(*  Title:      Pure/Isar/method.ML

    ID:         $Id$

    Author:     Markus Wenzel, TU Muenchen

Isar proof methods.

*)

signature BASIC_METHOD =

sig

  val FINDGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq

  val HEADGOAL: (int -> thm -> 'a Seq.seq) -> thm -> 'a Seq.seq

  type method

  val trace_rules: bool ref

  val print_methods: theory -> unit

end;

signature METHOD =

sig

  include BASIC_METHOD

  val apply: Position.T -> (Proof.context -> method) -> Proof.context -> thm list -> cases_tactic

  val RAW_METHOD_CASES: (thm list -> cases_tactic) -> method

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

  val METHOD_CASES: (thm list -> cases_tactic) -> method

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

  val fail: method

  val succeed: method

  val insert_tac: thm list -> int -> tactic

  val insert: thm list -> method

  val insert_facts: method

  val SIMPLE_METHOD: tactic -> method

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

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

  val defer: int option -> method

  val prefer: int -> method

  val cheating: bool -> Proof.context -> method

  val intro: thm list -> method

  val elim: thm list -> method

  val unfold: thm list -> Proof.context -> method

  val fold: thm list -> Proof.context -> method

  val atomize: bool -> method

  val this: method

  val fact: thm list -> Proof.context -> method

  val assumption: Proof.context -> method

  val close: bool -> Proof.context -> method

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

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

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

  val intros_tac: thm list -> thm list -> tactic

  val rule: thm list -> method

  val erule: int -> thm list -> method

  val drule: int -> thm list -> method

  val frule: int -> thm list -> method

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

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

  val tactic: string * Position.T -> Proof.context -> method

  val raw_tactic: string * Position.T -> Proof.context -> method

  type src

  datatype text =

    Basic of (Proof.context -> method) * Position.T |

    Source of src |

    Source_i of src |

    Then of text list |

    Orelse of text list |

    Try of text |

    Repeat1 of text |

    SelectGoals of int * text

  val primitive_text: (thm -> thm) -> text

  val succeed_text: text

  val default_text: text

  val this_text: text

  val done_text: text

  val sorry_text: bool -> text

  val finish_text: text option * bool -> Position.T -> text

  val intern: theory -> xstring -> string

  val defined: theory -> string -> bool

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

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

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

    -> theory -> theory

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

    -> theory -> theory

  val method_setup: bstring -> string * Position.T -> string -> theory -> theory

  val syntax: (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list))

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

  val simple_text: Args.T list -> text * Args.T list

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

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

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

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

  type modifier

  val sectioned_args: (Context.generic * Args.T list -> 'a * (Context.generic * 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 ->

    (Context.generic * Args.T list -> 'a * (Context.generic * 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

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

    -> src -> Proof.context -> method

  val goal_args': (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list))

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

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

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

  val goal_args_ctxt': (Context.generic * Args.T list -> 'a * (Context.generic * Args.T list)) ->

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

  val parse: OuterLex.token list -> text * OuterLex.token list

end;

structure Method: METHOD =

struct

(** generic tools **)

(* goal addressing *)

fun FINDGOAL tac st =

  let fun find i n = if i > n then Seq.fail else Seq.APPEND (tac i, find (i + 1) n)

  in find 1 (Thm.nprems_of st) st end;

fun HEADGOAL tac = tac 1;

(** proof methods **)

(* datatype method *)

datatype method = Meth of thm list -> cases_tactic;

fun apply pos meth_fun ctxt facts goal = Position.setmp_thread_data_seq pos

  (fn () => let val Meth meth = meth_fun ctxt in meth facts goal end) ();

val RAW_METHOD_CASES = Meth;

fun RAW_METHOD tac = RAW_METHOD_CASES (NO_CASES o tac);

fun METHOD_CASES tac = RAW_METHOD_CASES (fn facts =>

  Seq.THEN (ALLGOALS Goal.conjunction_tac, tac facts));

fun METHOD tac = RAW_METHOD (fn facts => ALLGOALS Goal.conjunction_tac THEN tac facts);

val fail = METHOD (K no_tac);

val succeed = METHOD (K all_tac);

