src/Provers/classical.ML
author wenzelm
Sat Dec 14 17:28:05 2013 +0100 (2013-12-14)
changeset 54742 7a86358a3c0b
parent 52732 b4da1f2ec73f
child 56334 6b3739fee456
permissions -rw-r--r--
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
clarified tool context in some boundary cases;
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(*  Title:      Provers/classical.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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Theorem prover for classical reasoning, including predicate calculus, set
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theory, etc.
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Rules must be classified as intro, elim, safe, hazardous (unsafe).
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A rule is unsafe unless it can be applied blindly without harmful results.
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For a rule to be safe, its premises and conclusion should be logically
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equivalent.  There should be no variables in the premises that are not in
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the conclusion.
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*)
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(*higher precedence than := facilitates use of references*)
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infix 4 addSIs addSEs addSDs addIs addEs addDs delrules
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  addSWrapper delSWrapper addWrapper delWrapper
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  addSbefore addSafter addbefore addafter
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  addD2 addE2 addSD2 addSE2;
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signature CLASSICAL_DATA =
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sig
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  val imp_elim: thm  (* P --> Q ==> (~ R ==> P) ==> (Q ==> R) ==> R *)
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  val not_elim: thm  (* ~P ==> P ==> R *)
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  val swap: thm  (* ~ P ==> (~ R ==> P) ==> R *)
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  val classical: thm  (* (~ P ==> P) ==> P *)
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  val sizef: thm -> int  (* size function for BEST_FIRST, typically size_of_thm *)
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  val hyp_subst_tacs: (Proof.context -> int -> tactic) list (* optional tactics for
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    substitution in the hypotheses; assumed to be safe! *)
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end;
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signature BASIC_CLASSICAL =
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sig
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  type wrapper = (int -> tactic) -> int -> tactic
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  type claset
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  val print_claset: Proof.context -> unit
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  val addDs: Proof.context * thm list -> Proof.context
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  val addEs: Proof.context * thm list -> Proof.context
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  val addIs: Proof.context * thm list -> Proof.context
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  val addSDs: Proof.context * thm list -> Proof.context
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  val addSEs: Proof.context * thm list -> Proof.context
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  val addSIs: Proof.context * thm list -> Proof.context
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  val delrules: Proof.context * thm list -> Proof.context
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  val addSWrapper: Proof.context * (string * (Proof.context -> wrapper)) -> Proof.context
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  val delSWrapper: Proof.context * string -> Proof.context
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  val addWrapper: Proof.context * (string * (Proof.context -> wrapper)) -> Proof.context
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  val delWrapper: Proof.context * string -> Proof.context
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  val addSbefore: Proof.context * (string * (Proof.context -> int -> tactic)) -> Proof.context
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  val addSafter: Proof.context * (string * (Proof.context -> int -> tactic)) -> Proof.context
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  val addbefore: Proof.context * (string * (Proof.context -> int -> tactic)) -> Proof.context
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  val addafter: Proof.context * (string * (Proof.context -> int -> tactic)) -> Proof.context
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  val addD2: Proof.context * (string * thm) -> Proof.context
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  val addE2: Proof.context * (string * thm) -> Proof.context
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  val addSD2: Proof.context * (string * thm) -> Proof.context
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  val addSE2: Proof.context * (string * thm) -> Proof.context
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  val appSWrappers: Proof.context -> wrapper
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  val appWrappers: Proof.context -> wrapper
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  val claset_of: Proof.context -> claset
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  val put_claset: claset -> Proof.context -> Proof.context
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  val map_theory_claset: (Proof.context -> Proof.context) -> theory -> theory
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  val fast_tac: Proof.context -> int -> tactic
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  val slow_tac: Proof.context -> int -> tactic
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  val astar_tac: Proof.context -> int -> tactic
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  val slow_astar_tac: Proof.context -> int -> tactic
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  val best_tac: Proof.context -> int -> tactic
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  val first_best_tac: Proof.context -> int -> tactic
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  val slow_best_tac: Proof.context -> int -> tactic
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  val depth_tac: Proof.context -> int -> int -> tactic
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  val deepen_tac: Proof.context -> int -> int -> tactic
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  val contr_tac: int -> tactic
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  val dup_elim: thm -> thm
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  val dup_intr: thm -> thm
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  val dup_step_tac: Proof.context -> int -> tactic
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  val eq_mp_tac: int -> tactic
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  val haz_step_tac: Proof.context -> int -> tactic
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  val joinrules: thm list * thm list -> (bool * thm) list
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  val mp_tac: int -> tactic
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  val safe_tac: Proof.context -> tactic
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  val safe_steps_tac: Proof.context -> int -> tactic
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  val safe_step_tac: Proof.context -> int -> tactic
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  val clarify_tac: Proof.context -> int -> tactic
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  val clarify_step_tac: Proof.context -> int -> tactic
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  val step_tac: Proof.context -> int -> tactic
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  val slow_step_tac: Proof.context -> int -> tactic
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  val swapify: thm list -> thm list
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  val swap_res_tac: thm list -> int -> tactic
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  val inst_step_tac: Proof.context -> int -> tactic
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  val inst0_step_tac: Proof.context -> int -> tactic
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  val instp_step_tac: Proof.context -> int -> tactic
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end;
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signature CLASSICAL =
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sig
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  include BASIC_CLASSICAL
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  val classical_rule: thm -> thm
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  type netpair = (int * (bool * thm)) Net.net * (int * (bool * thm)) Net.net
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  val rep_cs: claset ->
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   {safeIs: thm Item_Net.T,
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    safeEs: thm Item_Net.T,
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    hazIs: thm Item_Net.T,
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    hazEs: thm Item_Net.T,
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    swrappers: (string * (Proof.context -> wrapper)) list,
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    uwrappers: (string * (Proof.context -> wrapper)) list,
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    safe0_netpair: netpair,
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    safep_netpair: netpair,
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    haz_netpair: netpair,
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    dup_netpair: netpair,
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    xtra_netpair: Context_Rules.netpair}
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  val get_cs: Context.generic -> claset
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  val map_cs: (claset -> claset) -> Context.generic -> Context.generic
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  val safe_dest: int option -> attribute
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  val safe_elim: int option -> attribute
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  val safe_intro: int option -> attribute
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  val haz_dest: int option -> attribute
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  val haz_elim: int option -> attribute
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  val haz_intro: int option -> attribute
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  val rule_del: attribute
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  val cla_modifiers: Method.modifier parser list
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  val cla_method:
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    (Proof.context -> tactic) -> (Proof.context -> Proof.method) context_parser
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  val cla_method':
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    (Proof.context -> int -> tactic) -> (Proof.context -> Proof.method) context_parser
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  val setup: theory -> theory
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end;
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functor Classical(Data: CLASSICAL_DATA): CLASSICAL =
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struct
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(** classical elimination rules **)
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(*
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Classical reasoning requires stronger elimination rules.  For
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instance, make_elim of Pure transforms the HOL rule injD into
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    [| inj f; f x = f y; x = y ==> PROP W |] ==> PROP W
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Such rules can cause fast_tac to fail and blast_tac to report "PROOF
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FAILED"; classical_rule will strenthen this to
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    [| inj f; ~ W ==> f x = f y; x = y ==> W |] ==> W
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*)
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fun classical_rule rule =
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  if is_some (Object_Logic.elim_concl rule) then
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    let
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      val rule' = rule RS Data.classical;
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      val concl' = Thm.concl_of rule';
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      fun redundant_hyp goal =
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        concl' aconv Logic.strip_assums_concl goal orelse
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          (case Logic.strip_assums_hyp goal of
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            hyp :: hyps => exists (fn t => t aconv hyp) hyps
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          | _ => false);
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      val rule'' =
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        rule' |> ALLGOALS (SUBGOAL (fn (goal, i) =>
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          if i = 1 orelse redundant_hyp goal
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          then etac thin_rl i
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          else all_tac))
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        |> Seq.hd
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        |> Drule.zero_var_indexes;
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    in if Thm.equiv_thm (rule, rule'') then rule else rule'' end
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  else rule;
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(*flatten nested meta connectives in prems*)
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fun flat_rule opt_context th =
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  let
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    val ctxt =
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      (case opt_context of
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        NONE => Proof_Context.init_global (Thm.theory_of_thm th)
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      | SOME context => Context.proof_of context);
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  in Conv.fconv_rule (Conv.prems_conv ~1 (Object_Logic.atomize_prems ctxt)) th end;
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(*** Useful tactics for classical reasoning ***)
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(*Prove goal that assumes both P and ~P.
