(*  Title:      Pure/old_goals.ML

     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory

     Copyright   1993  University of Cambridge

 Old-style goal stack package.  The goal stack initially holds a dummy

 proof, and can never become empty.  Each goal stack consists of a list

 of levels.  The undo list is a list of goal stacks.  Finally, there

 may be a stack of pending proofs.

 *)

 signature OLD_GOALS =

 sig

   val mk_defpair: term * term -> string * term

   val strip_context: term -> (string * typ) list * term list * term

   val metahyps_thms: int -> thm -> thm list option

   val METAHYPS: (thm list -> tactic) -> int -> tactic

   val simple_read_term: theory -> typ -> string -> term

   val read_term: theory -> string -> term

   val read_prop: theory -> string -> term

   val get_def: theory -> xstring -> thm

   type proof

   val premises: unit -> thm list

   val reset_goals: unit -> unit

   val result_error_fn: (thm -> string -> thm) Unsynchronized.ref

   val print_sign_exn: theory -> exn -> 'a

   val prove_goalw_cterm: thm list->cterm->(thm list->tactic list)->thm

   val prove_goalw_cterm_nocheck: thm list->cterm->(thm list->tactic list)->thm

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

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

   val topthm: unit -> thm

   val result: unit -> thm

   val uresult: unit -> thm

   val getgoal: int -> term

   val gethyps: int -> thm list

   val print_exn: exn -> 'a

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

   val prlev: int -> unit

   val pr: unit -> unit

   val prlim: int -> unit

   val goalw_cterm: thm list -> cterm -> thm list

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

   val goal: theory -> string -> thm list

   val Goalw: thm list -> string -> thm list

   val Goal: string -> thm list

   val simple_prove_goal_cterm: cterm->(thm list->tactic list)->thm

   val by: tactic -> unit

   val byev: tactic list -> unit

   val back: unit -> unit

   val choplev: int -> unit

   val chop: unit -> unit

   val undo: unit -> unit

   val save_proof: unit -> proof

   val restore_proof: proof -> thm list

   val push_proof: unit -> unit

   val pop_proof: unit -> thm list

   val rotate_proof: unit -> thm list

   val qed: string -> unit

   val qed_goal: string -> theory -> string -> (thm list -> tactic list) -> unit

   val qed_goalw: string -> theory -> thm list -> string

     -> (thm list -> tactic list) -> unit

   val qed_spec_mp: string -> unit

   val qed_goal_spec_mp: string -> theory -> string -> (thm list -> tactic list) -> unit

   val qed_goalw_spec_mp: string -> theory -> thm list -> string

     -> (thm list -> tactic list) -> unit

 end;

 structure OldGoals: OLD_GOALS =

 struct

 fun mk_defpair (lhs, rhs) =

   (case Term.head_of lhs of

     Const (name, _) =>

       (Long_Name.base_name name ^ "_def", Logic.mk_equals (lhs, rhs))

   | _ => raise TERM ("Malformed definition: head of lhs not a constant", [lhs, rhs]));

 (**** METAHYPS -- tactical for using hypotheses as meta-level assumptions

        METAHYPS (fn prems => tac prems) i

 converts subgoal i, of the form !!x1...xm. [| A1;...;An] ==> A into a new

 proof state A==>A, supplying A1,...,An as meta-level assumptions (in

 "prems").  The parameters x1,...,xm become free variables.  If the

 resulting proof state is [| B1;...;Bk] ==> C (possibly assuming A1,...,An)

 then it is lifted back into the original context, yielding k subgoals.

 Replaces unknowns in the context by Frees having the prefix METAHYP_

 New unknowns in [| B1;...;Bk] ==> C are lifted over x1,...,xm.

 DOES NOT HANDLE TYPE UNKNOWNS.

 NOTE: This version does not observe the proof context, and thus cannot

 work reliably.  See also Subgoal.SUBPROOF and Subgoal.FOCUS for

 properly localized variants of the same idea.

 ****)

 (*Strips assumptions in goal yielding  ( [x1,...,xm], [H1,...,Hn], B )

     H1,...,Hn are the hypotheses;  x1...xm are variants of the parameters.

   Main difference from strip_assums concerns parameters:

     it replaces the bound variables by free variables.  *)

 fun strip_context_aux (params, Hs, Const ("==>", _) $ H $ B) =

       strip_context_aux (params, H :: Hs, B)

   | strip_context_aux (params, Hs, Const ("all",_) $ Abs (a, T, t)) =

       let val (b, u) = Syntax.variant_abs (a, T, t)

       in strip_context_aux ((b, T) :: params, Hs, u) end

   | strip_context_aux (params, Hs, B) = (rev params, rev Hs, B);

 fun strip_context A = strip_context_aux ([], [], A);

 local

   (*Left-to-right replacements: ctpairs = [...,(vi,ti),...].

