newgoals);  undo_list := newgoals :: !undo_list);
```
```   345
```
```   346 (*Given a proof state transformation, return a command that updates
```
```   347     the goal stack*)
```
```   348 fun make_command com = setstate (com (pop (getstate())));
```
```   349
```
```   350 (*Apply a function on proof states to the current goal stack*)
```
```   351 fun apply_fun f = f (pop(getstate()));
```
```   352
```
```   353 (*Return the top theorem, representing the proof state*)
```
```   354 fun topthm () = apply_fun  (fn ((th,_), _) => th);
```
```   355
```
```   356 (*Return the final result.  *)
```
```   357 fun result () = !curr_mkresult (true, topthm());
```
```   358
```
```   359 (*Return the result UNCHECKED that it equals the goal -- for synthesis,
```
```   360   answer extraction, or other instantiation of Vars *)
```
```   361 fun uresult () = !curr_mkresult (false, topthm());
```
```   362
```
```   363 (*Get subgoal i from goal stack*)
```
```   364 fun getgoal i = List.nth (prems_of (topthm()), i-1)
```
```   365                 handle Subscript => error"getgoal: Goal number out of range";
```
```   366
```
```   367 (*Return subgoal i's hypotheses as meta-level assumptions.
```
```   368   For debugging uses of METAHYPS*)
```
```   369 local exception GETHYPS of thm list
```
```   370 in
```
```   371 fun gethyps i =
```
```   372     (METAHYPS (fn hyps => raise (GETHYPS hyps)) i (topthm());  [])
```
```   373     handle GETHYPS hyps => hyps
```
```   374 end;
```
```   375
```
```   376 (*Which thms could apply to goal i? (debugs tactics involving filter_thms) *)
```
```   377 fun filter_goal could ths i = filter_thms could (999, getgoal i, ths);
```
```   378
```
```   379 (*For inspecting earlier levels of the backward proof*)
```
```   380 fun chop_level n (pair,pairs) =
```
```   381   let val level = length pairs
```
```   382   in  if n<0 andalso ~n <= level
```
```   383       then  List.drop (pair::pairs, ~n)
```
```   384       else if 0<=n andalso n<= level
```
```   385       then  List.drop (pair::pairs, level - n)
```
```   386       else  error ("Level number must lie between 0 and " ^
```
```   387 		   string_of_int level)
```
```   388   end;
```
```   389
```
```   390 (*Print the given level of the proof; prlev ~1 prints previous level*)
```
```   391 fun prlev n = (enable_pr (); apply_fun (print_top o pop o (chop_level n)));
```
```   392 fun pr () = (enable_pr (); apply_fun print_top);
```
```   393
```
```   394 (*Set goals_limit and print again*)
```
```   395 fun prlim n = (goals_limit:=n; pr());
```
```   396
```
```   397 (** the goal.... commands
```
```   398     Read main goal.  Set global variables curr_prems, curr_mkresult.
```
```   399     Initial subgoal and premises are rewritten using rths. **)
```
```   400
```
```   401 (*Version taking the goal as a cterm; if you have a term t and theory thy, use
```
```   402     goalw_cterm rths (cterm_of (Theory.sign_of thy) t);      *)
```
```   403 fun agoalw_cterm atomic rths chorn =
```
```   404   let val (prems, st0, mkresult) = prepare_proof atomic rths chorn
```
```   405   in  undo_list := [];
```
```   406       setstate [ (st0, Seq.empty) ];
```
```   407       curr_prems := prems;
```
```   408       curr_mkresult := mkresult;
```
```   409       prems
```
```   410   end;
```
```   411
```
```   412 val goalw_cterm = agoalw_cterm false;
```
```   413
```
```   414 (*Version taking the goal as a string*)
```
```   415 fun agoalw atomic thy rths agoal =
```
```   416     agoalw_cterm atomic rths (Locale.read_cterm(Theory.sign_of thy)(agoal,propT))
```
```   417     handle ERROR => error (*from type_assign, etc via prepare_proof*)
```
```   418 	("The error(s) above occurred for " ^ quote agoal);
```
```   419
```
```   420 val goalw = agoalw false;
```
```   421
```
```   422 (*String version with no meta-rewrite-rules*)
```
```   423 fun agoal atomic thy = agoalw atomic thy [];
```
```   424 val goal = agoal false;
```
```   425
```
```   426 (*now the versions that wrap the goal up in `Goal' to make it atomic*)
```
```   427 val atomic_goalw = agoalw true;
```
```   428 val atomic_goal = agoal true;
```
```   429
```
```   430 (*implicit context versions*)
```
```   431 fun Goal s = atomic_goal (Context.the_context ()) s;
```
```   432 fun Goalw thms s = atomic_goalw (Context.the_context ()) thms s;
```
```   433
```
```   434
```
```   435 (*Proof step "by" the given tactic -- apply tactic to the proof state*)
```
```   436 fun by_com tac ((th,ths), pairs) : gstack =
```
```   437   (case  Seq.pull(tac th)  of
```
```   438      None      => error"by: tactic failed"
```
```   439    | Some(th2,ths2) =>
```
```   440        (if eq_thm(th,th2)
```
```   441 	  then warning "Warning: same as previous level"
```
```   442 	  else if eq_thm_sg(th,th2) then ()
```
```   443 	  else warning ("Warning: signature of proof state has changed" ^
```
```   444 		       sign_error (#sign(rep_thm th), #sign(rep_thm th2)));
```
```   445        ((th2,ths2)::(th,ths)::pairs)));
```
```   446
```
```   447 fun by tac = cond_timeit (!Library.timing)
```
```   448     (fn() => make_command (by_com tac));
```
```   449
```
```   450 (* byev[tac1,...,tacn] applies tac1 THEN ... THEN tacn.