(* insert facts *)

local

fun cut_rule_tac rule =

  Tactic.rtac (Drule.forall_intr_vars rule COMP_INCR revcut_rl);

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));

val SIMPLE_METHOD' = SIMPLE_METHOD'' HEADGOAL;

end;

(* shuffle subgoals *)

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 (the_default 1 opt_i)));

(* cheating *)

fun cheating int ctxt = METHOD (K (setmp quick_and_dirty (int orelse ! quick_and_dirty)

    (SkipProof.cheat_tac (ProofContext.theory_of ctxt))));

(* unfold intro/elim rules *)

fun intro ths = SIMPLE_METHOD' (CHANGED_PROP o REPEAT_ALL_NEW (Tactic.match_tac ths));

fun elim ths = SIMPLE_METHOD' (CHANGED_PROP o REPEAT_ALL_NEW (Tactic.ematch_tac ths));

(* unfold/fold definitions *)

fun unfold_meth ths ctxt = SIMPLE_METHOD (CHANGED_PROP (LocalDefs.unfold_tac ctxt ths));

fun fold_meth ths ctxt = SIMPLE_METHOD (CHANGED_PROP (LocalDefs.fold_tac ctxt ths));

(* atomize rule statements *)

fun atomize false = SIMPLE_METHOD' (CHANGED_PROP o ObjectLogic.atomize_prems_tac)

  | atomize true = RAW_METHOD (K (HEADGOAL (CHANGED_PROP o ObjectLogic.full_atomize_tac)));

(* this -- resolve facts directly *)

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

(* fact -- composition by facts from context *)

fun fact [] ctxt = SIMPLE_METHOD' (ProofContext.some_fact_tac ctxt)

  | fact rules _ = SIMPLE_METHOD' (ProofContext.fact_tac rules);

(* assumption *)

local

fun cond_rtac cond rule = SUBGOAL (fn (prop, i) =>

  if cond (Logic.strip_assums_concl prop)

  then Tactic.rtac rule i else no_tac);

fun legacy_tac st =

  (legacy_feature

      ("Implicit use of prems in assumption proof" ^ Position.str_of (Position.thread_data ()));

    all_tac st);

fun assm_tac ctxt =

  assume_tac APPEND'

  Goal.assume_rule_tac ctxt APPEND'

  (CHANGED o solve_tac (Assumption.prems_of ctxt) THEN' K legacy_tac) APPEND'

  cond_rtac (can Logic.dest_equals) Drule.reflexive_thm APPEND'

  cond_rtac (can Logic.dest_term) Drule.termI;

in

fun assumption ctxt = METHOD (HEADGOAL o

  (fn [] => assm_tac ctxt

    | [fact] => solve_tac [fact]

    | _ => K no_tac));

fun close immed ctxt = METHOD (K

  (FILTER Thm.no_prems

    ((if immed then ALLGOALS (assm_tac ctxt) else all_tac) THEN flexflex_tac)));

end;

(* rule etc. -- single-step refinements *)

val trace_rules = ref false;

fun trace ctxt rules =

  if ! trace_rules andalso not (null rules) then

    Pretty.big_list "rules:" (map (ProofContext.pretty_thm ctxt) rules)

    |> Pretty.string_of |> tracing

  else ();

local

fun gen_rule_tac tac rules facts =

  (fn i => fn st =>

    if null facts then tac rules i st

    else Seq.maps (fn rule => (tac o single) rule i st) (Drule.multi_resolves facts rules))

  THEN_ALL_NEW Goal.norm_hhf_tac;

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;

(* intros_tac -- pervasive search spanned by intro rules *)

fun intros_tac intros facts =

  ALLGOALS (insert_tac facts THEN'

      REPEAT_ALL_NEW (resolve_tac intros))

    THEN Tactic.distinct_subgoals_tac;