     Instantiates distinct free variables by terms of same type.*)

   fun free_instantiate ctpairs =

     forall_elim_list (map snd ctpairs) o forall_intr_list (map fst ctpairs);

   fun free_of s ((a, i), T) =

     Free (s ^ (case i of 0 => a | _ => a ^ "_" ^ string_of_int i), T)

   fun mk_inst v = (Var v, free_of "METAHYP1_" v)

 in

 (*Common code for METAHYPS and metahyps_thms*)

 fun metahyps_split_prem prem =

   let (*find all vars in the hyps -- should find tvars also!*)

       val hyps_vars = fold Term.add_vars (Logic.strip_assums_hyp prem) []

       val insts = map mk_inst hyps_vars

       (*replace the hyps_vars by Frees*)

       val prem' = subst_atomic insts prem

       val (params,hyps,concl) = strip_context prem'

   in (insts,params,hyps,concl)  end;

 fun metahyps_aux_tac tacf (prem,gno) state =

   let val (insts,params,hyps,concl) = metahyps_split_prem prem

       val maxidx = Thm.maxidx_of state

       val cterm = Thm.cterm_of (Thm.theory_of_thm state)

       val chyps = map cterm hyps

       val hypths = map Thm.assume chyps

       val subprems = map (Thm.forall_elim_vars 0) hypths

       val fparams = map Free params

       val cparams = map cterm fparams

       fun swap_ctpair (t,u) = (cterm u, cterm t)

       (*Subgoal variables: make Free; lift type over params*)

       fun mk_subgoal_inst concl_vars (v, T) =

           if member (op =) concl_vars (v, T)

           then ((v, T), true, free_of "METAHYP2_" (v, T))

           else ((v, T), false, free_of "METAHYP2_" (v, map #2 params ---> T))

       (*Instantiate subgoal vars by Free applied to params*)

       fun mk_ctpair (v, in_concl, u) =

           if in_concl then (cterm (Var v), cterm u)

           else (cterm (Var v), cterm (list_comb (u, fparams)))

       (*Restore Vars with higher type and index*)

       fun mk_subgoal_swap_ctpair (((a, i), T), in_concl, u as Free (_, U)) =

           if in_concl then (cterm u, cterm (Var ((a, i), T)))

           else (cterm u, cterm (Var ((a, i + maxidx), U)))

       (*Embed B in the original context of params and hyps*)

       fun embed B = list_all_free (params, Logic.list_implies (hyps, B))

       (*Strip the context using elimination rules*)

       fun elim Bhyp = implies_elim_list (forall_elim_list cparams Bhyp) hypths

       (*A form of lifting that discharges assumptions.*)

       fun relift st =

         let val prop = Thm.prop_of st

             val subgoal_vars = (*Vars introduced in the subgoals*)

               fold Term.add_vars (Logic.strip_imp_prems prop) []

             and concl_vars = Term.add_vars (Logic.strip_imp_concl prop) []

             val subgoal_insts = map (mk_subgoal_inst concl_vars) subgoal_vars

             val st' = Thm.instantiate ([], map mk_ctpair subgoal_insts) st

             val emBs = map (cterm o embed) (prems_of st')

             val Cth  = implies_elim_list st' (map (elim o Thm.assume) emBs)

         in  (*restore the unknowns to the hypotheses*)

             free_instantiate (map swap_ctpair insts @

                               map mk_subgoal_swap_ctpair subgoal_insts)

                 (*discharge assumptions from state in same order*)

                 (implies_intr_list emBs

                   (forall_intr_list cparams (implies_intr_list chyps Cth)))

         end

       (*function to replace the current subgoal*)

       fun next st = Thm.bicompose false (false, relift st, nprems_of st) gno state

   in Seq.maps next (tacf subprems (Thm.trivial (cterm concl))) end;

 end;

