--- a/src/HOL/BNF/Tools/bnf_fp_def_sugar.ML Mon Apr 29 11:31:40 2013 +0200
+++ b/src/HOL/BNF/Tools/bnf_fp_def_sugar.ML Mon Apr 29 14:07:03 2013 +0200
@@ -7,6 +7,24 @@
signature BNF_FP_DEF_SUGAR =
sig
+ val derive_induct_fold_rec_thms_for_types: BNF_Def.BNF list -> thm -> thm list -> thm list ->
+ BNF_Def.BNF list -> BNF_Def.BNF list -> typ list -> typ list -> typ list list list ->
+ int list list -> int list -> term list list -> term list list -> term list list -> term list
+ list list -> thm list list -> term list -> term list -> thm list -> thm list -> Proof.context ->
+ (thm * thm list * Args.src list) * (thm list list * Args.src list)
+ * (thm list list * Args.src list)
+ val derive_coinduct_unfold_corec_thms_for_types: Proof.context -> Proof.context ->
+ BNF_Def.BNF list -> thm -> thm -> thm list -> thm list -> thm list -> BNF_Def.BNF list ->
+ BNF_Def.BNF list -> typ list -> typ list -> typ list -> int list list -> int list list ->
+ int list -> term list -> term list list -> term list list -> term list list list list ->
+ term list list list list -> term list list -> term list list list list ->
+ term list list list list -> term list list -> thm list list ->
+ BNF_Ctr_Sugar.ctr_wrap_result list -> term list -> term list -> thm list -> thm list ->
+ Proof.context ->
+ (thm * thm list * thm * thm list * Args.src list) * (thm list list * thm list list * 'e list)
+ * (thm list list * thm list list) * (thm list list * thm list list * Args.src list)
+ * (thm list list * thm list list * Args.src list) *
+ (thm list list * thm list list * Args.src list)
val datatypes: bool ->
(mixfix list -> (string * sort) list option -> binding list -> binding list -> binding list ->
binding list list -> typ list * typ list list -> BNF_Def.BNF list -> local_theory ->
@@ -56,6 +74,14 @@
let val (xs1, xs2, xs3, xs4) = split_list4 xs;
in (x1 :: xs1, x2 :: xs2, x3 :: xs3, x4 :: xs4) end;
+fun add_components_of_typ (Type (s, Ts)) =
+ fold add_components_of_typ Ts #> cons (Long_Name.base_name s)
+ | add_components_of_typ _ = I;
+
+fun base_name_of_typ T = space_implode "_" (add_components_of_typ T []);
+
+fun exists_subtype_in Ts = exists_subtype (member (op =) Ts);
+
fun resort_tfree S (TFree (s, _)) = TFree (s, S);
fun typ_subst inst (T as Type (s, Ts)) =
@@ -155,6 +181,447 @@
fun defaults_of ((_, ds), _) = ds;
fun ctr_mixfix_of (_, mx) = mx;
+fun build_map lthy build_arg (Type (s, Ts)) (Type (_, Us)) =
+ let
+ val bnf = the (bnf_of lthy s);
+ val live = live_of_bnf bnf;
+ val mapx = mk_map live Ts Us (map_of_bnf bnf);
+ val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
+ in Term.list_comb (mapx, map build_arg TUs') end;
+
+fun build_rel_step lthy build_arg (Type (s, Ts)) =
+ let
+ val bnf = the (bnf_of lthy s);
+ val live = live_of_bnf bnf;
+ val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
+ val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
+ in Term.list_comb (rel, map build_arg Ts') end;
+
+fun derive_induct_fold_rec_thms_for_types pre_bnfs ctor_induct ctor_fold_thms ctor_rec_thms
+ nesting_bnfs nested_bnfs fpTs Cs ctr_Tsss mss ns gss hss ctrss xsss ctr_defss folds recs
+ fold_defs rec_defs lthy =
+ let
+ val nn = length pre_bnfs;
+
+ val pre_map_defs = map map_def_of_bnf pre_bnfs;
+ val pre_set_defss = map set_defs_of_bnf pre_bnfs;
+ val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
+ val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
+ val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
+ val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
+
+ val fp_b_names = map base_name_of_typ fpTs;
+
+ val (((ps, ps'), us'), names_lthy) =
+ lthy
+ |> mk_Frees' "P" (map mk_pred1T fpTs)
+ ||>> Variable.variant_fixes fp_b_names;
+
+ val us = map2 (curry Free) us' fpTs;
+
+ fun mk_sets_nested bnf =
+ let
+ val Type (T_name, Us) = T_of_bnf bnf;
+ val lives = lives_of_bnf bnf;
+ val sets = sets_of_bnf bnf;
+ fun mk_set U =
+ (case find_index (curry (op =) U) lives of
+ ~1 => Term.dummy
+ | i => nth sets i);
+ in
+ (T_name, map mk_set Us)
+ end;
+
+ val setss_nested = map mk_sets_nested nested_bnfs;
+
+ val (induct_thms, induct_thm) =
+ let
+ fun mk_set Ts t =
+ let val Type (_, Ts0) = domain_type (fastype_of t) in
+ Term.subst_atomic_types (Ts0 ~~ Ts) t
+ end;
+
+ fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
+ (case find_index (curry (op =) T) fpTs of
+ ~1 =>
+ (case AList.lookup (op =) setss_nested T_name of
+ NONE => []
+ | SOME raw_sets0 =>
+ let
+ val (Ts, raw_sets) =
+ split_list (filter (exists_subtype_in fpTs o fst) (Ts0 ~~ raw_sets0));
+ val sets = map (mk_set Ts0) raw_sets;
+ val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
+ val xysets = map (pair x) (ys ~~ sets);
+ val ppremss = map (mk_raw_prem_prems names_lthy') ys;
+ in
+ flat (map2 (map o apfst o cons) xysets ppremss)
+ end)
+ | kk => [([], (kk + 1, x))])
+ | mk_raw_prem_prems _ _ = [];
+
+ fun close_prem_prem xs t =
+ fold_rev Logic.all (map Free (drop (nn + length xs)
