(*  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 multi_resolveq: thm list -> thm Seq.seq -> thm Seq.seq

  val resolveq_tac: thm Seq.seq -> int -> tactic

  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

  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 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 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 -> 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_resolveq facts rules = Seq.flat (Seq.map (multi_resolve facts) rules);

fun multi_resolves facts = multi_resolveq facts o Seq.of_list;

end;

(* rule *)

fun gen_resolveq_tac tac rules i st =

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

val resolveq_tac = gen_resolveq_tac Tactic.resolve_tac;

local

fun gen_rule_tac tac rules [] = tac rules

  | gen_rule_tac tac erules facts = gen_resolveq_tac tac (multi_resolves facts erules);

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;

(* 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: Proof.context -> thm list -> tactic) ctxt facts = " ^ txt ^

     "in Method.set_tactic tactic end")

    false (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_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 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 (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"),

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

(* 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;