 (*Returns the theorem list that METAHYPS would supply to its tactic*)

 fun metahyps_thms i state =

   let val prem = Logic.nth_prem (i, Thm.prop_of state)

       and cterm = cterm_of (Thm.theory_of_thm state)

       val (_,_,hyps,_) = metahyps_split_prem prem

   in SOME (map (Thm.forall_elim_vars 0 o Thm.assume o cterm) hyps) end

   handle TERM ("nth_prem", [A]) => NONE;

 local

 fun print_vars_terms thy (n,thm) =

   let

     fun typed ty = " has type: " ^ Syntax.string_of_typ_global thy ty;

     fun find_vars thy (Const (c, ty)) =

           if null (Term.add_tvarsT ty []) then I

           else insert (op =) (c ^ typed ty)

       | find_vars thy (Var (xi, ty)) = insert (op =) (Term.string_of_vname xi ^ typed ty)

       | find_vars _ (Free _) = I

       | find_vars _ (Bound _) = I

       | find_vars thy (Abs (_, _, t)) = find_vars thy t

       | find_vars thy (t1 $ t2) =

           find_vars thy t1 #> find_vars thy t1;

     val prem = Logic.nth_prem (n, Thm.prop_of thm)

     val tms = find_vars thy prem []

   in

     (warning "Found schematic vars in assumptions:"; warning (cat_lines tms))

   end;

 in

 fun METAHYPS tacf n thm = SUBGOAL (metahyps_aux_tac tacf) n thm

   handle THM("assume: variables",_,_) => (print_vars_terms (theory_of_thm thm) (n,thm); Seq.empty)

 end;

 (* old ways of reading terms *)

 fun simple_read_term thy T s =

   let

     val ctxt = ProofContext.init_global thy

       |> ProofContext.allow_dummies

       |> ProofContext.set_mode ProofContext.mode_schematic;

     val parse = if T = propT then Syntax.parse_prop else Syntax.parse_term;

   in parse ctxt s |> Type_Infer.constrain T |> Syntax.check_term ctxt end;

 fun read_term thy = simple_read_term thy dummyT;

 fun read_prop thy = simple_read_term thy propT;

 fun get_def thy = Thm.axiom thy o Name_Space.intern (Theory.axiom_space thy) o Thm.def_name;

 (*** Goal package ***)

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

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

 type gstack = (thm * thm Seq.seq) list;

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

 (*** References ***)

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

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

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

 fun premises() = !curr_prems;

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

 fun init_mkresult _ = error "No goal has been supplied in subgoal module";

 val curr_mkresult = Unsynchronized.ref (init_mkresult: bool*thm->thm);

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

   A list of lists!*)

 val undo_list = Unsynchronized.ref([[(asm_rl, Seq.empty)]] : gstack list);

 (* Stack of proof attempts *)

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

 (*reset all refs*)

 fun reset_goals () =

   (curr_prems := []; curr_mkresult := init_mkresult;

     undo_list := [[(asm_rl, Seq.empty)]]);

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

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

 fun thy_error (thy,thy') =

   let val names = subtract (op =) (Context.display_names thy) (Context.display_names thy')

   in  case names of

         [name] => "\nNew theory: " ^ name

       | _       => "\nNew theories: " ^ space_implode ", " names

   end;

 (*Default action is to print an error message; could be suppressed for

   special applications.*)

 fun result_error_default state msg : thm =

   Pretty.str "Bad final proof state:" ::

       Goal_Display.pretty_goals_without_context (!goals_limit) state @

     [Pretty.str msg, Pretty.str "Proof failed!"] |> Pretty.chunks |> Pretty.string_of |> error;

 val result_error_fn = Unsynchronized.ref result_error_default;

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

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

   "atomic" indicates if the goal should be wrapped up in the function

   "Goal::prop=>prop" to avoid assumptions being returned separately.

 *)

 fun prepare_proof atomic rths chorn =

   let

       val thy = Thm.theory_of_cterm chorn;

       val horn = Thm.term_of chorn;

       val _ = Term.no_dummy_patterns horn handle TERM (msg, _) => error msg;

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

       val atoms = atomic andalso

             forall (fn t => not (can Logic.dest_implies t orelse Logic.is_all t)) As;

       val (As,B) = if atoms then ([],horn) else (As,B);

       val cAs = map (cterm_of thy) As;

       val prems = map (rewrite_rule rths o Thm.forall_elim_vars 0 o Thm.assume) cAs;

       val cB = cterm_of thy B;

       val st0 = let val st = Goal.init cB |> fold Thm.weaken cAs

                 in  rewrite_goals_rule rths st end

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

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

       fun mkresult (check,state) =

         let val state = Seq.hd (Thm.flexflex_rule state)