(* iprover -- intuitionistic proof search *)

local

val remdups_tac = SUBGOAL (fn (g, i) =>

  let val prems = Logic.strip_assums_hyp g in

    REPEAT_DETERM_N (length prems - length (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;

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 intprover_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 member (fn ((ps1, c1), (ps2, c2)) =>

        c1 aconv c2 andalso

        length ps1 = length ps2 andalso

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

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

  end);

in

fun iprover_tac ctxt opt_lim =

  SELECT_GOAL (DEEPEN (2, the_default 20 opt_lim) (intprover_tac ctxt [] 0) 4 1);

end;

(* ML tactics *)

structure TacticData = ProofDataFun

(

  type T = thm list -> tactic;

  fun init _ = undefined;

);

val set_tactic = TacticData.put;

fun ml_tactic (txt, pos) ctxt =

  let

    val ctxt' = ctxt |> Context.proof_map

      (ML_Context.expression pos

        "fun tactic (facts: thm list) : tactic"

        "Context.map_proof (Method.set_tactic tactic)" txt);

  in Context.setmp_thread_data (SOME (Context.Proof ctxt)) (TacticData.get ctxt') end;

fun tactic txt ctxt = METHOD (ml_tactic txt ctxt);

fun raw_tactic txt ctxt = RAW_METHOD (ml_tactic txt ctxt);

(** method syntax **)

(* method text *)

type src = Args.src;

datatype text =

  Basic of (Proof.context -> method) * Position.T |

  Source of src |

  Source_i of src |

  Then of text list |

  Orelse of text list |

  Try of text |

  Repeat1 of text |

  SelectGoals of int * text;

fun primitive_text r = Basic (K (SIMPLE_METHOD (PRIMITIVE r)), Position.none);

val succeed_text = Basic (K succeed, Position.none);

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

val this_text = Basic (K this, Position.none);

val done_text = Basic (K (SIMPLE_METHOD all_tac), Position.none);

fun sorry_text int = Basic (cheating int, Position.none);

fun finish_text (NONE, immed) pos = Basic (close immed, pos)

  | finish_text (SOME txt, immed) pos = Then [txt, Basic (close immed, pos)];

(* method definitions *)

structure Methods = TheoryDataFun

(

  type T = (((src -> Proof.context -> method) * string) * stamp) NameSpace.table;

  val empty = NameSpace.empty_table;

  val copy = I;

  val extend = I;

  fun merge _ tables : T = NameSpace.merge_tables (eq_snd (op =)) tables handle Symtab.DUP dup =>

    error ("Attempt to merge different versions of method " ^ quote dup);

);

fun print_methods thy =

  let

    val meths = Methods.get thy;

    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 meths))]

    |> Pretty.chunks |> Pretty.writeln

  end;

(* get methods *)

val intern = NameSpace.intern o #1 o Methods.get;

val defined = Symtab.defined o #2 o Methods.get;

fun method_i thy =

  let

    val meths = #2 (Methods.get thy);

    fun meth src =

      let val ((name, _), pos) = Args.dest_src src in

        (case Symtab.lookup meths name of

          NONE => error ("Unknown proof method: " ^ quote name ^ Position.str_of pos)

        | SOME ((mth, _), _) => mth src)

      end;

  in meth end;

fun method thy = method_i thy o Args.map_name (NameSpace.intern (#1 (Methods.get thy)));

(* add method *)

fun add_methods raw_meths thy =

  let

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

      (name, ((f, comment), stamp ())));

    fun add meths = NameSpace.extend_table (Sign.naming_of thy) new_meths meths

      handle Symtab.DUP dup => error ("Duplicate declaration of method " ^ quote dup);

  in Methods.map add thy end;

val add_method = add_methods o Library.single;

(* method_setup *)

fun method_setup name (txt, pos) cmt =

  Context.theory_map (ML_Context.expression pos

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

    "Context.map_theory (Method.add_method method)"

    ("(" ^ quote name ^ ", " ^ txt ^ ", " ^ quote cmt ^ ")"));

