(*  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: (Proof.context -> thm list -> tactic) -> Proof.context -> Proof.context

   val 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 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_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 = Proof.context -> 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 Position.none

         "fun tactic (ctxt: Proof.context) (facts: thm list) : tactic"

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

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

 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;

 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;