(* Title: Pure/Isar/find_theorems.ML
ID: $Id$
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: (PureThy.thmref * Thm.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 = is_Const o 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;
val tsig = Sign.tsig_of thy;
fun matches pat =
is_nontrivial thy pat andalso
Pattern.matches tsig (if po then (pat,obj) else (obj,pat));
fun substsize pat =
let
val (_,subst) = Pattern.match tsig (if po then (pat,obj) else (obj,pat))
in Vartab.foldl (op + o apsnd (size_of_term o snd o snd)) (0, subst)
end;
fun bestmatch [] = NONE
| bestmatch (x :: xs) = SOME (foldl Int.min x 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 [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;
(*keep successful substitutions*)
val ss = prems |> List.map try_subst
|> List.filter isSome
|> List.map valOf;
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 ss)
then SOME (nprems_of thm - 1, foldl Int.min (hd ss) (tl ss)) else NONE
end;
fun filter_intro ctxt goal (_,thm) =
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 thm;
in
if is_some ss then SOME (nprems_of thm, valOf ss) else NONE
end;
fun filter_elim ctxt goal (_,thm) =
if not (Thm.no_prems thm) then
let
val rule = 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;
(*keep successful substitutions*)
val ss = prems |> List.map try_subst
|> List.filter isSome
|> List.map valOf;
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 ss)
then SOME (nprems_of thm - 1, foldl Int.min (hd ss) (tl ss)) 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 =
((List.map 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 (nprems_of thm, valOf ss) else NONE
end;
(* filter_pattern *)
fun filter_pattern ctxt pat (_, thm) =
let val tsig = Sign.tsig_of (ProofContext.theory_of ctxt)
in if Pattern.matches_subterm tsig (pat, Thm.prop_of thm) then SOME (0,0)
else NONE end;
(* 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 =
map (fn f => f thm) filters |> List.foldl opt_add (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));
val processed = List.map (fn t => (eval_filters filters t, t)) thms;
val filtered = List.filter (isSome o #1) processed;
in
filtered |> List.map (apfst valOf) |> 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;