(*  Title:      Pure/Isar/method.ML

     ID:         $Id$

     Author:     Markus Wenzel, TU Muenchen

 Proof methods.

 *)

 signature BASIC_METHOD =

 sig

   val print_methods: theory -> unit

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

 end;

 signature METHOD =

 sig

   include BASIC_METHOD

   val print_global_rules: theory -> unit

   val print_local_rules: Proof.context -> unit

   val dest_global: theory attribute

   val elim_global: theory attribute

   val intro_global: theory attribute

   val delrule_global: theory attribute

   val dest_local: Proof.context attribute

   val elim_local: Proof.context attribute

   val intro_local: Proof.context attribute

   val delrule_local: Proof.context attribute

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

   val METHOD0: 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 rule_tac: thm list -> thm list -> int -> tactic

   val rule: thm list -> Proof.method

   val erule: thm list -> Proof.method

   val drule: thm list -> Proof.method

   val frule: thm list -> Proof.method

   val this: Proof.method

   val assumption: Proof.context -> Proof.method

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

   val help_methods: theory option -> unit

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

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

   val bang_sectioned_args:

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

     (thm list -> Proof.context -> Proof.method) -> Args.src -> Proof.context -> Proof.method

   val only_sectioned_args:

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

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

   val thms_ctxt_args: (thm list -> Proof.context -> Proof.method)

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

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

   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: text option

     -> ({kind: string, name: string, thm: thm} -> unit) * (thm -> unit)

     -> Proof.state -> Proof.state Seq.seq

   val local_terminal_proof: text * text option

     -> ({kind: string, name: string, thm: thm} -> unit) * (thm -> unit)

     -> Proof.state -> Proof.state Seq.seq

   val local_immediate_proof: ({kind: string, name: string, thm: thm} -> unit) * (thm -> unit)

     -> Proof.state -> Proof.state Seq.seq

   val local_default_proof: ({kind: string, name: string, thm: thm} -> unit) * (thm -> unit)

     -> Proof.state -> Proof.state Seq.seq

   val global_qed: text option -> Proof.state -> theory * {kind: string, name: string, thm: thm}

   val global_terminal_proof: text * text option

     -> Proof.state -> theory * {kind: string, name: string, thm: thm}

   val global_immediate_proof: Proof.state -> theory * {kind: string, name: string, thm: thm}

   val global_default_proof: Proof.state -> theory * {kind: string, name: string, thm: thm}

   val setup: (theory -> theory) list

 end;

 structure Method: METHOD =

 struct

 (** global and local rule data **)

 fun prt_rules kind ths =

   Pretty.writeln (Pretty.big_list ("standard " ^ kind ^ " rules:") (map Display.pretty_thm ths));

 fun print_rules (intro, elim) =

   (prt_rules "introduction" intro; prt_rules "elimination" elim);

 fun merge_rules (ths1, ths2) = Library.generic_merge Thm.eq_thm I I ths1 ths2;

 (* theory data kind 'Isar/rules' *)

 structure GlobalRulesArgs =

 struct

   val name = "Isar/rules";

   type T = thm list * thm list;

   val empty = ([], []);

   val copy = I;

   val prep_ext = I;

   fun merge ((intro1, elim1), (intro2, elim2)) =

     (merge_rules (intro1, intro2), merge_rules (elim1, elim2));

   fun print _ = print_rules;

 end;

 structure GlobalRules = TheoryDataFun(GlobalRulesArgs);

 val print_global_rules = GlobalRules.print;

 (* proof data kind 'Isar/rules' *)

 structure LocalRulesArgs =

 struct

   val name = "Isar/rules";

   type T = thm list * thm list;

   val init = GlobalRules.get;

   fun print _ = print_rules;

 end;

 structure LocalRules = ProofDataFun(LocalRulesArgs);

 val print_local_rules = LocalRules.print;

 (** attributes **)

 (* add rules *)

 local

 fun add_rule thm rules = Library.gen_ins Thm.eq_thm (thm, rules);

 fun del_rule thm rules = Library.gen_rem Thm.eq_thm (rules, thm);

 fun add_dest thm (intro, elim) = (intro, add_rule (Tactic.make_elim thm) elim);

 fun add_elim thm (intro, elim) = (intro, add_rule thm elim);

 fun add_intro thm (intro, elim) = (add_rule thm intro, elim);

 fun delrule thm (intro, elim) = (del_rule thm intro, del_rule thm elim);

 fun mk_att f g (x, thm) = (f (g thm) x, thm);

 in

 val dest_global = mk_att GlobalRules.map add_dest;

 val elim_global = mk_att GlobalRules.map add_elim;

 val intro_global = mk_att GlobalRules.map add_intro;

 val delrule_global = mk_att GlobalRules.map delrule;

 val dest_local = mk_att LocalRules.map add_dest;

 val elim_local = mk_att LocalRules.map add_elim;

 val intro_local = mk_att LocalRules.map add_intro;

 val delrule_local = mk_att LocalRules.map delrule;

 end;

 (* concrete syntax *)

 val rule_atts =

  [("dest", (Attrib.no_args dest_global, Attrib.no_args dest_local), "destruction rule"),

   ("elim", (Attrib.no_args elim_global, Attrib.no_args elim_local), "elimination rule"),

   ("intro", (Attrib.no_args intro_global, Attrib.no_args intro_local), "introduction rule"),

   ("delrule", (Attrib.no_args delrule_global, Attrib.no_args delrule_local), "delete rule")];

 (** proof methods **)

 (* method from tactic *)

 val METHOD = Proof.method;

 fun METHOD0 tac = METHOD (fn [] => tac | _ => error "Method may not be used with 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));

 end;

