author | wenzelm |
Wed, 31 Dec 2008 15:30:10 +0100 | |
changeset 29269 | 5c25a2012975 |
parent 28900 | 53fd5cc685b4 |
child 29274 | 84e1729dda9c |
permissions | -rw-r--r-- |
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(* Title: Pure/Isar/find_theorems.ML |
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Author: Rafal Kolanski and Gerwin Klein, NICTA |
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Retrieve theorems from proof context. |
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*) |
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signature FIND_THEOREMS = |
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sig |
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val limit: int ref |
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datatype 'term criterion = |
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Name of string | Intro | Elim | Dest | Simp of 'term | Pattern of 'term |
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val print_theorems: Proof.context -> term option -> int option -> bool -> |
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(bool * string criterion) list -> unit |
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end; |
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structure FindTheorems: FIND_THEOREMS = |
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struct |
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(** search criteria **) |
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datatype 'term criterion = |
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Name of string | Intro | Elim | Dest | Simp of 'term | Pattern of 'term; |
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fun read_criterion _ (Name name) = Name name |
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| read_criterion _ Intro = Intro |
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| read_criterion _ Elim = Elim |
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| read_criterion _ Dest = Dest |
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| read_criterion ctxt (Simp str) = Simp (ProofContext.read_term_pattern ctxt str) |
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| read_criterion ctxt (Pattern str) = Pattern (ProofContext.read_term_pattern ctxt str); |
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fun pretty_criterion ctxt (b, c) = |
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let |
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fun prfx s = if b then s else "-" ^ s; |
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in |
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(case c of |
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Name name => Pretty.str (prfx "name: " ^ quote name) |
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| Intro => Pretty.str (prfx "intro") |
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| Elim => Pretty.str (prfx "elim") |
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| Dest => Pretty.str (prfx "dest") |
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| Simp pat => Pretty.block [Pretty.str (prfx "simp:"), Pretty.brk 1, |
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Pretty.quote (Syntax.pretty_term ctxt (Term.show_dummy_patterns pat))] |
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| Pattern pat => Pretty.enclose (prfx " \"") "\"" |
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[Syntax.pretty_term ctxt (Term.show_dummy_patterns pat)]) |
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end; |
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(** search criterion filters **) |
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(*generated filters are to be of the form |
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input: (Facts.ref * thm) |
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output: (p:int, s:int) option, where |
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NONE indicates no match |
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p is the primary sorting criterion |
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(eg. number of assumptions in the theorem) |
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s is the secondary sorting criterion |
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(eg. size of the substitution for intro, elim and dest) |
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when applying a set of filters to a thm, fold results in: |
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(biggest p, sum of all s) |
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currently p and s only matter for intro, elim, dest and simp filters, |
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otherwise the default ordering is used. |
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*) |
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(* matching theorems *) |
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fun is_nontrivial thy = Term.is_Const o Term.head_of o ObjectLogic.drop_judgment thy; |
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(*extract terms from term_src, refine them to the parts that concern us, |
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if po try match them against obj else vice versa. |
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trivial matches are ignored. |
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returns: smallest substitution size*) |
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fun is_matching_thm (extract_terms, refine_term) ctxt po obj term_src = |
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let |
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val thy = ProofContext.theory_of ctxt; |
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fun matches pat = |
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is_nontrivial thy pat andalso |
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Pattern.matches thy (if po then (pat, obj) else (obj, pat)); |
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fun substsize pat = |
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let val (_, subst) = |
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Pattern.match thy (if po then (pat, obj) else (obj, pat)) (Vartab.empty, Vartab.empty) |
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in Vartab.fold (fn (_, (_, t)) => fn n => size_of_term t + n) subst 0 end; |
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fun bestmatch [] = NONE |
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| bestmatch xs = SOME (foldr1 Int.min xs); |
