(*  Title:      Pure/Isar/method.ML

     ID:         $Id$

     Author:     Markus Wenzel, TU Muenchen

     License:    GPL (GNU GENERAL PUBLIC LICENSE)

 Proof methods.

 *)

 signature BASIC_METHOD =

 sig

   val trace_rules: bool ref

   val print_methods: theory -> unit

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

 end;

 signature METHOD =

 sig

   include BASIC_METHOD

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

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

   val RAW_METHOD_CASES:

     (thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq) -> Proof.method

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

   val METHOD_CASES:

     (thm list -> thm -> (thm * (string * RuleCases.T) list) Seq.seq) -> Proof.method

   val SIMPLE_METHOD: tactic -> Proof.method

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

   val fail: Proof.method

   val succeed: Proof.method

   val defer: int option -> Proof.method

   val prefer: int -> Proof.method

   val insert_tac: thm list -> int -> tactic

   val insert: thm list -> Proof.method

   val insert_facts: Proof.method

   val unfold: thm list -> Proof.method

   val fold: thm list -> Proof.method

   val multi_resolve: thm list -> thm -> thm Seq.seq

   val multi_resolves: thm list -> thm list -> thm Seq.seq

   val rules_tac: Proof.context -> int option -> int -> tactic

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

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

   val rule: thm list -> Proof.method

   val erule: int -> thm list -> Proof.method

   val drule: int -> thm list -> Proof.method

   val frule: int -> thm list -> Proof.method

   val this: Proof.method

   val assumption: Proof.context -> Proof.method

   val bires_inst_tac: bool -> Proof.context -> (indexname * string) list -> thm -> int -> tactic

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

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

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

   val method: theory -> Args.src -> Proof.context -> Proof.method

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

     -> theory -> theory

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

     -> theory -> theory

   val syntax: (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list)) ->

     Args.src -> Proof.context -> Proof.context * 'a

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

     -> ('a -> Proof.context -> Proof.method) -> Args.src -> Proof.context -> Proof.method

   val ctxt_args: (Proof.context -> Proof.method) -> Args.src -> Proof.context -> Proof.method

   val no_args: Proof.method -> Args.src -> Proof.context -> Proof.method

   type modifier

   val sectioned_args: (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list)) ->

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

     ('a -> Proof.context -> 'b) -> Args.src -> Proof.context -> 'b

   val bang_sectioned_args:

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

     (thm list -> Proof.context -> 'a) -> Args.src -> Proof.context -> 'a

   val bang_sectioned_args':

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

     (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list)) ->

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

   val only_sectioned_args:

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

     (Proof.context -> 'a) -> Args.src -> Proof.context -> 'a

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

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

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

   datatype text =

     Basic of (Proof.context -> Proof.method) |

     Source of Args.src |

     Then of text list |

     Orelse of text list |

     Try of text |

     Repeat1 of text

   val refine: text -> Proof.state -> Proof.state Seq.seq

   val refine_end: text -> Proof.state -> Proof.state Seq.seq

   val proof: text option -> Proof.state -> Proof.state Seq.seq

   val local_qed: bool -> text option

     -> (Proof.context -> string * (string * thm list) list -> unit) *

       (Proof.context -> thm -> unit) -> Proof.state -> Proof.state Seq.seq

   val local_terminal_proof: text * text option

     -> (Proof.context -> string * (string * thm list) list -> unit) *

       (Proof.context -> thm -> unit) -> Proof.state -> Proof.state Seq.seq

   val local_default_proof: (Proof.context -> string * (string * thm list) list -> unit) *

     (Proof.context -> thm -> unit) -> Proof.state -> Proof.state Seq.seq

   val local_immediate_proof: (Proof.context -> string * (string * thm list) list -> unit) *

     (Proof.context -> thm -> unit) -> Proof.state -> Proof.state Seq.seq

   val local_done_proof: (Proof.context -> string * (string * thm list) list -> unit) *

