src/Pure/old_goals.ML
author wenzelm
Wed Jun 11 18:03:38 2008 +0200 (2008-06-11)
changeset 27157 0ddb5576b387
parent 26939 1035c89b4c02
child 27233 224c830e7abe
permissions -rw-r--r--
qualified inst;
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(*  Title:      Pure/old_goals.ML
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    ID:         $Id$
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Copyright   1993  University of Cambridge
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Old-style goal stack package.  The goal stack initially holds a dummy
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proof, and can never become empty.  Each goal stack consists of a list
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of levels.  The undo list is a list of goal stacks.  Finally, there
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may be a stack of pending proofs.
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*)
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signature GOALS =
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sig
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  val the_context: unit -> theory
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  val premises: unit -> thm list
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  val prove_goal: theory -> string -> (thm list -> tactic list) -> thm
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  val prove_goalw: theory -> thm list -> string -> (thm list -> tactic list) -> thm
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  val topthm: unit -> thm
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  val result: unit -> thm
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  val uresult: unit -> thm
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  val getgoal: int -> term
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  val gethyps: int -> thm list
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  val prlev: int -> unit
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  val pr: unit -> unit
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  val prlim: int -> unit
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  val goal: theory -> string -> thm list
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  val goalw: theory -> thm list -> string -> thm list
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  val Goal: string -> thm list
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  val Goalw: thm list -> string -> thm list
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  val by: tactic -> unit
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  val back: unit -> unit
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  val choplev: int -> unit
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  val undo: unit -> unit
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  val qed: string -> unit
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  val qed_goal: string -> theory -> string -> (thm list -> tactic list) -> unit
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  val qed_goalw: string -> theory -> thm list -> string
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    -> (thm list -> tactic list) -> unit
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  val qed_spec_mp: string -> unit
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  val qed_goal_spec_mp: string -> theory -> string -> (thm list -> tactic list) -> unit
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  val qed_goalw_spec_mp: string -> theory -> thm list -> string
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    -> (thm list -> tactic list) -> unit
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  val no_qed: unit -> unit
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end;
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signature OLD_GOALS =
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sig
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  include GOALS
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  type proof
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  val chop: unit -> unit
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  val reset_goals: unit -> unit
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  val result_error_fn: (thm -> string -> thm) ref
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  val print_sign_exn: theory -> exn -> 'a
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  val prove_goalw_cterm: thm list->cterm->(thm list->tactic list)->thm
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  val prove_goalw_cterm_nocheck: thm list->cterm->(thm list->tactic list)->thm
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  val quick_and_dirty_prove_goalw_cterm: theory -> thm list -> cterm
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    -> (thm list -> tactic list) -> thm
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  val print_exn: exn -> 'a
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  val filter_goal: (term*term->bool) -> thm list -> int -> thm list
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  val goalw_cterm: thm list -> cterm -> thm list
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  val simple_prove_goal_cterm: cterm->(thm list->tactic list)->thm
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  val byev: tactic list -> unit
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  val save_proof: unit -> proof
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  val restore_proof: proof -> thm list
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  val push_proof: unit -> unit
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  val pop_proof: unit -> thm list
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  val rotate_proof: unit -> thm list
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  val bws: thm list -> unit
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  val bw: thm -> unit
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  val brs: thm list -> int -> unit
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  val br: thm -> int -> unit
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  val bes: thm list -> int -> unit
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  val be: thm -> int -> unit
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  val bds: thm list -> int -> unit
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  val bd: thm -> int -> unit
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  val ba: int -> unit
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  val ren: string -> int -> unit
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  val frs: thm list -> unit
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  val fr: thm -> unit
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  val fes: thm list -> unit
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  val fe: thm -> unit
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  val fds: thm list -> unit
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  val fd: thm -> unit
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  val fa: unit -> unit
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  val inst: string -> string -> thm -> thm
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end;
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structure OldGoals: OLD_GOALS =
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struct
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val the_context = ML_Context.the_global_context;
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(*** Goal package ***)
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(*Each level of goal stack includes a proof state and alternative states,
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  the output of the tactic applied to the preceeding level.  *)
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type gstack = (thm * thm Seq.seq) list;
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datatype proof = Proof of gstack list * thm list * (bool*thm->thm);
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(*** References ***)
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(*Current assumption list -- set by "goal".*)
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val curr_prems = ref([] : thm list);
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(*Return assumption list -- useful if you didn't save "goal"'s result. *)
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fun premises() = !curr_prems;
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(*Current result maker -- set by "goal", used by "result".  *)
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fun init_mkresult _ = error "No goal has been supplied in subgoal module";
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val curr_mkresult = ref (init_mkresult: bool*thm->thm);
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(*List of previous goal stacks, for the undo operation.  Set by setstate.
