(* 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
datatype theorem =
Internal of Facts.ref * thm | External of Facts.ref * term
type 'term query = {
goal: thm option,
limit: int option,
rem_dups: bool,
criteria: (bool * 'term criterion) list
}
val read_criterion: Proof.context -> string criterion -> term criterion
val query_parser: (bool * string criterion) list parser
val xml_of_query: term query -> XML.tree
val query_of_xml: XML.tree -> term query
val xml_of_result: int option * theorem list -> XML.tree
val result_of_xml: XML.tree -> int option * theorem 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 filter_theorems: Proof.context -> theorem list -> term query ->
int option * theorem list
val filter_theorems_cmd: Proof.context -> theorem list -> string query ->
int option * theorem list
val pretty_theorem: Proof.context -> theorem -> Pretty.T
val pretty_thm: Proof.context -> Facts.ref * thm -> Pretty.T
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 apply_dummies tm =
let
val (xs, _) = Term.strip_abs tm;
val tm' = Term.betapplys (tm, map (Term.dummy_pattern o #2) xs);
in #1 (Term.replace_dummy_patterns tm' 1) end;
fun parse_pattern ctxt nm =
let
val consts = Proof_Context.consts_of ctxt;
val nm' =
(case Syntax.parse_term ctxt nm of
Const (c, _) => c
| _ => Consts.intern consts nm);
in
(case try (Consts.the_abbreviation consts) nm' of
SOME (_, rhs) => apply_dummies (Proof_Context.expand_abbrevs ctxt rhs)
| NONE => Proof_Context.read_term_pattern ctxt nm)
end;
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 (parse_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};
fun xml_of_criterion (Name name) = XML.Elem (("Name", [("val", name)]), [])
| xml_of_criterion Intro = XML.Elem (("Intro", []) , [])
| xml_of_criterion Elim = XML.Elem (("Elim", []) , [])
| xml_of_criterion Dest = XML.Elem (("Dest", []) , [])
| xml_of_criterion Solves = XML.Elem (("Solves", []) , [])
| xml_of_criterion (Simp pat) = XML.Elem (("Simp", []), [Legacy_XML_Syntax.xml_of_term pat])
| xml_of_criterion (Pattern pat) = XML.Elem (("Pattern", []), [Legacy_XML_Syntax.xml_of_term pat]);
fun criterion_of_xml (XML.Elem (("Name", [("val", name)]), [])) = Name name
| criterion_of_xml (XML.Elem (("Intro", []) , [])) = Intro
| criterion_of_xml (XML.Elem (("Elim", []) , [])) = Elim
| criterion_of_xml (XML.Elem (("Dest", []) , [])) = Dest
| criterion_of_xml (XML.Elem (("Solves", []) , [])) = Solves
| criterion_of_xml (XML.Elem (("Simp", []), [tree])) = Simp (Legacy_XML_Syntax.term_of_xml tree)
| criterion_of_xml (XML.Elem (("Pattern", []), [tree])) = Pattern (Legacy_XML_Syntax.term_of_xml tree)
| criterion_of_xml tree = raise Legacy_XML_Syntax.XML ("criterion_of_xml: bad tree", tree);
fun xml_of_query {goal = NONE, limit, rem_dups, criteria} =
let
val properties = []
|> (if rem_dups then cons ("rem_dups", "") else I)
|> (if is_some limit then cons ("limit", Markup.print_int (the limit)) else I);
in
XML.Elem (("Query", properties), XML.Encode.list
(XML.Encode.pair XML.Encode.bool (single o xml_of_criterion)) criteria)
end
| xml_of_query _ = raise Fail "cannot serialize goal";
fun query_of_xml (XML.Elem (("Query", properties), body)) =
let
val rem_dups = Properties.defined properties "rem_dups";
val limit = Properties.get properties "limit" |> Option.map Markup.parse_int;
val criteria =
XML.Decode.list (XML.Decode.pair XML.Decode.bool
(criterion_of_xml o the_single)) body;
in
{goal = NONE, limit = limit, rem_dups = rem_dups, criteria = criteria}
end
| query_of_xml tree = raise Legacy_XML_Syntax.XML ("query_of_xml: bad tree", tree);
(** theorems, either internal or external (without proof) **)
datatype theorem =
Internal of Facts.ref * thm |
External of Facts.ref * term; (* FIXME: Facts.ref not appropriate *)
fun fact_ref_markup (Facts.Named ((name, pos), SOME [Facts.Single i])) =
Position.markup pos o Markup.properties [("name", name), ("index", Markup.print_int i)]
| fact_ref_markup (Facts.Named ((name, pos), NONE)) =
Position.markup pos o Markup.properties [("name", name)]
| fact_ref_markup fact_ref = raise Fail "bad fact ref";
fun xml_of_theorem (Internal _) = raise Fail "xml_of_theorem: Internal"
| xml_of_theorem (External (fact_ref, prop)) =
XML.Elem (fact_ref_markup fact_ref ("External", []), [Legacy_XML_Syntax.xml_of_term prop]);