     (Proof.context -> thm -> unit) -> Proof.state -> Proof.state Seq.seq

   val global_qed: bool -> text option

     -> Proof.state -> theory * ((string * string) * (string * thm list) list)

   val global_terminal_proof: text * text option

     -> Proof.state -> theory * ((string * string) * (string * thm list) list)

   val global_default_proof: Proof.state -> theory * ((string * string) * (string * thm list) list)

   val global_immediate_proof: Proof.state ->

     theory * ((string * string) * (string * thm list) list)

   val global_done_proof: Proof.state -> theory * ((string * string) * (string * thm list) list)

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

     -> Args.src -> Proof.context -> Proof.method

   val goal_args': (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list))

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

   val goal_args_ctxt: (Args.T list -> 'a * Args.T list) -> (Proof.context -> 'a -> int -> tactic)

     -> Args.src -> Proof.context -> Proof.method

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

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

   val setup: (theory -> theory) list

 end;

 structure Method: METHOD =

 struct

 (** proof methods **)

 (* tracing *)

 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);

 (* make methods *)

 val RAW_METHOD = Proof.method;

 val RAW_METHOD_CASES = Proof.method_cases;

 fun METHOD m = Proof.method (fn facts => TRY Tactic.conjunction_tac THEN m facts);

 fun METHOD_CASES m =

   Proof.method_cases (fn facts => Seq.THEN (TRY Tactic.conjunction_tac, m facts));

 (* primitive *)

 val fail = METHOD (K no_tac);

 val succeed = METHOD (K all_tac);

 (* shuffle *)

 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 (if_none opt_i 1)));

 (* insert *)

 local

 fun cut_rule_tac raw_rule =

   let

     val rule = Drule.forall_intr_vars raw_rule;

     val revcut_rl = Drule.incr_indexes_wrt [] [] [] [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;

 (* unfold/fold definitions *)

 fun unfold ths = SIMPLE_METHOD (CHANGED_PROP (rewrite_goals_tac ths));

 fun fold ths = SIMPLE_METHOD (CHANGED_PROP (fold_goals_tac 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)));

 (* 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));

 (* multi_resolve *)

 local

 fun res th i rule =

   Thm.biresolution false [(false, th)] i rule handle THM _ => Seq.empty;

 fun multi_res _ [] rule = Seq.single rule

   | multi_res i (th :: ths) rule = Seq.flat (Seq.map (res th i) (multi_res (i + 1) ths rule));

 in

 val multi_resolve = multi_res 1;

 fun multi_resolves facts rules = Seq.flat (Seq.map (multi_resolve facts) (Seq.of_list rules));

 end;

 (* rules_tac *)

 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 intpr_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 gen_mem (fn ((ps1, c1), (ps2, c2)) =>

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

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

   end);

 in

 fun rules_tac ctxt opt_lim =

   SELECT_GOAL (DEEPEN (2, if_none opt_lim 20) (intpr_tac ctxt [] 0) 4 1);

 end;

 (* rule_tac etc. *)

 local

 fun gen_rule_tac tac rules [] i st = tac rules i st

   | gen_rule_tac tac rules facts i st =

       Seq.flat (Seq.map (fn rule => (tac o single) rule i st) (multi_resolves facts rules));

 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 flat (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;

 (* this *)

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

 (* assumption *)

 fun asm_tac ths =

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

 fun assm_tac ctxt =

   assume_tac APPEND'

   asm_tac (ProofContext.prems_of ctxt) APPEND'

   Tactic.rtac Drule.reflexive_thm;

 fun assumption_tac ctxt [] = assm_tac ctxt

   | assumption_tac _ [fact] = asm_tac [fact]

   | assumption_tac _ _ = K no_tac;

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

 (* res_inst_tac etc. *)

 (* Reimplemented to support both static (Isar) and dynamic (proof state)

    context.  By Clemens Ballarin. *)

 fun bires_inst_tac bires_flag ctxt insts thm =

   let

     val sign = ProofContext.sign_of ctxt;

     (* Separate type and term insts *)

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

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

     val Tinsts = 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 (sign, sorts) s;

         in if Sign.typ_instance sign (T, TVar (xi, S)) then (xi, 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_TVars 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 assoc (params, a) of

