(*  Title:      Pure/Isar/method.ML

     ID:         $Id$

     Author:     Markus Wenzel, TU Muenchen

 Isar proof methods.

 *)

 signature BASIC_METHOD =

 sig

   val FINDGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq

   val HEADGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq

   type method

   val trace_rules: bool ref

   val print_methods: theory -> unit

   val Method: bstring -> (Args.src -> ProofContext.context -> method) -> string -> unit

 end;

 signature METHOD =

 sig

   include BASIC_METHOD

   val apply: method -> thm list -> cases_tactic

   val RAW_METHOD_CASES: (thm list -> cases_tactic) -> method

   val RAW_METHOD: (thm list -> tactic) -> method

   val METHOD_CASES: (thm list -> cases_tactic) -> method

   val METHOD: (thm list -> tactic) -> method

   val fail: method

   val succeed: method

   val insert_tac: thm list -> int -> tactic

   val insert: thm list -> method

   val insert_facts: method

   val SIMPLE_METHOD: tactic -> method

   val SIMPLE_METHOD': ((int -> tactic) -> tactic) -> (int -> tactic) -> method

   val defer: int option -> method

   val prefer: int -> method

   val cheating: bool -> ProofContext.context -> method

   val intro: thm list -> method

   val elim: thm list -> method

   val unfold: thm list -> ProofContext.context -> method

   val fold: thm list -> ProofContext.context -> method

   val atomize: bool -> method

   val this: method

   val fact: thm list -> ProofContext.context -> method

   val assumption: ProofContext.context -> method

   val close: bool -> ProofContext.context -> method

   val trace: ProofContext.context -> thm list -> unit

   val rule_tac: thm list -> thm list -> int -> tactic

   val some_rule_tac: thm list -> ProofContext.context -> thm list -> int -> tactic

   val rule: thm list -> method

   val erule: int -> thm list -> method

   val drule: int -> thm list -> method

   val frule: int -> thm list -> method

   val iprover_tac: ProofContext.context -> int option -> int -> tactic

   val bires_inst_tac: bool -> ProofContext.context -> (indexname * string) list ->

     thm -> int -> tactic

   val set_tactic: (ProofContext.context -> thm list -> tactic) -> unit

   val tactic: string -> ProofContext.context -> method

   type src

   datatype text =

     Basic of (ProofContext.context -> method) |

     Source of src |

     Then of text list |

     Orelse of text list |

     Try of text |

     Repeat1 of text

   val primitive_text: (thm -> thm) -> text

   val succeed_text: text

   val default_text: text

   val this_text: text

   val done_text: text

   val sorry_text: bool -> text

   val finish_text: text option * bool -> text

   exception METHOD_FAIL of (string * Position.T) * exn

   val method: theory -> src -> ProofContext.context -> method

   val add_methods: (bstring * (src -> ProofContext.context -> method) * string) list

     -> theory -> theory

   val add_method: bstring * (src -> ProofContext.context -> method) * string

     -> theory -> theory

   val method_setup: bstring * string * string -> theory -> theory

   val syntax: (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list))

     -> src -> ProofContext.context -> ProofContext.context * 'a

   val simple_args: (Args.T list -> 'a * Args.T list)

     -> ('a -> ProofContext.context -> method) -> src -> ProofContext.context -> method

   val ctxt_args: (ProofContext.context -> method) -> src -> ProofContext.context -> method

   val no_args: method -> src -> ProofContext.context -> method

   type modifier

   val sectioned_args: (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list)) ->

     (Args.T list -> modifier * Args.T list) list ->

     ('a -> ProofContext.context -> 'b) -> src -> ProofContext.context -> 'b

   val bang_sectioned_args:

     (Args.T list -> modifier * Args.T list) list ->

     (thm list -> ProofContext.context -> 'a) -> src -> ProofContext.context -> 'a

   val bang_sectioned_args':

     (Args.T list -> modifier * Args.T list) list ->

     (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list)) ->

     ('a -> thm list -> ProofContext.context -> 'b) -> src -> ProofContext.context -> 'b

   val only_sectioned_args:

