author  blanchet 
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permissions  rwrr 
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(* Title: HOL/Codatatype/Tools/bnf_fp_sugar.ML 
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Author: Jasmin Blanchette, TU Muenchen 

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Copyright 2012 

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Sugar for constructing LFPs and GFPs. 

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*) 

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signature BNF_FP_SUGAR = 

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sig 

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val datatyp: bool > 
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(mixfix list > (string * sort) list option > binding list > typ list * typ list list > 
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BNF_Def.BNF list > local_theory > 
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(term list * term list * term list * term list * thm * thm list * thm list * thm list * 
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thm list * thm list) * local_theory) > 

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bool * ((((typ * sort) list * binding) * mixfix) * ((((binding * binding) * 
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(binding * typ) list) * (binding * term) list) * mixfix) list) list > 
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local_theory > local_theory 

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val parse_datatype_cmd: bool > 
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(mixfix list > (string * sort) list option > binding list > typ list * typ list list > 
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BNF_Def.BNF list > local_theory > 
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(term list * term list * term list * term list * thm * thm list * thm list * thm list * 
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thm list * thm list) * local_theory) > 

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(local_theory > local_theory) parser 
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end; 
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structure BNF_FP_Sugar : BNF_FP_SUGAR = 

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struct 

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49119  29 
open BNF_Util 
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open BNF_Wrap 

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open BNF_Def 
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open BNF_FP_Util 
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open BNF_FP_Sugar_Tactics 
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val simp_attrs = @{attributes [simp]}; 
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49266  37 
fun split_list11 xs = 
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(map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs, 

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map #9 xs, map #10 xs, map #11 xs); 

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fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' >> cons T 
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 strip_map_type T = ([], T); 

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49342  44 
fun resort_tfree S (TFree (s, _)) = TFree (s, S); 
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fun typ_subst inst (T as Type (s, Ts)) = 
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(case AList.lookup (op =) inst T of 
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NONE => Type (s, map (typ_subst inst) Ts) 
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 SOME T' => T') 
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 typ_subst inst T = the_default T (AList.lookup (op =) inst T); 
49205  51 

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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs)); 
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49234  54 
fun mk_id T = Const (@{const_name id}, T > T); 
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49200  56 
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs)); 
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fun mk_uncurried_fun f xs = mk_tupled_fun (HOLogic.mk_tuple xs) f xs; 

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fun mk_uncurried2_fun f xss = 
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mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss); 
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49233  61 
fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v)); 
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fun tack z_name (c, v) f = 

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let val z = Free (z_name, mk_sumT (fastype_of v, fastype_of c)) in 
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Term.lambda z (mk_sum_case (Term.lambda v v, Term.lambda c (f $ c)) $ z) 
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end; 
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fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; 
49119  69 

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fun merge_type_arg T T' = if T = T' then T else cannot_merge_types (); 
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fun merge_type_args (As, As') = 
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if length As = length As' then map2 merge_type_arg As As' else cannot_merge_types (); 
49119  74 

49121  75 
fun type_args_constrained_of (((cAs, _), _), _) = cAs; 
49336  76 
fun type_binding_of (((_, b), _), _) = b; 
49181  77 
fun mixfix_of ((_, mx), _) = mx; 
49121  78 
fun ctr_specs_of (_, ctr_specs) = ctr_specs; 
49119  79 

49286  80 
fun disc_of ((((disc, _), _), _), _) = disc; 
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fun ctr_of ((((_, ctr), _), _), _) = ctr; 

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fun args_of (((_, args), _), _) = args; 

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fun defaults_of ((_, ds), _) = ds; 