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  A list of lists!*)
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val undo_list = ref([[(asm_rl, Seq.empty)]] : gstack list);
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(* Stack of proof attempts *)
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val proofstack = ref([]: proof list);
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(*reset all refs*)
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fun reset_goals () =
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  (curr_prems := []; curr_mkresult := init_mkresult;
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    undo_list := [[(asm_rl, Seq.empty)]]);
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(*** Setting up goal-directed proof ***)
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(*Generates the list of new theories when the proof state's theory changes*)
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fun thy_error (thy,thy') =
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  let val names = Context.names_of thy' \\ Context.names_of thy
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  in  case names of
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        [name] => "\nNew theory: " ^ name
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      | _       => "\nNew theories: " ^ space_implode ", " names
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  end;
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(*Default action is to print an error message; could be suppressed for
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  special applications.*)
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fun result_error_default state msg : thm =
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  Pretty.str "Bad final proof state:" :: Display.pretty_goals (!goals_limit) state @
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    [Pretty.str msg, Pretty.str "Proof failed!"] |> Pretty.chunks |> Pretty.string_of |> error;
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val result_error_fn = ref result_error_default;
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(*Common treatment of "goal" and "prove_goal":
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  Return assumptions, initial proof state, and function to make result.
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  "atomic" indicates if the goal should be wrapped up in the function
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  "Goal::prop=>prop" to avoid assumptions being returned separately.
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*)
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fun prepare_proof atomic rths chorn =
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  let
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      val _ = legacy_feature "Old goal command";
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      val thy = Thm.theory_of_cterm chorn;
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      val horn = Thm.term_of chorn;
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      val _ = Term.no_dummy_patterns horn handle TERM (msg, _) => error msg;
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      val (As, B) = Logic.strip_horn horn;
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      val atoms = atomic andalso
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            forall (fn t => not (can Logic.dest_implies t orelse can Logic.dest_all t)) As;
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      val (As,B) = if atoms then ([],horn) else (As,B);
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      val cAs = map (cterm_of thy) As;
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      val prems = map (rewrite_rule rths o Thm.forall_elim_vars 0 o Thm.assume) cAs;
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      val cB = cterm_of thy B;
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      val st0 = let val st = Goal.init cB |> fold Thm.weaken cAs
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                in  rewrite_goals_rule rths st end
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      (*discharges assumptions from state in the order they appear in goal;
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        checks (if requested) that resulting theorem is equivalent to goal. *)
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      fun mkresult (check,state) =
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        let val state = Seq.hd (flexflex_rule state)
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                        handle THM _ => state   (*smash flexflex pairs*)
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            val ngoals = nprems_of state
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            val ath = implies_intr_list cAs state
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            val th = Goal.conclude ath
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            val thy' = Thm.theory_of_thm th
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            val {hyps, prop, ...} = Thm.rep_thm th
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            val final_th = standard th
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        in  if not check then final_th
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            else if not (Theory.eq_thy(thy,thy')) then !result_error_fn state
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                ("Theory of proof state has changed!" ^
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                 thy_error (thy,thy'))
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            else if ngoals>0 then !result_error_fn state
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                (string_of_int ngoals ^ " unsolved goals!")
