(*  Title:      Pure/Isar/method.ML

    ID:         $Id$

    Author:     Markus Wenzel, TU Muenchen

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

  type src

  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 option) list) Seq.seq) -> Proof.method

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

  val METHOD_CASES:

    (thm list -> thm -> (thm * (string * RuleCases.T option) 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 -> src -> Proof.context -> Proof.method

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

    -> theory -> theory

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

    -> theory -> theory

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

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

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

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

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

  val no_args: Proof.method -> 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) -> src -> Proof.context -> 'b

  val bang_sectioned_args:

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

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

  val only_sectioned_args:

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

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

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

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

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

  datatype text =

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

    Source of 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)

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

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

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

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

    -> 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) -> src -> Proof.context -> Proof.method

end;

structure Method: METHOD =

struct

type src = Args.src;

(** 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_meth ths = SIMPLE_METHOD (CHANGED_PROP (rewrite_goals_tac ths));

fun fold_meth 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 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;

(* this *)

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

(* assumption *)

fun asm_tac ths =

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

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 = 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 (sign, sorts) s;

            val U = TVar (xi, S);

        in if Sign.typ_instance sign (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 assoc (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 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)

        val lifttvar = pairself (ctyp_of sign o incr_tvar inc);

        val rule = Drule.instantiate

              (map lifttvar envT', 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: Proof.context) (facts: thm list) : tactic = \

     \let val thm = ProofContext.get_thm_closure ctxt o rpair NONE\n\

     \  and thms = ProofContext.get_thms_closure ctxt o rpair NONE in\n"

     ^ txt ^

     "\nend in 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: (((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.extern_table space meths))]

      |> Pretty.chunks |> Pretty.writeln

    end;

end;

structure MethodsData = TheoryDataFun(MethodsDataArgs);

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(s) *)

fun add_methods raw_meths thy =

  let

    val sg = Theory.sign_of thy;

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

      (Sign.full_name sg name, ((f, comment), stamp ())));

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

    val space' = fold (Sign.declare_name sg) (map fst new_meths) space;

    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) >> List.concat;

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 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);

(* 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_meth, "unfold definitions"),

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

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

  ("fold", thms_args fold_meth, "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")];

val _ = Context.add_setup [add_methods pure_methods];

(*final declarations of this structure!*)

val unfold = unfold_meth;

val fold = fold_meth;

end;

structure BasicMethod: BASIC_METHOD = Method;

open BasicMethod;