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  No backtracking if it finds an equal assumption.  Perhaps should call
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  ematch_tac instead of eresolve_tac, but then cannot prove ZF/cantor.*)
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val contr_tac =
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  eresolve_tac [Data.not_elim] THEN' (eq_assume_tac ORELSE' assume_tac);
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(*Finds P-->Q and P in the assumptions, replaces implication by Q.
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  Could do the same thing for P<->Q and P... *)
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fun mp_tac i = eresolve_tac [Data.not_elim, Data.imp_elim] i THEN assume_tac i;
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(*Like mp_tac but instantiates no variables*)
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fun eq_mp_tac i = ematch_tac [Data.not_elim, Data.imp_elim] i THEN eq_assume_tac i;
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(*Creates rules to eliminate ~A, from rules to introduce A*)
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fun swapify intrs = intrs RLN (2, [Data.swap]);
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val swapped = Thm.rule_attribute (fn _ => fn th => th RSN (2, Data.swap));
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(*Uses introduction rules in the normal way, or on negated assumptions,
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  trying rules in order. *)
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fun swap_res_tac rls =
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  let fun addrl rl brls = (false, rl) :: (true, rl RSN (2, Data.swap)) :: brls in
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    assume_tac ORELSE'
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    contr_tac ORELSE'
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    biresolve_tac (fold_rev addrl rls [])
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  end;
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(*Duplication of hazardous rules, for complete provers*)
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fun dup_intr th = zero_var_indexes (th RS Data.classical);
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fun dup_elim th =  (* FIXME proper context!? *)
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  let
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    val rl = (th RSN (2, revcut_rl)) |> Thm.assumption 2 |> Seq.hd;
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    val ctxt = Proof_Context.init_global (Thm.theory_of_thm rl);
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  in rule_by_tactic ctxt (TRYALL (etac revcut_rl)) rl end;
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(**** Classical rule sets ****)
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type netpair = (int * (bool * thm)) Net.net * (int * (bool * thm)) Net.net;
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type wrapper = (int -> tactic) -> int -> tactic;
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datatype claset =
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  CS of
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   {safeIs         : thm Item_Net.T,          (*safe introduction rules*)
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    safeEs         : thm Item_Net.T,          (*safe elimination rules*)
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    hazIs          : thm Item_Net.T,          (*unsafe introduction rules*)
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    hazEs          : thm Item_Net.T,          (*unsafe elimination rules*)
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    swrappers      : (string * (Proof.context -> wrapper)) list, (*for transforming safe_step_tac*)
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    uwrappers      : (string * (Proof.context -> wrapper)) list, (*for transforming step_tac*)
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    safe0_netpair  : netpair,                 (*nets for trivial cases*)
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    safep_netpair  : netpair,                 (*nets for >0 subgoals*)
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    haz_netpair    : netpair,                 (*nets for unsafe rules*)
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    dup_netpair    : netpair,                 (*nets for duplication*)
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    xtra_netpair   : Context_Rules.netpair};  (*nets for extra rules*)
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(*Desired invariants are
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        safe0_netpair = build safe0_brls,
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        safep_netpair = build safep_brls,
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        haz_netpair = build (joinrules(hazIs, hazEs)),
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        dup_netpair = build (joinrules(map dup_intr hazIs,
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                                       map dup_elim hazEs))
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where build = build_netpair(Net.empty,Net.empty),
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      safe0_brls contains all brules that solve the subgoal, and
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      safep_brls contains all brules that generate 1 or more new subgoals.
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The theorem lists are largely comments, though they are used in merge_cs and print_cs.
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Nets must be built incrementally, to save space and time.
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*)
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val empty_netpair = (Net.empty, Net.empty);
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val empty_cs =
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  CS
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   {safeIs = Thm.full_rules,
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    safeEs = Thm.full_rules,
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    hazIs = Thm.full_rules,
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    hazEs = Thm.full_rules,
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    swrappers = [],
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    uwrappers = [],
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    safe0_netpair = empty_netpair,
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    safep_netpair = empty_netpair,
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    haz_netpair = empty_netpair,
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    dup_netpair = empty_netpair,
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    xtra_netpair = empty_netpair};
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fun rep_cs (CS args) = args;
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(*** Adding (un)safe introduction or elimination rules.
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    In case of overlap, new rules are tried BEFORE old ones!!
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***)
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(*For use with biresolve_tac.  Combines intro rules with swap to handle negated
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  assumptions.  Pairs elim rules with true. *)
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fun joinrules (intrs, elims) =
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  (map (pair true) (elims @ swapify intrs)) @ map (pair false) intrs;
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fun joinrules' (intrs, elims) =
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  map (pair true) elims @ map (pair false) intrs;
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(*Priority: prefer rules with fewest subgoals,
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  then rules added most recently (preferring the head of the list).*)
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fun tag_brls k [] = []
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  | tag_brls k (brl::brls) =
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      (1000000*subgoals_of_brl brl + k, brl) ::
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      tag_brls (k+1) brls;
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fun tag_brls' _ _ [] = []
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  | tag_brls' w k (brl::brls) = ((w, k), brl) :: tag_brls' w (k + 1) brls;
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fun insert_tagged_list rls = fold_rev Tactic.insert_tagged_brl rls;
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(*Insert into netpair that already has nI intr rules and nE elim rules.