     (Args.T list -> modifier * Args.T list) list ->

     (ProofContext.context -> 'a) -> src -> ProofContext.context -> 'a

   val thms_ctxt_args: (thm list -> ProofContext.context -> 'a) -> src ->

     ProofContext.context -> 'a

   val thms_args: (thm list -> 'a) -> src -> ProofContext.context -> 'a

   val thm_args: (thm -> 'a) -> src -> ProofContext.context -> 'a

   val goal_args: (Args.T list -> 'a * Args.T list) -> ('a -> int -> tactic)

     -> src -> ProofContext.context -> method

   val goal_args': (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list))

     -> ('a -> int -> tactic) -> src -> ProofContext.context -> method

   val goal_args_ctxt: (Args.T list -> 'a * Args.T list) ->

     (ProofContext.context -> 'a -> int -> tactic) -> src -> ProofContext.context -> method

   val goal_args_ctxt': (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list)) ->

     (ProofContext.context -> 'a -> int -> tactic) -> src -> ProofContext.context -> method

 end;

 structure Method: METHOD =

 struct

 (** generic tools **)

 (* goal addressing *)

 fun FINDGOAL tac st =

   let fun find i n = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1) n)

   in find 1 (Thm.nprems_of st) st end;

 fun HEADGOAL tac = tac 1;

 (** proof methods **)

 (* datatype method *)

 datatype method = Meth of thm list -> cases_tactic;

 fun apply (Meth m) = m;

 val RAW_METHOD_CASES = Meth;

 fun RAW_METHOD tac = RAW_METHOD_CASES (NO_CASES o tac);

 fun METHOD_CASES tac = RAW_METHOD_CASES (fn facts =>

   Seq.THEN (ALLGOALS Tactic.conjunction_tac, tac facts));

 fun METHOD tac = RAW_METHOD (fn facts => ALLGOALS Tactic.conjunction_tac THEN tac facts);

 val fail = METHOD (K no_tac);

 val succeed = METHOD (K all_tac);

 (* insert facts *)

 local

 fun cut_rule_tac raw_rule =

   let

     val rule = Drule.forall_intr_vars raw_rule;

     val revcut_rl = Drule.incr_indexes rule Drule.revcut_rl;

   in Tactic.rtac (rule COMP revcut_rl) end;

 in

 fun insert_tac [] i = all_tac

   | insert_tac facts i = EVERY (map (fn th => cut_rule_tac th i) facts);

 val insert_facts = METHOD (ALLGOALS o insert_tac);

 fun insert thms = METHOD (fn _ => ALLGOALS (insert_tac thms));

 fun SIMPLE_METHOD tac = METHOD (fn facts => ALLGOALS (insert_tac facts) THEN tac);

 fun SIMPLE_METHOD' quant tac = METHOD (fn facts => quant (insert_tac facts THEN' tac));

 end;

 (* shuffle subgoals *)

 fun prefer i = METHOD (K (Tactic.defer_tac i THEN PRIMITIVE (Thm.permute_prems 0 ~1)));

 fun defer opt_i = METHOD (K (Tactic.defer_tac (the_default 1 opt_i)));

 (* cheating *)

 fun cheating int ctxt = METHOD (K (setmp quick_and_dirty (int orelse ! quick_and_dirty)

     (SkipProof.cheat_tac (ProofContext.theory_of ctxt))));

 (* unfold intro/elim rules *)

 fun intro ths = SIMPLE_METHOD' HEADGOAL (CHANGED_PROP o REPEAT_ALL_NEW (Tactic.match_tac ths));

 fun elim ths = SIMPLE_METHOD' HEADGOAL (CHANGED_PROP o REPEAT_ALL_NEW (Tactic.ematch_tac ths));

 (* unfold/fold definitions *)

 fun unfold_meth ths ctxt = SIMPLE_METHOD (CHANGED_PROP (LocalDefs.unfold_tac ctxt ths));

 fun fold_meth ths ctxt = SIMPLE_METHOD (CHANGED_PROP (LocalDefs.fold_tac ctxt ths));