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val match_thm = matches o refine_term; |
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in |
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map (substsize o refine_term) (filter match_thm (extract_terms term_src)) |
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|> bestmatch |
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end; |
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(* filter_name *) |
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fun match_string pat str = |
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let |
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fun match [] _ = true |
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| match (p :: ps) s = |
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size p <= size s andalso |
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(case try (unprefix p) s of |
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SOME s' => match ps s' |
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| NONE => match (p :: ps) (String.substring (s, 1, size s - 1))); |
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in match (space_explode "*" pat) str end; |
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fun filter_name str_pat (thmref, _) = |
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if match_string str_pat (Facts.name_of_ref thmref) |
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then SOME (0, 0) else NONE; |
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(* filter intro/elim/dest rules *) |
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fun filter_dest ctxt goal (_, thm) = |
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let |
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val extract_dest = |
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(fn thm => if Thm.no_prems thm then [] else [Thm.full_prop_of thm], |
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hd o Logic.strip_imp_prems); |
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val prems = Logic.prems_of_goal goal 1; |
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fun try_subst prem = is_matching_thm extract_dest ctxt true prem thm; |
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val successful = prems |> map_filter try_subst; |
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in |
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(*if possible, keep best substitution (one with smallest size)*) |
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(*dest rules always have assumptions, so a dest with one |
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assumption is as good as an intro rule with none*) |
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if not (null successful) |
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then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE |
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end; |
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fun filter_intro ctxt goal (_, thm) = |
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let |
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val extract_intro = (single o Thm.full_prop_of, Logic.strip_imp_concl); |
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val concl = Logic.concl_of_goal goal 1; |
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val ss = is_matching_thm extract_intro ctxt true concl thm; |
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in |
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if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE |
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end; |
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fun filter_elim ctxt goal (_, thm) = |
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if not (Thm.no_prems thm) then |
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let |
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val rule = Thm.full_prop_of thm; |
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val prems = Logic.prems_of_goal goal 1; |
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val goal_concl = Logic.concl_of_goal goal 1; |
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val rule_mp = hd (Logic.strip_imp_prems rule); |
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val rule_concl = Logic.strip_imp_concl rule; |
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fun combine t1 t2 = Const ("*combine*", dummyT --> dummyT) $ (t1 $ t2); |
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val rule_tree = combine rule_mp rule_concl; |
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fun goal_tree prem = combine prem goal_concl; |
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fun try_subst prem = |
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is_matching_thm (single, I) ctxt true (goal_tree prem) rule_tree; |
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val successful = prems |> map_filter try_subst; |
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in |
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(*elim rules always have assumptions, so an elim with one |
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assumption is as good as an intro rule with none*) |
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if is_nontrivial (ProofContext.theory_of ctxt) (Thm.major_prem_of thm) |
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andalso not (null successful) |
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then SOME (Thm.nprems_of thm - 1, foldr1 Int.min successful) else NONE |
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end |
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else NONE |
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(* filter_simp *) |
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fun filter_simp ctxt t (_, thm) = |
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let |
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val (_, {mk_rews = {mk, ...}, ...}) = |
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MetaSimplifier.rep_ss (Simplifier.local_simpset_of ctxt); |
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val extract_simp = |
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(map Thm.full_prop_of o mk, #1 o Logic.dest_equals o Logic.strip_imp_concl); |
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val ss = is_matching_thm extract_simp ctxt false t thm |