```
```   451    Good for debugging proofs involving prove_goal.*)
```
```   452 val byev = by o EVERY;
```
```   453
```
```   454
```
```   455 (*Backtracking means find an alternative result from a tactic.
```
```   456   If none at this level, try earlier levels*)
```
```   457 fun backtrack [] = error"back: no alternatives"
```
```   458   | backtrack ((th,thstr) :: pairs) =
```
```   459      (case Seq.pull thstr of
```
```   460 	  None      => (writeln"Going back a level..."; backtrack pairs)
```
```   461 	| Some(th2,thstr2) =>
```
```   462 	   (if eq_thm(th,th2)
```
```   463 	      then warning "Warning: same as previous choice at this level"
```
```   464 	      else if eq_thm_sg(th,th2) then ()
```
```   465 	      else warning "Warning: signature of proof state has changed";
```
```   466 	    (th2,thstr2)::pairs));
```
```   467
```
```   468 fun back() = setstate (backtrack (getstate()));
```
```   469
```
```   470 (*Chop back to previous level of the proof*)
```
```   471 fun choplev n = make_command (chop_level n);
```
```   472
```
```   473 (*Chopping back the goal stack*)
```
```   474 fun chop () = make_command (fn (_,pairs) => pairs);
```
```   475
```
```   476 (*Restore the previous proof state;  discard current state. *)
```
```   477 fun undo() = case !undo_list of
```
```   478       [] => error"No proof state"
```
```   479     | [_] => error"Already at initial state"
```
```   480     | _::newundo =>  (undo_list := newundo;  pr()) ;
```
```   481
```
```   482
```
```   483 (*** Managing the proof stack ***)
```
```   484
```
```   485 fun save_proof() = Proof(!undo_list, !curr_prems, !curr_mkresult);
```
```   486
```
```   487 fun restore_proof(Proof(ul,prems,mk)) =
```
```   488  (undo_list:= ul;  curr_prems:= prems;  curr_mkresult := mk;  prems);
```
```   489
```
```   490
```
```   491 fun top_proof() = case !proofstack of
```
```   492 	[] => error("Stack of proof attempts is empty!")
```
```   493     | p::ps => (p,ps);
```
```   494
```
```   495 (*  push a copy of the current proof state on to the stack *)
```
```   496 fun push_proof() = (proofstack := (save_proof() :: !proofstack));
```
```   497
```
```   498 (* discard the top proof state of the stack *)
```
```   499 fun pop_proof() =
```
```   500   let val (p,ps) = top_proof()
```
```   501       val prems = restore_proof p
```
```   502   in proofstack := ps;  pr();  prems end;
```
```   503
```
```   504 (* rotate the stack so that the top element goes to the bottom *)
```
```   505 fun rotate_proof() = let val (p,ps) = top_proof()
```
```   506 		    in proofstack := ps@[save_proof()];
```
```   507 		       restore_proof p;
```
```   508 		       pr();
```
```   509 		       !curr_prems
```
```   510 		    end;
```
```   511
```
```   512
```
```   513 (** Shortcuts for commonly-used tactics **)
```
```   514
```
```   515 fun bws rls = by (rewrite_goals_tac rls);
```
```   516 fun bw rl = bws [rl];
```
```   517
```
```   518 fun brs rls i = by (resolve_tac rls i);
```
```   519 fun br rl = brs [rl];
```
```   520
```
```   521 fun bes rls i = by (eresolve_tac rls i);
```
```   522 fun be rl = bes [rl];
```
```   523
```
```   524 fun bds rls i = by (dresolve_tac rls i);
```
```   525 fun bd rl = bds [rl];
```
```   526
```
```   527 fun ba i = by (assume_tac i);
```
```   528
```
```   529 fun ren str i = by (rename_tac str i);
```
```   530
```
```   531 (** Shortcuts to work on the first applicable subgoal **)
```
```   532
```
```   533 fun frs rls = by (FIRSTGOAL (trace_goalno_tac (resolve_tac rls)));
```
```   534 fun fr rl = frs [rl];
```
```   535
```
```   536 fun fes rls = by (FIRSTGOAL (trace_goalno_tac (eresolve_tac rls)));
```
```   537 fun fe rl = fes [rl];
```
```   538
```
```   539 fun fds rls = by (FIRSTGOAL (trace_goalno_tac (dresolve_tac rls)));
```
```   540 fun fd rl = fds [rl];