+ (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
+
+ fun mk_prem_prem xs (xysets, (j, x)) =
+ close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
+ HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
+ HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
+
+ fun mk_raw_prem phi ctr ctr_Ts =
+ let
+ val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
+ val pprems = maps (mk_raw_prem_prems names_lthy') xs;
+ in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
+
+ fun mk_prem (xs, raw_pprems, concl) =
+ fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
+
+ val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss;
+
+ val goal =
+ Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
+ HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
+
+ val kksss = map (map (map (fst o snd) o #2)) raw_premss;
+
+ val ctor_induct' = ctor_induct OF (map mk_sumEN_tupled_balanced mss);
+
+ val thm =
+ Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
+ mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
+ pre_set_defss)
+ |> singleton (Proof_Context.export names_lthy lthy)
+ |> Thm.close_derivation;
+ in
+ `(conj_dests nn) thm
+ end;
+
+ val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
+
+ val (fold_thmss, rec_thmss) =
+ let
+ val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
+ val gfolds = map (lists_bmoc gss) folds;
+ val hrecs = map (lists_bmoc hss) recs;
+
+ fun mk_goal fss frec_like xctr f xs fxs =
+ fold_rev (fold_rev Logic.all) (xs :: fss)
+ (mk_Trueprop_eq (frec_like $ xctr, Term.list_comb (f, fxs)));
+
+ fun build_rec_like frec_likes (T, U) =
+ if T = U then
+ id_const T
+ else
+ (case find_index (curry (op =) T) fpTs of
+ ~1 => build_map lthy (build_rec_like frec_likes) T U
+ | kk => nth frec_likes kk);
+
+ val mk_U = typ_subst (map2 pair fpTs Cs);
+
+ fun unzip_rec_likes frec_likes combine (x as Free (_, T)) =
+ if exists_subtype_in fpTs T then
+ combine (x, build_rec_like frec_likes (T, mk_U T) $ x)
+ else
+ ([x], []);
+
+ val gxsss = map (map (flat_rec (unzip_rec_likes gfolds (fn (_, t) => ([t], []))))) xsss;
+ val hxsss = map (map (flat_rec (unzip_rec_likes hrecs (pairself single)))) xsss;
+
+ val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
+ val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
+
+ val fold_tacss =
+ map2 (map o mk_rec_like_tac pre_map_defs [] nesting_map_ids'' fold_defs) ctor_fold_thms
+ ctr_defss;
+ val rec_tacss =
+ map2 (map o mk_rec_like_tac pre_map_defs nested_map_comp's
+ (nested_map_ids'' @ nesting_map_ids'') rec_defs) ctor_rec_thms ctr_defss;
+
+ fun prove goal tac =
+ Goal.prove_sorry lthy [] [] goal (tac o #context)
+ |> Thm.close_derivation;
+ in
+ (map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss)
+ end;
+
+ val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
+ in
+ ((induct_thm, induct_thms, [induct_case_names_attr]),
+ (fold_thmss, code_simp_attrs), (rec_thmss, code_simp_attrs))
+ end;
+
+fun derive_coinduct_unfold_corec_thms_for_types names_lthy0 no_defs_lthy pre_bnfs dtor_coinduct
+ dtor_strong_induct dtor_ctors dtor_unfold_thms dtor_corec_thms nesting_bnfs nested_bnfs fpTs Cs
+ As kss mss ns cs cpss pgss crssss cgssss phss csssss chssss ctrss ctr_defss ctr_wrap_ress
+ unfolds corecs unfold_defs corec_defs lthy =
+ let
+ val nn = length pre_bnfs;
+
+ val pre_map_defs = map map_def_of_bnf pre_bnfs;
+ val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
+ val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
+ val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs;
+ val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
+ val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
+ val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
+
+ val fp_b_names = map base_name_of_typ fpTs;
+
+ val discss = map (map (mk_disc_or_sel As) o #1) ctr_wrap_ress;
+ val selsss = map (map (map (mk_disc_or_sel As)) o #2) ctr_wrap_ress;
+ val exhaust_thms = map #3 ctr_wrap_ress;
+ val disc_thmsss = map #7 ctr_wrap_ress;
+ val discIss = map #8 ctr_wrap_ress;
+ val sel_thmsss = map #9 ctr_wrap_ress;
+
+ val (((rs, us'), vs'), names_lthy) =
+ lthy
+ |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
+ ||>> Variable.variant_fixes fp_b_names
+ ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
+
+ val us = map2 (curry Free) us' fpTs;
+ val udiscss = map2 (map o rapp) us discss;
+ val uselsss = map2 (map o map o rapp) us selsss;
+
+ val vs = map2 (curry Free) vs' fpTs;
+ val vdiscss = map2 (map o rapp) vs discss;
+ val vselsss = map2 (map o map o rapp) vs selsss;
+
+ val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
+ let
+ val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
+ val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
+ val strong_rs =
+ map4 (fn u => fn v => fn uvr => fn uv_eq =>
+ fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
+
+ fun build_rel rs' T =
+ (case find_index (curry (op =) T) fpTs of
+ ~1 =>
+ if exists_subtype_in fpTs T then build_rel_step lthy (build_rel rs') T