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  Count the intr rules double (to account for swapify).  Negate to give the
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  new insertions the lowest priority.*)
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fun insert (nI, nE) = insert_tagged_list o (tag_brls (~(2*nI+nE))) o joinrules;
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fun insert' w (nI, nE) = insert_tagged_list o tag_brls' w (~(nI + nE)) o joinrules';
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fun delete_tagged_list rls = fold_rev Tactic.delete_tagged_brl rls;
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fun delete x = delete_tagged_list (joinrules x);
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fun delete' x = delete_tagged_list (joinrules' x);
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fun string_of_thm NONE = Display.string_of_thm_without_context
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  | string_of_thm (SOME context) = Display.string_of_thm (Context.proof_of context);
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fun make_elim context th =
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  if has_fewer_prems 1 th then
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    error ("Ill-formed destruction rule\n" ^ string_of_thm context th)
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  else Tactic.make_elim th;
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fun warn_thm (SOME (Context.Proof ctxt)) msg th =
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      if Context_Position.is_visible ctxt
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      then warning (msg ^ Display.string_of_thm ctxt th) else ()
wenzelm@52699
   314
  | warn_thm _ _ _ = ();
wenzelm@42793
   315
wenzelm@42807
   316
fun warn_rules context msg rules th =
wenzelm@42810
   317
  Item_Net.member rules th andalso (warn_thm context msg th; true);
wenzelm@42807
   318
wenzelm@42807
   319
fun warn_claset context th (CS {safeIs, safeEs, hazIs, hazEs, ...}) =
wenzelm@42807
   320
  warn_rules context "Rule already declared as safe introduction (intro!)\n" safeIs th orelse
wenzelm@42807
   321
  warn_rules context "Rule already declared as safe elimination (elim!)\n" safeEs th orelse
wenzelm@42807
   322
  warn_rules context "Rule already declared as introduction (intro)\n" hazIs th orelse
wenzelm@42807
   323
  warn_rules context "Rule already declared as elimination (elim)\n" hazEs th;
paulson@1927
   324
wenzelm@12376
   325
paulson@1800
   326
(*** Safe rules ***)
lcp@982
   327
wenzelm@42793
   328
fun addSI w context th
wenzelm@42790
   329
    (cs as CS {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers,
wenzelm@42790
   330
      safe0_netpair, safep_netpair, haz_netpair, dup_netpair, xtra_netpair}) =
wenzelm@42807
   331
  if warn_rules context "Ignoring duplicate safe introduction (intro!)\n" safeIs th then cs
paulson@1927
   332
  else
wenzelm@42790
   333
    let
wenzelm@54742
   334
      val th' = flat_rule context th;
wenzelm@23594
   335
      val (safe0_rls, safep_rls) = (*0 subgoals vs 1 or more*)
wenzelm@42790
   336
        List.partition Thm.no_prems [th'];
wenzelm@42810
   337
      val nI = Item_Net.length safeIs + 1;
wenzelm@42810
   338
      val nE = Item_Net.length safeEs;
wenzelm@42807
   339
      val _ = warn_claset context th cs;
wenzelm@42790
   340
    in
wenzelm@42790
   341
      CS
wenzelm@42810
   342
       {safeIs = Item_Net.update th safeIs,
lcp@1073
   343
        safe0_netpair = insert (nI,nE) (safe0_rls, []) safe0_netpair,
wenzelm@9938
   344
        safep_netpair = insert (nI,nE) (safep_rls, []) safep_netpair,
wenzelm@42790
   345
        safeEs = safeEs,
wenzelm@42790
   346
        hazIs = hazIs,
wenzelm@42790
   347
        hazEs = hazEs,
wenzelm@42790
   348
        swrappers = swrappers,
wenzelm@42790
   349
        uwrappers = uwrappers,
wenzelm@42790
   350
        haz_netpair = haz_netpair,
wenzelm@42790
   351
        dup_netpair = dup_netpair,
wenzelm@18691
   352
        xtra_netpair = insert' (the_default 0 w) (nI,nE) ([th], []) xtra_netpair}
wenzelm@42790
   353
    end;
lcp@1073
   354
wenzelm@42793
   355
fun addSE w context th
wenzelm@42790
   356
    (cs as CS {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers,
wenzelm@42790
   357
      safe0_netpair, safep_netpair, haz_netpair, dup_netpair, xtra_netpair}) =
wenzelm@42807
   358
  if warn_rules context "Ignoring duplicate safe elimination (elim!)\n" safeEs th then cs
paulson@18557
   359
  else if has_fewer_prems 1 th then
wenzelm@42793
   360
    error ("Ill-formed elimination rule\n" ^ string_of_thm context th)
paulson@1927
   361
  else
wenzelm@42790
   362
    let
wenzelm@54742
   363
      val th' = classical_rule (flat_rule context th);
wenzelm@18534
   364
      val (safe0_rls, safep_rls) = (*0 subgoals vs 1 or more*)
wenzelm@42790
   365
        List.partition (fn rl => nprems_of rl=1) [th'];
wenzelm@42810
   366
      val nI = Item_Net.length safeIs;
wenzelm@42810
   367
      val nE = Item_Net.length safeEs + 1;
wenzelm@42807
   368
      val _ = warn_claset context th cs;
wenzelm@42790
   369
    in
wenzelm@42790
   370
      CS
wenzelm@42810
   371
       {safeEs = Item_Net.update th safeEs,
lcp@1073
   372
        safe0_netpair = insert (nI,nE) ([], safe0_rls) safe0_netpair,
wenzelm@9938
   373
        safep_netpair = insert (nI,nE) ([], safep_rls) safep_netpair,
wenzelm@42790
   374
        safeIs = safeIs,
wenzelm@42790
   375
        hazIs = hazIs,
wenzelm@42790
   376
        hazEs = hazEs,
wenzelm@42790
   377
        swrappers = swrappers,
wenzelm@42790
   378
        uwrappers = uwrappers,
wenzelm@42790
   379
        haz_netpair = haz_netpair,
wenzelm@42790
   380
        dup_netpair = dup_netpair,
wenzelm@18691
   381
        xtra_netpair = insert' (the_default 0 w) (nI,nE) ([], [th]) xtra_netpair}
wenzelm@42790
   382
    end;
clasohm@0
   383
wenzelm@42793
   384
fun addSD w context th = addSE w context (make_elim context th);
wenzelm@42793
   385
lcp@1073
   386
paulson@1800
   387
(*** Hazardous (unsafe) rules ***)
clasohm@0
   388
wenzelm@42793
   389
fun addI w context th
wenzelm@42790
   390
    (cs as CS {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers,
wenzelm@42790
   391
      safe0_netpair, safep_netpair, haz_netpair, dup_netpair, xtra_netpair}) =
wenzelm@42807
   392
  if warn_rules context "Ignoring duplicate introduction (intro)\n" hazIs th then cs
paulson@1927
   393
  else
wenzelm@42790
   394
    let
wenzelm@54742
   395
      val th' = flat_rule context th;
wenzelm@42810
   396
      val nI = Item_Net.length hazIs + 1;
wenzelm@42810
   397
      val nE = Item_Net.length hazEs;
wenzelm@42807
   398
      val _ = warn_claset context th cs;
wenzelm@42790
   399
    in
wenzelm@42790
   400
      CS
wenzelm@42810
   401
       {hazIs = Item_Net.update th hazIs,
wenzelm@42790
   402
        haz_netpair = insert (nI, nE) ([th'], []) haz_netpair,
wenzelm@42790
   403
        dup_netpair = insert (nI, nE) ([dup_intr th'], []) dup_netpair,
wenzelm@42790
   404
        safeIs = safeIs,
wenzelm@42790
   405
        safeEs = safeEs,
wenzelm@42790
   406
        hazEs = hazEs,
wenzelm@42790
   407
        swrappers = swrappers,
wenzelm@42790
   408
        uwrappers = uwrappers,
wenzelm@9938
   409
        safe0_netpair = safe0_netpair,
wenzelm@9938
   410
        safep_netpair = safep_netpair,
wenzelm@42790
   411
        xtra_netpair = insert' (the_default 1 w) (nI, nE) ([th], []) xtra_netpair}
wenzelm@42790
   412
    end
wenzelm@42790
   413
    handle THM ("RSN: no unifiers", _, _) => (*from dup_intr*)  (* FIXME !? *)
wenzelm@42793
   414
      error ("Ill-formed introduction rule\n" ^ string_of_thm context th);
lcp@1073
   415
wenzelm@42793
   416
fun addE w context th
wenzelm@42790
   417
    (cs as CS {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers,
wenzelm@42790
   418
      safe0_netpair, safep_netpair, haz_netpair, dup_netpair, xtra_netpair}) =
wenzelm@42807
   419
  if warn_rules context "Ignoring duplicate elimination (elim)\n" hazEs th then cs
paulson@18557
   420
  else if has_fewer_prems 1 th then
wenzelm@42793
   421
    error ("Ill-formed elimination rule\n" ^ string_of_thm context th)
paulson@1927
   422
  else
wenzelm@42790
   423
    let
wenzelm@54742
   424
      val th' = classical_rule (flat_rule context th);
wenzelm@42810
   425
      val nI = Item_Net.length hazIs;
wenzelm@42810
   426
      val nE = Item_Net.length hazEs + 1;
wenzelm@42807
   427
      val _ = warn_claset context th cs;
wenzelm@42790
   428
    in
wenzelm@42790
   429
      CS
wenzelm@42810
   430
       {hazEs = Item_Net.update th hazEs,
wenzelm@42790
   431
        haz_netpair = insert (nI, nE) ([], [th']) haz_netpair,
wenzelm@42790
   432
        dup_netpair = insert (nI, nE) ([], [dup_elim th']) dup_netpair,
wenzelm@42790
   433
        safeIs = safeIs,
wenzelm@42790
   434
        safeEs = safeEs,
wenzelm@42790
   435
        hazIs = hazIs,
wenzelm@42790
   436
        swrappers = swrappers,
wenzelm@42790
   437
        uwrappers = uwrappers,
wenzelm@9938
   438
        safe0_netpair = safe0_netpair,
wenzelm@9938
   439
        safep_netpair = safep_netpair,
wenzelm@42790
   440
        xtra_netpair = insert' (the_default 1 w) (nI, nE) ([], [th]) xtra_netpair}
wenzelm@42790
   441
    end;
clasohm@0
   442
wenzelm@42793
   443
fun addD w context th = addE w context (make_elim context th);
wenzelm@42793
   444
clasohm@0
   445
lcp@1073
   446
wenzelm@10736
   447
(*** Deletion of rules
paulson@1800
   448
     Working out what to delete, requires repeating much of the code used
wenzelm@9938
   449
        to insert.