 (* atomize rule statements *)

 fun atomize false = SIMPLE_METHOD' HEADGOAL (CHANGED_PROP o ObjectLogic.atomize_tac)

   | atomize true = RAW_METHOD (K (HEADGOAL (CHANGED_PROP o ObjectLogic.full_atomize_tac)));

 (* this -- resolve facts directly *)

 val this = METHOD (EVERY o map (HEADGOAL o Tactic.rtac));

 (* fact -- composition by facts from context *)

 fun fact [] ctxt = SIMPLE_METHOD' HEADGOAL (ProofContext.some_fact_tac ctxt)

   | fact rules _ = SIMPLE_METHOD' HEADGOAL (ProofContext.fact_tac rules);

 (* assumption *)

 local

 fun asm_tac ths =

   foldr (op APPEND') (K no_tac) (map (fn th => Tactic.rtac th THEN_ALL_NEW assume_tac) ths);

 val refl_tac = SUBGOAL (fn (prop, i) =>

   if can Logic.dest_equals (Logic.strip_assums_concl prop)

   then Tactic.rtac Drule.reflexive_thm i else no_tac);

 fun assm_tac ctxt =

   assume_tac APPEND'

   asm_tac (ProofContext.prems_of ctxt) APPEND'

   refl_tac;

 fun assumption_tac ctxt [] = assm_tac ctxt

   | assumption_tac _ [fact] = asm_tac [fact]

   | assumption_tac _ _ = K no_tac;

 in

 fun assumption ctxt = METHOD (HEADGOAL o assumption_tac ctxt);

 fun close immed ctxt = METHOD (K

   (FILTER Thm.no_prems ((if immed then ALLGOALS (assm_tac ctxt) else all_tac) THEN flexflex_tac)));

 end;

 (* rule etc. -- single-step refinements *)

 val trace_rules = ref false;

 fun trace ctxt rules =

   conditional (! trace_rules andalso not (null rules)) (fn () =>

     Pretty.big_list "rules:" (map (ProofContext.pretty_thm ctxt) rules)

     |> Pretty.string_of |> tracing);

 local

 fun gen_rule_tac tac rules facts =

   (fn i => fn st =>

     if null facts then tac rules i st

     else Seq.maps (fn rule => (tac o single) rule i st) (Drule.multi_resolves facts rules))

   THEN_ALL_NEW Tactic.norm_hhf_tac;

 fun gen_arule_tac tac j rules facts =

   EVERY' (gen_rule_tac tac rules facts :: replicate j Tactic.assume_tac);

 fun gen_some_rule_tac tac arg_rules ctxt facts = SUBGOAL (fn (goal, i) =>

   let

     val rules =

       if not (null arg_rules) then arg_rules

       else List.concat (ContextRules.find_rules false facts goal ctxt)

   in trace ctxt rules; tac rules facts i end);

 fun meth tac x = METHOD (HEADGOAL o tac x);

 fun meth' tac x y = METHOD (HEADGOAL o tac x y);

 in

 val rule_tac = gen_rule_tac Tactic.resolve_tac;

 val rule = meth rule_tac;

 val some_rule_tac = gen_some_rule_tac rule_tac;

 val some_rule = meth' some_rule_tac;

 val erule = meth' (gen_arule_tac Tactic.eresolve_tac);

 val drule = meth' (gen_arule_tac Tactic.dresolve_tac);

 val frule = meth' (gen_arule_tac Tactic.forward_tac);

 end;

 (* iprover -- intuitionistic proof search *)

 local

 val remdups_tac = SUBGOAL (fn (g, i) =>

   let val prems = Logic.strip_assums_hyp g in

     REPEAT_DETERM_N (length prems - length (gen_distinct op aconv prems))