+ else HOLogic.eq_const T
+ | kk => nth rs' kk);
+
+ fun build_rel_app rs' usel vsel =
+ fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
+
+ fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
+ (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
+ (if null usels then
+ []
+ else
+ [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
+ Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
+
+ fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
+ Library.foldr1 HOLogic.mk_conj
+ (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
+ handle List.Empty => @{term True};
+
+ fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
+ fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
+ HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
+
+ val concl =
+ HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
+ (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
+ uvrs us vs));
+
+ fun mk_goal rs' =
+ Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
+ concl);
+
+ val goal = mk_goal rs;
+ val strong_goal = mk_goal strong_rs;
+
+ fun prove dtor_coinduct' goal =
+ Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
+ mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
+ exhaust_thms ctr_defss disc_thmsss sel_thmsss)
+ |> singleton (Proof_Context.export names_lthy lthy)
+ |> Thm.close_derivation;
+
+ fun postproc nn thm =
+ Thm.permute_prems 0 nn
+ (if nn = 1 then thm RS mp
+ else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
+ |> Drule.zero_var_indexes
+ |> `(conj_dests nn);
+ in
+ (postproc nn (prove dtor_coinduct goal), postproc nn (prove dtor_strong_induct strong_goal))
+ end;
+
+ fun mk_coinduct_concls ms discs ctrs =
+ let
+ fun mk_disc_concl disc = [name_of_disc disc];
+ fun mk_ctr_concl 0 _ = []
+ | mk_ctr_concl _ ctor = [name_of_ctr ctor];
+ val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
+ val ctr_concls = map2 mk_ctr_concl ms ctrs;
+ in
+ flat (map2 append disc_concls ctr_concls)
+ end;
+
+ val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
+ val coinduct_conclss =
+ map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
+
+ fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
+
+ val gunfolds = map (lists_bmoc pgss) unfolds;
+ val hcorecs = map (lists_bmoc phss) corecs;
+
+ val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
+ let
+ fun mk_goal pfss c cps fcorec_like n k ctr m cfs' =
+ fold_rev (fold_rev Logic.all) ([c] :: pfss)
+ (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
+ mk_Trueprop_eq (fcorec_like $ c, Term.list_comb (ctr, take m cfs'))));
+
+ fun build_corec_like fcorec_likes (T, U) =
+ if T = U then
+ id_const T
+ else
+ (case find_index (curry (op =) U) fpTs of
+ ~1 => build_map lthy (build_corec_like fcorec_likes) T U
+ | kk => nth fcorec_likes kk);
+
+ val mk_U = typ_subst (map2 pair Cs fpTs);
+
+ fun intr_corec_likes fcorec_likes [] [cf] =
+ let val T = fastype_of cf in
+ if exists_subtype_in Cs T then build_corec_like fcorec_likes (T, mk_U T) $ cf
+ else cf
+ end
+ | intr_corec_likes fcorec_likes [cq] [cf, cf'] =
+ mk_If cq (intr_corec_likes fcorec_likes [] [cf])
+ (intr_corec_likes fcorec_likes [] [cf']);
+
+ val crgsss = map2 (map2 (map2 (intr_corec_likes gunfolds))) crssss cgssss;
+ val cshsss = map2 (map2 (map2 (intr_corec_likes hcorecs))) csssss chssss;
+
+ val unfold_goalss =
+ map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss;
+ val corec_goalss =
+ map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss;
+
+ fun mk_map_if_distrib bnf =
+ let
+ val mapx = map_of_bnf bnf;
+ val live = live_of_bnf bnf;
+ val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
+ val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
+ val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
+ in
+ Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
+ @{thm if_distrib}
+ end;
+
+ val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
+
+ val unfold_tacss =
+ map3 (map oo mk_corec_like_tac unfold_defs [] [] nesting_map_ids'' [])
+ dtor_unfold_thms pre_map_defs ctr_defss;
+ val corec_tacss =
+ map3 (map oo mk_corec_like_tac corec_defs nested_map_comps'' nested_map_comp's
+ (nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
+ dtor_corec_thms pre_map_defs ctr_defss;
+
+ fun prove goal tac =
+ Goal.prove_sorry lthy [] [] goal (tac o #context)
+ |> Thm.close_derivation;
+
+ val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
+ val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss;
+
+ val filter_safesss =
+ map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
+ curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss);
+
+ val safe_unfold_thmss = filter_safesss unfold_thmss;
+ val safe_corec_thmss = filter_safesss corec_thmss;
+ in
+ (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
+ end;
+
+ val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
+ let
+ fun mk_goal c cps fcorec_like n k disc =
+ mk_Trueprop_eq (disc $ (fcorec_like $ c),