paulson@1800
   450
***)
paulson@1800
   451
wenzelm@54742
   452
fun delSI context th
wenzelm@42790
   453
    (cs as CS {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers,
wenzelm@42790
   454
      safe0_netpair, safep_netpair, haz_netpair, dup_netpair, xtra_netpair}) =
wenzelm@42810
   455
  if Item_Net.member safeIs th then
wenzelm@18534
   456
    let
wenzelm@54742
   457
      val th' = flat_rule context th;
wenzelm@42790
   458
      val (safe0_rls, safep_rls) = List.partition Thm.no_prems [th'];
wenzelm@42790
   459
    in
wenzelm@42790
   460
      CS
wenzelm@42790
   461
       {safe0_netpair = delete (safe0_rls, []) safe0_netpair,
wenzelm@42790
   462
        safep_netpair = delete (safep_rls, []) safep_netpair,
wenzelm@42810
   463
        safeIs = Item_Net.remove th safeIs,
wenzelm@42790
   464
        safeEs = safeEs,
wenzelm@42790
   465
        hazIs = hazIs,
wenzelm@42790
   466
        hazEs = hazEs,
wenzelm@42790
   467
        swrappers = swrappers,
wenzelm@42790
   468
        uwrappers = uwrappers,
wenzelm@42790
   469
        haz_netpair = haz_netpair,
wenzelm@42790
   470
        dup_netpair = dup_netpair,
wenzelm@42790
   471
        xtra_netpair = delete' ([th], []) xtra_netpair}
wenzelm@18534
   472
    end
wenzelm@18534
   473
  else cs;
paulson@1800
   474
wenzelm@54742
   475
fun delSE context th
wenzelm@42790
   476
    (cs as CS {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers,
wenzelm@42790
   477
      safe0_netpair, safep_netpair, haz_netpair, dup_netpair, xtra_netpair}) =
wenzelm@42810
   478
  if Item_Net.member safeEs th then
wenzelm@42790
   479
    let
wenzelm@54742
   480
      val th' = classical_rule (flat_rule context th);
wenzelm@42790
   481
      val (safe0_rls, safep_rls) = List.partition (fn rl => nprems_of rl = 1) [th'];
wenzelm@42790
   482
    in
wenzelm@42790
   483
      CS
wenzelm@42790
   484
       {safe0_netpair = delete ([], safe0_rls) safe0_netpair,
wenzelm@42790
   485
        safep_netpair = delete ([], safep_rls) safep_netpair,
wenzelm@42790
   486
        safeIs = safeIs,
wenzelm@42810
   487
        safeEs = Item_Net.remove th safeEs,
wenzelm@42790
   488
        hazIs = hazIs,
wenzelm@42790
   489
        hazEs = hazEs,
wenzelm@42790
   490
        swrappers = swrappers,
wenzelm@42790
   491
        uwrappers = uwrappers,
wenzelm@42790
   492
        haz_netpair = haz_netpair,
wenzelm@42790
   493
        dup_netpair = dup_netpair,
wenzelm@42790
   494
        xtra_netpair = delete' ([], [th]) xtra_netpair}
wenzelm@42790
   495
    end
wenzelm@42790
   496
  else cs;
paulson@1800
   497
wenzelm@42793
   498
fun delI context th
wenzelm@42790
   499
    (cs as CS {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers,
wenzelm@42790
   500
      safe0_netpair, safep_netpair, haz_netpair, dup_netpair, xtra_netpair}) =
wenzelm@42810
   501
  if Item_Net.member hazIs th then
wenzelm@54742
   502
    let val th' = flat_rule context th in
wenzelm@42790
   503
      CS
wenzelm@42790
   504
       {haz_netpair = delete ([th'], []) haz_netpair,
wenzelm@23594
   505
        dup_netpair = delete ([dup_intr th'], []) dup_netpair,
wenzelm@42790
   506
        safeIs = safeIs,
wenzelm@42790
   507
        safeEs = safeEs,
wenzelm@42810
   508
        hazIs = Item_Net.remove th hazIs,
wenzelm@42790
   509
        hazEs = hazEs,
wenzelm@42790
   510
        swrappers = swrappers,
wenzelm@42790
   511
        uwrappers = uwrappers,
wenzelm@9938
   512
        safe0_netpair = safe0_netpair,
wenzelm@9938
   513
        safep_netpair = safep_netpair,
wenzelm@12401
   514
        xtra_netpair = delete' ([th], []) xtra_netpair}
wenzelm@23594
   515
    end
wenzelm@42790
   516
  else cs
wenzelm@42790
   517
  handle THM ("RSN: no unifiers", _, _) => (*from dup_intr*)  (* FIXME !? *)
wenzelm@42793
   518
    error ("Ill-formed introduction rule\n" ^ string_of_thm context th);
paulson@1800
   519
wenzelm@54742
   520
fun delE context th
wenzelm@42790
   521
    (cs as CS {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers,
wenzelm@42790
   522
      safe0_netpair, safep_netpair, haz_netpair, dup_netpair, xtra_netpair}) =
wenzelm@42810
   523
  if Item_Net.member hazEs th then
wenzelm@54742
   524
    let val th' = classical_rule (flat_rule context th) in
wenzelm@42790
   525
      CS
wenzelm@42790
   526
       {haz_netpair = delete ([], [th']) haz_netpair,
wenzelm@18534
   527
        dup_netpair = delete ([], [dup_elim th']) dup_netpair,
wenzelm@42790
   528
        safeIs = safeIs,
wenzelm@42790
   529
        safeEs = safeEs,
wenzelm@42790
   530
        hazIs = hazIs,
wenzelm@42810
   531
        hazEs = Item_Net.remove th hazEs,
wenzelm@42790
   532
        swrappers = swrappers,
wenzelm@42790
   533
        uwrappers = uwrappers,
wenzelm@9938
   534
        safe0_netpair = safe0_netpair,
wenzelm@9938
   535
        safep_netpair = safep_netpair,
wenzelm@12401
   536
        xtra_netpair = delete' ([], [th]) xtra_netpair}
wenzelm@42790
   537
    end
wenzelm@42790
   538
  else cs;
paulson@1800
   539
paulson@2813
   540
(*Delete ALL occurrences of "th" in the claset (perhaps from several lists)*)
wenzelm@42793
   541
fun delrule context th (cs as CS {safeIs, safeEs, hazIs, hazEs, ...}) =
wenzelm@42793
   542
  let val th' = Tactic.make_elim th in
wenzelm@42810
   543
    if Item_Net.member safeIs th orelse Item_Net.member safeEs th orelse
wenzelm@42810
   544
      Item_Net.member hazIs th orelse Item_Net.member hazEs th orelse
wenzelm@42810
   545
      Item_Net.member safeEs th' orelse Item_Net.member hazEs th'
wenzelm@54742
   546
    then
wenzelm@54742
   547
      delSI context th
wenzelm@54742
   548
        (delSE context th
wenzelm@54742
   549
          (delI context th
wenzelm@54742
   550
            (delE context th (delSE context th' (delE context th' cs)))))
wenzelm@42807
   551
    else (warn_thm context "Undeclared classical rule\n" th; cs)
wenzelm@9938
   552
  end;
paulson@1800
   553
paulson@1800
   554
wenzelm@42793
   555
wenzelm@42793
   556
(** claset data **)
wenzelm@42790
   557
wenzelm@42793
   558
(* wrappers *)
wenzelm@42790
   559
haftmann@22674
   560
fun map_swrappers f
haftmann@22674
   561