     (Tactic.ematch_tac [Drule.remdups_rl] i THEN Tactic.eq_assume_tac i)

   end);

 fun REMDUPS tac = tac THEN_ALL_NEW remdups_tac;

 fun gen_eq_set e s1 s2 =

   length s1 = length s2 andalso

   gen_subset e (s1, s2) andalso gen_subset e (s2, s1);

 val bires_tac = Tactic.biresolution_from_nets_tac ContextRules.orderlist;

 fun safe_step_tac ctxt =

   ContextRules.Swrap ctxt

    (eq_assume_tac ORELSE'

     bires_tac true (ContextRules.netpair_bang ctxt));

 fun unsafe_step_tac ctxt =

   ContextRules.wrap ctxt

    (assume_tac APPEND'

     bires_tac false (ContextRules.netpair_bang ctxt) APPEND'

     bires_tac false (ContextRules.netpair ctxt));

 fun step_tac ctxt i =

   REPEAT_DETERM1 (REMDUPS (safe_step_tac ctxt) i) ORELSE

   REMDUPS (unsafe_step_tac ctxt) i;

 fun intprover_tac ctxt gs d lim = SUBGOAL (fn (g, i) => if d > lim then no_tac else

   let

     val ps = Logic.strip_assums_hyp g;

     val c = Logic.strip_assums_concl g;

   in

     if member (fn ((ps1, c1), (ps2, c2)) =>

       c1 aconv c2 andalso gen_eq_set op aconv ps1 ps2) gs (ps, c) then no_tac

     else (step_tac ctxt THEN_ALL_NEW intprover_tac ctxt ((ps, c) :: gs) (d + 1) lim) i

   end);

 in

 fun iprover_tac ctxt opt_lim =

   SELECT_GOAL (DEEPEN (2, the_default 20 opt_lim) (intprover_tac ctxt [] 0) 4 1);

 end;

 (* rule_tac etc. -- refer to dynamic goal state!! *)

 fun bires_inst_tac bires_flag ctxt insts thm =

   let

     val thy = ProofContext.theory_of ctxt;

     (* Separate type and term insts *)

     fun has_type_var ((x, _), _) = (case Symbol.explode x of

           "'"::cs => true | cs => false);

     val Tinsts = List.filter has_type_var insts;

     val tinsts = filter_out has_type_var insts;

     (* Tactic *)

     fun tac i st =

       let

         (* Preprocess state: extract environment information:

            - variables and their types

            - type variables and their sorts

            - parameters and their types *)

         val (types, sorts) = types_sorts st;

     (* Process type insts: Tinsts_env *)

     fun absent xi = error

           ("No such variable in theorem: " ^ Syntax.string_of_vname xi);

     val (rtypes, rsorts) = types_sorts thm;

     fun readT (xi, s) =

         let val S = case rsorts xi of SOME S => S | NONE => absent xi;

             val T = Sign.read_typ (thy, sorts) s;

             val U = TVar (xi, S);

         in if Sign.typ_instance thy (T, U) then (U, T)

            else error

              ("Instantiation of " ^ Syntax.string_of_vname xi ^ " fails")

         end;

     val Tinsts_env = map readT Tinsts;

     (* Preprocess rule: extract vars and their types, apply Tinsts *)

     fun get_typ xi =

       (case rtypes xi of

            SOME T => typ_subst_atomic Tinsts_env T

          | NONE => absent xi);

     val (xis, ss) = Library.split_list tinsts;

     val Ts = map get_typ xis;

         val (_, _, Bi, _) = dest_state(st,i)

         val params = Logic.strip_params Bi

                              (* params of subgoal i as string typ pairs *)

         val params = rev(Term.rename_wrt_term Bi params)

                            (* as they are printed: bound variables with *)

