src/Pure/Tools/find_theorems.ML
author Timothy Bourke
Wed May 06 10:55:47 2009 +1000 (2009-05-06)
changeset 31042 d452117ba564
parent 30822 8aac4b974280
child 31684 d5d830979a54
permissions -rw-r--r--
Prototype introiff option for find_theorems.

This feature was suggested by Jeremy Avigad / Tobias Nipkow.

It adds an introiff keyword for find_theorems that returns, in
addition to the usual results for intro, any theorems of the
form ([| ... |] ==> (P = Q)) where either P or Q matches the
conclusions of the current goal. Such theorems can be made
introduction rules with [THEN iffDx].

The current patch is for evaluation only. It assumes an
(op = : 'a -> 'a -> bool) operator, which is specific to HOL.
It is not clear how this should be generalised.
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(*  Title:      Pure/Tools/find_theorems.ML
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    Author:     Rafal Kolanski and Gerwin Klein, NICTA
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Retrieve theorems from proof context.
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*)
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signature FIND_THEOREMS =
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sig
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  datatype 'term criterion =
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    Name of string | Intro | IntroIff | Elim | Dest | Solves | Simp of 'term |
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    Pattern of 'term
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  val tac_limit: int ref
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  val limit: int ref
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  val find_theorems: Proof.context -> thm option -> int option -> bool ->
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    (bool * string criterion) list -> int option * (Facts.ref * thm) list
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  val pretty_thm: Proof.context -> Facts.ref * thm -> Pretty.T
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  val print_theorems: Proof.context -> thm option -> int option -> bool ->
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    (bool * string criterion) list -> unit
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end;
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structure FindTheorems: FIND_THEOREMS =
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struct
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(** search criteria **)
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datatype 'term criterion =
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  Name of string | Intro | IntroIff | Elim | Dest | Solves | Simp of 'term |
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  Pattern of 'term;
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fun read_criterion _ (Name name) = Name name
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  | read_criterion _ Intro = Intro
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  | read_criterion _ IntroIff = IntroIff
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  | read_criterion _ Elim = Elim
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  | read_criterion _ Dest = Dest
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  | read_criterion _ Solves = Solves
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  | read_criterion ctxt (Simp str) = Simp (ProofContext.read_term_pattern ctxt str)
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  | read_criterion ctxt (Pattern str) = Pattern (ProofContext.read_term_pattern ctxt str);
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fun pretty_criterion ctxt (b, c) =
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  let
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    fun prfx s = if b then s else "-" ^ s;
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  in
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    (case c of
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      Name name => Pretty.str (prfx "name: " ^ quote name)
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    | Intro => Pretty.str (prfx "intro")
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    | IntroIff => Pretty.str (prfx "introiff")
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    | Elim => Pretty.str (prfx "elim")
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    | Dest => Pretty.str (prfx "dest")
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    | Solves => Pretty.str (prfx "solves")
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    | Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1,
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        Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))]
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    | Pattern pat => Pretty.enclose (prfx " \"") "\""
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        [Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)])
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  end;
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(** search criterion filters **)
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(*generated filters are to be of the form
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  input: (Facts.ref * thm)
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  output: (p:int, s:int) option, where
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    NONE indicates no match
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    p is the primary sorting criterion
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      (eg. number of assumptions in the theorem)
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    s is the secondary sorting criterion
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      (eg. size of the substitution for intro, elim and dest)
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  when applying a set of filters to a thm, fold results in:
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    (biggest p, sum of all s)
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  currently p and s only matter for intro, elim, dest and simp filters,
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  otherwise the default ordering is used.
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*)
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(* matching theorems *)
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fun is_nontrivial thy = Term.is_Const o Term.head_of o ObjectLogic.drop_judgment thy;
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(* Note: ("op =" : "bool --> bool --> bool") does not exist in Pure. *)
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fun is_Iff c =
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  (case dest_Const c of
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     ("op =", ty) =>
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       (ty
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        |> strip_type
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        |> swap
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        |> (op ::)
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        |> map (fst o dest_Type)
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        |> forall (curry (op =) "bool")
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        handle TYPE _ => false)
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   | _ => false);
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(*extract terms from term_src, refine them to the parts that concern us,
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  if po try match them against obj else vice versa.
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  trivial matches are ignored.
