(*  Title:      Pure/Isar/find_theorems.ML

    Author:     Rafal Kolanski and Gerwin Klein, NICTA

Retrieve theorems from proof context.

*)

signature FIND_THEOREMS =

sig

  val limit: int ref

  val tac_limit: int ref

  datatype 'term criterion =

    Name of string | Intro | Elim | Dest | Solves | Simp of 'term |

    Pattern of 'term

  val find_theorems: Proof.context -> thm option -> bool ->

    (bool * string criterion) list -> (Facts.ref * thm) list

  val print_theorems: Proof.context -> thm option -> int option -> bool ->

    (bool * string criterion) list -> unit

end;

structure FindTheorems: FIND_THEOREMS =

struct

(** search criteria **)

datatype 'term criterion =

  Name of string | Intro | Elim | Dest | Solves | Simp of 'term |

  Pattern of 'term;

fun read_criterion _ (Name name) = Name name

  | read_criterion _ Intro = Intro

  | read_criterion _ Elim = Elim

  | read_criterion _ Dest = Dest

  | read_criterion _ Solves = Solves

  | read_criterion ctxt (Simp str) = Simp (ProofContext.read_term_pattern ctxt str)

  | read_criterion ctxt (Pattern str) = Pattern (ProofContext.read_term_pattern ctxt str);

fun pretty_criterion ctxt (b, c) =

  let

    fun prfx s = if b then s else "-" ^ s;

  in

    (case c of

      Name name => Pretty.str (prfx "name: " ^ quote name)

    | Intro => Pretty.str (prfx "intro")

    | Elim => Pretty.str (prfx "elim")

    | Dest => Pretty.str (prfx "dest")

    | Solves => Pretty.str (prfx "solves")

    | Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1,

        Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))]

    | Pattern pat => Pretty.enclose (prfx " \"") "\""

        [Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)])

  end;

(** search criterion filters **)

(*generated filters are to be of the form

  input: (Facts.ref * thm)

  output: (p:int, s:int) option, where

    NONE indicates no match

    p is the primary sorting criterion

      (eg. number of assumptions in the theorem)

    s is the secondary sorting criterion

      (eg. size of the substitution for intro, elim and dest)

  when applying a set of filters to a thm, fold results in:

    (biggest p, sum of all s)

  currently p and s only matter for intro, elim, dest and simp filters,

  otherwise the default ordering is used.

*)

(* matching theorems *)

fun is_nontrivial thy = Term.is_Const o Term.head_of o ObjectLogic.drop_judgment thy;

(*extract terms from term_src, refine them to the parts that concern us,

  if po try match them against obj else vice versa.

  trivial matches are ignored.

  returns: smallest substitution size*)

fun is_matching_thm (extract_terms, refine_term) ctxt po obj term_src =

  let

    val thy = ProofContext.theory_of ctxt;

    fun matches pat =

      is_nontrivial thy pat andalso

      Pattern.matches thy (if po then (pat, obj) else (obj, pat));

    fun substsize pat =

      let val (_, subst) =

        Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty)

      in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end;

    fun bestmatch [] = NONE

     |  bestmatch xs = SOME (foldr1 Int.min xs);

    val match_thm = matches o refine_term;

  in

    map (substsize o refine_term) (filter match_thm (extract_terms term_src))

    |> bestmatch

  end;

(* filter_name *)

fun filter_name str_pat (thmref, _) =

  if match_string str_pat (Facts.name_of_ref thmref)

  then SOME (0, 0) else NONE;

(* filter intro/elim/dest/solves rules *)

fun filter_dest ctxt goal (_, thm) =

  let

    val extract_dest =

     (fn thm => if Thm.no_prems thm then [] else [Thm.full_prop_of thm],

      hd o Logic.strip_imp_prems);

    val prems = Logic.prems_of_goal goal 1;

    fun try_subst prem = is_matching_thm extract_dest ctxt true prem thm;

    val successful = prems |> map_filter try_subst;

  in

    (*if possible, keep best substitution (one with smallest size)*)