  (CS {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers,
haftmann@22674
   562
    safe0_netpair, safep_netpair, haz_netpair, dup_netpair, xtra_netpair}) =
haftmann@22674
   563
  CS {safeIs = safeIs, safeEs = safeEs, hazIs = hazIs, hazEs = hazEs,
oheimb@4767
   564
    swrappers = f swrappers, uwrappers = uwrappers,
oheimb@4767
   565
    safe0_netpair = safe0_netpair, safep_netpair = safep_netpair,
wenzelm@6955
   566
    haz_netpair = haz_netpair, dup_netpair = dup_netpair, xtra_netpair = xtra_netpair};
oheimb@4767
   567
haftmann@22674
   568
fun map_uwrappers f
wenzelm@42793
   569
  (CS {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers,
haftmann@22674
   570
    safe0_netpair, safep_netpair, haz_netpair, dup_netpair, xtra_netpair}) =
haftmann@22674
   571
  CS {safeIs = safeIs, safeEs = safeEs, hazIs = hazIs, hazEs = hazEs,
oheimb@4767
   572
    swrappers = swrappers, uwrappers = f uwrappers,
oheimb@4767
   573
    safe0_netpair = safe0_netpair, safep_netpair = safep_netpair,
wenzelm@6955
   574
    haz_netpair = haz_netpair, dup_netpair = dup_netpair, xtra_netpair = xtra_netpair};
oheimb@4767
   575
haftmann@22674
   576
wenzelm@42793
   577
(* merge_cs *)
lcp@982
   578
wenzelm@42810
   579
(*Merge works by adding all new rules of the 2nd claset into the 1st claset,
wenzelm@42810
   580
  in order to preserve priorities reliably.*)
wenzelm@42810
   581
wenzelm@42810
   582
fun merge_thms add thms1 thms2 =
wenzelm@42810
   583
  fold_rev (fn thm => if Item_Net.member thms1 thm then I else add thm) (Item_Net.content thms2);
wenzelm@42810
   584
haftmann@22674
   585
fun merge_cs (cs as CS {safeIs, safeEs, hazIs, hazEs, ...},
wenzelm@24358
   586
    cs' as CS {safeIs = safeIs2, safeEs = safeEs2, hazIs = hazIs2, hazEs = hazEs2,
haftmann@22674
   587
      swrappers, uwrappers, ...}) =
wenzelm@24358
   588
  if pointer_eq (cs, cs') then cs
wenzelm@24358
   589
  else
wenzelm@42810
   590
    cs
wenzelm@42810
   591
    |> merge_thms (addSI NONE NONE) safeIs safeIs2
wenzelm@42810
   592
    |> merge_thms (addSE NONE NONE) safeEs safeEs2
wenzelm@42810
   593
    |> merge_thms (addI NONE NONE) hazIs hazIs2
wenzelm@42810
   594
    |> merge_thms (addE NONE NONE) hazEs hazEs2
wenzelm@42810
   595
    |> map_swrappers (fn ws => AList.merge (op =) (K true) (ws, swrappers))
wenzelm@42810
   596
    |> map_uwrappers (fn ws => AList.merge (op =) (K true) (ws, uwrappers));
wenzelm@42793
   597
wenzelm@42793
   598
wenzelm@42793
   599
(* data *)
wenzelm@42793
   600
wenzelm@42793
   601
structure Claset = Generic_Data
wenzelm@42793
   602
(
wenzelm@42793
   603
  type T = claset;
wenzelm@42793
   604
  val empty = empty_cs;
wenzelm@42793
   605
  val extend = I;
wenzelm@42793
   606
  val merge = merge_cs;
wenzelm@42793
   607
);
wenzelm@42793
   608
wenzelm@42793
   609
val claset_of = Claset.get o Context.Proof;
wenzelm@42793
   610
val rep_claset_of = rep_cs o claset_of;
wenzelm@42793
   611
wenzelm@42793
   612
val get_cs = Claset.get;
wenzelm@42793
   613
val map_cs = Claset.map;
wenzelm@42793
   614
wenzelm@51703
   615
fun map_theory_claset f thy =
wenzelm@51703
   616
  let
wenzelm@51703
   617
    val ctxt' = f (Proof_Context.init_global thy);
wenzelm@51703
   618
    val thy' = Proof_Context.theory_of ctxt';
wenzelm@51703
   619
  in Context.theory_map (Claset.map (K (claset_of ctxt'))) thy' end;
wenzelm@51703
   620
wenzelm@42793
   621
fun map_claset f = Context.proof_map (map_cs f);
wenzelm@42793
   622
fun put_claset cs = map_claset (K cs);
wenzelm@42793
   623
wenzelm@42793
   624
fun print_claset ctxt =
wenzelm@42793
   625
  let
wenzelm@42793
   626
    val {safeIs, safeEs, hazIs, hazEs, swrappers, uwrappers, ...} = rep_claset_of ctxt;
wenzelm@51584
   627
    val pretty_thms = map (Display.pretty_thm_item ctxt) o Item_Net.content;
wenzelm@42793
   628
  in
wenzelm@42793
   629
    [Pretty.big_list "safe introduction rules (intro!):" (pretty_thms safeIs),
wenzelm@42793
   630
      Pretty.big_list "introduction rules (intro):" (pretty_thms hazIs),
wenzelm@42793
   631
      Pretty.big_list "safe elimination rules (elim!):" (pretty_thms safeEs),
wenzelm@42793
   632
      Pretty.big_list "elimination rules (elim):" (pretty_thms hazEs),
wenzelm@42793
   633
      Pretty.strs ("safe wrappers:" :: map #1 swrappers),
wenzelm@42793
   634
      Pretty.strs ("unsafe wrappers:" :: map #1 uwrappers)]
wenzelm@42793
   635
    |> Pretty.chunks |> Pretty.writeln
wenzelm@42793
   636
  end;
wenzelm@42793
   637
wenzelm@42793
   638
wenzelm@42793
   639
(* old-style declarations *)
wenzelm@42793
   640
wenzelm@42793
   641
fun decl f (ctxt, ths) = map_claset (fold_rev (f (SOME (Context.Proof ctxt))) ths) ctxt;
wenzelm@42793
   642
wenzelm@42793
   643
val op addSIs = decl (addSI NONE);
wenzelm@42793
   644
val op addSEs = decl (addSE NONE);
wenzelm@42793
   645
val op addSDs = decl (addSD NONE);
wenzelm@42793
   646
val op addIs = decl (addI NONE);
wenzelm@42793
   647
val op addEs = decl (addE NONE);
wenzelm@42793
   648
val op addDs = decl (addD NONE);
wenzelm@42793
   649
val op delrules = decl delrule;
wenzelm@42793
   650
wenzelm@42793
   651
wenzelm@42793
   652
wenzelm@42793
   653
(*** Modifying the wrapper tacticals ***)
wenzelm@42793
   654
wenzelm@42793
   655
fun appSWrappers ctxt = fold (fn (_, w) => w ctxt) (#swrappers (rep_claset_of ctxt));
wenzelm@42793
   656
fun appWrappers ctxt = fold (fn (_, w) => w ctxt) (#uwrappers (rep_claset_of ctxt));
wenzelm@42793
   657
wenzelm@42793
   658
fun update_warn msg (p as (key : string, _)) xs =
wenzelm@42793
   659
  (if AList.defined (op =) xs key then warning msg else (); AList.update (op =) p xs);
wenzelm@42793
   660
wenzelm@42793
   661
fun delete_warn msg (key : string) xs =
wenzelm@42793
   662
  if AList.defined (op =) xs key then AList.delete (op =) key xs
wenzelm@42793
   663
  else (warning msg; xs);
wenzelm@42793
   664
wenzelm@42793
   665
(*Add/replace a safe wrapper*)
wenzelm@51703
   666
fun ctxt addSWrapper new_swrapper = ctxt |> map_claset
wenzelm@51703
   667
  (map_swrappers (update_warn ("Overwriting safe wrapper " ^ fst new_swrapper) new_swrapper));
wenzelm@42793
   668
wenzelm@42793
   669
(*Add/replace an unsafe wrapper*)