                            (* the same name are renamed during printing *)

         fun types' (a, ~1) = (case AList.lookup (op =) params a of

                 NONE => types (a, ~1)

               | some => some)

           | types' xi = types xi;

         fun internal x = is_some (types' (x, ~1));

         val used = Drule.add_used thm (Drule.add_used st []);

         val (ts, envT) =

           ProofContext.read_termTs_schematic ctxt internal types' sorts used (ss ~~ Ts);

         val envT' = map (fn (ixn, T) =>

           (TVar (ixn, the (rsorts ixn)), T)) envT @ Tinsts_env;

         val cenv =

           map

             (fn (xi, t) =>

               pairself (Thm.cterm_of thy) (Var (xi, fastype_of t), t))

             (gen_distinct

               (fn ((x1, t1), (x2, t2)) => x1 = x2 andalso t1 aconv t2)

               (xis ~~ ts));

         (* Lift and instantiate rule *)

         val {maxidx, ...} = rep_thm st;

         val paramTs = map #2 params

         and inc = maxidx+1

         fun liftvar (Var ((a,j), T)) =

               Var((a, j+inc), paramTs ---> Logic.incr_tvar inc T)

           | liftvar t = raise TERM("Variable expected", [t]);

         fun liftterm t = list_abs_free

               (params, Logic.incr_indexes(paramTs,inc) t)

         fun liftpair (cv,ct) =

               (cterm_fun liftvar cv, cterm_fun liftterm ct)

         val lifttvar = pairself (ctyp_of thy o Logic.incr_tvar inc);

         val rule = Drule.instantiate

               (map lifttvar envT', map liftpair cenv)

               (Thm.lift_rule (Thm.cprem_of st i) thm)

       in

         if i > nprems_of st then no_tac st

         else st |>

           compose_tac (bires_flag, rule, nprems_of thm) i

       end

            handle TERM (msg,_)   => (warning msg; no_tac st)

                 | THM  (msg,_,_) => (warning msg; no_tac st);

   in

     tac

   end;

 local

 fun gen_inst _ tac _ (quant, ([], thms)) =

       METHOD (fn facts => quant (insert_tac facts THEN' tac thms))

   | gen_inst inst_tac _ ctxt (quant, (insts, [thm])) =

       METHOD (fn facts =>

         quant (insert_tac facts THEN' inst_tac ctxt insts thm))

   | gen_inst _ _ _ _ = error "Cannot have instantiations with multiple rules";

 (* Preserve Var indexes of rl; increment revcut_rl instead.

    Copied from tactic.ML *)

 fun make_elim_preserve rl =

   let val {maxidx,...} = rep_thm rl

       fun cvar xi = cterm_of ProtoPure.thy (Var(xi,propT));

       val revcut_rl' =

           instantiate ([],  [(cvar("V",0), cvar("V",maxidx+1)),

                              (cvar("W",0), cvar("W",maxidx+1))]) revcut_rl

       val arg = (false, rl, nprems_of rl)

       val [th] = Seq.list_of (bicompose false arg 1 revcut_rl')

   in  th  end

   handle Bind => raise THM("make_elim_preserve", 1, [rl]);

 in

 val res_inst_meth = gen_inst (bires_inst_tac false) Tactic.resolve_tac;

 val eres_inst_meth = gen_inst (bires_inst_tac true) Tactic.eresolve_tac;

 val cut_inst_meth =

   gen_inst

     (fn ctxt => fn insts => bires_inst_tac false ctxt insts o make_elim_preserve)

     Tactic.cut_rules_tac;

 val dres_inst_meth =

   gen_inst

     (fn ctxt => fn insts => bires_inst_tac true ctxt insts o make_elim_preserve)

     Tactic.dresolve_tac;

 val forw_inst_meth =

   gen_inst

     (fn ctxt => fn insts => fn rule =>

        bires_inst_tac false ctxt insts (make_elim_preserve rule) THEN'

        assume_tac)

     Tactic.forward_tac;

 fun subgoal_tac ctxt sprop =

   DETERM o bires_inst_tac false ctxt [(("psi", 0), sprop)] cut_rl;

 fun subgoals_tac ctxt sprops = EVERY' (map (subgoal_tac ctxt) sprops);

 fun thin_tac ctxt s =

   bires_inst_tac true ctxt [(("V", 0), s)] thin_rl;

 end;