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fun ctr_mixfix_of (_, mx) = mx; 
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fun define_datatype prepare_constraint prepare_typ prepare_term lfp construct (no_dests, specs) 
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no_defs_lthy0 = 
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let 
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(* TODO: sanity checks on arguments *) 
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val _ = if not lfp andalso no_dests then error "Cannot define destructorless codatatypes" 
49278  92 
else (); 
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val N = length specs; 
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val fp_bs = map type_binding_of specs; 
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val fp_common_name = mk_common_name fp_bs; 
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fun prepare_type_arg (ty, c) = 
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let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in 
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TFree (s, prepare_constraint no_defs_lthy0 c) 
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end; 
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val Ass0 = map (map prepare_type_arg o type_args_constrained_of) specs; 
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val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0; 
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val unsorted_As = Library.foldr1 merge_type_args unsorted_Ass0; 
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val (((Bs, Cs), vs'), no_defs_lthy) = 
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no_defs_lthy0 
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> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As 
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> mk_TFrees N 
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>> mk_TFrees N 
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>> Variable.variant_fixes (map Binding.name_of fp_bs); 
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(* TODO: cleaner handling of fake contexts, without "background_theory" *) 
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(*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a 
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locale and shadows an existing global type*) 
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val fake_thy = 
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Theory.copy #> fold (fn spec => perhaps (try (Sign.add_type no_defs_lthy 
49336  119 
(type_binding_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs; 
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val fake_lthy = Proof_Context.background_theory fake_thy no_defs_lthy; 
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fun mk_fake_T b = 
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Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), 
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unsorted_As); 
49121  125 

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val fake_Ts = map mk_fake_T fp_bs; 
49121  127 

49181  128 
val mixfixes = map mixfix_of specs; 
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val _ = (case duplicates Binding.eq_name fp_bs of [] => () 
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 b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); 
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49121  133 
val ctr_specss = map ctr_specs_of specs; 
49119  134 

49336  135 
val disc_bindingss = map (map disc_of) ctr_specss; 
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val ctr_bindingss = 

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map2 (fn fp_b => map (Binding.qualify false (Binding.name_of fp_b) o ctr_of)) 
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fp_bs ctr_specss; 
49121  139 
val ctr_argsss = map (map args_of) ctr_specss; 
49181  140 
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; 
49119  141 

49336  142 
val sel_bindingsss = map (map (map fst)) ctr_argsss; 
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val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; 
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val raw_sel_defaultsss = map (map defaults_of) ctr_specss; 
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val (As :: _) :: fake_ctr_Tsss = 
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burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0); 
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val _ = (case duplicates (op =) unsorted_As of [] => () 
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 A :: _ => error ("Duplicate type parameter " ^ 
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quote (Syntax.string_of_typ no_defs_lthy A))); 
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val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; 
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val _ = (case subtract (op =) (map dest_TFree As) rhs_As' of 
49165  155 
[] => () 
49342  156 
 A' :: _ => error ("Extra type variable on righthand side: " ^ 
49204  157 
quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); 
49165  158 

49204  159 
fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) = 
49146  160 
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ 
161 
quote (Syntax.string_of_typ fake_lthy T))) 

49204  162 
 eq_fpT _ _ = false; 
49146  163 

49204  164 
fun freeze_fp (T as Type (s, Us)) = 
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(case find_index (eq_fpT T) fake_Ts of ~1 => Type (s, map freeze_fp Us)  j => nth Bs j) 
49204  166 
 freeze_fp T = T; 
49121  167 

49297  168 
val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss; 
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val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs; 

49119  170 

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val fp_eqs = 
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map dest_TFree Bs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctr_sum_prod_TsBs; 
49121  173 

49337  174 
val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, fp_induct, unf_flds, fld_unfs, fld_injects, 
49207  175 
fp_iter_thms, fp_rec_thms), lthy)) = 
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fp_bnf construct fp_bs mixfixes (map dest_TFree unsorted_As) fp_eqs no_defs_lthy0; 
49121  177 

49363  178 
fun add_nesty_bnf_names Us = 
49226  179 
let 
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fun add (Type (s, Ts)) ss = 

181 
let val (needs, ss') = fold_map add Ts ss in 

182 
if exists I needs then (true, insert (op =) s ss') else (false, ss') 