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            else if not (null hyps) then !result_error_fn state
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                ("Additional hypotheses:\n" ^
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                 cat_lines (map (Syntax.string_of_term_global thy) hyps))
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            else if Pattern.matches thy
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                                    (Envir.beta_norm (term_of chorn), Envir.beta_norm prop)
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                 then final_th
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            else  !result_error_fn state "proved a different theorem"
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        end
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  in
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     if Theory.eq_thy(thy, Thm.theory_of_thm st0)
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     then (prems, st0, mkresult)
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     else error ("Definitions would change the proof state's theory" ^
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                 thy_error (thy, Thm.theory_of_thm st0))
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  end
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  handle THM(s,_,_) => error("prepare_proof: exception THM was raised!\n" ^ s);
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(*Prints exceptions readably to users*)
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fun print_sign_exn_unit thy e =
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  case e of
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     THM (msg,i,thms) =>
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         (writeln ("Exception THM " ^ string_of_int i ^ " raised:\n" ^ msg);
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          List.app Display.print_thm thms)
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   | THEORY (msg,thys) =>
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         (writeln ("Exception THEORY raised:\n" ^ msg);
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          List.app (writeln o Context.str_of_thy) thys)
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   | TERM (msg,ts) =>
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         (writeln ("Exception TERM raised:\n" ^ msg);
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          List.app (writeln o Syntax.string_of_term_global thy) ts)
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   | TYPE (msg,Ts,ts) =>
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         (writeln ("Exception TYPE raised:\n" ^ msg);
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          List.app (writeln o Syntax.string_of_typ_global thy) Ts;
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          List.app (writeln o Syntax.string_of_term_global thy) ts)
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   | e => raise e;
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(*Prints an exception, then fails*)
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fun print_sign_exn thy e = (print_sign_exn_unit thy e; raise ERROR "");
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(** the prove_goal.... commands
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    Prove theorem using the listed tactics; check it has the specified form.
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    Augment theory with all type assignments of goal.
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    Syntax is similar to "goal" command for easy keyboard use. **)
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(*Version taking the goal as a cterm*)
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fun prove_goalw_cterm_general check rths chorn tacsf =
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  let val (prems, st0, mkresult) = prepare_proof false rths chorn
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      val tac = EVERY (tacsf prems)
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      fun statef() =
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          (case Seq.pull (tac st0) of
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               SOME(st,_) => st
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             | _ => error ("prove_goal: tactic failed"))
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  in  mkresult (check, cond_timeit (!Output.timing) "" statef)  end
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  handle e => (print_sign_exn_unit (Thm.theory_of_cterm chorn) e;
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               writeln ("The exception above was raised for\n" ^
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                      Display.string_of_cterm chorn); raise e);
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(*Two variants: one checking the result, one not.
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  Neither prints runtime messages: they are for internal packages.*)
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fun prove_goalw_cterm rths chorn =
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        setmp Output.timing false (prove_goalw_cterm_general true rths chorn)
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and prove_goalw_cterm_nocheck rths chorn =
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        setmp Output.timing false (prove_goalw_cterm_general false rths chorn);
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(*Version taking the goal as a string*)
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fun prove_goalw thy rths agoal tacsf =
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  let val chorn = Thm.read_cterm thy (agoal, propT)
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  in prove_goalw_cterm_general true rths chorn tacsf end
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  handle ERROR msg => cat_error msg (*from read_cterm?*)
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                ("The error(s) above occurred for " ^ quote agoal);
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(*String version with no meta-rewrite-rules*)
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fun prove_goal thy = prove_goalw thy [];
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(*quick and dirty version (conditional)*)
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fun quick_and_dirty_prove_goalw_cterm thy rews ct tacs =
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  prove_goalw_cterm rews ct
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    (if ! quick_and_dirty then (K [SkipProof.cheat_tac thy]) else tacs);
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(*** Commands etc ***)
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(*Return the current goal stack, if any, from undo_list*)
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fun getstate() : gstack = case !undo_list of
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      []   => error"No current state in subgoal module"
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    | x::_ => x;
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(*Pops the given goal stack*)
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fun pop [] = error"Cannot go back past the beginning of the proof!"
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  | pop (pair::pairs) = (pair,pairs);
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(* Print a level of the goal stack *)
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fun print_top ((th, _), pairs) =
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  let
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    val n = length pairs;
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    val m = (! goals_limit);
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    val ngoals = nprems_of th;
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  in
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    [Pretty.str ("Level " ^ string_of_int n ^
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      (if ngoals > 0 then " (" ^ string_of_int ngoals ^ " subgoal" ^
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        (if ngoals <> 1 then "s" else "") ^ ")"
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      else ""))] @
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    Display.pretty_goals m th
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  end |> Pretty.chunks |> Pretty.writeln;
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(*Printing can raise exceptions, so the assignment occurs last.