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in |
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if is_some ss then SOME (Thm.nprems_of thm, the ss) else NONE |
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end; |
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(* filter_pattern *) |
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fun get_names (_, thm) = let |
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val t = Thm.full_prop_of thm; |
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in (term_consts t) union (add_term_free_names (t, [])) end; |
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fun add_pat_names (t, cs) = |
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case strip_comb t of |
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(Const (c, _), args) => foldl add_pat_names (insert (op =) c cs) args |
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| (Free (c, _), args) => foldl add_pat_names (insert (op =) c cs) args |
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| (Abs (_, _, t), _) => add_pat_names (t, cs) |
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| _ => cs; |
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(* Only include constants and frees that cannot be thrown away. |
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for example, from "(% x y z. y + 1) 7 8 9" give [1]. |
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191 |
The result [1, 8] would be more accurate, but only a |
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sound approximation is required and variables must |
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be ignored: e.g. "_ 7 8 9". *) |
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194 |
|
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fun filter_pattern ctxt pat = let |
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val pat_consts = add_pat_names (pat, []); |
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197 |
|
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fun check (t, NONE) = check (t, SOME (get_names t)) |
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| check ((_, thm), c as SOME thm_consts) = |
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(if pat_consts subset_string thm_consts |
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andalso (Pattern.matches_subterm (ProofContext.theory_of ctxt) |
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(pat, Thm.full_prop_of thm)) |
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then SOME (0, 0) else NONE, c); |
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in check end; |
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|
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(* interpret criteria as filters *) |
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local |
209 |
||
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fun err_no_goal c = |
|
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error ("Current goal required for " ^ c ^ " search criterion"); |
|
212 |
||
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fun filter_crit _ _ (Name name) = apfst (filter_name name) |
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| filter_crit _ NONE Intro = err_no_goal "intro" |
215 |
| filter_crit _ NONE Elim = err_no_goal "elim" |
|
216 |
| filter_crit _ NONE Dest = err_no_goal "dest" |
|
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| filter_crit ctxt (SOME goal) Intro = apfst (filter_intro ctxt goal) |
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| filter_crit ctxt (SOME goal) Elim = apfst (filter_elim ctxt goal) |
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| filter_crit ctxt (SOME goal) Dest = apfst (filter_dest ctxt goal) |
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| filter_crit ctxt _ (Simp pat) = apfst (filter_simp ctxt pat) |
16088 | 221 |
| filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat; |
16036 | 222 |
|
19502 | 223 |
fun opt_not x = if is_some x then NONE else SOME (0, 0); |
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224 |
|
17756 | 225 |
fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int) |
26283 | 226 |
| opt_add _ _ = NONE; |
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|
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228 |
fun app_filters thm = let |
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fun app (NONE, _, _) = NONE |
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| app (SOME v, consts, []) = SOME (v, thm) |
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| app (r, consts, f::fs) = let val (r', consts') = f (thm, consts) |
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in app (opt_add r r', consts', fs) end; |
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in app end; |
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234 |
|
16036 | 235 |
in |
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236 |
|
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fun filter_criterion ctxt opt_goal (b, c) = |
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(if b then I else (apfst opt_not)) o filter_crit ctxt opt_goal c; |
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239 |
|
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fun all_filters filters thms = |
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let |
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fun eval_filters thm = app_filters thm (SOME (0, 0), NONE, filters); |
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243 |
|
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(*filters return: (number of assumptions, substitution size) option, so |
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sort (desc. in both cases) according to number of assumptions first, |
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then by the substitution size*) |
17205 | 247 |
fun thm_ord (((p0, s0), _), ((p1, s1), _)) = |
248 |
prod_ord int_ord int_ord ((p1, s1), (p0, s0)); |
|
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in map_filter eval_filters thms |> sort thm_ord |> map #2 end; |
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250 |
|
16036 | 251 |
end; |
252 |
||
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253 |
|
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(* removing duplicates, preferring nicer names, roughly n log n *) |
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255 |
|
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256 |
local |
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257 |
|