+ if n = 1 then @{const True}
+ else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
+
+ val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
+ val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
+
+ fun mk_case_split' cp =
+ Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
+
+ val case_splitss' = map (map mk_case_split') cpss;
+
+ val unfold_tacss =
+ map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' unfold_thmss disc_thmsss;
+ val corec_tacss =
+ map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' corec_thmss disc_thmsss;
+
+ fun prove goal tac =
+ Goal.prove_sorry lthy [] [] goal (tac o #context)
+ |> singleton (Proof_Context.export names_lthy0 no_defs_lthy)
+ |> Thm.close_derivation;
+
+ fun proves [_] [_] = []
+ | proves goals tacs = map2 prove goals tacs;
+ in
+ (map2 proves unfold_goalss unfold_tacss,
+ map2 proves corec_goalss corec_tacss)
+ end;
+
+ val is_triv_discI = is_triv_implies orf is_concl_refl;
+
+ fun mk_disc_corec_like_thms corec_likes discIs =
+ map (op RS) (filter_out (is_triv_discI o snd) (corec_likes ~~ discIs));
+
+ val disc_unfold_thmss = map2 mk_disc_corec_like_thms unfold_thmss discIss;
+ val disc_corec_thmss = map2 mk_disc_corec_like_thms corec_thmss discIss;
+
+ fun mk_sel_corec_like_thm corec_like_thm sel sel_thm =
+ let
+ val (domT, ranT) = dest_funT (fastype_of sel);
+ val arg_cong' =
+ Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
+ [NONE, NONE, SOME (certify lthy sel)] arg_cong
+ |> Thm.varifyT_global;
+ val sel_thm' = sel_thm RSN (2, trans);
+ in
+ corec_like_thm RS arg_cong' RS sel_thm'
+ end;
+
+ fun mk_sel_corec_like_thms corec_likess =
+ map3 (map3 (map2 o mk_sel_corec_like_thm)) corec_likess selsss sel_thmsss |> map flat;
+
+ val sel_unfold_thmss = mk_sel_corec_like_thms unfold_thmss;
+ val sel_corec_thmss = mk_sel_corec_like_thms corec_thmss;
+
+ val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
+ val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
+ val coinduct_case_concl_attrs =
+ map2 (fn casex => fn concls =>
+ Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
+ coinduct_cases coinduct_conclss;
+ val coinduct_case_attrs =
+ coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
+ in
+ ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms, coinduct_case_attrs),
+ (unfold_thmss, corec_thmss, []),
+ (safe_unfold_thmss, safe_corec_thmss),
+ (disc_unfold_thmss, disc_corec_thmss, simp_attrs),
+ (disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
+ (sel_unfold_thmss, sel_corec_thmss, simp_attrs))
+ end;
+
fun define_datatypes prepare_constraint prepare_typ prepare_term lfp construct_fp
(wrap_opts as (no_dests, rep_compat), specs) no_defs_lthy0 =
let
@@ -264,22 +731,6 @@
val timer = time (Timer.startRealTimer ());
- fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) =
- let
- val bnf = the (bnf_of lthy s);
- val live = live_of_bnf bnf;
- val mapx = mk_map live Ts Us (map_of_bnf bnf);
- val TUs' = map dest_funT (fst (strip_typeN live (fastype_of mapx)));
- in Term.list_comb (mapx, map build_arg TUs') end;
-
- fun build_rel_step build_arg (Type (s, Ts)) =
- let
- val bnf = the (bnf_of lthy s);
- val live = live_of_bnf bnf;
- val rel = mk_rel live Ts Ts (rel_of_bnf bnf);
- val Ts' = map domain_type (fst (strip_typeN live (fastype_of rel)));
- in Term.list_comb (rel, map build_arg Ts') end;
-
fun add_nesty_bnf_names Us =
let
fun add (Type (s, Ts)) ss =
@@ -298,10 +749,6 @@
val pre_map_defs = map map_def_of_bnf pre_bnfs;
val pre_set_defss = map set_defs_of_bnf pre_bnfs;
val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
- val nested_map_comps'' = map ((fn thm => thm RS sym) o map_comp_of_bnf) nested_bnfs;
- val nested_map_comp's = map map_comp'_of_bnf nested_bnfs;
- val nested_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nested_bnfs;
- val nesting_map_ids'' = map (unfold_thms lthy @{thms id_def} o map_id_of_bnf) nesting_bnfs;
val nested_set_map's = maps set_map'_of_bnf nested_bnfs;
val nesting_set_map's = maps set_map'_of_bnf nesting_bnfs;
@@ -332,9 +779,6 @@
((qualify true fp_b_name (Binding.name thmN), attrs T_name),
[(thms, [])])) fp_b_names fpTs thmss);
- val exists_fp_subtype = exists_subtype (member (op =) fpTs);
- val exists_Cs_subtype = exists_subtype (member (op =) Cs);
-
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs;
val ns = map length ctr_Tsss;
val kss = map (fn n => 1 upto n) ns;
@@ -368,7 +812,7 @@
| proj_recT _ T = T;
fun unzip_recT T =
- if exists_fp_subtype T then ([proj_recT fst T], [proj_recT snd T]) else ([T], []);
+ if exists_subtype_in fpTs T then ([proj_recT fst T], [proj_recT snd T]) else ([T], []);
val z_Tsss =
map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type)
@@ -422,7 +866,7 @@
| proj_corecT _ T = T;
fun unzip_corecT T =
- if exists_fp_subtype T then [proj_corecT fst T, proj_corecT snd T] else [T];
+ if exists_subtype_in fpTs T then [proj_corecT fst T, proj_corecT snd T] else [T];
val (s_Tssss, h_sum_prod_Ts, h_Tsss, h_Tssss, ph_Tss) =