 (* ML tactics *)

 val tactic_ref = ref ((fn _ => raise Match): ProofContext.context -> thm list -> tactic);

 fun set_tactic f = tactic_ref := f;

 fun tactic txt ctxt = METHOD (fn facts =>

   (Context.use_mltext

     ("let fun tactic (ctxt: ProofContext.context) (facts: thm list) : tactic = \

        \let val thm = ProofContext.get_thm_closure ctxt o PureThy.Name\n\

        \  and thms = ProofContext.get_thms_closure ctxt o PureThy.Name in\n"

        ^ txt ^

        "\nend in Method.set_tactic tactic end")

     false NONE;

     Context.setmp (SOME (ProofContext.theory_of ctxt)) (! tactic_ref ctxt) facts));

 (** method syntax **)

 (* method text *)

 type src = Args.src;

 datatype text =

   Basic of (ProofContext.context -> method) |

   Source of src |

   Then of text list |

   Orelse of text list |

   Try of text |

   Repeat1 of text;

 val primitive_text = Basic o K o SIMPLE_METHOD o PRIMITIVE;

 val succeed_text = Basic (K succeed);

 val default_text = Source (Args.src (("default", []), Position.none));

 val this_text = Basic (K this);

 val done_text = Basic (K (SIMPLE_METHOD all_tac));

 val sorry_text = Basic o cheating;

 fun finish_text (NONE, immed) = Basic (close immed)

   | finish_text (SOME txt, immed) = Then [txt, Basic (close immed)];

 (* method definitions *)

 structure MethodsData = TheoryDataFun

 (struct

   val name = "Isar/methods";

   type T = (((src -> ProofContext.context -> method) * string) * stamp) NameSpace.table;

   val empty = NameSpace.empty_table;

   val copy = I;

   val extend = I;

   fun merge _ tables = NameSpace.merge_tables (eq_snd (op =)) tables handle Symtab.DUPS dups =>

     error ("Attempt to merge different versions of method(s) " ^ commas_quote dups);

   fun print _ meths =

     let

       fun prt_meth (name, ((_, comment), _)) = Pretty.block

         [Pretty.str (name ^ ":"), Pretty.brk 2, Pretty.str comment];

     in

       [Pretty.big_list "methods:" (map prt_meth (NameSpace.extern_table meths))]

       |> Pretty.chunks |> Pretty.writeln

     end;

 end);

 val _ = Context.add_setup MethodsData.init;

 val print_methods = MethodsData.print;

 (* get methods *)

 exception METHOD_FAIL of (string * Position.T) * exn;

 fun method thy =

   let

     val (space, meths) = MethodsData.get thy;

     fun meth src =

       let

         val ((raw_name, _), pos) = Args.dest_src src;

         val name = NameSpace.intern space raw_name;

       in

         (case Symtab.lookup meths name of

           NONE => error ("Unknown proof method: " ^ quote name ^ Position.str_of pos)

         | SOME ((mth, _), _) => transform_failure (curry METHOD_FAIL (name, pos)) (mth src))

       end;

   in meth end;

 (* add method *)

 fun add_methods raw_meths thy =

   let

     val new_meths = raw_meths |> map (fn (name, f, comment) =>

       (name, ((f, comment), stamp ())));

     fun add meths = NameSpace.extend_table (Sign.naming_of thy) (meths, new_meths)

       handle Symtab.DUPS dups =>

         error ("Duplicate declaration of method(s) " ^ commas_quote dups);

   in MethodsData.map add thy end;

 val add_method = add_methods o Library.single;

 fun Method name meth cmt = Context.>> (add_method (name, meth, cmt));

 (* method_setup *)

 fun method_setup (name, txt, cmt) =

   Context.use_let

     "val thm = PureThy.get_thm_closure (Context.the_context ()) o PureThy.Name;\n\

     \val thms = PureThy.get_thms_closure (Context.the_context ()) o PureThy.Name;\n\

     \val method: bstring * (Method.src -> ProofContext.context -> Proof.method) * string"