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  returns: smallest substitution size*)
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fun is_matching_thm doiff (extract_terms, refine_term) ctxt po obj term_src =
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  let
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    val thy = ProofContext.theory_of ctxt;
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    val chkmatch = obj |> (if po then rpair else pair) #> Pattern.matches thy;
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    fun matches pat =
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      let
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        val jpat = ObjectLogic.drop_judgment thy pat;
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        val c = Term.head_of jpat;
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        val pats =
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          if Term.is_Const c
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          then if doiff andalso is_Iff c
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               then pat :: map (ObjectLogic.ensure_propT thy) ((snd o strip_comb) jpat)
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                    |> filter (is_nontrivial thy)
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               else [pat]
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          else [];
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      in filter chkmatch pats end;
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    fun substsize pat =
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      let val (_, subst) =
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        Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)
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      in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;
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    fun bestmatch [] = NONE
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     |  bestmatch xs = SOME (foldr1 Int.min xs);
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    val match_thm = matches o refine_term;
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  in
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    map match_thm (extract_terms term_src)
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    |> flat
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    |> map substsize
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    |> bestmatch
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  end;
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(* filter_name *)
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fun filter_name str_pat (thmref, _) =
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  if match_string str_pat (Facts.name_of_ref thmref)
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  then SOME (0, 0) else NONE;
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(* filter intro/elim/dest/solves rules *)
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fun filter_dest ctxt goal (_, thm) =
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  let
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    val extract_dest =
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     (fn thm => if Thm.no_prems thm then [] else [Thm.full_prop_of thm],
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      hd o Logic.strip_imp_prems);
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    val prems = Logic.prems_of_goal goal 1;
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    fun try_subst prem = is_matching_thm false extract_dest ctxt true prem thm;
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    val successful = prems |> map_filter try_subst;
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  in
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    (*if possible, keep best substitution (one with smallest size)*)
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    (*dest rules always have assumptions, so a dest with one
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      assumption is as good as an intro rule with none*)
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    if not (null successful)
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    then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE
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  end;
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fun filter_intro doiff ctxt goal (_, thm) =
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  let
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    val extract_intro = (single o Thm.full_prop_of, Logic.strip_imp_concl);
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    val concl = Logic.concl_of_goal goal 1;
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    val ss = is_matching_thm doiff extract_intro ctxt true concl thm;
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  in
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    if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
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  end;
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fun filter_elim ctxt goal (_, thm) =
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  if not (Thm.no_prems thm) then
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    let
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      val rule = Thm.full_prop_of thm;
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      val prems = Logic.prems_of_goal goal 1;
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      val goal_concl = Logic.concl_of_goal goal 1;
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      val rule_mp = hd (Logic.strip_imp_prems rule);
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      val rule_concl = Logic.strip_imp_concl rule;
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      fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) $ (t1 $ t2);
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      val rule_tree = combine rule_mp rule_concl;
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      fun goal_tree prem = combine prem goal_concl;
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      fun try_subst prem =
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        is_matching_thm false (single, I) ctxt true (goal_tree prem) rule_tree;
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      val successful = prems |> map_filter try_subst;
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    in
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    (*elim rules always have assumptions, so an elim with one
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      assumption is as good as an intro rule with none*)
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      if is_nontrivial (ProofContext.theory_of ctxt) (Thm.major_prem_of thm)
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        andalso not (null successful)
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      then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE
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    end
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  else NONE
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val tac_limit = ref 5;
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fun filter_solves ctxt goal =
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  let
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    val baregoal = Logic.get_goal (Thm.prop_of goal) 1;
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    fun etacn thm i = Seq.take (! tac_limit) o etac thm i;
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    fun try_thm thm =
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      if Thm.no_prems thm then rtac thm 1 goal
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      else (etacn thm THEN_ALL_NEW (Goal.norm_hhf_tac THEN' Method.assm_tac ctxt)) 1 goal;
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  in
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    fn (_, thm) =>
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      if (is_some o Seq.pull o try_thm) thm
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      then SOME (Thm.nprems_of thm, 0) else NONE
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  end;
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(* filter_simp *)
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fun filter_simp ctxt t (_, thm) =
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  let
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    val mksimps = Simplifier.mksimps (Simplifier.local_simpset_of ctxt);
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    val extract_simp =
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      (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl);
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    val ss = is_matching_thm false extract_simp ctxt false t thm;
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  in
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    if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE
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  end;
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(* filter_pattern *)
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fun get_names t = (Term.add_const_names t []) union (Term.add_free_names t []);
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fun get_thm_names (_, thm) = get_names (Thm.full_prop_of thm);
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(*Including all constants and frees is only sound because
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  matching uses higher-order patterns. If full matching
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  were used, then constants that may be subject to
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  beta-reduction after substitution of frees should
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  not be included for LHS set because they could be
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  thrown away by the substituted function.