wenzelm@51703
   670
fun ctxt addWrapper new_uwrapper = ctxt |> map_claset
wenzelm@51703
   671
  (map_uwrappers (update_warn ("Overwriting unsafe wrapper " ^ fst new_uwrapper) new_uwrapper));
wenzelm@42793
   672
wenzelm@42793
   673
(*Remove a safe wrapper*)
wenzelm@51703
   674
fun ctxt delSWrapper name = ctxt |> map_claset
wenzelm@51703
   675
  (map_swrappers (delete_warn ("No such safe wrapper in claset: " ^ name) name));
wenzelm@42793
   676
wenzelm@42793
   677
(*Remove an unsafe wrapper*)
wenzelm@51703
   678
fun ctxt delWrapper name = ctxt |> map_claset
wenzelm@51703
   679
  (map_uwrappers (delete_warn ("No such unsafe wrapper in claset: " ^ name) name));
wenzelm@42793
   680
wenzelm@42793
   681
(* compose a safe tactic alternatively before/after safe_step_tac *)
wenzelm@51717
   682
fun ctxt addSbefore (name, tac1) =
wenzelm@51717
   683
  ctxt addSWrapper (name, fn ctxt => fn tac2 => tac1 ctxt ORELSE' tac2);
wenzelm@51717
   684
fun ctxt addSafter (name, tac2) =
wenzelm@51717
   685
  ctxt addSWrapper (name, fn ctxt => fn tac1 => tac1 ORELSE' tac2 ctxt);
wenzelm@42793
   686
wenzelm@42793
   687
(*compose a tactic alternatively before/after the step tactic *)
wenzelm@51717
   688
fun ctxt addbefore (name, tac1) =
wenzelm@51717
   689
  ctxt addWrapper (name, fn ctxt => fn tac2 => tac1 ctxt APPEND' tac2);
wenzelm@51717
   690
fun ctxt addafter (name, tac2) =
wenzelm@51717
   691
  ctxt addWrapper (name, fn ctxt => fn tac1 => tac1 APPEND' tac2 ctxt);
wenzelm@42793
   692
wenzelm@51717
   693
fun ctxt addD2 (name, thm) = ctxt addafter (name, fn _ => dtac thm THEN' assume_tac);
wenzelm@51717
   694
fun ctxt addE2 (name, thm) = ctxt addafter (name, fn _ => etac thm THEN' assume_tac);
wenzelm@51717
   695
fun ctxt addSD2 (name, thm) = ctxt addSafter (name, fn _ => dmatch_tac [thm] THEN' eq_assume_tac);
wenzelm@51717
   696
fun ctxt addSE2 (name, thm) = ctxt addSafter (name, fn _ => ematch_tac [thm] THEN' eq_assume_tac);
wenzelm@42793
   697
paulson@1711
   698
lcp@982
   699
paulson@1800
   700
(**** Simple tactics for theorem proving ****)
clasohm@0
   701
clasohm@0
   702
(*Attack subgoals using safe inferences -- matching, not resolution*)
wenzelm@42793
   703
fun safe_step_tac ctxt =
wenzelm@42793
   704
  let val {safe0_netpair, safep_netpair, ...} = rep_claset_of ctxt in
wenzelm@42793
   705
    appSWrappers ctxt
wenzelm@42793
   706
      (FIRST'
wenzelm@42793
   707
       [eq_assume_tac,
wenzelm@9938
   708
        eq_mp_tac,
wenzelm@9938
   709
        bimatch_from_nets_tac safe0_netpair,
wenzelm@51798
   710
        FIRST' (map (fn tac => tac ctxt) Data.hyp_subst_tacs),
wenzelm@42793
   711
        bimatch_from_nets_tac safep_netpair])
wenzelm@42793
   712
  end;
clasohm@0
   713
oheimb@5757
   714
(*Repeatedly attack a subgoal using safe inferences -- it's deterministic!*)
wenzelm@42793
   715
fun safe_steps_tac ctxt =
wenzelm@42793
   716
  REPEAT_DETERM1 o (fn i => COND (has_fewer_prems i) no_tac (safe_step_tac ctxt i));
oheimb@5757
   717
clasohm@0
   718
(*Repeatedly attack subgoals using safe inferences -- it's deterministic!*)
wenzelm@42793
   719
fun safe_tac ctxt = REPEAT_DETERM1 (FIRSTGOAL (safe_steps_tac ctxt));
lcp@747
   720
paulson@3705
   721
paulson@3705
   722
(*** Clarify_tac: do safe steps without causing branching ***)
paulson@3705
   723
wenzelm@42790
   724
fun nsubgoalsP n (k, brl) = (subgoals_of_brl brl = n);
paulson@3705
   725
paulson@3705
   726
(*version of bimatch_from_nets_tac that only applies rules that
paulson@3705
   727
  create precisely n subgoals.*)
wenzelm@10736
   728
fun n_bimatch_from_nets_tac n =
wenzelm@42790
   729
  biresolution_from_nets_tac (order_list o filter (nsubgoalsP n)) true;
paulson@3705
   730
wenzelm@42792
   731
fun eq_contr_tac i = ematch_tac [Data.not_elim] i THEN eq_assume_tac i;
paulson@3705
   732
val eq_assume_contr_tac = eq_assume_tac ORELSE' eq_contr_tac;
paulson@3705
   733
paulson@3705
   734
(*Two-way branching is allowed only if one of the branches immediately closes*)
paulson@3705
   735
fun bimatch2_tac netpair i =
wenzelm@42790
   736
  n_bimatch_from_nets_tac 2 netpair i THEN
wenzelm@42790
   737
  (eq_assume_contr_tac i ORELSE eq_assume_contr_tac (i + 1));
paulson@3705
   738
paulson@3705
   739
(*Attack subgoals using safe inferences -- matching, not resolution*)
wenzelm@42793
   740
fun clarify_step_tac ctxt =
wenzelm@42793
   741
  let val {safe0_netpair, safep_netpair, ...} = rep_claset_of ctxt in
wenzelm@42793
   742
    appSWrappers ctxt
wenzelm@42793
   743
     (FIRST'
wenzelm@42793
   744
       [eq_assume_contr_tac,
wenzelm@9938
   745
        bimatch_from_nets_tac safe0_netpair,
wenzelm@51798
   746
        FIRST' (map (fn tac => tac ctxt) Data.hyp_subst_tacs),
wenzelm@9938
   747
        n_bimatch_from_nets_tac 1 safep_netpair,
wenzelm@42793
   748
        bimatch2_tac safep_netpair])
wenzelm@42793
   749
  end;
paulson@3705
   750
wenzelm@42793
   751
fun clarify_tac ctxt = SELECT_GOAL (REPEAT_DETERM (clarify_step_tac ctxt 1));
paulson@3705
   752
paulson@3705
   753
paulson@3705
   754
(*** Unsafe steps instantiate variables or lose information ***)
paulson@3705
   755
paulson@4066
   756
(*Backtracking is allowed among the various these unsafe ways of
paulson@4066
   757
  proving a subgoal.  *)
wenzelm@42793
   758
fun inst0_step_tac ctxt =
wenzelm@32862
   759
  assume_tac APPEND'
wenzelm@32862
   760
  contr_tac APPEND'
wenzelm@42793
   761
  biresolve_from_nets_tac (#safe0_netpair (rep_claset_of ctxt));
lcp@747
   762
paulson@4066
   763
(*These unsafe steps could generate more subgoals.*)
wenzelm@42793
   764
fun instp_step_tac ctxt =
wenzelm@42793
   765
  biresolve_from_nets_tac (#safep_netpair (rep_claset_of ctxt));
clasohm@0
   766
clasohm@0
   767
(*These steps could instantiate variables and are therefore unsafe.*)
wenzelm@42793
   768
fun inst_step_tac ctxt = inst0_step_tac ctxt APPEND' instp_step_tac ctxt;
clasohm@0
   769
wenzelm@42793
   770
fun haz_step_tac ctxt =
wenzelm@42793
   771
  biresolve_from_nets_tac (#haz_netpair (rep_claset_of ctxt));
lcp@681
   772
clasohm@0
   773
(*Single step for the prover.  FAILS unless it makes progress. *)
wenzelm@42793
   774
fun step_tac ctxt i =
