author | haftmann |
Fri, 19 Oct 2007 15:08:33 +0200 | |
changeset 25096 | b8950f7cf92e |
parent 24920 | 2a45e400fdad |
child 25226 | 502d8676cdd6 |
permissions | -rw-r--r-- |
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(* Title: Pure/Isar/find_theorems.ML |
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ID: $Id$ |
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Author: Rafal Kolanski, NICTA and Tobias Nipkow, TU Muenchen |
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|
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Retrieve theorems from proof context. |
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*) |
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|
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val thms_containing_limit = ref 40; |
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signature FIND_THEOREMS = |
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sig |
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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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|
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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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|
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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: (thmref * 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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|
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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) |
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(filter match_thm (extract_terms term_src)) |> bestmatch |
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end; |
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||
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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 (PureThy.name_of_thmref 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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|
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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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|
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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 o 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 filter_pattern ctxt pat (_, thm) = |
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if Pattern.matches_subterm (ProofContext.theory_of ctxt) (pat, Thm.full_prop_of thm) |
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then SOME (0, 0) else NONE; |
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||
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(* interpret criteria as filters *) |
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local |
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fun err_no_goal c = |
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error ("Current goal required for " ^ c ^ " search criterion"); |
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fun filter_crit _ _ (Name name) = filter_name name |
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| filter_crit _ NONE Intro = err_no_goal "intro" |
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| filter_crit _ NONE Elim = err_no_goal "elim" |
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| filter_crit _ NONE Dest = err_no_goal "dest" |
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| filter_crit ctxt (SOME goal) Intro = filter_intro ctxt goal |
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| filter_crit ctxt (SOME goal) Elim = filter_elim ctxt goal |
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| filter_crit ctxt (SOME goal) Dest = filter_dest ctxt goal |
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| filter_crit ctxt _ (Simp pat) = filter_simp ctxt pat |
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| filter_crit ctxt _ (Pattern pat) = filter_pattern ctxt pat; |
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fun opt_not x = if is_some x then NONE else SOME (0, 0); |
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fun opt_add (SOME (a, x)) (SOME (b, y)) = SOME (Int.max (a, b), x + y : int) |
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| opt_add _ _ = NONE; |
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|
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in |
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|
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fun filter_criterion ctxt opt_goal (b, c) = |
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(if b then I else opt_not) o filter_crit ctxt opt_goal c; |
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|
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fun all_filters filters thms = |
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let |
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fun eval_filters filters thm = |
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fold opt_add (map (fn f => f thm) filters) (SOME (0, 0)); |
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|
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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*) |
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fun thm_ord (((p0, s0), _), ((p1, s1), _)) = |
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prod_ord int_ord int_ord ((p1, s1), (p0, s0)); |
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in |
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map (`(eval_filters filters)) thms |
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|> map_filter (fn (SOME x, y) => SOME (x, y) | (NONE, _) => NONE) |
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|> sort thm_ord |> map #2 |
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end; |
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|
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end; |
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||
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(* removing duplicates, preferring nicer names, roughly n log n *) |
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|
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fun rem_thm_dups xs = |
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let |
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fun nicer (Fact x) (Fact y) = size x <= size y |
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| nicer (Fact _) _ = true |
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| nicer (PureThy.Name x) (PureThy.Name y) = size x <= size y |
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| nicer (PureThy.Name _) (Fact _) = false |
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| nicer (PureThy.Name _) _ = true |
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| nicer (NameSelection (x, _)) (NameSelection (y, _)) = size x <= size y |
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| nicer (NameSelection _) _ = false; |
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|
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fun rem_cdups xs = |
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let |
|
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fun rem_c rev_seen [] = rev rev_seen |
|
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| rem_c rev_seen [x] = rem_c (x::rev_seen) [] |
|
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| rem_c rev_seen ((x as ((n,t),_))::(y as ((n',t'),_))::xs) = |
|
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if Thm.eq_thm_prop (t,t') |
|
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then if nicer n n' |
|
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then rem_c rev_seen (x::xs) |
|
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else rem_c rev_seen (y::xs) |
|
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else rem_c (x::rev_seen) (y::xs) |
|
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in rem_c [] xs end; |
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|
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in ListPair.zip (xs, 1 upto length xs) |
259 |
|> sort (Term.fast_term_ord o pairself (prop_of o #2 o #1)) |
|
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|> rem_cdups |
|
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|> sort (int_ord o pairself #2) |
|
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|> map #1 |
|
263 |
end; |
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|
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(* print_theorems *) |
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|
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fun find_thms ctxt spec = |
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(PureThy.thms_containing (ProofContext.theory_of ctxt) spec |
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|> maps PureThy.selections) @ |
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(ProofContext.lthms_containing ctxt spec |
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|> maps PureThy.selections |
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|> distinct (fn ((r1, th1), (r2, th2)) => |
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r1 = r2 andalso Thm.eq_thm_prop (th1, th2))); |
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|
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fun print_theorems ctxt opt_goal opt_limit rem_dups raw_criteria = |
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let |
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val criteria = map (apsnd (read_criterion ctxt)) raw_criteria; |
279 |
val filters = map (filter_criterion ctxt opt_goal) criteria; |
|
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|
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val raw_matches = all_filters filters (find_thms ctxt ([], [])); |
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val matches = |
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if rem_dups |
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then rem_thm_dups raw_matches |
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else raw_matches; |
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|
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val len = length matches; |
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val limit = the_default (! thms_containing_limit) opt_limit; |
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val thms = Library.drop (len - limit, matches); |
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|
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fun prt_fact (thmref, thm) = |
292 |
ProofContext.pretty_fact ctxt (PureThy.string_of_thmref thmref, [thm]); |
|
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293 |
in |
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Pretty.big_list "searched for:" (map (pretty_criterion ctxt) criteria) :: Pretty.str "" :: |
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(if null thms then [Pretty.str "nothing found"] |
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296 |
else |
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[Pretty.str ("found " ^ string_of_int len ^ " theorems" ^ |
298 |
(if len <= limit then "" else " (" ^ string_of_int limit ^ " displayed)") ^ ":"), |
|
299 |
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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304 |
end; |