mk_types unzip_corecT fp_rec_fun_Ts;
@@ -547,7 +991,7 @@
(sel_bindingss, sel_defaultss))) lthy
end;
- fun derive_maps_sets_rels (wrap_res, lthy) =
+ fun derive_maps_sets_rels (ctr_wrap_res, lthy) =
let
val rel_flip = rel_flip_of_bnf fp_bnf;
val nones = replicate live NONE;
@@ -623,7 +1067,7 @@
(setsN, flat set_thmss, code_simp_attrs)]
|> massage_simple_notes fp_b_name;
in
- (wrap_res, lthy |> Local_Theory.notes notes |> snd)
+ (ctr_wrap_res, lthy |> Local_Theory.notes notes |> snd)
end;
fun define_fold_rec no_defs_lthy =
@@ -636,7 +1080,7 @@
else
(case (T, U) of
(Type (s, _), Type (s', _)) =>
- if s = s' then build_map (build_prod_proj mk_proj) T U else mk_proj T
+ if s = s' then build_map lthy (build_prod_proj mk_proj) T U else mk_proj T
| _ => mk_proj T);
(* TODO: Avoid these complications; cf. corec case *)
@@ -646,7 +1090,7 @@
| mk_U _ T = T;
fun unzip_rec (x as Free (_, T)) =
- if exists_fp_subtype T then
+ if exists_subtype_in fpTs T then
([build_prod_proj fst_const (T, mk_U fst T) $ x],
[build_prod_proj snd_const (T, mk_U snd T) $ x])
else
@@ -696,7 +1140,7 @@
else
(case (T, U) of
(Type (s, _), Type (s', _)) =>
- if s = s' then build_map (build_sum_inj mk_inj) T U
+ if s = s' then build_map lthy (build_sum_inj mk_inj) T U
else uncurry mk_inj (dest_sumT U)
| _ => uncurry mk_inj (dest_sumT U));
@@ -746,8 +1190,8 @@
val define_rec_likes = if lfp then define_fold_rec else define_unfold_corec;
- fun massage_res ((wrap_res, rec_like_res), lthy) =
- (((ctrs, xss, ctr_defs, wrap_res), rec_like_res), lthy);
+ fun massage_res ((ctr_wrap_res, rec_like_res), lthy) =
+ (((ctrs, xss, ctr_defs, ctr_wrap_res), rec_like_res), lthy);
in
(wrap #> (live > 0 ? derive_maps_sets_rels) ##>> define_rec_likes #> massage_res, lthy')
end;
@@ -761,406 +1205,56 @@
map3 (fn (_, _, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn fold_likes =>
injects @ distincts @ cases @ rec_likes @ fold_likes);
- fun derive_induct_fold_rec_thms_for_types (((ctrss, xsss, ctr_defss, wrap_ress), (folds, recs,
- fold_defs, rec_defs)), lthy) =
+ fun derive_and_note_induct_fold_rec_thms_for_types
+ (((ctrss, xsss, ctr_defss, ctr_wrap_ress), (folds, recs, fold_defs, rec_defs)), lthy) =
let
- val (((ps, ps'), us'), names_lthy) =
- lthy
- |> mk_Frees' "P" (map mk_pred1T fpTs)
- ||>> Variable.variant_fixes fp_b_names;
-
- val us = map2 (curry Free) us' fpTs;
-
- fun mk_sets_nested bnf =
- let
- val Type (T_name, Us) = T_of_bnf bnf;
- val lives = lives_of_bnf bnf;
- val sets = sets_of_bnf bnf;
- fun mk_set U =
- (case find_index (curry (op =) U) lives of
- ~1 => Term.dummy
- | i => nth sets i);
- in
- (T_name, map mk_set Us)
- end;
-
- val setss_nested = map mk_sets_nested nested_bnfs;
-
- val (induct_thms, induct_thm) =
- let
- fun mk_set Ts t =
- let val Type (_, Ts0) = domain_type (fastype_of t) in
- Term.subst_atomic_types (Ts0 ~~ Ts) t
- end;
-
- fun mk_raw_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) =
- (case find_index (curry (op =) T) fpTs of
- ~1 =>
- (case AList.lookup (op =) setss_nested T_name of
- NONE => []
- | SOME raw_sets0 =>
- let
- val (Ts, raw_sets) =
- split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0));
- val sets = map (mk_set Ts0) raw_sets;
- val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
- val xysets = map (pair x) (ys ~~ sets);
- val ppremss = map (mk_raw_prem_prems names_lthy') ys;
- in
- flat (map2 (map o apfst o cons) xysets ppremss)
- end)
- | kk => [([], (kk + 1, x))])
- | mk_raw_prem_prems _ _ = [];
-
- fun close_prem_prem xs t =
- fold_rev Logic.all (map Free (drop (nn + length xs)
- (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
-
- fun mk_prem_prem xs (xysets, (j, x)) =
- close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
- HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
- HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
-
- fun mk_raw_prem phi ctr ctr_Ts =
- let
- val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
- val pprems = maps (mk_raw_prem_prems names_lthy') xs;
- in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
-
- fun mk_prem (xs, raw_pprems, concl) =
- fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
+ val ((induct_thm, induct_thms, induct_attrs),
+ (fold_thmss, fold_attrs),
+ (rec_thmss, rec_attrs)) =
+ derive_induct_fold_rec_thms_for_types pre_bnfs fp_induct fp_fold_thms fp_rec_thms
+ nesting_bnfs nested_bnfs fpTs Cs ctr_Tsss mss ns gss hss ctrss xsss ctr_defss folds recs
+ fold_defs rec_defs lthy;
- val raw_premss = map3 (map2 o mk_raw_prem) ps ctrss ctr_Tsss;
-
- val goal =
- Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
- HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
-
- val kksss = map (map (map (fst o snd) o #2)) raw_premss;
-
- val ctor_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss);
-
- val thm =
- Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
- mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' nested_set_map's
- pre_set_defss)
