src/Pure/Isar/find_theorems.ML

removed obsolete ProofGeneral/pgml_isabelle.ML;

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−(*  Title:      Pure/Isar/find_theorems.ML
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−    ID:         $Id$
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−    Author:     Rafal Kolanski and Gerwin Klein, NICTA
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−
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−Retrieve theorems from proof context.
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−*)
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−
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−signature FIND_THEOREMS =
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−sig
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−  val limit: int ref
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−  datatype 'term criterion =
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−    Name of string | Intro | Elim | Dest | Simp of 'term | Pattern of 'term
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−  val print_theorems: Proof.context -> term option -> int option -> bool ->
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−    (bool * string criterion) list -> unit
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−end;
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−
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−structure FindTheorems: FIND_THEOREMS =
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−struct
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−
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−(** search criteria **)
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−
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−datatype 'term criterion =
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−  Name of string | Intro | Elim | Dest | Simp of 'term | Pattern of 'term;
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−
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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 _ Elim = Elim
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−  | read_criterion _ Dest = Dest
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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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−
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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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−    | Elim => Pretty.str (prfx "elim")
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−    | Dest => Pretty.str (prfx "dest")
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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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−
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−
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−
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−(** search criterion filters **)
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−
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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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−
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−
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−(* matching theorems *)
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−
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−fun is_nontrivial thy = Term.is_Const o Term.head_of o ObjectLogic.drop_judgment thy;
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−
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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 (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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−
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−    fun matches pat =
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−      is_nontrivial thy pat andalso
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−      Pattern.matches thy (if po then (pat, obj) else (obj, pat));
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−
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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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−
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−    fun bestmatch [] = NONE
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−     |  bestmatch xs = SOME (foldr1 Int.min xs);
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−
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−    val match_thm = matches o refine_term;
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−  in
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−    map (substsize o refine_term) (filter match_thm (extract_terms term_src))
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−    |> bestmatch
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−  end;
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−
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−
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−(* filter_name *)
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−
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−fun match_string pat str =
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−  let
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−    fun match [] _ = true
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−      | match (p :: ps) s =
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−          size p <= size s andalso
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−            (case try (unprefix p) s of
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−              SOME s' => match ps s'
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−            | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));
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−  in match (space_explode "*" pat) str end;
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−
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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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−
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−
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−(* filter intro/elim/dest rules *)
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−
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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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−
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−    fun try_subst prem = is_matching_thm 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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−
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−fun filter_intro 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 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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−
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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 (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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−
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−
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−(* filter_simp *)
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−
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−fun filter_simp ctxt t (_, thm) =
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−  let
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−    val (_, {mk_rews = {mk, ...}, ...}) =
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−      MetaSimplifier.rep_ss (Simplifier.local_simpset_of ctxt);
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−    val extract_simp =
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−      (map Thm.full_prop_of o mk, #1 o Logic.dest_equals o Logic.strip_imp_concl);
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−    val ss = is_matching_thm 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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−
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−
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−(* filter_pattern *)
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−
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−fun filter_pattern ctxt pat (_, thm) =
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−  if Pattern.matches_subterm (ProofContext.theory_of ctxt) (pat, Thm.full_prop_of thm)
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−  then SOME (0, 0) else NONE;
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−
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−
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−(* interpret criteria as filters *)
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−
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−local
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−
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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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−
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−fun filter_crit _ _ (Name name) = 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 ctxt (SOME goal) Intro = filter_intro ctxt goal
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−  | filter_crit ctxt (SOME goal) Elim = filter_elim ctxt goal
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−  | filter_crit ctxt (SOME goal) Dest = filter_dest ctxt goal
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−  | filter_crit ctxt _ (Simp pat) = filter_simp ctxt pat
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−  | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;
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−
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−fun opt_not x = if is_some x then NONE else SOME (0, 0);
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−
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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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−
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−in
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−
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−fun filter_criterion ctxt opt_goal (b, c) =
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−  (if b then I else opt_not) o filter_crit ctxt opt_goal c;
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−
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−fun all_filters filters thms =
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−  let
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−    fun eval_filters thm =
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−      fold opt_add (map (fn f => f thm) filters) (SOME (0, 0));
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−
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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
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−    map (`eval_filters) thms
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−    |> map_filter (fn (SOME x, y) => SOME (x, y) | (NONE, _) => NONE)
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−    |> sort thm_ord |> map #2
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−  end;
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−
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−end;
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−
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−
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−(* removing duplicates, preferring nicer names, roughly n log n *)
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−
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−local
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−
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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 NameSpace.explode);
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−val txt_ord = int_ord o pairself size;
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−
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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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−      (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)
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−    | ord => ord)
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−  | ord => ord) <> GREATER;
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−
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−fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =
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−      nicer_name (x, i) (y, j)
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−  | nicer (Facts.Fact _) (Facts.Named _) = true
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−  | nicer (Facts.Named _) (Facts.Fact _) = false;
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−
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−fun rem_cdups xs =
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−  let
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−    fun rem_c rev_seen [] = rev rev_seen
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−      | rem_c rev_seen [x] = rem_c (x :: rev_seen) []
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−      | rem_c rev_seen ((x as ((n, t), _)) :: (y as ((n', t'), _)) :: xs) =
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−        if Thm.eq_thm_prop (t, t')
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−        then rem_c rev_seen ((if nicer n n' then x else y) :: xs)
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−        else rem_c (x :: rev_seen) (y :: xs)
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−  in rem_c [] xs end;
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−
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−in
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−
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−fun rem_thm_dups xs =
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−  xs ~~ (1 upto length xs)
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−  |> sort (Term.fast_term_ord o pairself (Thm.prop_of o #2 o #1))
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−  |> rem_cdups
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−  |> sort (int_ord o pairself #2)
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−  |> map #1;
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−
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−end;
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−
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−
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−(* print_theorems *)
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−
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−fun all_facts_of ctxt =
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−  maps Facts.selections
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−   (Facts.dest_static [] (PureThy.facts_of (ProofContext.theory_of ctxt)) @
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−    Facts.dest_static [] (ProofContext.facts_of ctxt));
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−
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−val limit = ref 40;
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−
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−fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
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−  let
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−    val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
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−    val filters = map (filter_criterion ctxt opt_goal) criteria;
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−
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−    val raw_matches = all_filters filters (all_facts_of ctxt);
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−    val matches =
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−      if rem_dups
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−      then rem_thm_dups raw_matches
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−      else raw_matches;
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−
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−    val len = length matches;
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−    val lim = the_default (! limit) opt_limit;
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−    val thms = Library.drop (len - lim, matches);
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−
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−    fun prt_fact (thmref, thm) =
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−      ProofContext.pretty_fact ctxt (Facts.string_of_ref thmref, [thm]);
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−  in
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−    Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria) :: Pretty.str "" ::
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−     (if null thms then [Pretty.str "nothing found"]
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−      else
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−        [Pretty.str ("found " ^ string_of_int len ^ " theorems" ^
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−          (if len <= lim then "" else " (" ^ string_of_int lim ^ " displayed)") ^ ":"),
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−         Pretty.str ""] @
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−        map prt_fact thms)
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−    |> Pretty.chunks |> Pretty.writeln
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−  end;
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−
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−end;