183 
end 

49363  184 
 add T ss = (member (op =) Us T, ss); 
49226  185 
in snd oo add end; 
186 

49363  187 
fun nesty_bnfs Us = 
188 
map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssBs []); 

189 

190 
val nesting_bnfs = nesty_bnfs As; 

191 
val nested_bnfs = nesty_bnfs Bs; 

49226  192 

49167  193 
val timer = time (Timer.startRealTimer ()); 
194 

49176  195 
fun mk_unf_or_fld get_T Ts t = 
196 
let val Type (_, Ts0) = get_T (fastype_of t) in 

49124  197 
Term.subst_atomic_types (Ts0 ~~ Ts) t 
49121  198 
end; 
49119  199 

49126  200 
val mk_unf = mk_unf_or_fld domain_type; 
201 
val mk_fld = mk_unf_or_fld range_type; 

49121  202 

49203  203 
val unfs = map (mk_unf As) unfs0; 
204 
val flds = map (mk_fld As) flds0; 

49124  205 

49201  206 
val fpTs = map (domain_type o fastype_of) unfs; 
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val exists_fp_subtype = exists_subtype (member (op =) fpTs); 
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val vs = map2 (curry Free) vs' fpTs; 
49204  211 

49297  212 
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs; 
49203  213 
val ns = map length ctr_Tsss; 
49212  214 
val kss = map (fn n => 1 upto n) ns; 
49203  215 
val mss = map (map length) ctr_Tsss; 
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val Css = map2 replicate ns Cs; 

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fun mk_iter_like Ts Us t = 
49121  219 
let 
49336  220 
val (bindings, body) = strip_type (fastype_of t); 
221 
val (f_Us, prebody) = split_last bindings; 

49210  222 
val Type (_, Ts0) = if lfp then prebody else body; 
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val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us); 

49176  224 
in 
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Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
49176  226 
end; 
227 

49210  228 
val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0; 
229 
val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0; 

230 

49212  231 
val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1))); 
232 
val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1))); 

49204  233 

49256  234 
val ((iter_only as (gss, _, _), rec_only as (hss, _, _)), 
49276  235 
(zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) = 
49208  236 
if lfp then 
237 
let 

238 
val y_Tsss = 

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239 
map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type) 
49212  240 
ns mss fp_iter_fun_Ts; 
49208  241 
val g_Tss = map2 (map2 (curry (op >))) y_Tsss Css; 
242 

243 
val ((gss, ysss), _) = 

244 
lthy 

245 
> mk_Freess "f" g_Tss 

246 
>> mk_Freesss "x" y_Tsss; 

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247 
val yssss = map (map (map single)) ysss; 
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248 

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249 
fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) = 
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250 
if member (op =) Cs U then Us else [T] 
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251 
 dest_rec_prodT T = [T]; 
49204  252 

49208  253 
val z_Tssss = 
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254 
map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o 
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255 
dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts; 
49208  256 
val h_Tss = map2 (map2 (fold_rev (curry (op >)))) z_Tssss Css; 
49204  257 

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258 
val hss = map2 (map2 retype_free) h_Tss gss; 
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259 
val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss; 
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260 
val (zssss_tl, _) = 
49208  261 
lthy 
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262 
> mk_Freessss "y" (map (map (map tl)) z_Tssss); 
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263 
val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl; 
49210  264 
in 
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265 
(((gss, g_Tss, yssss), (hss, h_Tss, zssss)), 
49276  266 
([], [], [], (([], []), ([], [])), (([], []), ([], [])))) 
49210  267 
end 
49208  268 
else 
49210  269 
let 
49221
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270 
(*avoid "'a itself" arguments in coiterators and corecursors*) 
6d8d5fe9f3a2
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271 
val mss' = map (fn [0] => [1]  ms => ms) mss; 
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272 

49275  273 
val p_Tss = map2 (fn n => replicate (Int.max (0, n  1)) o mk_predT) ns Cs; 
274 