                 None => types (a, ~1)

               | some => some)

           | types' xi = types xi;

         val used = add_term_tvarnames

                   (prop_of st $ prop_of thm,[])

 	val (ts, envT) =

 	  ProofContext.read_termTs_env (types', sorts, used) ctxt (ss ~~ Ts);

 	val cenvT = map (apsnd (Thm.ctyp_of sign)) (envT @ Tinsts_env);

 	val cenv =

 	  map

 	    (fn (xi, t) =>

 	      pairself (Thm.cterm_of sign) (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 ---> 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)

 	fun lifttvar((a,i),ctyp) =

 	    let val {T,sign} = rep_ctyp ctyp

 	    in  ((a,i+inc), ctyp_of sign (incr_tvar inc T)) end

 	val rule = Drule.instantiate

 	      (map lifttvar cenvT, map liftpair cenv)

 	      (lift_rule (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;

 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";

 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;

 (* 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 (Theory.sign_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]);

 val cut_inst_meth =

   gen_inst

     (fn ctxt => fn insts => fn thm =>

        bires_inst_tac false ctxt insts (make_elim_preserve thm))

     Tactic.cut_rules_tac;

 val dres_inst_meth =

   gen_inst

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

        bires_inst_tac true ctxt insts (make_elim_preserve rule))

     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 THEN'

   SUBGOAL (fn (prop, _) =>

     let val concl' = Logic.strip_assums_concl prop in

       if null (term_tvars concl') then ()

       else warning "Type variables in new subgoal: add a type constraint?";

       all_tac

   end);

 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;

 (* simple Prolog interpreter *)

 fun prolog_tac rules facts =

   DEPTH_SOLVE_1 (HEADGOAL (Tactic.assume_tac APPEND' Tactic.resolve_tac (facts @ rules)));

 val prolog = METHOD o prolog_tac;

 (* ML tactics *)

 val tactic_ref = ref ((fn _ => raise Match): Proof.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: PureIsar.Proof.context) (facts: thm list) : tactic = \

      \let val thm = PureIsar.ProofContext.get_thm_closure ctxt\n\

      \  and thms = PureIsar.ProofContext.get_thms_closure ctxt in\n"

      ^ txt ^

      "\nend in PureIsar.Method.set_tactic tactic end")

     false None;

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

 (** methods theory data **)

 (* data kind 'Isar/methods' *)

 structure MethodsDataArgs =

 struct

   val name = "Isar/methods";

   type T =

     {space: NameSpace.T,

      meths: (((Args.src -> Proof.context -> Proof.method) * string) * stamp) Symtab.table};

   val empty = {space = NameSpace.empty, meths = Symtab.empty};

   val copy = I;

   val prep_ext = I;

   fun merge ({space = space1, meths = meths1}, {space = space2, meths = meths2}) =

     {space = NameSpace.merge (space1, space2),

       meths = Symtab.merge eq_snd (meths1, meths2) handle Symtab.DUPS dups =>

         error ("Attempt to merge different versions of methods " ^ commas_quote dups)};

   fun print _ {space, 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.cond_extern_table space meths))]

       |> Pretty.chunks |> Pretty.writeln

     end;

 end;

 structure MethodsData = TheoryDataFun(MethodsDataArgs);

 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(s) *)

 fun add_methods raw_meths thy =

   let

     val full = Sign.full_name (Theory.sign_of thy);

     val new_meths =

       map (fn (name, f, comment) => (full name, ((f, comment), stamp ()))) raw_meths;

     val {space, meths} = MethodsData.get thy;

     val space' = NameSpace.extend (space, map fst new_meths);

     val meths' = Symtab.extend (meths, new_meths) handle Symtab.DUPS dups =>

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

   in

     thy |> MethodsData.put {space = space', meths = meths'}

   end;

 val add_method = add_methods o Library.single;

 (*implicit version*)

 fun Method name meth cmt = Context.>> (add_methods [(name, meth, cmt)]);

 (** method syntax **)

 (* basic *)

 fun syntax (scan: (Proof.context * Args.T list -> 'a * (Proof.context * Args.T list))) =

   Args.syntax "method" scan;

 fun simple_args scan f src ctxt : Proof.method =

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

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

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

 fun no_args m = ctxt_args (K m);

 (* sections *)