wenzelm@42793
   775
  safe_tac ctxt ORELSE appWrappers ctxt (inst_step_tac ctxt ORELSE' haz_step_tac ctxt) i;
clasohm@0
   776
clasohm@0
   777
(*Using a "safe" rule to instantiate variables is unsafe.  This tactic
clasohm@0
   778
  allows backtracking from "safe" rules to "unsafe" rules here.*)
wenzelm@42793
   779
fun slow_step_tac ctxt i =
wenzelm@42793
   780
  safe_tac ctxt ORELSE appWrappers ctxt (inst_step_tac ctxt APPEND' haz_step_tac ctxt) i;
clasohm@0
   781
wenzelm@42791
   782
paulson@1800
   783
(**** The following tactics all fail unless they solve one goal ****)
clasohm@0
   784
clasohm@0
   785
(*Dumb but fast*)
wenzelm@42793
   786
fun fast_tac ctxt =
wenzelm@54742
   787
  Object_Logic.atomize_prems_tac ctxt THEN' SELECT_GOAL (DEPTH_SOLVE (step_tac ctxt 1));
clasohm@0
   788
clasohm@0
   789
(*Slower but smarter than fast_tac*)
wenzelm@42793
   790
fun best_tac ctxt =
wenzelm@54742
   791
  Object_Logic.atomize_prems_tac ctxt THEN'
wenzelm@42793
   792
  SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, Data.sizef) (step_tac ctxt 1));
clasohm@0
   793
oheimb@9402
   794
(*even a bit smarter than best_tac*)
wenzelm@42793
   795
fun first_best_tac ctxt =
wenzelm@54742
   796
  Object_Logic.atomize_prems_tac ctxt THEN'
wenzelm@42793
   797
  SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, Data.sizef) (FIRSTGOAL (step_tac ctxt)));
oheimb@9402
   798
wenzelm@42793
   799
fun slow_tac ctxt =
wenzelm@54742
   800
  Object_Logic.atomize_prems_tac ctxt THEN'
wenzelm@42793
   801
  SELECT_GOAL (DEPTH_SOLVE (slow_step_tac ctxt 1));
clasohm@0
   802
wenzelm@42793
   803
fun slow_best_tac ctxt =
wenzelm@54742
   804
  Object_Logic.atomize_prems_tac ctxt THEN'
wenzelm@42793
   805
  SELECT_GOAL (BEST_FIRST (has_fewer_prems 1, Data.sizef) (slow_step_tac ctxt 1));
clasohm@0
   806
lcp@681
   807
wenzelm@10736
   808
(***ASTAR with weight weight_ASTAR, by Norbert Voelker*)
wenzelm@42791
   809
wenzelm@42791
   810
val weight_ASTAR = 5;
paulson@1587
   811
wenzelm@42793
   812
fun astar_tac ctxt =
wenzelm@54742
   813
  Object_Logic.atomize_prems_tac ctxt THEN'
wenzelm@10382
   814
  SELECT_GOAL
wenzelm@52462
   815
    (ASTAR (has_fewer_prems 1, fn lev => fn thm => Data.sizef thm + weight_ASTAR * lev)
wenzelm@42793
   816
      (step_tac ctxt 1));
paulson@1587
   817
wenzelm@42793
   818
fun slow_astar_tac ctxt =
wenzelm@54742
   819
  Object_Logic.atomize_prems_tac ctxt THEN'
wenzelm@10382
   820
  SELECT_GOAL
wenzelm@52462
   821
    (ASTAR (has_fewer_prems 1, fn lev => fn thm => Data.sizef thm + weight_ASTAR * lev)
wenzelm@42793
   822
      (slow_step_tac ctxt 1));
paulson@1587
   823
wenzelm@42790
   824
paulson@1800
   825
(**** Complete tactic, loosely based upon LeanTaP.  This tactic is the outcome
lcp@747
   826
  of much experimentation!  Changing APPEND to ORELSE below would prove
lcp@747
   827
  easy theorems faster, but loses completeness -- and many of the harder
paulson@1800
   828
  theorems such as 43. ****)
lcp@681
   829
lcp@747
   830
(*Non-deterministic!  Could always expand the first unsafe connective.
lcp@747
   831
  That's hard to implement and did not perform better in experiments, due to
lcp@747
   832
  greater search depth required.*)
wenzelm@42793
   833
fun dup_step_tac ctxt =
wenzelm@42793
   834
  biresolve_from_nets_tac (#dup_netpair (rep_claset_of ctxt));
lcp@681
   835
oheimb@5523
   836
(*Searching to depth m. A variant called nodup_depth_tac appears in clasimp.ML*)
oheimb@5757
   837
local
wenzelm@42793
   838
  fun slow_step_tac' ctxt = appWrappers ctxt (instp_step_tac ctxt APPEND' dup_step_tac ctxt);
wenzelm@42790
   839
in
wenzelm@42793
   840
  fun depth_tac ctxt m i state = SELECT_GOAL
wenzelm@42793
   841
    (safe_steps_tac ctxt 1 THEN_ELSE
wenzelm@42793
   842
      (DEPTH_SOLVE (depth_tac ctxt m 1),
wenzelm@42793
   843
        inst0_step_tac ctxt 1 APPEND COND (K (m = 0)) no_tac
wenzelm@42793
   844
          (slow_step_tac' ctxt 1 THEN DEPTH_SOLVE (depth_tac ctxt (m - 1) 1)))) i state;
oheimb@5757
   845
end;
lcp@747
   846
wenzelm@10736
   847
(*Search, with depth bound m.
paulson@2173
   848
  This is the "entry point", which does safe inferences first.*)
wenzelm@42793
   849
fun safe_depth_tac ctxt m = SUBGOAL (fn (prem, i) =>
wenzelm@42793
   850
  let
wenzelm@42793
   851
    val deti = (*No Vars in the goal?  No need to backtrack between goals.*)
wenzelm@42793
   852
      if exists_subterm (fn Var _ => true | _ => false) prem then DETERM else I;
wenzelm@42790
   853
  in
wenzelm@42793
   854
    SELECT_GOAL (TRY (safe_tac ctxt) THEN DEPTH_SOLVE (deti (depth_tac ctxt m 1))) i
wenzelm@42790
   855
  end);
lcp@681
   856
wenzelm@42793
   857
fun deepen_tac ctxt = DEEPEN (2, 10) (safe_depth_tac ctxt);
wenzelm@24021
   858
wenzelm@24021
   859
wenzelm@5885
   860
(* attributes *)
wenzelm@5885
   861
wenzelm@42793
   862
fun attrib f =
wenzelm@42793
   863
  Thm.declaration_attribute (fn th => fn context => map_cs (f (SOME context) th) context);
wenzelm@5885
   864
wenzelm@18691
   865
val safe_elim = attrib o addSE;
wenzelm@18691
   866
val safe_intro = attrib o addSI;
wenzelm@42793
   867
val safe_dest = attrib o addSD;
wenzelm@18691
   868
val haz_elim = attrib o addE;
wenzelm@18691
   869
val haz_intro = attrib o addI;
wenzelm@42793
   870
val haz_dest = attrib o addD;
wenzelm@45375
   871
wenzelm@45375
   872
val rule_del =
wenzelm@45375
   873
  Thm.declaration_attribute (fn th => fn context =>
wenzelm@45375
   874
    context |> map_cs (delrule (SOME context) th) |>
wenzelm@45375
   875
    Thm.attribute_declaration Context_Rules.rule_del th);
wenzelm@5885
   876
wenzelm@5885
   877
wenzelm@5841
   878
wenzelm@5885
   879
(** concrete syntax of attributes **)
wenzelm@5841
   880
wenzelm@5841
   881
val introN = "intro";
wenzelm@5841
   882
val elimN = "elim";
wenzelm@5841
   883
val destN = "dest";
wenzelm@5841
   884
wenzelm@30528
   885
val setup_attrs =
wenzelm@30528
   886
  Attrib.setup @{binding swapped} (Scan.succeed swapped)
wenzelm@30528
   887
    "classical swap of introduction rule" #>
wenzelm@33369
   888
  Attrib.setup @{binding dest} (Context_Rules.add safe_dest haz_dest Context_Rules.dest_query)
wenzelm@30528
   889