fun theorem_of_xml (XML.Elem (("External", properties), [tree])) =
let
val name = the (Properties.get properties "name");
val pos = Position.of_properties properties;
val intvs_opt =
Option.map (single o Facts.Single o Markup.parse_int)
(Properties.get properties "index");
in
External (Facts.Named ((name, pos), intvs_opt), Legacy_XML_Syntax.term_of_xml tree)
end
| theorem_of_xml tree = raise Legacy_XML_Syntax.XML ("theorem_of_xml: bad tree", tree);
fun xml_of_result (opt_found, theorems) =
let
val properties =
if is_some opt_found then [("found", Markup.print_int (the opt_found))] else [];
in
XML.Elem (("Result", properties), XML.Encode.list (single o xml_of_theorem) theorems)
end;
fun result_of_xml (XML.Elem (("Result", properties), body)) =
(Properties.get properties "found" |> Option.map Markup.parse_int,
XML.Decode.list (theorem_of_xml o the_single) body)
| result_of_xml tree = raise Legacy_XML_Syntax.XML ("result_of_xml: bad tree", tree);
fun prop_of (Internal (_, thm)) = Thm.full_prop_of thm
| prop_of (External (_, prop)) = prop;
fun nprems_of (Internal (_, thm)) = Thm.nprems_of thm
| nprems_of (External (_, prop)) = Logic.count_prems prop;
fun major_prem_of (Internal (_, thm)) = Thm.major_prem_of thm
| major_prem_of (External (_, prop)) =
Logic.strip_assums_concl (hd (Logic.strip_imp_prems prop));
fun fact_ref_of (Internal (fact_ref, _)) = fact_ref
| fact_ref_of (External (fact_ref, _)) = fact_ref;
(** search criterion filters **)
(*generated filters are to be of the form
input: theorem
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 Object_Logic.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 = Proof_Context.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 (foldl1 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 theorem =
if match_string str_pat (Facts.name_of_ref (fact_ref_of theorem))
then SOME (0, 0) else NONE;
(* filter intro/elim/dest/solves rules *)
fun filter_dest ctxt goal theorem =
let
val extract_dest =
(fn theorem => if nprems_of theorem = 0 then [] else [prop_of theorem],
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 theorem;
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 (nprems_of theorem - 1, foldl1 Int.min successful) else NONE
end;
fun filter_intro ctxt goal theorem =
let
val extract_intro = (single o prop_of, Logic.strip_imp_concl);
val concl = Logic.concl_of_goal goal 1;
val ss = is_matching_thm extract_intro ctxt true concl theorem;
in
if is_some ss then SOME (nprems_of theorem, the ss) else NONE
end;
fun filter_elim ctxt goal theorem =
if nprems_of theorem > 0 then
let
val rule = prop_of theorem;
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 (Proof_Context.theory_of ctxt) (major_prem_of theorem)
andalso not (null successful)
then SOME (nprems_of theorem - 1, foldl1 Int.min successful) else NONE
end
else NONE;
fun filter_solves ctxt goal =
let
fun etacn thm i =
Seq.take (Options.default_int @{option find_theorems_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.assm_tac ctxt)) 1 goal;
in
fn Internal (_, thm) =>
if is_some (Seq.pull (try_thm thm))
then SOME (Thm.nprems_of thm, 0) else NONE
| External _ => NONE
end;
(* filter_simp *)
fun filter_simp ctxt t (Internal (_, 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);
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_simp _ _ (External _) = NONE;
(* filter_pattern *)
fun get_names t = Term.add_const_names t (Term.add_free_names t []);
(*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 (theorem, NONE) = check (theorem, SOME (get_names (prop_of theorem)))
| check (theorem, c as SOME thm_consts) =
(if subset (op =) (pat_consts, thm_consts) andalso
Pattern.matches_subterm (Proof_Context.theory_of ctxt) (pat, prop_of theorem)
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;
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, _, []) = 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 theorems =
let
fun eval_filters theorem = app_filters theorem (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 result_ord (((p0, s0), _), ((p1, s1), _)) =
prod_ord int_ord int_ord ((p1, s1), (p0, s0));
in
grouped 100 Par_List.map eval_filters theorems
|> 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), 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 n log n *)
local
val index_ord = option_ord (K EQUAL);