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  Can do   setstate[(st,Seq.empty)]  to set st as the state.  *)
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fun setstate newgoals =
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  (print_top (pop newgoals);  undo_list := newgoals :: !undo_list);
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(*Given a proof state transformation, return a command that updates
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    the goal stack*)
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fun make_command com = setstate (com (pop (getstate())));
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(*Apply a function on proof states to the current goal stack*)
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fun apply_fun f = f (pop(getstate()));
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(*Return the top theorem, representing the proof state*)
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fun topthm () = apply_fun  (fn ((th,_), _) => th);
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(*Return the final result.  *)
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fun result () = !curr_mkresult (true, topthm());
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(*Return the result UNCHECKED that it equals the goal -- for synthesis,
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  answer extraction, or other instantiation of Vars *)
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fun uresult () = !curr_mkresult (false, topthm());
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(*Get subgoal i from goal stack*)
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fun getgoal i = Logic.get_goal (prop_of (topthm())) i;
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(*Return subgoal i's hypotheses as meta-level assumptions.
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  For debugging uses of METAHYPS*)
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local exception GETHYPS of thm list
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in
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fun gethyps i =
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    (METAHYPS (fn hyps => raise (GETHYPS hyps)) i (topthm());  [])
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    handle GETHYPS hyps => hyps
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end;
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(*Prints exceptions nicely at top level;
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  raises the exception in order to have a polymorphic type!*)
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fun print_exn e = (print_sign_exn_unit (Thm.theory_of_thm (topthm())) e;  raise e);
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(*Which thms could apply to goal i? (debugs tactics involving filter_thms) *)
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fun filter_goal could ths i = filter_thms could (999, getgoal i, ths);
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(*For inspecting earlier levels of the backward proof*)
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fun chop_level n (pair,pairs) =
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  let val level = length pairs
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  in  if n<0 andalso ~n <= level
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      then  List.drop (pair::pairs, ~n)
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      else if 0<=n andalso n<= level
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      then  List.drop (pair::pairs, level - n)
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      else  error ("Level number must lie between 0 and " ^
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                   string_of_int level)
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  end;
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(*Print the given level of the proof; prlev ~1 prints previous level*)
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fun prlev n = apply_fun (print_top o pop o (chop_level n));
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fun pr () = apply_fun print_top;
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(*Set goals_limit and print again*)
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fun prlim n = (goals_limit:=n; pr());
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(** the goal.... commands
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    Read main goal.  Set global variables curr_prems, curr_mkresult.
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    Initial subgoal and premises are rewritten using rths. **)
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(*Version taking the goal as a cterm; if you have a term t and theory thy, use
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    goalw_cterm rths (cterm_of thy t);      *)
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fun agoalw_cterm atomic rths chorn =
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  let val (prems, st0, mkresult) = prepare_proof atomic rths chorn
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  in  undo_list := [];
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      setstate [ (st0, Seq.empty) ];
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      curr_prems := prems;
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      curr_mkresult := mkresult;
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      prems
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  end;
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val goalw_cterm = agoalw_cterm false;
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(*Version taking the goal as a string*)
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fun agoalw atomic thy rths agoal =
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    agoalw_cterm atomic rths (Thm.read_cterm thy (agoal, propT))
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    handle ERROR msg => cat_error msg (*from type_assign, etc via prepare_proof*)
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        ("The error(s) above occurred for " ^ quote agoal);
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val goalw = agoalw false;
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fun goal thy = goalw thy [];
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(*now the versions that wrap the goal up in `Goal' to make it atomic*)
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fun Goalw thms s = agoalw true (ML_Context.the_global_context ()) thms s;
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val Goal = Goalw [];
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(*simple version with minimal amount of checking and postprocessing*)
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fun simple_prove_goal_cterm G f =
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  let
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    val _ = legacy_feature "Old goal command";
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    val As = Drule.strip_imp_prems G;
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    val B = Drule.strip_imp_concl G;
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    val asms = map Assumption.assume As;
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    fun check NONE = error "prove_goal: tactic failed"
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      | check (SOME (thm, _)) = (case nprems_of thm of
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   387
            0 => thm
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          | i => !result_error_fn thm (string_of_int i ^ " unsolved goals!"))
