(*  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 LIFT: tactic -> thm -> (thm * (indexname * term) list * (string * tthm list) list) Seq.seq

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

  val METHOD0: tactic -> Proof.method

  val fail: Proof.method

  val succeed: Proof.method

  val trivial: Proof.method

  val assumption: Proof.method

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

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

  val rule: tthm list -> Proof.method

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

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

    -> theory -> theory

  datatype text =

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

    Source of Args.src |

    Then of text list |

    Orelse of text list |

    Try of text |

    Repeat of text |

    Repeat1 of text

  val dynamic_method: string -> (Proof.context -> Proof.method)

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

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

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

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

  val end_block: Proof.state -> Proof.state Seq.seq

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

  val trivial_proof: Proof.state -> Proof.state Seq.seq

  val default_proof: Proof.state -> Proof.state Seq.seq

  val qed: bstring option -> theory attribute list option -> Proof.state

    -> theory * (string * string * tthm)

  val syntax: (Args.T list -> 'a * Args.T list) -> ('a -> 'b) -> Args.src -> 'b

  val no_args: 'a -> Args.src -> Proof.context -> 'a

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

  val sectioned_args: (Proof.context -> 'a) -> ('a * tthm list -> 'b) ->

    (string * ('b * tthm list -> 'b)) list -> ('b -> 'c) -> Args.src -> Proof.context -> 'c

  val setup: (theory -> theory) list

end;

structure Method: METHOD =

struct

(** proof methods **)

(* method from tactic *)

fun LIFT tac goal = Seq.map (fn x => (x, [], [])) (tac goal);

fun METHOD tacf = Proof.method (LIFT o tacf);

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);

(* trivial, assumption *)

fun trivial_tac [] = K all_tac

  | trivial_tac facts =

      let

        val thms = map Attribute.thm_of facts;

        val r = ~ (length facts);

      in metacuts_tac thms THEN' rotate_tac r end;

val trivial = METHOD (ALLGOALS o trivial_tac);

val assumption = METHOD (fn facts => FIRSTGOAL (trivial_tac facts THEN' assume_tac));

val asm_finish = METHOD (K (TRYALL assume_tac));

(* rule *)

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

fun multi_resolve facts rule =

  let

    fun multi_res i [] = Seq.single rule

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

  in multi_res 1 facts end;

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

fun rule_tac rules [] = resolve_tac (map Attribute.thm_of rules)

  | rule_tac erules facts =

      let

        val rules = forward_chain (map Attribute.thm_of facts) (map Attribute.thm_of erules);

        fun tac i state = Seq.flat (Seq.map (fn rule => Tactic.rtac rule i state) rules);

      in tac end;

fun rule rules = METHOD (FIRSTGOAL o rule_tac rules);

(** 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 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 (NameSpace.cond_extern space name ^ ":"), Pretty.brk 2, Pretty.str comment];

    in

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

      Pretty.writeln (Pretty.big_list "methods:" (map prt_meth (Symtab.dest meths)))

    end;

end;

structure MethodsData = TheoryDataFun(MethodsDataArgs);

val print_methods = MethodsData.print;

(* get methods *)

fun method thy =

  let

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

    fun meth ((raw_name, args), pos) =

      let 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, _), _) => mth ((name, args), pos))

      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)]);

(* argument syntax *)

val methodN = "method";

fun syntax scan = Args.syntax methodN scan;

fun no_args x = syntax (Scan.succeed (fn (_: Proof.context) => x)) I;

(* FIXME move? *)

fun thm_args f = syntax (Scan.repeat Args.name)

  (fn names => fn ctxt => f (ProofContext.get_tthmss ctxt names));

fun sectioned_args get_data def_sect sects f =

  syntax (Args.sectioned (map fst sects))

    (fn (names, sect_names) => fn ctxt =>

      let

        val get_thms = ProofContext.get_tthmss ctxt;

        val thms = get_thms names;

        val sect_thms = map (apsnd get_thms) sect_names;

        fun apply_sect (data, (s, ths)) =

          (case assoc (sects, s) of

            Some add => add (data, ths)

          | None => error ("Unknown argument section " ^ quote s));

       in f (foldl apply_sect (def_sect (get_data ctxt, thms), sect_thms)) end);

(** 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 |

  Repeat of text |

  Repeat1 of text;

(* dynamic methods *)

fun dynamic_method name = (fn ctxt =>

  method (ProofContext.theory_of ctxt) ((name, []), Position.none) ctxt);

(* refine *)

fun refine text state =

  let

    val thy = Proof.theory_of state;

    fun eval (Basic mth) = Proof.refine mth

      | eval (Source src) = Proof.refine (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 (Repeat txt) = Seq.REPEAT (eval txt)

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

  in eval text state end;

(* unstructured steps *)

fun tac text state =

  state

  |> Proof.goal_facts (K [])

  |> refine text;

fun etac text state =

  state

  |> Proof.goal_facts Proof.the_facts

  |> refine text;

(* proof steps *)

val default_txt = Source (("default", []), Position.none);

val finishN = "finish";

fun proof opt_text state =

  state

  |> Proof.assert_backward

  |> refine (if_none opt_text default_txt)

  |> Seq.map Proof.enter_forward;

(* conclusions *)

val end_block = Proof.end_block (dynamic_method finishN);

fun terminal_proof text = Seq.THEN (proof (Some text), end_block);

val trivial_proof = terminal_proof (Basic (K trivial));

val default_proof = terminal_proof default_txt;

val qed = Proof.qed (dynamic_method finishN);

(** theory setup **)

(* pure_methods *)

val pure_methods =

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

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

  ("trivial", no_args trivial, "proof all goals trivially"),

  ("assumption", no_args assumption, "proof by assumption"),

  ("finish", no_args asm_finish, "finish proof by assumption"),

  ("rule", thm_args rule, "apply primitive rule")];

(* setup *)

val setup = [MethodsData.init, add_methods pure_methods];

end;

structure BasicMethod: BASIC_METHOD = Method;

open BasicMethod;