```
```   541
```
```   542 fun fa() = by (FIRSTGOAL (trace_goalno_tac assume_tac));
```
```   543
```
```   544 (** Reading and printing terms wrt the current theory **)
```
```   545
```
```   546 fun top_sg() = #sign(rep_thm(topthm()));
```
```   547
```
```   548 fun read s = term_of (read_cterm (top_sg()) (s, TypeInfer.logicT));
```
```   549
```
```   550 (*Print a term under the current signature of the proof state*)
```
```   551 fun prin t = writeln (Sign.string_of_term (top_sg()) t);
```
```   552
```
```   553 fun printyp T = writeln (Sign.string_of_typ (top_sg()) T);
```
```   554
```
```   555 fun pprint_term t = Sign.pprint_term (top_sg()) t;
```
```   556
```
```   557 fun pprint_typ T = Sign.pprint_typ (top_sg()) T;
```
```   558
```
```   559
```
```   560 (*Prints exceptions nicely at top level;
```
```   561   raises the exception in order to have a polymorphic type!*)
```
```   562 fun print_exn e = (print_sign_exn_unit (top_sg()) e;  raise e);
```
```   563
```
```   564
```
```   565
```
```   566 (** theorem database operations **)
```
```   567
```
```   568 (* storing *)
```
```   569
```
```   570 fun bind_thm (name, thm) = ThmDatabase.ml_store_thm (name, standard thm);
```
```   571 fun bind_thms (name, thms) = ThmDatabase.ml_store_thms (name, map standard thms);
```
```   572
```
```   573 fun qed name = ThmDatabase.ml_store_thm (name, result ());
```
```   574 fun qed_goal name thy goal tacsf = ThmDatabase.ml_store_thm (name, prove_goal thy goal tacsf);
```
```   575 fun qed_goalw name thy rews goal tacsf =
```
```   576   ThmDatabase.ml_store_thm (name, prove_goalw thy rews goal tacsf);
```
```   577 fun qed_spec_mp name =
```
```   578   ThmDatabase.ml_store_thm (name, ObjectLogic.rulify_no_asm (result ()));
```
```   579 fun qed_goal_spec_mp name thy s p =
```
```   580   bind_thm (name, ObjectLogic.rulify_no_asm (prove_goal thy s p));
```
```   581 fun qed_goalw_spec_mp name thy defs s p =
```
```   582   bind_thm (name, ObjectLogic.rulify_no_asm (prove_goalw thy defs s p));
```
```   583
```
```   584 fun no_qed () = ();
```
```   585
```
```   586
```
```   587 (* retrieval *)
```
```   588
```
```   589 fun theory_of_goal () = ThyInfo.theory_of_sign (Thm.sign_of_thm (topthm ()));
```
```   590
```
```   591 fun thms_containing raw_consts =
```
```   592   let
```
```   593     val thy = theory_of_goal ();
```
```   594     val consts = map (Sign.intern_const (Theory.sign_of thy)) raw_consts;
```
```   595   in ThmDatabase.thms_containing thy consts end;
```
```   596
```
```   597
```
```   598 (*top_const: main constant, ignoring Trueprop*)
```
```   599 fun top_const (_ \$ t) = (case head_of t of Const (c, _) => Some c | _ => None)
```
```   600   | top_const _ = None;
```
```   601
```
```   602 val intro_const = top_const o concl_of;
```
```   603
```
```   604 fun elim_const thm = case prems_of thm of [] => None | p::_ => top_const p;
```
```   605
```
```   606 (* In case faster access is necessary, the thm db should provide special
```
```   607 functions
```
```   608
```
```   609 index_intros, index_elims: string -> (string * thm) list
```
```   610
```
```   611 where thm [| A1 ; ...; An |] ==> B is returned by
```
```   612 - index_intros c if B  is of the form c t1 ... tn
```
```   613 - index_elims c  if A1 is of the form c t1 ... tn
```
```   614 *)
```
```   615
```
```   616 (* could be provided by thm db *)
```
```   617 fun index_intros c =
```
```   618   let fun topc(_,thm) = intro_const thm = Some(c);
```
```   619       val named_thms = ThmDatabase.thms_containing (theory_of_goal ()) [c]
```
```   620   in filter topc named_thms end;
```
```   621
```
```   622 (* could be provided by thm db *)
```
```   623 fun index_elims c =
```
```   624   let fun topc(_,thm) = elim_const thm = Some(c);
```