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  e.g. for (?F 1 2) do not include 1 or 2, if it were
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       possible for ?F to be (% x y. 3)
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  The largest possible set should always be included on
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  the RHS.*)
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fun filter_pattern ctxt pat =
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  let
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    val pat_consts = get_names pat;
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    fun check (t, NONE) = check (t, SOME (get_thm_names t))
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      | check ((_, thm), c as SOME thm_consts) =
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          (if pat_consts subset_string thm_consts
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              andalso (Pattern.matches_subterm (ProofContext.theory_of ctxt)
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                                               (pat, Thm.full_prop_of thm))
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           then SOME (0, 0) else NONE, c);
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  in check end;
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(* interpret criteria as filters *)
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local
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fun err_no_goal c =
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  error ("Current goal required for " ^ c ^ " search criterion");
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val fix_goal = Thm.prop_of;
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val fix_goalo = Option.map fix_goal;
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fun filter_crit _ _ (Name name) = apfst (filter_name name)
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  | filter_crit _ NONE Intro = err_no_goal "intro"
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  | filter_crit _ NONE Elim = err_no_goal "elim"
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  | filter_crit _ NONE Dest = err_no_goal "dest"
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  | filter_crit _ NONE Solves = err_no_goal "solves"
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  | filter_crit ctxt (SOME goal) Intro = apfst (filter_intro false ctxt (fix_goal goal))
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  | filter_crit ctxt (SOME goal) IntroIff = apfst (filter_intro true ctxt (fix_goal goal))
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  | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (fix_goal goal))
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  | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (fix_goal goal))
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  | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)
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  | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)
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  | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;
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fun opt_not x = if is_some x then NONE else SOME (0, 0);
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fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)
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  | opt_add _ _ = NONE;
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fun app_filters thm =
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  let
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    fun app (NONE, _, _) = NONE
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      | app (SOME v, consts, []) = SOME (v, thm)
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      | app (r, consts, f :: fs) =
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          let val (r', consts') = f (thm, consts)
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          in app (opt_add r r', consts', fs) end;
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  in app end;
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in
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fun filter_criterion ctxt opt_goal (b, c) =
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  (if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c;
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fun sorted_filter filters thms =
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  let
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    fun eval_filters thm = app_filters thm (SOME (0, 0), NONE, filters);
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    (*filters return: (number of assumptions, substitution size) option, so
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      sort (desc. in both cases) according to number of assumptions first,
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      then by the substitution size*)