                         handle THM _ => state   (*smash flexflex pairs*)

             val ngoals = nprems_of state

             val ath = implies_intr_list cAs state

             val th = Goal.conclude ath

             val thy' = Thm.theory_of_thm th

             val {hyps, prop, ...} = Thm.rep_thm th

             val final_th = Drule.export_without_context th

         in  if not check then final_th

             else if not (Theory.eq_thy(thy,thy')) then !result_error_fn state

                 ("Theory of proof state has changed!" ^

                  thy_error (thy,thy'))

             else if ngoals>0 then !result_error_fn state

                 (string_of_int ngoals ^ " unsolved goals!")

             else if not (null hyps) then !result_error_fn state

                 ("Additional hypotheses:\n" ^

                  cat_lines (map (Syntax.string_of_term_global thy) hyps))

             else if Pattern.matches thy

                                     (Envir.beta_norm (term_of chorn), Envir.beta_norm prop)

                  then final_th

             else  !result_error_fn state "proved a different theorem"

         end

   in

      if Theory.eq_thy(thy, Thm.theory_of_thm st0)

      then (prems, st0, mkresult)

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

                  thy_error (thy, Thm.theory_of_thm st0))

   end

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

 (*Prints exceptions readably to users*)

 fun print_sign_exn_unit thy e =

   case e of

      THM (msg,i,thms) =>

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

           List.app (writeln o Display.string_of_thm_global thy) thms)

    | THEORY (msg,thys) =>

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

           List.app (writeln o Context.str_of_thy) thys)

    | TERM (msg,ts) =>

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

           List.app (writeln o Syntax.string_of_term_global thy) ts)

    | TYPE (msg,Ts,ts) =>

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

           List.app (writeln o Syntax.string_of_typ_global thy) Ts;

           List.app (writeln o Syntax.string_of_term_global thy) ts)

    | e => raise e;

 (*Prints an exception, then fails*)

 fun print_sign_exn thy e = (print_sign_exn_unit thy e; raise ERROR "");

 (** the prove_goal.... commands

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

     Augment theory with all type assignments of goal.

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

 (*Version taking the goal as a cterm*)

 fun prove_goalw_cterm_general check rths chorn tacsf =

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

       val tac = EVERY (tacsf prems)

       fun statef() =

           (case Seq.pull (tac st0) of

                SOME(st,_) => st

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

   in  mkresult (check, cond_timeit (!Output.timing) "" statef)  end;

 (*Two variants: one checking the result, one not.

   Neither prints runtime messages: they are for internal packages.*)

 fun prove_goalw_cterm rths chorn =

         setmp_CRITICAL Output.timing false (prove_goalw_cterm_general true rths chorn)

 and prove_goalw_cterm_nocheck rths chorn =

         setmp_CRITICAL Output.timing false (prove_goalw_cterm_general false rths chorn);

 (*Version taking the goal as a string*)

 fun prove_goalw thy rths agoal tacsf =

   let val chorn = cterm_of thy (read_prop thy agoal)

   in prove_goalw_cterm_general true rths chorn tacsf end

   handle ERROR msg => cat_error msg (*from read_prop?*)

                 ("The error(s) above occurred for " ^ quote agoal);

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

 fun prove_goal thy = prove_goalw thy [];

 (*** Commands etc ***)

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

 fun getstate() : gstack = case !undo_list of

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

     | x::_ => x;

 (*Pops the given goal stack*)

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

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

 (* Print a level of the goal stack *)

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

   let

     val n = length pairs;

     val m = (! goals_limit);

     val ngoals = nprems_of th;

   in

     [Pretty.str ("Level " ^ string_of_int n ^

       (if ngoals > 0 then " (" ^ string_of_int ngoals ^ " subgoal" ^

         (if ngoals <> 1 then "s" else "") ^ ")"

       else ""))] @

     Goal_Display.pretty_goals_without_context m th

   end |> Pretty.chunks |> Pretty.writeln;

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

   Can do   setstate[(st,Seq.empty)]  to set st as the state.  *)

 fun setstate newgoals =

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

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

     the goal stack*)

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

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

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

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

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

 (*Return the final result.  *)

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

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

   answer extraction, or other instantiation of Vars *)

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

 (*Get subgoal i from goal stack*)

 fun getgoal i = Logic.get_goal (prop_of (topthm())) i;

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

   For debugging uses of METAHYPS*)

 local exception GETHYPS of thm list

 in

 fun gethyps i =

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

     handle GETHYPS hyps => hyps

 end;

 (*Prints exceptions nicely at top level;

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

 fun print_exn e = (print_sign_exn_unit (Thm.theory_of_thm (topthm())) e;  raise e);

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

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

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

 fun chop_level n (pair,pairs) =

   let val level = length pairs

   in  if n<0 andalso ~n <= level

       then  List.drop (pair::pairs, ~n)

       else if 0<=n andalso n<= level

       then  List.drop (pair::pairs, level - n)

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

                    string_of_int level)

   end;

 (*Print the given level of the proof; prlev ~1 prints previous level*)

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

 fun pr () = apply_fun print_top;

 (*Set goals_limit and print again*)

 fun prlim n = (goals_limit:=n; pr());

 (** the goal.... commands

     Read main goal.  Set global variables curr_prems, curr_mkresult.