- |> singleton (Proof_Context.export names_lthy lthy)
- |> Thm.close_derivation;
- in
- `(conj_dests nn) thm
- end;
-
- val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
-
- val (fold_thmss, rec_thmss) =
- let
- val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
- val gfolds = map (lists_bmoc gss) folds;
- val hrecs = map (lists_bmoc hss) recs;
-
- fun mk_goal fss frec_like xctr f xs fxs =
- fold_rev (fold_rev Logic.all) (xs :: fss)
- (mk_Trueprop_eq (frec_like $ xctr, Term.list_comb (f, fxs)));
-
- fun build_rec_like frec_likes (T, U) =
- if T = U then
- id_const T
- else
- (case find_index (curry (op =) T) fpTs of
- ~1 => build_map (build_rec_like frec_likes) T U
- | kk => nth frec_likes kk);
-
- val mk_U = typ_subst (map2 pair fpTs Cs);
-
- fun unzip_rec_likes frec_likes combine (x as Free (_, T)) =
- if exists_fp_subtype T then
- combine (x, build_rec_like frec_likes (T, mk_U T) $ x)
- else
- ([x], []);
-
- val gxsss = map (map (flat_rec (unzip_rec_likes gfolds (fn (_, t) => ([t], []))))) xsss;
- val hxsss = map (map (flat_rec (unzip_rec_likes hrecs (pairself single)))) xsss;
-
- val fold_goalss = map5 (map4 o mk_goal gss) gfolds xctrss gss xsss gxsss;
- val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss;
-
- val fold_tacss =
- map2 (map o mk_rec_like_tac pre_map_defs [] nesting_map_ids'' fold_defs) fp_fold_thms
- ctr_defss;
- val rec_tacss =
- map2 (map o mk_rec_like_tac pre_map_defs nested_map_comp's
- (nested_map_ids'' @ nesting_map_ids'') rec_defs) fp_rec_thms ctr_defss;
-
- fun prove goal tac =
- Goal.prove_sorry lthy [] [] goal (tac o #context)
- |> Thm.close_derivation;
- in
- (map2 (map2 prove) fold_goalss fold_tacss, map2 (map2 prove) rec_goalss rec_tacss)
- end;
-
- val simp_thmss = mk_simp_thmss wrap_ress rec_thmss fold_thmss;
-
- val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name));
+ val simp_thmss = mk_simp_thmss ctr_wrap_ress rec_thmss fold_thmss;
+
val common_notes =
- (if nn > 1 then [(inductN, [induct_thm], [induct_case_names_attr])] else [])
+ (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
|> massage_simple_notes fp_common_name;
val notes =
- [(foldN, fold_thmss, K code_simp_attrs),
- (inductN, map single induct_thms,
- fn T_name => [induct_case_names_attr, induct_type_attr T_name]),
- (recN, rec_thmss, K code_simp_attrs),
+ [(foldN, fold_thmss, K fold_attrs),
+ (inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
+ (recN, rec_thmss, K rec_attrs),
(simpsN, simp_thmss, K [])]
|> massage_multi_notes;
in
lthy |> Local_Theory.notes (common_notes @ notes) |> snd
end;
- fun derive_coinduct_unfold_corec_thms_for_types (((ctrss, _, ctr_defss, wrap_ress), (unfolds,
- corecs, unfold_defs, corec_defs)), lthy) =
+ fun derive_and_note_coinduct_unfold_corec_thms_for_types
+ (((ctrss, _, ctr_defss, ctr_wrap_ress), (unfolds, corecs, unfold_defs, corec_defs)), lthy) =
let
- val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
-
- val discss = map (map (mk_disc_or_sel As) o #1) wrap_ress;
- val selsss = map (map (map (mk_disc_or_sel As)) o #2) wrap_ress;
- val exhaust_thms = map #3 wrap_ress;
- val disc_thmsss = map #7 wrap_ress;
- val discIss = map #8 wrap_ress;
- val sel_thmsss = map #9 wrap_ress;
-
- val (((rs, us'), vs'), names_lthy) =
- lthy
- |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
- ||>> Variable.variant_fixes fp_b_names
- ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
-
- val us = map2 (curry Free) us' fpTs;
- val udiscss = map2 (map o rapp) us discss;
- val uselsss = map2 (map o map o rapp) us selsss;
-
- val vs = map2 (curry Free) vs' fpTs;
- val vdiscss = map2 (map o rapp) vs discss;
- val vselsss = map2 (map o map o rapp) vs selsss;
-
- val ((coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)) =
- let
- val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
- val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
- val strong_rs =
- map4 (fn u => fn v => fn uvr => fn uv_eq =>
- fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
-
- fun build_rel rs' T =
- (case find_index (curry (op =) T) fpTs of
- ~1 =>
- if exists_fp_subtype T then build_rel_step (build_rel rs') T else HOLogic.eq_const T
- | kk => nth rs' kk);
-
- fun build_rel_app rs' usel vsel =
- fold rapp [usel, vsel] (build_rel rs' (fastype_of usel));
-
- fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels =
- (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
- (if null usels then
- []
- else
- [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
- Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app rs') usels vsels))]);
-
- fun mk_prem_concl rs' n udiscs uselss vdiscs vselss =
- Library.foldr1 HOLogic.mk_conj
- (flat (map5 (mk_prem_ctr_concls rs' n) (1 upto n) udiscs uselss vdiscs vselss))
- handle List.Empty => @{term True};
-
- fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss =
- fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
- HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss)));
-
- val concl =
- HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
- (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
- uvrs us vs));
-
- fun mk_goal rs' =
- Logic.list_implies (map8 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss,
- concl);
-
- val goal = mk_goal rs;
- val strong_goal = mk_goal strong_rs;
-
- fun prove dtor_coinduct' goal =
- Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
- mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs dtor_ctors
- exhaust_thms ctr_defss disc_thmsss sel_thmsss)
- |> singleton (Proof_Context.export names_lthy lthy)
- |> Thm.close_derivation;
-
- fun postproc nn thm =
- Thm.permute_prems 0 nn
- (if nn = 1 then thm RS mp
- else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
- |> Drule.zero_var_indexes
- |> `(conj_dests nn);
- in
- (postproc nn (prove fp_induct goal), postproc nn (prove fp_strong_induct strong_goal))
- end;
-
- fun mk_coinduct_concls ms discs ctrs =
- let
- fun mk_disc_concl disc = [name_of_disc disc];
- fun mk_ctr_concl 0 _ = []
- | mk_ctr_concl _ ctor = [name_of_ctr ctor];
- val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
- val ctr_concls = map2 mk_ctr_concl ms ctrs;
- in
- flat (map2 append disc_concls ctr_concls)
- end;
-
- val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
- val coinduct_conclss =
- map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
-
- fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
-
- val gunfolds = map (lists_bmoc pgss) unfolds;
- val hcorecs = map (lists_bmoc phss) corecs;
-
- val (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss) =
- let
- fun mk_goal pfss c cps fcorec_like n k ctr m cfs' =
- fold_rev (fold_rev Logic.all) ([c] :: pfss)
- (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
- mk_Trueprop_eq (fcorec_like $ c, Term.list_comb (ctr, take m cfs'))));
+ val ((coinduct_thm, coinduct_thms, strong_coinduct_thm, strong_coinduct_thms,
+ coinduct_attrs),
+ (unfold_thmss, corec_thmss, corec_like_attrs),
+ (safe_unfold_thmss, safe_corec_thmss),
+ (disc_unfold_thmss, disc_corec_thmss, disc_corec_like_attrs),
+ (disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_corec_like_iff_attrs),
+ (sel_unfold_thmss, sel_corec_thmss, sel_corec_like_attrs)) =
+ derive_coinduct_unfold_corec_thms_for_types names_lthy0 no_defs_lthy pre_bnfs fp_induct
+ fp_strong_induct dtor_ctors fp_fold_thms fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs As
+ kss mss ns cs cpss pgss crssss cgssss phss csssss chssss ctrss ctr_defss ctr_wrap_ress
+ unfolds corecs unfold_defs corec_defs lthy;
- fun build_corec_like fcorec_likes (T, U) =
- if T = U then
- id_const T
- else
- (case find_index (curry (op =) U) fpTs of
- ~1 => build_map (build_corec_like fcorec_likes) T U
- | kk => nth fcorec_likes kk);
-
- val mk_U = typ_subst (map2 pair Cs fpTs);
-
- fun intr_corec_likes fcorec_likes [] [cf] =
- let val T = fastype_of cf in
- if exists_Cs_subtype T then build_corec_like fcorec_likes (T, mk_U T) $ cf else cf
- end
- | intr_corec_likes fcorec_likes [cq] [cf, cf'] =
- mk_If cq (intr_corec_likes fcorec_likes [] [cf])
- (intr_corec_likes fcorec_likes [] [cf']);
-
- val crgsss = map2 (map2 (map2 (intr_corec_likes gunfolds))) crssss cgssss;
- val cshsss = map2 (map2 (map2 (intr_corec_likes hcorecs))) csssss chssss;
-
- val unfold_goalss =
- map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss;
- val corec_goalss =
- map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss;
-
- fun mk_map_if_distrib bnf =
- let
- val mapx = map_of_bnf bnf;
- val live = live_of_bnf bnf;
- val ((Ts, T), U) = strip_typeN (live + 1) (fastype_of mapx) |>> split_last;
- val fs = Variable.variant_frees lthy [mapx] (map (pair "f") Ts);
- val t = Term.list_comb (mapx, map (Var o apfst (rpair 0)) fs);
- in
- Drule.instantiate' (map (SOME o certifyT lthy) [U, T]) [SOME (certify lthy t)]
- @{thm if_distrib}
- end;
-
- val nested_map_if_distribs = map mk_map_if_distrib nested_bnfs;
-
- val unfold_tacss =
- map3 (map oo mk_corec_like_tac unfold_defs [] [] nesting_map_ids'' [])
- fp_fold_thms pre_map_defs ctr_defss;
- val corec_tacss =
- map3 (map oo mk_corec_like_tac corec_defs nested_map_comps'' nested_map_comp's
- (nested_map_ids'' @ nesting_map_ids'') nested_map_if_distribs)
- fp_rec_thms pre_map_defs ctr_defss;
-
- fun prove goal tac =
- Goal.prove_sorry lthy [] [] goal (tac o #context) |> Thm.close_derivation;
-
- val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
- val corec_thmss = map2 (map2 prove) corec_goalss corec_tacss;
-
- val filter_safesss =
- map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo
- curry (op ~~)) (map2 (map2 (map2 (member (op =)))) cgssss crgsss);
-
- val safe_unfold_thmss = filter_safesss unfold_thmss;
- val safe_corec_thmss = filter_safesss corec_thmss;
- in
- (unfold_thmss, corec_thmss, safe_unfold_thmss, safe_corec_thmss)
- end;
-
- val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
- let
- fun mk_goal c cps fcorec_like n k disc =