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    fun thm_ord (((p0, s0), _), ((p1, s1), _)) =
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      prod_ord int_ord int_ord ((p1, s1), (p0, s0));
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  in map_filter eval_filters thms |> sort thm_ord |> map #2 end;
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fun lazy_filter filters =
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  let
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    fun lazy_match thms = Seq.make (fn () => first_match thms)
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    and first_match [] = NONE
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      | first_match (thm :: thms) =
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          (case app_filters thm (SOME (0, 0), NONE, filters) of
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            NONE => first_match thms
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          | SOME (_, t) => SOME (t, lazy_match thms));
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  in lazy_match end;
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end;
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(* removing duplicates, preferring nicer names, roughly n log n *)
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local
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val index_ord = option_ord (K EQUAL);
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val hidden_ord = bool_ord o pairself NameSpace.is_hidden;
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val qual_ord = int_ord o pairself (length o Long_Name.explode);
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val txt_ord = int_ord o pairself size;
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fun nicer_name (x, i) (y, j) =
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  (case hidden_ord (x, y) of EQUAL =>
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    (case index_ord (i, j) of EQUAL =>
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   328
      (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)
huffman@27486
   329
    | ord => ord)
wenzelm@25226
   330
  | ord => ord) <> GREATER;
wenzelm@25226
   331
Timothy@29848
   332
fun rem_cdups nicer xs =
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   333
  let
wenzelm@26336
   334
    fun rem_c rev_seen [] = rev rev_seen
wenzelm@26336
   335
      | rem_c rev_seen [x] = rem_c (x :: rev_seen) []
wenzelm@26336
   336
      | rem_c rev_seen ((x as ((n, t), _)) :: (y as ((n', t'), _)) :: xs) =
wenzelm@30822
   337
          if Thm.eq_thm_prop (t, t')
wenzelm@30822
   338
          then rem_c rev_seen ((if nicer n n' then x else y) :: xs)
wenzelm@30822
   339
          else rem_c (x :: rev_seen) (y :: xs)
wenzelm@26336
   340
  in rem_c [] xs end;
wenzelm@25226
   341
wenzelm@26336
   342
in
wenzelm@25226
   343
wenzelm@30143
   344
fun nicer_shortest ctxt =
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   345
  let
wenzelm@30216
   346
    (* FIXME global name space!? *)
wenzelm@30216
   347
    val space = Facts.space_of (PureThy.facts_of (ProofContext.theory_of ctxt));
Timothy@29848
   348
wenzelm@30216
   349
    val shorten =
wenzelm@30216
   350
      NameSpace.extern_flags {long_names = false, short_names = false, unique_names = false} space;
Timothy@29848
   351
Timothy@29848
   352
    fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
Timothy@29848
   353
          nicer_name (shorten x, i) (shorten y, j)
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   354
      | nicer (Facts.Fact _) (Facts.Named _) = true
Timothy@29848
   355
      | nicer (Facts.Named _) (Facts.Fact _) = false;
Timothy@29848
   356
  in nicer end;
Timothy@29848
   357
Timothy@29848
   358
fun rem_thm_dups nicer xs =
wenzelm@26336
   359
  xs ~~ (1 upto length xs)
wenzelm@29269
   360
  |> sort (TermOrd.fast_term_ord o pairself (Thm.prop_of o #2 o #1))
Timothy@29848
   361
  |> rem_cdups nicer
wenzelm@26336
   362
  |> sort (int_ord o pairself #2)
wenzelm@26336
   363
  |> map #1;
kleing@22340
   364
wenzelm@26336
   365
end;
kleing@22340
   366
kleing@22340
   367
wenzelm@16033
   368
(* print_theorems *)
wenzelm@16033
   369
wenzelm@26283
   370
fun all_facts_of ctxt =
wenzelm@26336
   371
  maps Facts.selections
wenzelm@27173
   372
   (Facts.dest_static [] (PureThy.facts_of (ProofContext.theory_of ctxt)) @
wenzelm@27173
   373
    Facts.dest_static [] (ProofContext.facts_of ctxt));
wenzelm@17972
   374
wenzelm@25992
   375
val limit = ref 40;
wenzelm@25992
   376
Timothy@30785
   377
fun find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
wenzelm@16033
   378
  let
wenzelm@30822
   379
    val assms =
wenzelm@30822
   380
      ProofContext.get_fact ctxt (Facts.named "local.assms")
wenzelm@30822
   381
        handle ERROR _ => [];
wenzelm@30822
   382
    val add_prems = Seq.hd o TRY (Method.insert_tac assms 1);
kleing@29857
   383
    val opt_goal' = Option.map add_prems opt_goal;