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

 local

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

 fun thms ss = Scan.unless (sect ss) Attrib.local_thms;

 fun thmss ss = Scan.repeat (thms ss) >> flat;

 fun apply (f, att) (ctxt, ths) = Thm.applys_attributes ((f ctxt, ths), [att]);

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

   Scan.succeed (apply m (ctxt, 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 (thmss []) [] 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;

 (* rules 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: Proof.context -> Proof.context) o att);

 val rules_modifiers =

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

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

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

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

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

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

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

 in

 fun rules_args m = bang_sectioned_args' rules_modifiers (Scan.lift (Scan.option Args.nat)) m;

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

   HEADGOAL (insert_tac (prems @ facts) THEN' ObjectLogic.atomize_tac THEN' rules_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.local_thmss));

 val insts =

   Scan.optional

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

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

 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.local_thmss;

 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;

 (** method text **)

 (* datatype text *)

 datatype text =

   Basic of (Proof.context -> Proof.method) |

   Source of Args.src |

   Then of text list |

   Orelse of text list |

   Try of text |

   Repeat1 of text;

 (* refine *)

 fun gen_refine f text state =

   let

     val thy = Proof.theory_of state;

     fun eval (Basic mth) = f mth

       | eval (Source src) = f (method thy src)

       | eval (Then txts) = Seq.EVERY (map eval txts)

       | eval (Orelse txts) = Seq.FIRST (map eval txts)

       | eval (Try txt) = Seq.TRY (eval txt)

       | eval (Repeat1 txt) = Seq.REPEAT1 (eval txt);

   in eval text state end;

 val refine = gen_refine Proof.refine;

 val refine_end = gen_refine Proof.refine_end;

 (* structured proof steps *)

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

 val this_text = Basic (K this);

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

 fun close_text asm = Basic (fn ctxt => METHOD (K

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

 fun finish_text asm None = close_text asm

   | finish_text asm (Some txt) = Then [txt, close_text asm];

 fun proof opt_text state =

   state

   |> Proof.assert_backward

   |> refine (if_none opt_text default_text)

   |> Seq.map (Proof.goal_facts (K []))

   |> Seq.map Proof.enter_forward;

 fun local_qed asm opt_text = Proof.local_qed (refine (finish_text asm opt_text));

 fun local_terminal_proof (text, opt_text) pr =

   Seq.THEN (proof (Some text), local_qed true opt_text pr);

 val local_default_proof = local_terminal_proof (default_text, None);

 val local_immediate_proof = local_terminal_proof (this_text, None);

 fun local_done_proof pr = Seq.THEN (proof (Some done_text), local_qed false None pr);

 fun global_qeds asm opt_text = Proof.global_qed (refine (finish_text asm opt_text));

 fun global_qed asm opt_text state =

   state

   |> global_qeds asm opt_text

   |> Proof.check_result "Failed to finish proof" state

   |> Seq.hd;

 fun global_term_proof asm (text, opt_text) state =

   state

   |> proof (Some text)

   |> Proof.check_result "Terminal proof method failed" state

   |> (Seq.flat o Seq.map (global_qeds asm opt_text))

   |> Proof.check_result "Failed to finish proof (after successful terminal method)" state

   |> Seq.hd;

 val global_terminal_proof = global_term_proof true;

 val global_default_proof = global_terminal_proof (default_text, None);

 val global_immediate_proof = global_terminal_proof (this_text, None);

 val global_done_proof = global_term_proof false (done_text, None);

 (** theory setup **)

 (* 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;

 (* pure_methods *)

 val pure_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)"),

   ("unfold", thms_args unfold, "unfold definitions"),

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

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

   ("fold", thms_args fold, "fold definitions"),

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

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

   ("rules", rules_args rules_meth, "apply many rules, including 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"),

   ("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"),

   ("prolog", thms_args prolog, "simple prolog interpreter"),

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

 (* setup *)

 val setup =

  [MethodsData.init, add_methods pure_methods,

   (#1 o PureThy.add_thms [(("", Drule.equal_intr_rule), [ContextRules.intro_query_global None])])];

 end;

 structure BasicMethod: BASIC_METHOD = Method;

 open BasicMethod;