val hidden_ord = bool_ord o pairself Name_Space.is_hidden;
val qual_ord = int_ord o pairself (length o Long_Name.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 (t, _)) :: (y as (t', _)) :: xs) =
if (prop_of t) aconv (prop_of t')
then rem_c rev_seen ((if nicer (fact_ref_of t) (fact_ref_of t') then x else y) :: xs)
else rem_c (x :: rev_seen) (y :: xs)
in rem_c [] xs end;
in
fun nicer_shortest ctxt =
let
(* FIXME Why global name space!?? *)
val space = Facts.space_of (Global_Theory.facts_of (Proof_Context.theory_of ctxt));
val shorten =
Name_Space.extern
(ctxt
|> Config.put Name_Space.names_long false
|> Config.put Name_Space.names_short false
|> Config.put Name_Space.names_unique false) space;
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 (Term_Ord.fast_term_ord o pairself (prop_of o #1))
|> rem_cdups nicer
|> sort (int_ord o pairself #2)
|> map #1;
end;
(* print_theorems *)
fun all_facts_of ctxt =
let
fun visible_facts facts =
Facts.dest_static [] facts
|> filter_out (Facts.is_concealed facts o #1);
in
maps Facts.selections
(visible_facts (Global_Theory.facts_of (Proof_Context.theory_of ctxt)) @
visible_facts (Proof_Context.facts_of ctxt))
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 @{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);
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 assms 1);
val opt_goal' = Option.map add_prems opt_goal;
in
filter ctxt (map Internal (all_facts_of ctxt))
{goal = opt_goal', limit = opt_limit, rem_dups = rem_dups, criteria = raw_criteria}
|> apsnd (map (fn Internal f => f))
end;
val find_theorems = gen_find_theorems filter_theorems;
val find_theorems_cmd = gen_find_theorems filter_theorems_cmd;
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.mark (Proof_Context.markup_fact ctxt name) (Pretty.str name),
Pretty.str (Facts.string_of_selection sel), Pretty.str ":", Pretty.brk 1]
end;
fun pretty_theorem ctxt (Internal (thmref, thm)) =
Pretty.block (pretty_ref ctxt thmref @ [Display.pretty_thm ctxt thm])
| pretty_theorem ctxt (External (thmref, prop)) =
Pretty.block (pretty_ref ctxt thmref @ [Syntax.unparse_term ctxt prop]);
fun pretty_thm ctxt (thmref, thm) = pretty_theorem ctxt (Internal (thmref, thm));
fun gen_print_theorems find ctxt opt_goal opt_limit rem_dups raw_criteria =
let
val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
val (foundo, theorems) = find
{goal = opt_goal, limit = opt_limit, rem_dups = rem_dups, criteria = criteria};
val returned = length theorems;
val tally_msg =
(case foundo 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 ""));
in
Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria) ::
Pretty.str "" ::
(if null theorems then [Pretty.str "nothing found"]
else
[Pretty.str (tally_msg ^ ":"), Pretty.str ""] @
grouped 10 Par_List.map (pretty_theorem ctxt) theorems)
end |> Pretty.fbreaks |> curry Pretty.blk 0 |> Pretty.writeln;
fun print_theorems ctxt =
gen_print_theorems (filter_theorems ctxt (map Internal (all_facts_of ctxt))) ctxt;
(** command syntax **)
local
val criterion =
Parse.reserved "name" |-- Parse.!!! (Parse.$$$ ":" |-- Parse.xname) >> Name ||
Parse.reserved "intro" >> K Intro ||
Parse.reserved "elim" >> K Elim ||
Parse.reserved "dest" >> K Dest ||
Parse.reserved "solves" >> K Solves ||
Parse.reserved "simp" |-- Parse.!!! (Parse.$$$ ":" |-- Parse.term) >> Simp ||
Parse.term >> Pattern;
val options =
Scan.optional
(Parse.$$$ "(" |--
Parse.!!! (Scan.option Parse.nat -- Scan.optional (Parse.reserved "with_dups" >> K false) true
--| Parse.$$$ ")")) (NONE, true);
in
val query_parser = Scan.repeat (((Scan.option Parse.minus >> is_none) -- criterion));
val _ =
Outer_Syntax.improper_command @{command_spec "find_theorems"}
"find theorems meeting specified criteria"
(options -- query_parser
>> (fn ((opt_lim, rem_dups), spec) =>
Toplevel.keep (fn state =>
let
val ctxt = Toplevel.context_of state;
val thy' =
Proof_Context.theory_of ctxt
|> Theory.copy
|> Context_Position.set_visible_global (Context_Position.is_visible ctxt)
|> Theory.checkpoint;
val opt_goal = try (Proof.simple_goal o Toplevel.proof_of) state |> Option.map #goal;
val (ctxt', opt_goal') =
(case opt_goal of
NONE => (ctxt, NONE)
| SOME th => (Proof_Context.transfer thy' ctxt, SOME (Thm.transfer thy' th)));
in print_theorems ctxt' opt_goal' opt_lim rem_dups spec end)));
end;
end;