(*  Title:      Pure/Isar/find_theorems.ML

    ID:         $Id$

    Author:     Rafal Kolanski, NICTA and Tobias Nipkow, TU Muenchen

Retrieve theorems from proof context.

*)

val thms_containing_limit = ref 40;

signature FIND_THEOREMS =

sig

  datatype 'term criterion =

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

  val print_theorems: Proof.context -> term 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 | 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 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")

    | 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: (thmref * 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 match_string pat str =

  let

    fun match [] _ = true

      | match (p :: ps) s =

          size p <= size s andalso

            (case try (unprefix p) s of

              SOME s' => match ps s'

            | NONE => match (p :: ps) (String.substring (s, 1, size s - 1)));

  in match (space_explode "*" pat) str end;

fun filter_name str_pat (thmref, _) =

  if match_string str_pat (PureThy.name_of_thmref thmref)

  then SOME (0, 0) else NONE;

(* filter intro/elim/dest 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 o 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

(* filter_simp *)

fun filter_simp ctxt t (_, thm) =

  let

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

      MetaSimplifier.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 filter_pattern ctxt pat (_, thm) =

  if Pattern.matches_subterm (ProofContext.theory_of ctxt) (pat, Thm.full_prop_of thm)

  then SOME (0, 0) else NONE;

(* interpret criteria as filters *)

local

fun err_no_goal c =

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

fun filter_crit _ _ (Name name) = 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 ctxt (SOME goal) Intro = filter_intro ctxt goal

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

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

  | filter_crit ctxt _ (Simp pat) = 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;

in

fun filter_criterion ctxt opt_goal (b, c) =

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

fun all_filters filters thms =

  let

    fun eval_filters filters thm =

      fold opt_add (map (fn f => f thm) filters) (SOME (0, 0));

    (*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 (`(eval_filters filters)) thms

    |> map_filter (fn (SOME x, y) => SOME (x, y) | (NONE, _) => NONE)

    |> sort thm_ord |> map #2

  end;

end;

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

fun rem_thm_dups xs =

  let

    fun nicer (Fact x) (Fact y) = size x <= size y

      | nicer (Fact _) _        = true

      | nicer (PureThy.Name x) (PureThy.Name y) = size x <= size y

      | nicer (PureThy.Name _) (Fact _) = false

      | nicer (PureThy.Name _) _ = true

      | nicer (NameSelection (x, _)) (NameSelection (y, _)) = size x <= size y

      | nicer (NameSelection _) _ = false;

    fun rem_cdups 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 if nicer n n'

                 then rem_c rev_seen (x::xs)

                 else rem_c rev_seen (y::xs)

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

      in rem_c [] xs end;

  in ListPair.zip (xs, 1 upto length xs)

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

     |> rem_cdups

     |> sort (int_ord o pairself #2)

     |> map #1

  end;

(* print_theorems *)

fun find_thms ctxt spec =

  (PureThy.thms_containing (ProofContext.theory_of ctxt) spec

    |> maps PureThy.selections) @

  (ProofContext.lthms_containing ctxt spec

    |> maps PureThy.selections

    |> distinct (fn ((r1, th1), (r2, th2)) =>

        r1 = r2 andalso Thm.eq_thm_prop (th1, th2)));

fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =

  let

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

    val filters = map (filter_criterion ctxt opt_goal) criteria;

    val raw_matches = all_filters filters (find_thms ctxt ([], []));

    val matches =

      if rem_dups

      then rem_thm_dups raw_matches

      else raw_matches;

    val len = length matches;

    val limit = the_default (! thms_containing_limit) opt_limit;

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

    fun prt_fact (thmref, thm) =

      ProofContext.pretty_fact ctxt (PureThy.string_of_thmref thmref, [thm]);

  in

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

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

      else

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

          (if len <= limit then "" else " (" ^ string_of_int limit ^ " displayed)") ^ ":"),

         Pretty.str ""] @

        map prt_fact thms)

    |> Pretty.chunks |> Pretty.writeln

  end;

end;