27486 | 258 |
val index_ord = option_ord (K EQUAL); |
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259 |
val hidden_ord = bool_ord o pairself NameSpace.is_hidden; |
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260 |
val qual_ord = int_ord o pairself (length o NameSpace.explode); |
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261 |
val txt_ord = int_ord o pairself size; |
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262 |
|
27486 | 263 |
fun nicer_name (x, i) (y, j) = |
264 |
(case hidden_ord (x, y) of EQUAL => |
|
265 |
(case index_ord (i, j) of EQUAL => |
|
266 |
(case qual_ord (x, y) of EQUAL => txt_ord (x, y) | ord => ord) |
|
267 |
| ord => ord) |
|
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| ord => ord) <> GREATER; |
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269 |
|
27486 | 270 |
fun nicer (Facts.Named ((x, _), i)) (Facts.Named ((y, _), j)) = |
271 |
nicer_name (x, i) (y, j) |
|
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| nicer (Facts.Fact _) (Facts.Named _) = true |
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273 |
| nicer (Facts.Named _) (Facts.Fact _) = false; |
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274 |
|
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275 |
fun rem_cdups xs = |
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276 |
let |
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277 |
fun rem_c rev_seen [] = rev rev_seen |
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278 |
| rem_c rev_seen [x] = rem_c (x :: rev_seen) [] |
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279 |
| rem_c rev_seen ((x as ((n, t), _)) :: (y as ((n', t'), _)) :: xs) = |
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280 |
if Thm.eq_thm_prop (t, t') |
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281 |
then rem_c rev_seen ((if nicer n n' then x else y) :: xs) |
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282 |
else rem_c (x :: rev_seen) (y :: xs) |
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283 |
in rem_c [] xs end; |
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284 |
|
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285 |
in |
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286 |
|
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287 |
fun rem_thm_dups xs = |
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288 |
xs ~~ (1 upto length xs) |
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289 |
|> sort (TermOrd.fast_term_ord o pairself (Thm.prop_of o #2 o #1)) |
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290 |
|> rem_cdups |
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291 |
|> sort (int_ord o pairself #2) |
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292 |
|> map #1; |
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293 |
|
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294 |
end; |
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295 |
|
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296 |
|
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(* print_theorems *) |
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298 |
|
26283 | 299 |
fun all_facts_of ctxt = |
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300 |
maps Facts.selections |
27173 | 301 |
(Facts.dest_static [] (PureThy.facts_of (ProofContext.theory_of ctxt)) @ |
302 |
Facts.dest_static [] (ProofContext.facts_of ctxt)); |
|
17972 | 303 |
|
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304 |
val limit = ref 40; |
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305 |
|
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fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria = |
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307 |
let |
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308 |
val start = start_timing (); |
16036 | 309 |
val criteria = map (apsnd (read_criterion ctxt)) raw_criteria; |
310 |
val filters = map (filter_criterion ctxt opt_goal) criteria; |
|
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311 |
|
26283 | 312 |
val raw_matches = all_filters filters (all_facts_of ctxt); |
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313 |
|
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314 |
val matches = |
22414 | 315 |
if rem_dups |
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316 |
then rem_thm_dups raw_matches |
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317 |
else raw_matches; |
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318 |
|
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319 |
val len = length matches; |
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320 |
val lim = the_default (! limit) opt_limit; |
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321 |
val thms = Library.drop (len - lim, matches); |
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322 |
|
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323 |
val end_msg = " in " ^ |
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|
324 |
(List.nth (String.tokens Char.isSpace (end_timing start), 3)) |
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325 |
^ " secs" |
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326 |
|
28211 | 327 |
fun prt_fact (thmref, thm) = Pretty.block |
328 |
[Pretty.str (Facts.string_of_ref thmref), Pretty.str ":", Pretty.brk 1, |
|
329 |
ProofContext.pretty_thm ctxt thm]; |
|
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330 |
in |
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|
331 |
Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria) |
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332 |
:: Pretty.str "" :: |
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|
333 |
(if null thms then [Pretty.str ("nothing found" ^ end_msg)] |
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else |
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[Pretty.str ("found " ^ string_of_int len ^ " theorems" ^ |
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(if len <= lim then "" |
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else " (" ^ string_of_int lim ^ " displayed)") |
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^ end_msg ^ ":"), Pretty.str ""] @ |
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map prt_fact thms) |
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|> Pretty.chunks |> Pretty.writeln |
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end; |
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|
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end; |