49276  275 
fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss); 
49211  276 

49276  277 
fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss 
278 
 zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) = 

279 
p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss; 

49274
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280 

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281 
fun mk_types maybe_dest_sumT fun_Ts = 
49212  282 
let 
283 
val f_sum_prod_Ts = map range_type fun_Ts; 

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284 
val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts; 
49275  285 
val f_Tssss = 
286 
map3 (fn C => map2 (map (map (curry (op >) C) o maybe_dest_sumT) oo dest_tupleT)) 

287 
Cs mss' f_prod_Tss; 

288 
val q_Tssss = 

289 
map (map (map (fn [_] => []  [_, C] => [mk_predT (domain_type C)]))) f_Tssss; 

49276  290 
val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss; 
49275  291 
in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end; 
49176  292 

49275  293 
val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts; 
49211  294 

49275  295 
val ((((Free (z, _), cs), pss), gssss), _) = 
49210  296 
lthy 
49233  297 
> yield_singleton (mk_Frees "z") dummyT 
298 
>> mk_Frees "a" Cs 

49211  299 
>> mk_Freess "p" p_Tss 
49275  300 
>> mk_Freessss "g" g_Tssss; 
301 
val rssss = map (map (map (fn [] => []))) r_Tssss; 

49274
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302 

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303 
fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) = 
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304 
if member (op =) Cs U then Us else [T] 
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305 
 dest_corec_sumT T = [T]; 
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306 

49275  307 
val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts; 
49210  308 

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309 
val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss; 
49275  310 
val ((sssss, hssss_tl), _) = 
311 
lthy 

312 
> mk_Freessss "q" s_Tssss 

313 
>> mk_Freessss "h" (map (map (map tl)) h_Tssss); 

314 
val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl; 

49211  315 

49212  316 
val cpss = map2 (fn c => map (fn p => p $ c)) cs pss; 
317 

49276  318 
fun mk_preds_getters_join [] [cf] = cf 
319 
 mk_preds_getters_join [cq] [cf, cf'] = 

320 
mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf'); 

321 

49275  322 
fun mk_terms qssss fssss = 
49212  323 
let 
49276  324 
val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss; 
49275  325 
val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss; 
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326 
val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss; 
49276  327 
val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss; 
328 
in (pfss, cqfsss) end; 

49210  329 
in 
49212  330 
((([], [], []), ([], [], [])), 
49275  331 
([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)), 
332 
(mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss)))) 

49210  333 
end; 
334 

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changeset

335 
fun define_ctrs_case_for_type (((((((((((((((((((fp_b, fpT), C), v), fld), unf), fp_iter), 
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changeset

336 
fp_rec), fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_bindings), ctr_mixfixes), 
cc1d39529dd1
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diff
changeset

337 
ctr_Tss), disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy = 
49176  338 
let 
49201  339 
val unfT = domain_type (fastype_of fld); 
49210  340 
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
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341 
val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts; 
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342 
val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  343 

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changeset

344 
val (((u, fs), xss), _) = 
49204  345 
no_defs_lthy 
49201  346 
> yield_singleton (mk_Frees "u") unfT 
49176  347 
>> mk_Frees "f" case_Ts 
49124  348 
>> mk_Freess "x" ctr_Tss; 
49121  349 

49129  350 
val ctr_rhss = 
49256  351 
map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $ 
352 
mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss; 

49121  353 

49336  354 
val case_binding = Binding.suffix_name ("_" ^ caseN) fp_b; 
49129  355 

49134
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356 
val case_rhs = 
49255
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357 
fold_rev Term.lambda (fs @ [v]) 
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358 
(mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v)); 
49129  359 

49201  360 
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy 
49169  361 
> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => 
49302
f5bd87aac224
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blanchet
parents:
49300
diff
changeset

362 
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 
49336  363 
(case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) 
49121  364 
> `Local_Theory.restore; 
365 

