--- a/src/Pure/Isar/find_theorems.ML Thu Feb 26 10:13:43 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,378 +0,0 @@
-(* 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;