    (*dest rules always have assumptions, so a dest with one

      assumption is as good as an intro rule with none*)

    if not (null successful)

    then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE

  end;

fun filter_intro ctxt goal (_, thm) =

  let

    val extract_intro = (single o Thm.full_prop_of, Logic.strip_imp_concl);

    val concl = Logic.concl_of_goal goal 1;

    val ss = is_matching_thm extract_intro ctxt true concl thm;

  in

    if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE

  end;

fun filter_elim ctxt goal (_, thm) =

  if not (Thm.no_prems thm) then

    let

      val rule = Thm.full_prop_of thm;

      val prems = Logic.prems_of_goal goal 1;

      val goal_concl = Logic.concl_of_goal goal 1;

      val rule_mp = hd (Logic.strip_imp_prems rule);

      val rule_concl = Logic.strip_imp_concl rule;

      fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) $ (t1 $ t2);

      val rule_tree = combine rule_mp rule_concl;

      fun goal_tree prem = combine prem goal_concl;

      fun try_subst prem =

        is_matching_thm (single, I) ctxt true (goal_tree prem) rule_tree;

      val successful = prems |> map_filter try_subst;

    in

    (*elim rules always have assumptions, so an elim with one

      assumption is as good as an intro rule with none*)

      if is_nontrivial (ProofContext.theory_of ctxt) (Thm.major_prem_of thm)

        andalso not (null successful)

      then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE

    end

  else NONE

val tac_limit = ref 5;

fun filter_solves ctxt goal = let

    val baregoal = Logic.get_goal (prop_of goal) 1;

    fun etacn thm i = Seq.take (!tac_limit) o etac thm i;

    fun try_thm thm = if Thm.no_prems thm then rtac thm 1 goal

                      else (etacn thm THEN_ALL_NEW

                             (Goal.norm_hhf_tac THEN'

                               Method.assumption_tac ctxt)) 1 goal;

  in

    fn (_, thm) => if (is_some o Seq.pull o try_thm) thm

                   then SOME (Thm.nprems_of thm, 0) else NONE

  end;

(* filter_simp *)

fun filter_simp ctxt t (_, thm) =

  let

    val (_, {mk_rews = {mk, ...}, ...}) =

      Simplifier.rep_ss (Simplifier.local_simpset_of ctxt);

    val extract_simp =

      (map Thm.full_prop_of o mk, #1 o Logic.dest_equals o Logic.strip_imp_concl);

    val ss = is_matching_thm extract_simp ctxt false t thm

  in

    if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE

  end;

(* filter_pattern *)

fun get_names t = (Term.add_const_names t []) union (Term.add_free_names t []);

fun get_thm_names (_, thm) = get_names (Thm.full_prop_of thm);

  (* Including all constants and frees is only sound because

     matching uses higher-order patterns. If full matching

     were used, then constants that may be subject to

     beta-reduction after substitution of frees should

     not be included for LHS set because they could be

     thrown away by the substituted function.

     e.g. for (?F 1 2) do not include 1 or 2, if it were

          possible for ?F to be (% x y. 3)

     The largest possible set should always be included on

     the RHS. *)

fun filter_pattern ctxt pat = let

    val pat_consts = get_names pat;

    fun check (t, NONE) = check (t, SOME (get_thm_names t))

      | check ((_, thm), c as SOME thm_consts) =

          (if pat_consts subset_string thm_consts

              andalso (Pattern.matches_subterm (ProofContext.theory_of ctxt)

                                               (pat, Thm.full_prop_of thm))

           then SOME (0, 0) else NONE, c);

  in check end;

(* interpret criteria as filters *)

local

fun err_no_goal c =

  error ("Current goal required for " ^ c ^ " search criterion");

val fix_goal = Thm.prop_of;

val fix_goalo = Option.map fix_goal;

fun filter_crit _ _ (Name name) = apfst (filter_name name)

  | filter_crit _ NONE Intro = err_no_goal "intro"

  | filter_crit _ NONE Elim = err_no_goal "elim"

  | filter_crit _ NONE Dest = err_no_goal "dest"

  | filter_crit _ NONE Solves = err_no_goal "solves"

  | filter_crit ctxt (SOME goal) Intro = apfst (filter_intro ctxt

                                                  (fix_goal goal))

  | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt 

                                                  (fix_goal goal))

  | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt

                                                  (fix_goal goal))

  | filter_crit ctxt (SOME goal) Solves = apfst (filter_solves ctxt goal)

  | filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat)

  | filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat;

fun opt_not x = if is_some x then NONE else SOME (0, 0);

fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int)

  | opt_add _ _ = NONE;

fun app_filters thm = let

    fun app (NONE, _, _) = NONE

      | app (SOME v, consts, []) = SOME (v, thm)

      | app (r, consts, f::fs) = let val (r', consts') = f (thm, consts)