 (* unfold / fold definitions *)

 fun unfold thms = METHOD (fn facts => ALLGOALS (insert_tac facts) THEN rewrite_goals_tac thms);

 fun fold thms = METHOD (fn facts => ALLGOALS (insert_tac facts) THEN fold_goals_tac thms);

 (* 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;

 (* rule *)

 local

 fun gen_rule_tac tac rules [] = tac rules

   | gen_rule_tac tac erules facts =

       let

         val rules = multi_resolves facts erules;

         fun tactic i state = Seq.flat (Seq.map (fn rule => tac [rule] i state) rules);

       in tactic end;

 fun gen_rule tac rules = METHOD (FINDGOAL o tac rules);

 fun gen_rule' tac arg_rules ctxt = METHOD (fn facts =>

   let val rules =

     if not (null arg_rules) then arg_rules

     else if null facts then #1 (LocalRules.get ctxt)

     else op @ (LocalRules.get ctxt);

   in FINDGOAL (tac rules facts) end);

 fun setup raw_tac =

   let val tac = gen_rule_tac raw_tac

   in (tac, gen_rule tac, gen_rule' tac) end;

 in

 val (rule_tac, rule, some_rule) = setup Tactic.resolve_tac;

 val (erule_tac, erule, some_erule) = setup Tactic.eresolve_tac;

 val (drule_tac, drule, some_drule) = setup Tactic.dresolve_tac;

 val (frule_tac, frule, some_frule) = setup Tactic.forward_tac;

 end;

 (* this *)

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

 (* assumption *)

 fun assm_tac ctxt =

   assume_tac APPEND' resolve_tac (filter Thm.no_prems (ProofContext.prems_of ctxt));

 fun assumption_tac ctxt [] = assm_tac ctxt

   | assumption_tac _ [fact] = resolve_tac [fact]

   | assumption_tac _ _ = K no_tac;

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

 (* res_inst_tac emulations *)

 (*Note: insts refer to the implicit (!) goal context; use at your own risk*)

 fun gen_res_inst tac ((i, insts), thm) =

   METHOD (fn facts => (insert_tac facts THEN' tac insts thm) i);

 val res_inst = gen_res_inst Tactic.res_inst_tac;

 val eres_inst = gen_res_inst Tactic.eres_inst_tac;

 val dres_inst = gen_res_inst Tactic.dres_inst_tac;

 val forw_inst = gen_res_inst Tactic.forw_inst_tac;

 (* 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;

 (** 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_meths verbose {space, meths} =

     let

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

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

     in

       if not verbose then ()

       else Pretty.writeln (Display.pretty_name_space ("method name space", space));

       Pretty.writeln (Pretty.big_list "methods:"

         (map prt_meth (NameSpace.cond_extern_table space meths)))

     end;

   fun print _ = print_meths true;

 end;

 structure MethodsData = TheoryDataFun(MethodsDataArgs);

 val print_methods = MethodsData.print;

 fun help_methods None = writeln "methods: (unkown theory context)"

   | help_methods (Some thy) = MethodsDataArgs.print_meths false (MethodsData.get thy);

 (* 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_methods *)

 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;

 (*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 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 (fn s => Scan.lift (s --| Args.$$$ ":")) 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 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);

 end;

 (* insts *)

 val insts =

   Scan.lift (Scan.optional (Args.$$$ "(" |-- Args.!!! (Args.nat --| Args.$$$ ")")) 1) --

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

     (Scan.lift (Args.$$$ "in") |-- Attrib.local_thm);

 fun inst_args f = f oo (#2 oo syntax insts);

 (** 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);

 fun finish ctxt = METHOD (K (FILTER Thm.no_prems (ALLGOALS (assm_tac ctxt) THEN flexflex_tac)));

 fun finish_text None = Basic finish

   | finish_text (Some txt) = Then [txt, Basic finish];

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

 fun local_terminal_proof (text, opt_text) pr = Seq.THEN (proof (Some text), local_qed opt_text pr);

 val local_immediate_proof = local_terminal_proof (this_text, None);

 val local_default_proof = local_terminal_proof (default_text, None);

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

 fun global_qed opt_text state =

   state

   |> global_qeds opt_text

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

   |> Seq.hd;

 fun global_terminal_proof (text, opt_text) state =

   state

   |> proof (Some text)

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

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

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

   |> Seq.hd;

 val global_immediate_proof = global_terminal_proof (this_text, None);

 val global_default_proof = global_terminal_proof (default_text, None);

 (** theory setup **)

 (* pure_methods *)

 val pure_methods =

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

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

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

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

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

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

   ("default", thms_ctxt_args some_rule, "apply some rule"),

   ("rule", thms_ctxt_args some_rule, "apply some rule"),

   ("erule", thms_ctxt_args some_erule, "apply some rule in elimination manner (improper!)"),

   ("drule", thms_ctxt_args some_drule, "apply some rule in destruct manner (improper!)"),

   ("frule", thms_ctxt_args some_frule, "apply some rule in forward manner (improper!)"),

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

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

   ("res_inst_tac", inst_args res_inst, "res_inst_tac emulation (beware!)"),

   ("eres_inst_tac", inst_args eres_inst, "eres_inst_tac emulation (beware!)"),

   ("dres_inst_tac", inst_args dres_inst, "dres_inst_tac emulation (beware!)"),

   ("forw_inst_tac", inst_args forw_inst, "forw_inst_tac emulation (beware!)"),

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

 (* setup *)

 val setup =

  [GlobalRules.init, LocalRules.init, Attrib.add_attributes rule_atts,

   MethodsData.init, add_methods pure_methods];

 end;

 structure BasicMethod: BASIC_METHOD = Method;

 open BasicMethod;