(* Title: Pure/Tools/find_theorems.ML Author: Rafal Kolanski and Gerwin Klein, NICTA Author: Lars Noschinski and Alexander Krauss, TU Muenchen Retrieve theorems from proof context. *) signature FIND_THEOREMS = sig datatype 'term criterion = Name of string | Intro | Elim | Dest | Solves | Simp of 'term | Pattern of 'term type 'term query = { goal: thm option, limit: int option, rem_dups: bool, criteria: (bool * 'term criterion) list } val query_parser: (bool * string criterion) list parser val read_query: Position.T -> string -> (bool * string criterion) list val find_theorems: Proof.context -> thm option -> int option -> bool -> (bool * term criterion) list -> int option * (Facts.ref * thm) list val find_theorems_cmd: Proof.context -> thm option -> int option -> bool -> (bool * string criterion) list -> int option * (Facts.ref * thm) list val pretty_thm: Proof.context -> Facts.ref * thm -> Pretty.T val pretty_theorems: Proof.state -> int option -> bool -> (bool * string criterion) list -> Pretty.T val proof_state: Toplevel.state -> Proof.state end; structure Find_Theorems: 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 (Proof_Context.read_term_pattern ctxt str) | read_criterion ctxt (Pattern str) = Pattern (Proof_Context.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; (** queries **) type 'term query = { goal: thm option, limit: int option, rem_dups: bool, criteria: (bool * 'term criterion) list }; fun map_criteria f {goal, limit, rem_dups, criteria} = {goal = goal, limit = limit, rem_dups = rem_dups, criteria = f criteria}; (** search criterion filters **) (*generated filters are to be of the form input: (Facts.ref * thm) output: (p:int, s:int, t:int) option, where NONE indicates no match p is the primary sorting criterion (eg. size of term) s is the secondary sorting criterion (eg. number of assumptions in the theorem) t is the tertiary sorting criterion (eg. size of the substitution for intro, elim and dest) when applying a set of filters to a thm, fold results in: (max p, max s, sum of all t) *) (* matching theorems *) fun is_nontrivial ctxt = Term.is_Const o Term.head_of o Object_Logic.drop_judgment ctxt; (*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 = Proof_Context.theory_of ctxt; fun matches pat = is_nontrivial ctxt pat andalso Pattern.matches thy (if po then (pat, obj) else (obj, pat)); fun subst_size 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 best_match [] = NONE | best_match xs = SOME (foldl1 Int.min xs); val match_thm = matches o refine_term; in map (subst_size o refine_term) (filter match_thm (extract_terms term_src)) |> best_match end; (* filter_name *) fun filter_name str_pat (thmref, _) = if match_string str_pat (Facts.ref_name thmref) then SOME (0, 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 (size_of_term (Thm.prop_of thm), Thm.nprems_of thm - 1, foldl1 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; in (case is_matching_thm extract_intro ctxt true concl thm of SOME k => SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, k) | NONE => NONE) end; fun filter_elim ctxt goal (_, thm) = if Thm.nprems_of thm > 0 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); (* FIXME ?!? *) 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 ctxt (Thm.major_prem_of thm) andalso not (null successful) then SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm - 1, foldl1 Int.min successful) else NONE end else NONE; fun filter_solves ctxt goal = let val thy' = Proof_Context.theory_of ctxt |> Context_Position.set_visible_global false; val ctxt' = Proof_Context.transfer thy' ctxt |> Context_Position.set_visible false; val goal' = Thm.transfer thy' goal; fun limited_etac thm i = Seq.take (Options.default_int \<^system_option>\find_theorems_tactic_limit\) o eresolve_tac ctxt' [thm] i; fun try_thm thm = if Thm.no_prems thm then resolve_tac ctxt' [thm] 1 goal' else (limited_etac thm THEN_ALL_NEW (Goal.norm_hhf_tac ctxt' THEN' Method.assm_tac ctxt')) 1 goal'; in fn (_, thm) => if is_some (Seq.pull (try_thm thm)) then SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, 0) else NONE end; (* filter_simp *) fun filter_simp ctxt t (_, thm) = let val mksimps = Simplifier.mksimps ctxt; val extract_simp = (map Thm.full_prop_of o mksimps, #1 o Logic.dest_equals o Logic.strip_imp_concl); in (case is_matching_thm extract_simp ctxt false t thm of SOME ss => SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, ss) | NONE => NONE) end; (* filter_pattern *) fun expand_abs t = let val m = Term.maxidx_of_term t + 1; val vs = strip_abs_vars t; val ts = map_index (fn (k, (_, T)) => Var ((Name.aT, m + k), T)) vs; in betapplys (t, ts) end; fun get_names t = Term.add_const_names t (Term.add_free_names t []); (* Does pat match a subterm of obj? *) fun matches_subterm thy (pat, obj) = let fun msub bounds obj = Pattern.matches thy (pat, obj) orelse (case obj of Abs (_, T, t) => msub (bounds + 1) (snd (Term.dest_abs (Name.bound bounds, T, t))) | t $ u => msub bounds t orelse msub bounds u | _ => false) in msub 0 obj end; (*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' = (expand_abs o Envir.eta_contract) pat; val pat_consts = get_names pat'; fun check ((x, thm), NONE) = check ((x, thm), SOME (get_names (Thm.full_prop_of thm))) | check ((_, thm), c as SOME thm_consts) = (if subset (op =) (pat_consts, thm_consts) andalso matches_subterm (Proof_Context.theory_of ctxt) (pat', Thm.full_prop_of thm) then SOME (size_of_term (Thm.prop_of thm), Thm.nprems_of thm, 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"); 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 (Thm.prop_of goal)) | filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt (Thm.prop_of goal)) | filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt (Thm.prop_of 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, 0); fun opt_add (SOME (a, c, x)) (SOME (b, d, y)) = SOME (Int.max (a,b), Int.max (c, d), x + y : int) | opt_add _ _ = NONE; fun app_filters thm = let fun app (NONE, _, _) = NONE | app (SOME v, _, []) = 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 sorted_filter filters thms = let fun eval_filters thm = app_filters thm (SOME (0, 0, 0), NONE, filters); (*filters return: (thm size, number of assumptions, substitution size) option, so sort according to size of thm first, then number of assumptions, then by the substitution size, then by term order *) fun result_ord (((p0, s0, t0), (_, thm0)), ((p1, s1, t1), (_, thm1))) = prod_ord int_ord (prod_ord int_ord (prod_ord int_ord Term_Ord.term_ord)) ((p1, (s1, (t1, Thm.full_prop_of thm1))), (p0, (s0, (t0, Thm.full_prop_of thm0)))); in grouped 100 Par_List.map eval_filters thms |> map_filter I |> sort result_ord |> map #2 end; fun lazy_filter filters = let fun lazy_match thms = Seq.make (fn () => first_match thms) and first_match [] = NONE | first_match (thm :: thms) = (case app_filters thm (SOME (0, 0, 0), NONE, filters) of NONE => first_match thms | SOME (_, t) => SOME (t, lazy_match thms)); in lazy_match end; end; (* removing duplicates, preferring nicer names, roughly O(n log n) *) local val index_ord = option_ord (K EQUAL); val hidden_ord = bool_ord o apply2 Long_Name.is_hidden; val qual_ord = int_ord o apply2 Long_Name.qualification; val txt_ord = int_ord o apply2 size; fun nicer_name ((a, x), i) ((b, y), j) = (case bool_ord (a, b) of EQUAL => (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) | 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, thm), _)) :: (y as ((n', thm'), _)) :: rest) = if Thm.eq_thm_prop (thm, thm') then rem_c rev_seen ((if nicer n n' then x else y) :: rest) else rem_c (x :: rev_seen) (y :: rest); in rem_c [] xs end; in fun nicer_shortest ctxt = let fun extern_shortest name = let val facts = Proof_Context.facts_of_fact ctxt name; val space = Facts.space_of facts; in (Facts.is_dynamic facts name, Name_Space.extern_shortest ctxt space name) end; fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) = nicer_name (extern_shortest x, i) (extern_shortest y, j) | nicer (Facts.Fact _) (Facts.Named _) = true | nicer (Facts.Named _) (Facts.Fact _) = false | nicer (Facts.Fact _) (Facts.Fact _) = true; in nicer end; fun rem_thm_dups nicer xs = (xs ~~ (1 upto length xs)) |> sort (Term_Ord.fast_term_ord o apply2 (Thm.full_prop_of o #2 o #1)) |> rem_cdups nicer |> sort (int_ord o apply2 #2) |> map #1; end; (** main operations **) (* filter_theorems *) fun all_facts_of ctxt = let val thy = Proof_Context.theory_of ctxt; val transfer = Global_Theory.transfer_theories thy; val local_facts = Proof_Context.facts_of ctxt; val global_facts = Global_Theory.facts_of thy; in (Facts.dest_all (Context.Proof ctxt) false [global_facts] local_facts @ Facts.dest_all (Context.Proof ctxt) false [] global_facts) |> maps Facts.selections |> map (apsnd transfer) end; fun filter_theorems ctxt theorems query = let val {goal = opt_goal, limit = opt_limit, rem_dups, criteria} = query; val filters = map (filter_criterion ctxt opt_goal) criteria; fun find_all theorems = let val raw_matches = sorted_filter filters theorems; val matches = if rem_dups then rem_thm_dups (nicer_shortest ctxt) raw_matches else raw_matches; val len = length matches; val lim = the_default (Options.default_int \<^system_option>\find_theorems_limit\) opt_limit; in (SOME len, drop (Int.max (len - lim, 0)) matches) end; val find = if rem_dups orelse is_none opt_limit then find_all else pair NONE o Seq.list_of o Seq.take (the opt_limit) o lazy_filter filters; in find theorems end; fun filter_theorems_cmd ctxt theorems raw_query = filter_theorems ctxt theorems (map_criteria (map (apsnd (read_criterion ctxt))) raw_query); (* find_theorems *) local fun gen_find_theorems filter ctxt opt_goal opt_limit rem_dups raw_criteria = let val assms = Proof_Context.get_fact ctxt (Facts.named "local.assms") handle ERROR _ => []; val add_prems = Seq.hd o TRY (Method.insert_tac ctxt assms 1); val opt_goal' = Option.map add_prems opt_goal; in filter ctxt (all_facts_of ctxt) {goal = opt_goal', limit = opt_limit, rem_dups = rem_dups, criteria = raw_criteria} end; in val find_theorems = gen_find_theorems filter_theorems; val find_theorems_cmd = gen_find_theorems filter_theorems_cmd; end; (* pretty_theorems *) local fun pretty_ref ctxt thmref = let val (name, sel) = (case thmref of Facts.Named ((name, _), sel) => (name, sel) | Facts.Fact _ => raise Fail "Illegal literal fact"); in [Pretty.marks_str (#1 (Proof_Context.markup_extern_fact ctxt name), name), Pretty.str (Facts.string_of_selection sel), Pretty.str ":", Pretty.brk 1] end; in fun pretty_thm ctxt (thmref, thm) = Pretty.block (pretty_ref ctxt thmref @ [Thm.pretty_thm ctxt thm]); fun pretty_theorems state opt_limit rem_dups raw_criteria = let val ctxt = Proof.context_of state; val opt_goal = try (#goal o Proof.simple_goal) state; val criteria = map (apsnd (read_criterion ctxt)) raw_criteria; val (opt_found, theorems) = filter_theorems ctxt (all_facts_of ctxt) {goal = opt_goal, limit = opt_limit, rem_dups = rem_dups, criteria = criteria}; val returned = length theorems; val tally_msg = (case opt_found of NONE => "displaying " ^ string_of_int returned ^ " theorem(s)" | SOME found => "found " ^ string_of_int found ^ " theorem(s)" ^ (if returned < found then " (" ^ string_of_int returned ^ " displayed)" else "")); val position_markup = Position.markup (Position.thread_data ()) Markup.position; in Pretty.block (Pretty.fbreaks (Pretty.mark position_markup (Pretty.keyword1 "find_theorems") :: map (pretty_criterion ctxt) criteria)) :: Pretty.str "" :: (if null theorems then [Pretty.str "found nothing"] else Pretty.str (tally_msg ^ ":") :: grouped 10 Par_List.map (Pretty.item o single o pretty_thm ctxt) (rev theorems)) end |> Pretty.fbreaks |> curry Pretty.blk 0; end; (** Isar command syntax **) local val criterion = Parse.reserved "name" |-- Parse.!!! (Parse.$$$ ":" |-- Parse.name) >> Name || Parse.reserved "intro" >> K Intro || Parse.reserved "elim" >> K Elim || Parse.reserved "dest" >> K Dest || Parse.reserved "solves" >> K Solves || Parse.reserved "simp" |-- Parse.!!! (Parse.$$$ ":" |-- Parse.term) >> Simp || Parse.term >> Pattern; val query_keywords = Keyword.add_keywords [((":", \<^here>), Keyword.no_spec)] Keyword.empty_keywords; in val query_parser = Scan.repeat ((Scan.option Parse.minus >> is_none) -- criterion); fun read_query pos str = Token.explode query_keywords pos str |> filter Token.is_proper |> Scan.error (Scan.finite Token.stopper (Parse.!!! (query_parser --| Scan.ahead Parse.eof))) |> #1; end; (** PIDE query operation **) fun proof_state st = (case try Toplevel.proof_of st of SOME state => state | NONE => Proof.init (Toplevel.context_of st)); val _ = Query_Operation.register {name = "find_theorems", pri = Task_Queue.urgent_pri} (fn {state = st, args, writeln_result, ...} => if can Toplevel.context_of st then let val [limit_arg, allow_dups_arg, query_arg] = args; val state = proof_state st; val opt_limit = Int.fromString limit_arg; val rem_dups = allow_dups_arg = "false"; val criteria = read_query Position.none query_arg; in writeln_result (Pretty.string_of (pretty_theorems state opt_limit rem_dups criteria)) end else error "Unknown context"); end;