(* Title: Pure/Tools/find_theorems.ML
Author: Rafal Kolanski and Gerwin Klein, NICTA
Retrieve theorems from proof context.
*)
signature FIND_THEOREMS =
sig
datatype 'term criterion =
Name of string | Intro | IntroIff | Elim | Dest | Solves | Simp of 'term |
Pattern of 'term
datatype theorem =
Internal of Facts.ref * thm |
External of Facts.ref * term
val tac_limit: int Unsynchronized.ref
val limit: int Unsynchronized.ref
val find_theorems: Proof.context -> thm option -> int option -> bool ->
(bool * string criterion) list -> int option * (Facts.ref * thm) list
val filter_theorems: Proof.context -> theorem list -> thm option ->
int option -> bool -> (bool * string criterion) list ->
int option * theorem list
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 | IntroIff | 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 = ProofContext.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 (ProofContext.expand_abbrevs ctxt rhs)
| NONE => ProofContext.read_term_pattern ctxt nm)
end;
fun read_criterion _ (Name name) = Name name
| read_criterion _ Intro = Intro
| read_criterion _ IntroIff = IntroIff
| 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 (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")
| IntroIff => Pretty.str (prfx "introiff")
| 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;
(** theorems, either internal or external (without proof) *)
datatype theorem =
Internal of Facts.ref * thm |
External of Facts.ref * term;
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;
(*educated guesses on HOL*) (* FIXME broken *)
val boolT = Type ("bool", []);
val iff_const = Const ("op =", boolT --> boolT --> boolT);
(*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 doiff (extract_terms, refine_term) ctxt po obj term_src =
let
val thy = ProofContext.theory_of ctxt;
fun check_match pat = Pattern.matches thy (if po then (pat, obj) else (obj, pat));
fun matches pat =
let
val jpat = Object_Logic.drop_judgment thy pat;
val c = Term.head_of jpat;
val pats =
if Term.is_Const c
then
if doiff andalso c = iff_const then
(pat :: map (Object_Logic.ensure_propT thy) (snd (strip_comb jpat)))
|> filter (is_nontrivial thy)
else [pat]
else [];
in filter check_match pats end;
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
maps match_thm (extract_terms term_src)
|> map substsize
|> 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 false 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 doiff 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 doiff 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 false (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) (major_prem_of theorem)
andalso not (null successful)
then SOME (nprems_of theorem - 1, foldl1 Int.min successful) else NONE
end
else NONE
val tac_limit = Unsynchronized.ref 5;
fun filter_solves ctxt goal =
let
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.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 (simpset_of 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 false 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 (ProofContext.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 IntroIff = err_no_goal "introiff"
| 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 false ctxt (fix_goal goal))
| filter_crit ctxt (SOME goal) IntroIff = apfst (filter_intro true 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 map_filter eval_filters theorems |> 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 global name space!? *)
val space = Facts.space_of (Global_Theory.facts_of (ProofContext.theory_of ctxt));
val shorten =
Name_Space.extern_flags
{long_names = false, short_names = false, unique_names = 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 (ProofContext.theory_of ctxt)) @
visible_facts (ProofContext.facts_of ctxt))
end;
val limit = Unsynchronized.ref 40;
fun filter_theorems ctxt theorems opt_goal opt_limit rem_dups raw_criteria =
let
val assms =
ProofContext.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;
val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
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 (! 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 find_theorems ctxt opt_goal opt_limit rem_dups raw_criteria =
filter_theorems ctxt (map Internal (all_facts_of ctxt)) opt_goal opt_limit
rem_dups raw_criteria
|> apsnd (map (fn Internal f => f));
fun pretty_thm ctxt (thmref, thm) = Pretty.block
[Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1,
Display.pretty_thm ctxt thm];
fun print_theorems ctxt (foundo, thms) raw_criteria =
let
val start = start_timing ();
val criteria = map (apsnd (read_criterion ctxt)) raw_criteria;
val returned = length thms;
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 ""));
val end_msg = " in " ^ Time.toString (#cpu (end_timing start)) ^ " 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 (tally_msg ^ end_msg ^ ":"), Pretty.str ""] @
map (pretty_thm ctxt) thms)
end |> Pretty.chunks |> Pretty.writeln;
(** command syntax **)
local
val criterion =
Parse.reserved "name" |-- Parse.!!! (Parse.$$$ ":" |-- Parse.xname) >> Name ||
Parse.reserved "intro" >> K Intro ||
Parse.reserved "introiff" >> K IntroIff ||
Parse.reserved "elim" >> K Elim ||
Parse.reserved "dest" >> K Dest ||
Parse.reserved "solves" >> K Solves ||
Parse.reserved "simp" |-- Parse.!!! (Parse.$$$ ":" |-- 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 _ =
Outer_Syntax.improper_command "find_theorems" "print theorems meeting specified criteria"
Keyword.diag
(options -- Scan.repeat (((Scan.option Parse.minus >> is_none) -- criterion))
>> (fn ((opt_lim, rem_dups), spec) =>
Toplevel.no_timing o
Toplevel.keep (fn state =>
let
val ctxt = Toplevel.context_of state;
val opt_goal = try (Proof.simple_goal o Toplevel.proof_of) state |> Option.map #goal;
val found = find_theorems ctxt opt_goal opt_lim rem_dups spec;
in print_theorems ctxt found spec end)));
end;
end;