    "declaration of Classical destruction rule" #>
wenzelm@33369
   890
  Attrib.setup @{binding elim} (Context_Rules.add safe_elim haz_elim Context_Rules.elim_query)
wenzelm@30528
   891
    "declaration of Classical elimination rule" #>
wenzelm@33369
   892
  Attrib.setup @{binding intro} (Context_Rules.add safe_intro haz_intro Context_Rules.intro_query)
wenzelm@30528
   893
    "declaration of Classical introduction rule" #>
wenzelm@30528
   894
  Attrib.setup @{binding rule} (Scan.lift Args.del >> K rule_del)
wenzelm@30528
   895
    "remove declaration of intro/elim/dest rule";
wenzelm@5841
   896
wenzelm@5841
   897
wenzelm@5841
   898
wenzelm@7230
   899
(** proof methods **)
wenzelm@7230
   900
wenzelm@7230
   901
local
wenzelm@7230
   902
wenzelm@30609
   903
fun some_rule_tac ctxt facts = SUBGOAL (fn (goal, i) =>
wenzelm@5841
   904
  let
wenzelm@33369
   905
    val [rules1, rules2, rules4] = Context_Rules.find_rules false facts goal ctxt;
wenzelm@42793
   906
    val {xtra_netpair, ...} = rep_claset_of ctxt;
wenzelm@33369
   907
    val rules3 = Context_Rules.find_rules_netpair true facts goal xtra_netpair;
wenzelm@12376
   908
    val rules = rules1 @ rules2 @ rules3 @ rules4;
wenzelm@18223
   909
    val ruleq = Drule.multi_resolves facts rules;
wenzelm@52732
   910
    val _ = Method.trace ctxt rules;
wenzelm@12376
   911
  in
wenzelm@52732
   912
    fn st => Seq.maps (fn rule => rtac rule i st) ruleq
wenzelm@18834
   913
  end)
wenzelm@54742
   914
  THEN_ALL_NEW Goal.norm_hhf_tac ctxt;
wenzelm@5841
   915
wenzelm@30609
   916
in
wenzelm@7281
   917
wenzelm@30609
   918
fun rule_tac ctxt [] facts = some_rule_tac ctxt facts
wenzelm@54742
   919
  | rule_tac ctxt rules facts = Method.rule_tac ctxt rules facts;
wenzelm@30609
   920
wenzelm@30609
   921
fun default_tac ctxt rules facts =
wenzelm@30609
   922
  HEADGOAL (rule_tac ctxt rules facts) ORELSE
haftmann@26470
   923
  Class.default_intro_tac ctxt facts;
wenzelm@10309
   924
wenzelm@7230
   925
end;
wenzelm@5841
   926
wenzelm@5841
   927
wenzelm@6502
   928
(* automatic methods *)
wenzelm@5841
   929
wenzelm@5927
   930
val cla_modifiers =
wenzelm@18728
   931
 [Args.$$$ destN -- Args.bang_colon >> K ((I, safe_dest NONE): Method.modifier),
wenzelm@18728
   932
  Args.$$$ destN -- Args.colon >> K (I, haz_dest NONE),
wenzelm@18728
   933
  Args.$$$ elimN -- Args.bang_colon >> K (I, safe_elim NONE),
wenzelm@18728
   934
  Args.$$$ elimN -- Args.colon >> K (I, haz_elim NONE),
wenzelm@18728
   935
  Args.$$$ introN -- Args.bang_colon >> K (I, safe_intro NONE),
wenzelm@18728
   936
  Args.$$$ introN -- Args.colon >> K (I, haz_intro NONE),
wenzelm@18728
   937
  Args.del -- Args.colon >> K (I, rule_del)];
wenzelm@5927
   938
wenzelm@42793
   939
fun cla_method tac = Method.sections cla_modifiers >> K (SIMPLE_METHOD o tac);
wenzelm@42793
   940
fun cla_method' tac = Method.sections cla_modifiers >> K (SIMPLE_METHOD' o tac);
wenzelm@5841
   941
wenzelm@5841
   942
wenzelm@5841
   943
wenzelm@5841
   944
(** setup_methods **)
wenzelm@5841
   945
wenzelm@30541
   946
val setup_methods =
wenzelm@30609
   947
  Method.setup @{binding default}
wenzelm@30609
   948
   (Attrib.thms >> (fn rules => fn ctxt => METHOD (default_tac ctxt rules)))
wenzelm@30541
   949
    "apply some intro/elim rule (potentially classical)" #>
wenzelm@30609
   950
  Method.setup @{binding rule}
wenzelm@30609
   951
    (Attrib.thms >> (fn rules => fn ctxt => METHOD (HEADGOAL o rule_tac ctxt rules)))
wenzelm@30541
   952
    "apply some intro/elim rule (potentially classical)" #>
wenzelm@50112
   953
  Method.setup @{binding contradiction}
wenzelm@54742
   954
    (Scan.succeed (fn ctxt => Method.rule ctxt [Data.not_elim, Drule.rotate_prems 1 Data.not_elim]))
wenzelm@30541
   955
    "proof by contradiction" #>
wenzelm@30541
   956
  Method.setup @{binding clarify} (cla_method' (CHANGED_PROP oo clarify_tac))
wenzelm@30541
   957
    "repeatedly apply safe steps" #>
wenzelm@30541
   958
  Method.setup @{binding fast} (cla_method' fast_tac) "classical prover (depth-first)" #>
wenzelm@30541
   959
  Method.setup @{binding slow} (cla_method' slow_tac) "classical prover (slow depth-first)" #>
wenzelm@30541
   960
  Method.setup @{binding best} (cla_method' best_tac) "classical prover (best-first)" #>
wenzelm@42798
   961
  Method.setup @{binding deepen}
wenzelm@42798
   962
    (Scan.lift (Scan.optional Parse.nat 4) --| Method.sections cla_modifiers
wenzelm@42798
   963
      >> (fn n => fn ctxt => SIMPLE_METHOD' (deepen_tac ctxt n)))
wenzelm@30541
   964
    "classical prover (iterative deepening)" #>
wenzelm@30541
   965
  Method.setup @{binding safe} (cla_method (CHANGED_PROP o safe_tac))
wenzelm@50108
   966
    "classical prover (apply safe rules)" #>
wenzelm@50108
   967
  Method.setup @{binding safe_step} (cla_method' safe_step_tac)
wenzelm@50108
   968
    "single classical step (safe rules)" #>
wenzelm@50108
   969
  Method.setup @{binding inst_step} (cla_method' inst_step_tac)
wenzelm@50108
   970
    "single classical step (safe rules, allow instantiations)" #>
wenzelm@50108
   971
  Method.setup @{binding step} (cla_method' step_tac)
wenzelm@50108
   972
    "single classical step (safe and unsafe rules)" #>
wenzelm@50108
   973
  Method.setup @{binding slow_step} (cla_method' slow_step_tac)
wenzelm@50108
   974
    "single classical step (safe and unsafe rules, allow backtracking)" #>
wenzelm@50108
   975
  Method.setup @{binding clarify_step} (cla_method' clarify_step_tac)
wenzelm@50108
   976
    "single classical step (safe rules, without splitting)";
wenzelm@5841
   977
wenzelm@5841
   978
wenzelm@5841
   979
wenzelm@5841
   980
(** theory setup **)
wenzelm@5841
   981
wenzelm@26497
   982
val setup = setup_attrs #> setup_methods;
wenzelm@5841
   983
wenzelm@5841
   984
wenzelm@8667
   985
wenzelm@8667
   986
(** outer syntax **)
wenzelm@8667
   987
wenzelm@24867
   988
val _ =
wenzelm@46961
   989
  Outer_Syntax.improper_command @{command_spec "print_claset"} "print context of Classical Reasoner"
wenzelm@51658
   990
    (Scan.succeed (Toplevel.unknown_context o Toplevel.keep (print_claset o Toplevel.context_of)));
wenzelm@8667
   991
wenzelm@5841
   992
end;