     "Method.add_method method"

     ("(" ^ Library.quote name ^ ", " ^ txt ^ ", " ^ Library.quote cmt ^ ")");

 (** concrete syntax **)

 (* basic *)

 fun syntax scan = Args.context_syntax "method" scan;

 fun simple_args scan f src ctxt : method =

   #2 (syntax (Scan.lift (scan >> (fn x => f x ctxt))) src ctxt);

 fun ctxt_args (f: ProofContext.context -> method) src ctxt =

   #2 (syntax (Scan.succeed (f ctxt)) src ctxt);

 fun no_args m = ctxt_args (K m);

 (* sections *)

 type modifier = (ProofContext.context -> ProofContext.context) * attribute;

 local

 fun sect ss = Scan.first (map Scan.lift ss);

 fun thms ss = Scan.repeat (Scan.unless (sect ss) Attrib.multi_thm) >> List.concat;

 fun apply (f, att) (context, ths) = foldl_map att (Context.map_proof f context, ths);

 fun section ss = (sect ss -- thms ss) :-- (fn (m, ths) => Scan.depend (fn context =>

   Scan.succeed (apply m (context, ths)))) >> #2;

 fun sectioned args ss = args -- Scan.repeat (section ss);

 in

 fun sectioned_args args ss f src ctxt =

   let val (ctxt', (x, _)) = syntax (sectioned args ss) src ctxt

   in f x ctxt' end;

 fun bang_sectioned_args ss f = sectioned_args Args.bang_facts ss f;

 fun bang_sectioned_args' ss scan f =

   sectioned_args (Args.bang_facts -- scan >> swap) ss (uncurry f);

 fun only_sectioned_args ss f = sectioned_args (Scan.succeed ()) ss (fn () => f);

 fun thms_ctxt_args f = sectioned_args (thms []) [] f;

 fun thms_args f = thms_ctxt_args (K o f);

 fun thm_args f = thms_args (fn [thm] => f thm | _ => error "Single theorem expected");

 end;

 (* iprover syntax *)

 local

 val introN = "intro";

 val elimN = "elim";

 val destN = "dest";

 val ruleN = "rule";

 fun modifier name kind kind' att =

   Args.$$$ name |-- (kind >> K NONE || kind' |-- Args.nat --| Args.colon >> SOME)

     >> (pair (I: ProofContext.context -> ProofContext.context) o att);

 val iprover_modifiers =

  [modifier destN Args.bang_colon Args.bang ContextRules.dest_bang,

   modifier destN Args.colon (Scan.succeed ()) ContextRules.dest,

   modifier elimN Args.bang_colon Args.bang ContextRules.elim_bang,

   modifier elimN Args.colon (Scan.succeed ()) ContextRules.elim,

   modifier introN Args.bang_colon Args.bang ContextRules.intro_bang,

   modifier introN Args.colon (Scan.succeed ()) ContextRules.intro,

   Args.del -- Args.colon >> K (I, ContextRules.rule_del)];

 in

 val iprover_meth =

   bang_sectioned_args' iprover_modifiers (Scan.lift (Scan.option Args.nat))

     (fn n => fn prems => fn ctxt => METHOD (fn facts =>

       HEADGOAL (insert_tac (prems @ facts) THEN'

       ObjectLogic.atomize_tac THEN' iprover_tac ctxt n)));

 end;

 (* tactic syntax *)

 fun nat_thms_args f = uncurry f oo

   (#2 oo syntax (Scan.lift (Scan.optional (Args.parens Args.nat) 0) -- Attrib.thms));

 val insts =

   Scan.optional

     (Args.enum1 "and" (Scan.lift (Args.name -- (Args.$$$ "=" |-- Args.!!! Args.name))) --|

       Scan.lift (Args.$$$ "in")) [] -- Attrib.thms;

 fun inst_args f src ctxt = f ctxt (#2 (syntax (Args.goal_spec HEADGOAL -- insts) src ctxt));

 val insts_var =

   Scan.optional

     (Args.enum1 "and" (Scan.lift (Args.var -- (Args.$$$ "=" |-- Args.!!! Args.name))) --|