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  in
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    standard (implies_intr_list As
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      (check (Seq.pull (EVERY (f asms) (trivial B)))))
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  end;
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   393
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   394
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   395
(*Proof step "by" the given tactic -- apply tactic to the proof state*)
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fun by_com tac ((th,ths), pairs) : gstack =
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   397
  (case  Seq.pull(tac th)  of
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   398
     NONE      => error"by: tactic failed"
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   399
   | SOME(th2,ths2) =>
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   400
       (if Thm.eq_thm(th,th2)
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   401
          then warning "Warning: same as previous level"
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   402
          else if Thm.eq_thm_thy(th,th2) then ()
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   403
          else warning ("Warning: theory of proof state has changed" ^
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   404
                       thy_error (Thm.theory_of_thm th, Thm.theory_of_thm th2));
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   405
       ((th2,ths2)::(th,ths)::pairs)));
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   406
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   407
fun by tac = cond_timeit (!Output.timing) ""
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   408
    (fn() => make_command (by_com tac));
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   409
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   410
(* byev[tac1,...,tacn] applies tac1 THEN ... THEN tacn.
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   411
   Good for debugging proofs involving prove_goal.*)
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   412
val byev = by o EVERY;
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   413
wenzelm@18120
   414
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   415
(*Backtracking means find an alternative result from a tactic.
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   416
  If none at this level, try earlier levels*)
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   417
fun backtrack [] = error"back: no alternatives"
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   418
  | backtrack ((th,thstr) :: pairs) =
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   419
     (case Seq.pull thstr of
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   420
          NONE      => (writeln"Going back a level..."; backtrack pairs)
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   421
        | SOME(th2,thstr2) =>
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   422
           (if Thm.eq_thm(th,th2)
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   423
              then warning "Warning: same as previous choice at this level"
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   424
              else if Thm.eq_thm_thy(th,th2) then ()
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   425
              else warning "Warning: theory of proof state has changed";
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   426
            (th2,thstr2)::pairs));
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   427
wenzelm@18120
   428
fun back() = setstate (backtrack (getstate()));
wenzelm@18120
   429
wenzelm@18120
   430
(*Chop back to previous level of the proof*)
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   431
fun choplev n = make_command (chop_level n);
wenzelm@18120
   432
wenzelm@18120
   433
(*Chopping back the goal stack*)
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   434
fun chop () = make_command (fn (_,pairs) => pairs);
wenzelm@18120
   435
wenzelm@18120
   436
(*Restore the previous proof state;  discard current state. *)
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   437
fun undo() = case !undo_list of
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   438
      [] => error"No proof state"
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   439
    | [_] => error"Already at initial state"
wenzelm@18120
   440
    | _::newundo =>  (undo_list := newundo;  pr()) ;
wenzelm@18120
   441
wenzelm@18120
   442
wenzelm@18120
   443
(*** Managing the proof stack ***)
wenzelm@18120
   444
wenzelm@18120
   445
fun save_proof() = Proof(!undo_list, !curr_prems, !curr_mkresult);
wenzelm@18120
   446
wenzelm@18120
   447
fun restore_proof(Proof(ul,prems,mk)) =
wenzelm@18120
   448
 (undo_list:= ul;  curr_prems:= prems;  curr_mkresult := mk;  prems);
wenzelm@18120
   449
wenzelm@18120
   450
wenzelm@18120
   451
fun top_proof() = case !proofstack of
wenzelm@18120
   452
        [] => error("Stack of proof attempts is empty!")