- mk_Trueprop_eq (disc $ (fcorec_like $ c),
- if n = 1 then @{const True}
- else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
-
- val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
- val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
-
- fun mk_case_split' cp =
- Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
-
- val case_splitss' = map (map mk_case_split') cpss;
-
- val unfold_tacss =
- map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' unfold_thmss disc_thmsss;
- val corec_tacss =
- map3 (map oo mk_disc_corec_like_iff_tac) case_splitss' corec_thmss disc_thmsss;
-
- fun prove goal tac =
- Goal.prove_sorry lthy [] [] goal (tac o #context)
- |> singleton (Proof_Context.export names_lthy0 no_defs_lthy)
- |> Thm.close_derivation;
-
- fun proves [_] [_] = []
- | proves goals tacs = map2 prove goals tacs;
- in
- (map2 proves unfold_goalss unfold_tacss,
- map2 proves corec_goalss corec_tacss)
- end;
-
- val is_triv_discI = is_triv_implies orf is_concl_refl;
-
- fun mk_disc_corec_like_thms corec_likes discIs =
- map (op RS) (filter_out (is_triv_discI o snd) (corec_likes ~~ discIs));
-
- val disc_unfold_thmss = map2 mk_disc_corec_like_thms unfold_thmss discIss;
- val disc_corec_thmss = map2 mk_disc_corec_like_thms corec_thmss discIss;
-
- fun mk_sel_corec_like_thm corec_like_thm sel sel_thm =
- let
- val (domT, ranT) = dest_funT (fastype_of sel);
- val arg_cong' =
- Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
- [NONE, NONE, SOME (certify lthy sel)] arg_cong
- |> Thm.varifyT_global;
- val sel_thm' = sel_thm RSN (2, trans);
- in
- corec_like_thm RS arg_cong' RS sel_thm'
- end;
-
- fun mk_sel_corec_like_thms corec_likess =
- map3 (map3 (map2 o mk_sel_corec_like_thm)) corec_likess selsss sel_thmsss |> map flat;
-
- val sel_unfold_thmss = mk_sel_corec_like_thms unfold_thmss;
- val sel_corec_thmss = mk_sel_corec_like_thms corec_thmss;
+ fun coinduct_type_attr T_name = Attrib.internal (K (Induct.coinduct_type T_name));
fun flat_corec_like_thms corec_likes disc_corec_likes sel_corec_likes =
corec_likes @ disc_corec_likes @ sel_corec_likes;
val simp_thmss =
- mk_simp_thmss wrap_ress
+ mk_simp_thmss ctr_wrap_ress
(map3 flat_corec_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss)
(map3 flat_corec_like_thms safe_unfold_thmss disc_unfold_thmss sel_unfold_thmss);
@@ -1168,37 +1262,27 @@
[(flat safe_unfold_thmss @ flat safe_corec_thmss, simp_attrs)]
|> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
- val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
- val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
- val coinduct_case_concl_attrs =
- map2 (fn casex => fn concls =>
- Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
- coinduct_cases coinduct_conclss;
- val coinduct_case_attrs =
- coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
- fun coinduct_type_attr T_name = Attrib.internal (K (Induct.coinduct_type T_name));
-
val common_notes =
(if nn > 1 then
- [(coinductN, [coinduct_thm], coinduct_case_attrs),
- (strong_coinductN, [strong_coinduct_thm], coinduct_case_attrs)]
+ [(coinductN, [coinduct_thm], coinduct_attrs),
+ (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
else
[])
|> massage_simple_notes fp_common_name;
val notes =
[(coinductN, map single coinduct_thms,
- fn T_name => coinduct_case_attrs @ [coinduct_type_attr T_name]),
- (corecN, corec_thmss, K []),
- (disc_corecN, disc_corec_thmss, K simp_attrs),
- (disc_corec_iffN, disc_corec_iff_thmss, K simp_attrs),
- (disc_unfoldN, disc_unfold_thmss, K simp_attrs),
- (disc_unfold_iffN, disc_unfold_iff_thmss, K simp_attrs),
- (sel_corecN, sel_corec_thmss, K simp_attrs),
- (sel_unfoldN, sel_unfold_thmss, K simp_attrs),
+ fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
+ (corecN, corec_thmss, K corec_like_attrs),
+ (disc_corecN, disc_corec_thmss, K disc_corec_like_attrs),
+ (disc_corec_iffN, disc_corec_iff_thmss, K disc_corec_like_iff_attrs),
+ (disc_unfoldN, disc_unfold_thmss, K disc_corec_like_attrs),
+ (disc_unfold_iffN, disc_unfold_iff_thmss, K disc_corec_like_iff_attrs),
+ (sel_corecN, sel_corec_thmss, K sel_corec_like_attrs),
+ (sel_unfoldN, sel_unfold_thmss, K sel_corec_like_attrs),
(simpsN, simp_thmss, K []),
- (strong_coinductN, map single strong_coinduct_thms, K coinduct_case_attrs),
- (unfoldN, unfold_thmss, K [])]
+ (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
+ (unfoldN, unfold_thmss, K corec_like_attrs)]
|> massage_multi_notes;
in
lthy |> Local_Theory.notes (anonymous_notes @ common_notes @ notes) |> snd
@@ -1211,8 +1295,8 @@
mss ~~ ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
raw_sel_defaultsss)
|> wrap_types_and_more
- |> (if lfp then derive_induct_fold_rec_thms_for_types
- else derive_coinduct_unfold_corec_thms_for_types);
+ |> (if lfp then derive_and_note_induct_fold_rec_thms_for_types
+ else derive_and_note_coinduct_unfold_corec_thms_for_types);
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
(if lfp then "" else "co") ^ "datatype"));