       Scan.lift (Args.$$$ "in")) [] -- Attrib.thms;

 fun inst_args_var f src ctxt =

   f ctxt (#2 (syntax (Args.goal_spec HEADGOAL -- insts_var) src ctxt));

 fun goal_args' args tac src ctxt = #2 (syntax (Args.goal_spec HEADGOAL -- args >>

   (fn (quant, s) => SIMPLE_METHOD' quant (tac s))) src ctxt);

 fun goal_args args tac = goal_args' (Scan.lift args) tac;

 fun goal_args_ctxt' args tac src ctxt =

   #2 (syntax (Args.goal_spec HEADGOAL -- args >>

   (fn (quant, s) => SIMPLE_METHOD' quant (tac ctxt s))) src ctxt);

 fun goal_args_ctxt args tac = goal_args_ctxt' (Scan.lift args) tac;

 (* misc tactic emulations *)

 val subgoal_meth = goal_args_ctxt (Scan.repeat1 Args.name) subgoals_tac;

 val thin_meth = goal_args_ctxt Args.name thin_tac;

 val rename_meth = goal_args (Scan.repeat1 Args.name) Tactic.rename_params_tac;

 val rotate_meth = goal_args (Scan.optional Args.int 1) Tactic.rotate_tac;

 (* theory setup *)

 val _ = Context.add_setup (add_methods

  [("fail", no_args fail, "force failure"),

   ("succeed", no_args succeed, "succeed"),

   ("-", no_args insert_facts, "do nothing (insert current facts only)"),

   ("insert", thms_args insert, "insert theorems, ignoring facts (improper)"),

   ("intro", thms_args intro, "repeatedly apply introduction rules"),

   ("elim", thms_args elim, "repeatedly apply elimination rules"),

   ("unfold", thms_ctxt_args unfold_meth, "unfold definitions"),

   ("fold", thms_ctxt_args fold_meth, "fold definitions"),

   ("atomize", (atomize o #2) oo syntax (Args.mode "full"),

     "present local premises as object-level statements"),

   ("iprover", iprover_meth, "intuitionistic proof search"),

   ("rule", thms_ctxt_args some_rule, "apply some intro/elim rule"),

   ("erule", nat_thms_args erule, "apply rule in elimination manner (improper)"),

   ("drule", nat_thms_args drule, "apply rule in destruct manner (improper)"),

   ("frule", nat_thms_args frule, "apply rule in forward manner (improper)"),

   ("this", no_args this, "apply current facts as rules"),

   ("fact", thms_ctxt_args fact, "composition by facts from context"),

   ("assumption", ctxt_args assumption, "proof by assumption, preferring facts"),

   ("rule_tac", inst_args_var res_inst_meth, "apply rule (dynamic instantiation)"),

   ("erule_tac", inst_args_var eres_inst_meth, "apply rule in elimination manner (dynamic instantiation)"),

   ("drule_tac", inst_args_var dres_inst_meth, "apply rule in destruct manner (dynamic instantiation)"),

   ("frule_tac", inst_args_var forw_inst_meth, "apply rule in forward manner (dynamic instantiation)"),

   ("cut_tac", inst_args_var cut_inst_meth, "cut rule (dynamic instantiation)"),

   ("subgoal_tac", subgoal_meth, "insert subgoal (dynamic instantiation)"),

   ("thin_tac", thin_meth, "remove premise (dynamic instantiation)"),

   ("rename_tac", rename_meth, "rename parameters of goal (dynamic instantiation)"),

   ("rotate_tac", rotate_meth, "rotate assumptions of goal"),

   ("tactic", simple_args Args.name tactic, "ML tactic as proof method")]);

 (*final declarations of this structure!*)

 val unfold = unfold_meth;

 val fold = fold_meth;

 end;

 structure BasicMethod: BASIC_METHOD = Method;

 open BasicMethod;