                                 in app (opt_add r r', consts', fs) end;

  in app end;

in

fun filter_criterion ctxt opt_goal (b, c) =

  (if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c;

fun all_filters filters thms =

  let

    fun eval_filters thm = app_filters thm (SOME (0, 0), NONE, filters);

    (*filters return: (number of assumptions, substitution size) option, so

      sort (desc. in both cases) according to number of assumptions first,

      then by the substitution size*)

    fun thm_ord (((p0, s0), _), ((p1, s1), _)) =

      prod_ord int_ord int_ord ((p1, s1), (p0, s0));

  in map_filter eval_filters thms |> sort thm_ord |> map #2 end;

end;

(* removing duplicates, preferring nicer names, roughly n log n *)

local

val index_ord = option_ord (K EQUAL);

val hidden_ord = bool_ord o pairself NameSpace.is_hidden;

val qual_ord = int_ord o pairself (length o NameSpace.explode);

val txt_ord = int_ord o pairself size;

fun nicer_name (x, i) (y, j) =

  (case hidden_ord (x, y) of EQUAL =>

    (case index_ord (i, j) of EQUAL =>

      (case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord)

    | ord => ord)

  | ord => ord) <> GREATER;

fun rem_cdups nicer xs =

  let

    fun rem_c rev_seen [] = rev rev_seen

      | rem_c rev_seen [x] = rem_c (x :: rev_seen) []

      | rem_c rev_seen ((x as ((n, t), _)) :: (y as ((n', t'), _)) :: xs) =

        if Thm.eq_thm_prop (t, t')

        then rem_c rev_seen ((if nicer n n' then x else y) :: xs)

        else rem_c (x :: rev_seen) (y :: xs)

  in rem_c [] xs end;

in

fun nicer_shortest ctxt = let

    val ns = ProofContext.theory_of ctxt

             |> PureThy.facts_of

             |> Facts.space_of;

    val len_sort = sort (int_ord o (pairself size));

    fun shorten s = (case len_sort (NameSpace.get_accesses ns s) of

                       [] => s

                     | s'::_ => s');

    fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) =

          nicer_name (shorten x, i) (shorten y, j)

      | nicer (Facts.Fact _) (Facts.Named _) = true

      | nicer (Facts.Named _) (Facts.Fact _) = false;

  in nicer end;

fun rem_thm_dups nicer xs =

  xs ~~ (1 upto length xs)

  |> sort (TermOrd.fast_term_ord o pairself (Thm.prop_of o #2 o #1))

  |> rem_cdups nicer

  |> sort (int_ord o pairself #2)

  |> map #1;

end;

(* print_theorems *)

fun all_facts_of ctxt =

  maps Facts.selections

   (Facts.dest_static [] (PureThy.facts_of (ProofContext.theory_of ctxt)) @

    Facts.dest_static [] (ProofContext.facts_of ctxt));

val limit = ref 40;

fun find_theorems ctxt opt_goal rem_dups raw_criteria =

  let

    val add_prems = Seq.hd o (TRY (Method.insert_tac

                                     (Assumption.prems_of ctxt) 1));

    val opt_goal' = Option.map add_prems opt_goal;

    val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;

    val filters = map (filter_criterion ctxt opt_goal') criteria;

    val raw_matches = all_filters filters (all_facts_of ctxt);

    val matches =

      if rem_dups

      then rem_thm_dups (nicer_shortest ctxt) raw_matches

      else raw_matches;

  in matches end;

fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria = let

    val start = start_timing ();

    val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;

    val matches = find_theorems ctxt opt_goal rem_dups raw_criteria;

    val len = length matches;

    val lim = the_default (! limit) opt_limit;

    val thms = Library.drop (len - lim, matches);

    val end_msg = " in " ^

                  (List.nth (String.tokens Char.isSpace (end_timing start), 3))

                  ^ " secs"

  in

    Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria)

        :: Pretty.str "" ::

     (if null thms then [Pretty.str ("nothing found" ^ end_msg)]

      else

        [Pretty.str ("found " ^ string_of_int len ^ " theorems" ^

          (if len <= lim then ""

           else " (" ^ string_of_int lim ^ " displayed)")

           ^ end_msg ^ ":"), Pretty.str ""] @

        map Display.pretty_fact thms)

    |> Pretty.chunks |> Pretty.writeln

  end

end;