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

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

     goalw_cterm rths (cterm_of thy t);      *)

 fun agoalw_cterm atomic rths chorn =

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

   in  undo_list := [];

       setstate [ (st0, Seq.empty) ];

       curr_prems := prems;

       curr_mkresult := mkresult;

       prems

   end;

 val goalw_cterm = agoalw_cterm false;

 (*Version taking the goal as a string*)

 fun agoalw atomic thy rths agoal =

     agoalw_cterm atomic rths (cterm_of thy (read_prop thy agoal))

     handle ERROR msg => cat_error msg (*from type_assign, etc via prepare_proof*)

         ("The error(s) above occurred for " ^ quote agoal);

 val goalw = agoalw false;

 fun goal thy = goalw thy [];

 (*now the versions that wrap the goal up in `Goal' to make it atomic*)

 fun Goalw thms s = agoalw true (ML_Context.the_global_context ()) thms s;

 val Goal = Goalw [];

 (*simple version with minimal amount of checking and postprocessing*)

 fun simple_prove_goal_cterm G f =

   let

     val As = Drule.strip_imp_prems G;

     val B = Drule.strip_imp_concl G;

     val asms = map Assumption.assume As;

     fun check NONE = error "prove_goal: tactic failed"

       | check (SOME (thm, _)) = (case nprems_of thm of

             0 => thm

           | i => !result_error_fn thm (string_of_int i ^ " unsolved goals!"))

   in

     Drule.export_without_context (implies_intr_list As

       (check (Seq.pull (EVERY (f asms) (Thm.trivial B)))))

   end;

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

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

   (case  Seq.pull(tac th)  of

      NONE      => error"by: tactic failed"

    | SOME(th2,ths2) =>

        (if Thm.eq_thm(th,th2)

           then warning "Warning: same as previous level"

           else if Thm.eq_thm_thy(th,th2) then ()

           else warning ("Warning: theory of proof state has changed" ^

                        thy_error (Thm.theory_of_thm th, Thm.theory_of_thm th2));

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

 fun by tac = cond_timeit (!Output.timing) ""

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

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

    Good for debugging proofs involving prove_goal.*)

 val byev = by o EVERY;

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

   If none at this level, try earlier levels*)

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

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

      (case Seq.pull thstr of

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

         | SOME(th2,thstr2) =>

            (if Thm.eq_thm(th,th2)

               then warning "Warning: same as previous choice at this level"

               else if Thm.eq_thm_thy(th,th2) then ()

               else warning "Warning: theory of proof state has changed";

             (th2,thstr2)::pairs));

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

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

 fun choplev n = make_command (chop_level n);

 (*Chopping back the goal stack*)

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

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

 fun undo() = case !undo_list of

       [] => error"No proof state"

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

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

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

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

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

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

 fun top_proof() = case !proofstack of

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

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

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

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

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

 fun pop_proof() =

   let val (p,ps) = top_proof()

       val prems = restore_proof p

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

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

 fun rotate_proof() =

   let val (p,ps) = top_proof()

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

      restore_proof p;

      pr();

      !curr_prems

   end;

 (** theorem bindings **)

 fun qed name = ML_Context.ml_store_thm (name, result ());

 fun qed_goal name thy goal tacsf = ML_Context.ml_store_thm (name, prove_goal thy goal tacsf);

 fun qed_goalw name thy rews goal tacsf =

   ML_Context.ml_store_thm (name, prove_goalw thy rews goal tacsf);

 fun qed_spec_mp name =

   ML_Context.ml_store_thm (name, Object_Logic.rulify_no_asm (result ()));

 fun qed_goal_spec_mp name thy s p =

   bind_thm (name, Object_Logic.rulify_no_asm (prove_goal thy s p));

 fun qed_goalw_spec_mp name thy defs s p =

   bind_thm (name, Object_Logic.rulify_no_asm (prove_goalw thy defs s p));

 end;