366 
val phi = Proof_Context.export_morphism lthy lthy'; 

367 

368 
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; 

49130
3c26e17b2849
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49129
diff
changeset

369 
val case_def = Morphism.thm phi raw_case_def; 
3c26e17b2849
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parents:
49129
diff
changeset

370 

49203  371 
val ctrs0 = map (Morphism.term phi) raw_ctrs; 
372 
val casex0 = Morphism.term phi raw_case; 

373 

374 
val ctrs = map (mk_ctr As) ctrs0; 

49121  375 

49135  376 
fun exhaust_tac {context = ctxt, ...} = 
49123
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49121
diff
changeset

377 
let 
49135  378 
val fld_iff_unf_thm = 
379 
let 

380 
val goal = 

381 
fold_rev Logic.all [u, v] 

382 
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u))); 

383 
in 

384 
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => 

49201  385 
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT]) 
49176  386 
(certify lthy fld) (certify lthy unf) fld_unf unf_fld) 
49135  387 
> Thm.close_derivation 
388 
> Morphism.thm phi 

389 
end; 

390 

391 
val sumEN_thm' = 

392 
Local_Defs.unfold lthy @{thms all_unit_eq} 

49255
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changeset

393 
(Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) [] 
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49254
diff
changeset

394 
(mk_sumEN_balanced n)) 
49135  395 
> Morphism.thm phi; 
49123
263b0e330d8b
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blanchet
parents:
49121
diff
changeset

396 
in 
49161
a8e74375d971
fixed (n + 1)st bug in "mk_exhaust_tac"  arose with uncurried constructors
blanchet
parents:
49157
diff
changeset

397 
mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm' 
49123
263b0e330d8b
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49121
diff
changeset

398 
end; 
49121  399 

49126  400 
val inject_tacss = 
49205  401 
map2 (fn 0 => K []  _ => fn ctr_def => [fn {context = ctxt, ...} => 
402 
mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs; 

49126  403 

49127  404 
val half_distinct_tacss = 
405 
map (map (fn (def, def') => fn {context = ctxt, ...} => 

406 
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs); 

407 

49130
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset

408 
val case_tacs = 
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset

409 
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => 
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset

410 
mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs; 
49121  411 

412 
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; 

49134
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changeset

413 

49287
ebe2a5cec4bf
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blanchet
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49286
diff
changeset

414 
fun define_iter_rec ((selss0, discIs, sel_thmss), no_defs_lthy) = 
49134
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49130
diff
changeset

415 
let 
49208  416 
val fpT_to_C = fpT > C; 
49199  417 

49215  418 
fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) = 
419 
let 

420 
val res_T = fold_rev (curry (op >)) f_Tss fpT_to_C; 

49336  421 
val binding = Binding.suffix_name ("_" ^ suf) fp_b; 
49215  422 
val spec = 
49336  423 
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)), 
49215  424 
Term.list_comb (fp_iter_like, 
49255
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changeset

425 
map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss)); 
49336  426 
in (binding, spec) end; 
49199  427 

49300  428 
val iter_like_infos = 
49215  429 
[(iterN, fp_iter, iter_only), 
430 
(recN, fp_rec, rec_only)]; 

431 

49336  432 
val (bindings, specs) = map generate_iter_like iter_like_infos > split_list; 
49215  433 

434 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49201  435 
> apfst split_list o fold_map2 (fn b => fn spec => 
49199  436 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 
49336  437 
#>> apsnd snd) bindings specs 
49199  438 
> `Local_Theory.restore; 
49201  439 

440 
val phi = Proof_Context.export_morphism lthy lthy'; 

441 

49215  442 
val [iter_def, rec_def] = map (Morphism.thm phi) defs; 
49201  443 

49215  444 
val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts; 
49134
846264f80f16
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parents:
49130
diff
changeset

445 
in 
49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

446 
((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def), 
49266  447 
lthy) 
49134
846264f80f16
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parents:
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diff
changeset