(** concrete syntax **)

(* basic *)

fun syntax scan = Args.context_syntax "method" scan;

val simple_text = (Args.$$$ "(" |-- Args.name

    -- Scan.repeat (Scan.one (fn x => not (Args.string_of x = ")"))) --| Args.$$$ ")"

  || Args.name -- Scan.succeed [])

  >> (fn (name, args) => Source (Args.src ((name, args), Position.none)));

fun simple_args scan f src ctxt : method =

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

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

  fst (syntax (Scan.succeed (f ctxt)) src ctxt);

fun no_args m = ctxt_args (K m);

(* sections *)

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

local

fun thms ss = Scan.repeat (Scan.unless (Scan.lift (Scan.first ss)) Attrib.multi_thm) >> flat;

fun app (f, att) (context, ths) = foldl_map att (Context.map_proof f context, ths);

fun section ss = Scan.depend (fn context => (Scan.first ss -- Scan.pass context (thms ss)) :|--

  (fn (m, ths) => Scan.succeed (app m (context, ths))));

fun sectioned args ss = args -- Scan.repeat (section ss);

in

fun sectioned_args args ss f src ctxt =

  let val ((x, _), ctxt') = 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 (thms []) [] 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;

(* iprover 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 iprover_modifiers =

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

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

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

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

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

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

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

in

val iprover_meth =

  bang_sectioned_args' iprover_modifiers (Scan.lift (Scan.option Args.nat))

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

      HEADGOAL (insert_tac (prems @ facts) THEN'

      ObjectLogic.atomize_prems_tac THEN' iprover_tac ctxt n)));

end;

(* tactic syntax *)

fun nat_thms_args f = uncurry f oo

  (fst oo syntax (Scan.lift (Scan.optional (Args.parens Args.nat) 0) -- Attrib.thms));

fun goal_args' args tac src ctxt = fst (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 =

  fst (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;

(* theory setup *)

val _ = Context.>> (Context.map_theory

  (add_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)"),

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

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

    ("unfold", thms_ctxt_args unfold_meth, "unfold definitions"),

    ("fold", thms_ctxt_args fold_meth, "fold definitions"),

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

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

    ("iprover", iprover_meth, "intuitionistic 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"),

    ("fact", thms_ctxt_args fact, "composition by facts from context"),

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

    ("rename_tac", goal_args (Scan.repeat1 Args.name) Tactic.rename_params_tac,

      "rename parameters of goal"),

    ("rotate_tac", goal_args (Scan.optional Args.int 1) Tactic.rotate_tac,

      "rotate assumptions of goal"),

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

    ("raw_tactic", simple_args (Args.position Args.name) raw_tactic,

      "ML tactic as raw proof method")]));

(* outer parser *)

local

structure T = OuterLex;

structure P = OuterParse;

fun is_symid_meth s =

  s <> "|" andalso s <> "?" andalso s <> "+" andalso T.is_sid s;

fun meth4 x =

 (P.position (P.xname >> rpair []) >> (Source o Args.src) ||

  P.$$$ "(" |-- P.!!! (meth0 --| P.$$$ ")")) x

and meth3 x =

 (meth4 --| P.$$$ "?" >> Try ||

  meth4 --| P.$$$ "+" >> Repeat1 ||

  meth4 -- (P.$$$ "[" |-- Scan.optional P.nat 1 --| P.$$$ "]") >> (SelectGoals o swap) ||

  meth4) x

and meth2 x =

 (P.position (P.xname -- P.args1 is_symid_meth false) >> (Source o Args.src) ||

  meth3) x

and meth1 x = (P.enum1 "," meth2 >> (fn [m] => m | ms => Then ms)) x

and meth0 x = (P.enum1 "|" meth1 >> (fn [m] => m | ms => Orelse ms)) x;

in val parse = meth3 end;

(*final declarations of this structure!*)

val unfold = unfold_meth;

val fold = fold_meth;

end;

structure BasicMethod: BASIC_METHOD = Method;

open BasicMethod;