(* Title: Pure/Isar/find_theorems.ML ID: $Id: find_theorems.ML,v 1.11 2005/08/31 13:46:44 wenzelm Exp $ Author: Rafal Kolanski, NICTA and Tobias Nipkow, TU Muenchen Retrieve theorems from proof context. *) val thms_containing_limit = ref 40; signature FIND_THEOREMS = sig val find_thms: Proof.context -> FactIndex.spec -> (thmref * thm) list 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 * string criterion) list -> unit end; structure FindTheorems: FIND_THEOREMS = struct (* find_thms *) fun find_thms ctxt spec = (PureThy.thms_containing (ProofContext.theory_of ctxt) spec @ ProofContext.lthms_containing ctxt spec) |> map PureThy.selections |> List.concat; (** 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 (hd (ProofContext.read_term_pats TypeInfer.logicT ctxt [str])) | read_criterion ctxt (Pattern str) = Pattern (hd (ProofContext.read_term_pats TypeInfer.logicT 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 (ProofContext.pretty_term ctxt (Term.show_dummy_patterns pat))] | Pattern pat => Pretty.enclose (prfx " \"") "\"" [ProofContext.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)) 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) (List.filter match_thm (extract_terms term_src)) |> bestmatch end; (* filter_name *) fun is_substring pat str = if String.size pat = 0 then true else if String.size pat > String.size str then false else if String.substring (str, 0, String.size pat) = pat then true else is_substring pat (String.extract (str, 1, NONE)); (*filter that just looks for a string in the name, substring match only (no regexps are performed)*) fun filter_name str_pat (thmref, _) = if is_substring 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 |> List.mapPartial 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, valOf 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 |> List.mapPartial 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, valOf 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 isSome x then NONE else SOME (0, 0); fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y) | 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 |> List.mapPartial (fn (SOME x, y) => SOME (x, y) | (NONE, _) => NONE) |> sort thm_ord |> map #2 end; end; (* print_theorems *) fun print_theorems ctxt opt_goal opt_limit raw_criteria = let val criteria = map (apsnd (read_criterion ctxt)) raw_criteria; val filters = map (filter_criterion ctxt opt_goal) criteria; val matches = all_filters filters (find_thms ctxt ([], [])); val len = length matches; val limit = if_none opt_limit (! thms_containing_limit); 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 matches 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 (Library.drop (len - limit, matches))) |> Pretty.chunks |> Pretty.writeln end; end;