```   625       val named_thms = ThmDatabase.thms_containing (theory_of_goal ()) [c]
```
```   626   in filter topc named_thms end;
```
```   627
```
```   628 (*assume that parameters have unique names; reverse them for substitution*)
```
```   629 fun goal_params i =
```
```   630   let val gi = getgoal i
```
```   631       val rfrees = rev(map Free (Logic.strip_params gi))
```
```   632   in (gi,rfrees) end;
```
```   633
```
```   634 fun concl_of_goal i =
```
```   635   let val (gi,rfrees) = goal_params i
```
```   636       val B = Logic.strip_assums_concl gi
```
```   637   in subst_bounds(rfrees,B) end;
```
```   638
```
```   639 fun prems_of_goal i =
```
```   640   let val (gi,rfrees) = goal_params i
```
```   641       val As = Logic.strip_assums_hyp gi
```
```   642   in map (fn A => subst_bounds(rfrees,A)) As end;
```
```   643
```
```   644 (*returns all those named_thms whose subterm extracted by extract can be
```
```   645   instantiated to obj; the list is sorted according to the number of premises
```
```   646   and the size of the required substitution.*)
```
```   647 fun select_match(obj, signobj, named_thms, extract) =
```
```   648   let fun matches(prop, tsig) =
```
```   649             case extract prop of
```
```   650               None => false
```
```   651             | Some pat => Pattern.matches tsig (pat, obj);
```
```   652
```
```   653       fun substsize(prop, tsig) =
```
```   654             let val Some pat = extract prop
```
```   655                 val (_,subst) = Pattern.match tsig (pat,obj)
```
```   656             in foldl op+
```
```   657                 (0, map (fn (_,t) => size_of_term t) subst)
```
```   658             end
```
```   659
```
```   660       fun thm_ord ((p0,s0,_),(p1,s1,_)) =
```
```   661             prod_ord (int_ord o pairself (fn 0 => 0 | x => 1)) int_ord ((p0,s0),(p1,s1));
```
```   662
```
```   663       fun select((p as (_,thm))::named_thms, sels) =
```
```   664             let val {prop, sign, ...} = rep_thm thm
```
```   665             in select(named_thms,
```
```   666                       if Sign.subsig(sign, signobj) andalso
```
```   667                          matches(prop,#tsig(Sign.rep_sg signobj))
```
```   668                       then
```
```   669                         (nprems_of thm,substsize(prop,#tsig(Sign.rep_sg signobj)),p)::sels
```
```   670                       else sels)
```
```   671             end
```
```   672         | select([],sels) = sels
```
```   673
```
```   674   in map (fn (_,_,t) => t) (sort thm_ord (select(named_thms, []))) end;
```
```   675
```
```   676 fun find_matching(prop,sign,index,extract) =
```
```   677   (case top_const prop of
```
```   678      Some c => select_match(prop,sign,index c,extract)
```
```   679    | _      => []);
```
```   680
```
```   681 fun find_intros(prop,sign) =
```
```   682   find_matching(prop,sign,index_intros,Some o Logic.strip_imp_concl);
```
```   683
```
```   684 fun find_elims sign prop =
```
```   685   let fun major prop = case Logic.strip_imp_prems prop of
```
```   686                          [] => None | p::_ => Some p
```
```   687   in find_matching(prop,sign,index_elims,major) end;
```
```   688
```
```   689 fun findI i = find_intros(concl_of_goal i,#sign(rep_thm(topthm())));
```
```   690
```
```   691 fun findEs i =
```
```   692   let fun eq_nth((n1,th1),(n2,th2)) = n1=n2 andalso eq_thm(th1,th2);
```
```   693       val sign = #sign(rep_thm(topthm()))
```
```   694       val thmss = map (find_elims sign) (prems_of_goal i)
```
```   695   in foldl (gen_union eq_nth) ([],thmss) end;
```
```   696
```
```   697 fun findE i j =
```
```   698   let val sign = #sign(rep_thm(topthm()))
```
```   699   in find_elims sign (nth_elem(j-1, prems_of_goal i)) end;
```
```   700
```
```   701 end;
```
```   702
```
```   703 open Goals;
```