wenzelm@18120
   453
    | p::ps => (p,ps);
wenzelm@18120
   454
wenzelm@18120
   455
(*  push a copy of the current proof state on to the stack *)
wenzelm@18120
   456
fun push_proof() = (proofstack := (save_proof() :: !proofstack));
wenzelm@18120
   457
wenzelm@18120
   458
(* discard the top proof state of the stack *)
wenzelm@18120
   459
fun pop_proof() =
wenzelm@18120
   460
  let val (p,ps) = top_proof()
wenzelm@18120
   461
      val prems = restore_proof p
wenzelm@18120
   462
  in proofstack := ps;  pr();  prems end;
wenzelm@18120
   463
wenzelm@18120
   464
(* rotate the stack so that the top element goes to the bottom *)
wenzelm@18120
   465
fun rotate_proof() = let val (p,ps) = top_proof()
wenzelm@18120
   466
                    in proofstack := ps@[save_proof()];
wenzelm@18120
   467
                       restore_proof p;
wenzelm@18120
   468
                       pr();
wenzelm@18120
   469
                       !curr_prems
wenzelm@18120
   470
                    end;
wenzelm@18120
   471
wenzelm@18120
   472
wenzelm@18120
   473
(** Shortcuts for commonly-used tactics **)
wenzelm@18120
   474
wenzelm@18120
   475
fun bws rls = by (rewrite_goals_tac rls);
wenzelm@18120
   476
fun bw rl = bws [rl];
wenzelm@18120
   477
wenzelm@18120
   478
fun brs rls i = by (resolve_tac rls i);
wenzelm@18120
   479
fun br rl = brs [rl];
wenzelm@18120
   480
wenzelm@18120
   481
fun bes rls i = by (eresolve_tac rls i);
wenzelm@18120
   482
fun be rl = bes [rl];
wenzelm@18120
   483
wenzelm@18120
   484
fun bds rls i = by (dresolve_tac rls i);
wenzelm@18120
   485
fun bd rl = bds [rl];
wenzelm@18120
   486
wenzelm@18120
   487
fun ba i = by (assume_tac i);
wenzelm@18120
   488
wenzelm@18120
   489
fun ren str i = by (rename_tac str i);
wenzelm@18120
   490
wenzelm@18120
   491
(** Shortcuts to work on the first applicable subgoal **)
wenzelm@18120
   492
wenzelm@18120
   493
fun frs rls = by (FIRSTGOAL (trace_goalno_tac (resolve_tac rls)));
wenzelm@18120
   494
fun fr rl = frs [rl];
wenzelm@18120
   495
wenzelm@18120
   496
fun fes rls = by (FIRSTGOAL (trace_goalno_tac (eresolve_tac rls)));
wenzelm@18120
   497
fun fe rl = fes [rl];
wenzelm@18120
   498
wenzelm@18120
   499
fun fds rls = by (FIRSTGOAL (trace_goalno_tac (dresolve_tac rls)));
wenzelm@18120
   500
fun fd rl = fds [rl];
wenzelm@18120
   501
wenzelm@18120
   502
fun fa() = by (FIRSTGOAL (trace_goalno_tac assume_tac));
wenzelm@18120
   503
wenzelm@18120
   504
wenzelm@26414
   505
(** theorem bindings **)
wenzelm@18120
   506
wenzelm@26414
   507
fun qed name = ML_Context.ml_store_thm (name, result ());
wenzelm@26414
   508
fun qed_goal name thy goal tacsf = ML_Context.ml_store_thm (name, prove_goal thy goal tacsf);
wenzelm@18120
   509
fun qed_goalw name thy rews goal tacsf =
wenzelm@26414
   510
  ML_Context.ml_store_thm (name, prove_goalw thy rews goal tacsf);
wenzelm@18120
   511
fun qed_spec_mp name =
wenzelm@26414
   512
  ML_Context.ml_store_thm (name, ObjectLogic.rulify_no_asm (result ()));
wenzelm@18120
   513
fun qed_goal_spec_mp name thy s p =
wenzelm@18120
   514
  bind_thm (name, ObjectLogic.rulify_no_asm (prove_goal thy s p));
wenzelm@18120
   515
fun qed_goalw_spec_mp name thy defs s p =
wenzelm@18120
   516
  bind_thm (name, ObjectLogic.rulify_no_asm (prove_goalw thy defs s p));
wenzelm@18120
   517
wenzelm@18120
   518
fun no_qed () = ();
wenzelm@18120
   519
wenzelm@22109
   520
(*shorthand for instantiating just one variable in the current theory*)
wenzelm@27157
   521
fun inst x t = Drule.read_instantiate_sg (ML_Context.the_global_context()) [(x,t)];
wenzelm@22109
   522
wenzelm@18120
   523
end;
wenzelm@18120
   524
wenzelm@18120
   525
structure Goals: GOALS = OldGoals;
wenzelm@18120
   526
open Goals;