# HG changeset patch # User blanchet # Date 1367228763 -7200 # Node ID 7b75fab5ebf549663f0ee235846d7b42d10fc41a # Parent d4c1abbb4095c04fbff868597ef7c4635a234fc1 factored out derivation of coinduction, unfold, corec diff -r d4c1abbb4095 -r 7b75fab5ebf5 src/HOL/BNF/Tools/bnf_fp_def_sugar.ML --- a/src/HOL/BNF/Tools/bnf_fp_def_sugar.ML Mon Apr 29 11:04:56 2013 +0200 +++ b/src/HOL/BNF/Tools/bnf_fp_def_sugar.ML Mon Apr 29 11:46:03 2013 +0200 @@ -173,16 +173,16 @@ 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 - nn fp_b_names 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 = +fun derive_induct_fold_rec_thms_for_types nn fp_b_names 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 = let 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 nested_set_map's = maps set_map'_of_bnf nested_bnfs; val (((ps, ps'), us'), names_lthy) = lthy @@ -319,13 +319,276 @@ end; 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)); in - ((induct_thm, [induct_case_names_attr]), - (induct_thms, fn T_name => [induct_case_names_attr, induct_type_attr T_name]), + ((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 nn fp_b_names 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 = + let + 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 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 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')))); + + 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'' []) + 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; + + 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 @@ -453,10 +716,6 @@ 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; @@ -699,7 +958,7 @@ (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; @@ -775,7 +1034,7 @@ (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 = @@ -898,8 +1157,8 @@ 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; @@ -913,14 +1172,18 @@ map3 (fn (_, _, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn fold_likes => injects @ distincts @ cases @ rec_likes @ fold_likes); - fun derive_and_note_induct_fold_rec_thms_for_types (info as ((_, _, _, wrap_ress), _), lthy) = + fun derive_and_note_induct_fold_rec_thms_for_types + (info as ((_, _, _, ctr_wrap_ress), _), lthy) = let - val ((induct_thm, induct_attrs), (induct_thms, inducts_attrs), (fold_thmss, fold_attrs), + val ((induct_thm, induct_thms, induct_attrs), + (fold_thmss, fold_attrs), (rec_thmss, rec_attrs)) = derive_induct_fold_rec_thms_for_types nn fp_b_names pre_bnfs fp_induct fp_fold_thms fp_rec_thms nesting_bnfs nested_bnfs fpTs Cs ctr_Tsss mss ns gss hss info lthy; - val simp_thmss = mk_simp_thmss wrap_ress rec_thmss fold_thmss; + 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_attrs)] else []) @@ -928,7 +1191,7 @@ val notes = [(foldN, fold_thmss, K fold_attrs), - (inductN, map single induct_thms, inducts_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; @@ -936,251 +1199,28 @@ lthy |> Local_Theory.notes (common_notes @ notes) |> snd end; - fun derive_and_note_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 + (info as ((_, _, _, ctr_wrap_ress), _), 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_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 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 nn fp_b_names + 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 info + 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 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'' []) - 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); @@ -1188,37 +1228,27 @@ [(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