kleing@29857
   384
wenzelm@16036
   385
    val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
kleing@29857
   386
    val filters = map (filter_criterion ctxt opt_goal') criteria;
wenzelm@16033
   387
Timothy@30785
   388
    fun find_all facts =
Timothy@30785
   389
      let
Timothy@30785
   390
        val raw_matches = sorted_filter filters facts;
Timothy@30785
   391
Timothy@30785
   392
        val matches =
Timothy@30785
   393
          if rem_dups
Timothy@30785
   394
          then rem_thm_dups (nicer_shortest ctxt) raw_matches
Timothy@30785
   395
          else raw_matches;
kleing@28900
   396
Timothy@30785
   397
        val len = length matches;
Timothy@30785
   398
        val lim = the_default (! limit) opt_limit;
Timothy@30785
   399
      in (SOME len, Library.drop (len - lim, matches)) end;
Timothy@30785
   400
Timothy@30785
   401
    val find =
Timothy@30785
   402
      if rem_dups orelse is_none opt_limit
Timothy@30785
   403
      then find_all
wenzelm@30822
   404
      else pair NONE o Seq.list_of o Seq.take (the opt_limit) o lazy_filter filters;
Timothy@30785
   405
Timothy@30785
   406
  in find (all_facts_of ctxt) end;
kleing@29857
   407
wenzelm@30186
   408
wenzelm@30186
   409
fun pretty_thm ctxt (thmref, thm) = Pretty.block
wenzelm@30186
   410
  [Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,
wenzelm@30186
   411
    ProofContext.pretty_thm ctxt thm];
wenzelm@30186
   412
wenzelm@30143
   413
fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
wenzelm@30143
   414
  let
kleing@29857
   415
    val start = start_timing ();
kleing@29857
   416
kleing@29857
   417
    val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
Timothy@30785
   418
    val (foundo, thms) = find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria;
Timothy@30785
   419
    val returned = length thms;
Timothy@30785
   420
    
Timothy@30785
   421
    val tally_msg =
wenzelm@30822
   422
      (case foundo of
Timothy@30785
   423
        NONE => "displaying " ^ string_of_int returned ^ " theorems"
wenzelm@30822
   424
      | SOME found =>
wenzelm@30822
   425
          "found " ^ string_of_int found ^ " theorems" ^
wenzelm@30822
   426
            (if returned < found
wenzelm@30822
   427
             then " (" ^ string_of_int returned ^ " displayed)"
wenzelm@30822
   428
             else ""));
wenzelm@16033
   429
wenzelm@30188
   430
    val end_msg = " in " ^ Time.toString (#all (end_timing start)) ^ " secs";
wenzelm@16033
   431
  in
kleing@28900
   432
    Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria)
kleing@29857
   433
        :: Pretty.str "" ::
kleing@28900
   434
     (if null thms then [Pretty.str ("nothing found" ^ end_msg)]
wenzelm@16033
   435
      else
Timothy@30785
   436
        [Pretty.str (tally_msg ^ end_msg ^ ":"), Pretty.str ""] @
wenzelm@30186
   437
        map (pretty_thm ctxt) thms)
wenzelm@16033
   438
    |> Pretty.chunks |> Pretty.writeln
wenzelm@30142
   439
  end;
wenzelm@30142
   440
wenzelm@30142
   441
wenzelm@30142
   442
(** command syntax **)
wenzelm@30142
   443
wenzelm@30142
   444
fun find_theorems_cmd ((opt_lim, rem_dups), spec) =
wenzelm@30142
   445
  Toplevel.unknown_theory o Toplevel.keep (fn state =>
wenzelm@30822
   446
    let
wenzelm@30822
   447
      val proof_state = Toplevel.enter_proof_body state;
wenzelm@30822
   448
      val ctxt = Proof.context_of proof_state;
wenzelm@30822
   449
      val opt_goal = try Proof.get_goal proof_state |> Option.map (#2 o #2);
wenzelm@30822
   450
    in print_theorems ctxt opt_goal opt_lim rem_dups spec end);
wenzelm@30142
   451
wenzelm@30142
   452
local
wenzelm@30142
   453
wenzelm@30142
   454
structure P = OuterParse and K = OuterKeyword;
wenzelm@30142
   455
wenzelm@30142
   456
val criterion =
wenzelm@30142
   457
  P.reserved "name" |-- P.!!! (P.$$$ ":" |-- P.xname) >> Name ||
wenzelm@30142
   458
  P.reserved "intro" >> K Intro ||
Timothy@31042
   459
  P.reserved "introiff" >> K IntroIff ||
wenzelm@30142
   460
  P.reserved "elim" >> K Elim ||
wenzelm@30142
   461
  P.reserved "dest" >> K Dest ||
wenzelm@30142
   462
  P.reserved "solves" >> K Solves ||
wenzelm@30142
   463
  P.reserved "simp" |-- P.!!! (P.$$$ ":" |-- P.term) >> Simp ||
wenzelm@30142
   464
  P.term >> Pattern;
wenzelm@30142
   465
wenzelm@30142
   466
val options =
wenzelm@30142
   467
  Scan.optional
wenzelm@30142
   468
    (P.$$$ "(" |--
wenzelm@30142
   469
      P.!!! (Scan.option P.nat -- Scan.optional (P.reserved "with_dups" >> K false) true
wenzelm@30142
   470
        --| P.$$$ ")")) (NONE, true);
wenzelm@30142
   471
in
wenzelm@30142
   472
wenzelm@30142
   473
val _ =
wenzelm@30142
   474
  OuterSyntax.improper_command "find_theorems" "print theorems meeting specified criteria" K.diag
wenzelm@30142
   475
    (options -- Scan.repeat (((Scan.option P.minus >> is_none) -- criterion))
wenzelm@30142
   476
      >> (Toplevel.no_timing oo find_theorems_cmd));
wenzelm@16033
   477
wenzelm@16033
   478
end;
wenzelm@30142
   479
wenzelm@30142
   480
end;