448 
end; 
846264f80f16
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parents:
49130
diff
changeset

449 

49287
ebe2a5cec4bf
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blanchet
parents:
49286
diff
changeset

450 
fun define_coiter_corec ((selss0, discIs, sel_thmss), no_defs_lthy) = 
49210  451 
let 
452 
val B_to_fpT = C > fpT; 

49211  453 

49276  454 
fun mk_preds_getterss_join c n cps sum_prod_T cqfss = 
455 
Term.lambda c (mk_IfN sum_prod_T cps 

456 
(map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n))); 

49275  457 

49276  458 
fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts, 
49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
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parents:
49273
diff
changeset

459 
pf_Tss))) = 
49211  460 
let 
461 
val res_T = fold_rev (curry (op >)) pf_Tss B_to_fpT; 

49336  462 
val binding = Binding.suffix_name ("_" ^ suf) fp_b; 
49211  463 
val spec = 
49336  464 
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)), 
49211  465 
Term.list_comb (fp_iter_like, 
49276  466 
map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss)); 
49336  467 
in (binding, spec) end; 
49210  468 

49300  469 
val coiter_like_infos = 
49215  470 
[(coiterN, fp_iter, coiter_only), 
471 
(corecN, fp_rec, corec_only)]; 

49212  472 

49336  473 
val (bindings, specs) = map generate_coiter_like coiter_like_infos > split_list; 
49211  474 

475 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49210  476 
> apfst split_list o fold_map2 (fn b => fn spec => 
477 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 

49336  478 
#>> apsnd snd) bindings specs 
49210  479 
> `Local_Theory.restore; 
480 

481 
val phi = Proof_Context.export_morphism lthy lthy'; 

482 

49211  483 
val [coiter_def, corec_def] = map (Morphism.thm phi) defs; 
49210  484 

49211  485 
val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts; 
49210  486 
in 
49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

487 
((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def, 
49266  488 
corec_def), lthy) 
49210  489 
end; 
49286  490 

49287
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

491 
fun wrap lthy = 
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

492 
let val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss in 
49336  493 
wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_bindings, (sel_bindingss, 
49287
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

494 
sel_defaultss))) lthy 
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

495 
end; 
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

496 

ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

497 
val define_iter_likes = if lfp then define_iter_rec else define_coiter_corec; 
49119  498 
in 
49287
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

499 
((wrap, define_iter_likes), lthy') 
49119  500 
end; 
49167  501 

49226  502 
val pre_map_defs = map map_def_of_bnf pre_bnfs; 
49342  503 
val pre_set_defss = map set_defs_of_bnf pre_bnfs; 
49363  504 
val nesting_map_ids = map map_id_of_bnf nesting_bnfs; 
49226  505 

49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

506 
fun mk_map Ts Us t = 
49217  507 
let val (Type (_, Ts0), Type (_, Us0)) = strip_map_type (fastype_of t) >> List.last in 
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

508 
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

509 
end; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

510 

49234  511 
fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) = 
512 
let 

49236  513 
val map0 = map_of_bnf (the (bnf_of lthy s)); 
49234  514 
val mapx = mk_map Ts Us map0; 
515 
val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx))))); 

516 
val args = map build_arg TUs; 

517 
in Term.list_comb (mapx, args) end; 

518 

49337  519 
fun derive_induct_iter_rec_thms_for_types ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, 
520 
iter_defs, rec_defs), lthy) = 

49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

521 
let 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

522 
fun mk_sets_nested bnf = 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

523 
let 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

524 
val Type (T_name, Us) = T_of_bnf bnf; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
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parents:
49361
diff
changeset

525 
val lives = lives_of_bnf bnf; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

526 
val sets = sets_of_bnf bnf; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

527 
fun mk_set U = 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

528 
(case find_index (curry (op =) U) lives of 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

529 
~1 => Term.dummy 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

530 
 i => nth sets i); 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

531 
in 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

532 
(T_name, map mk_set Us) 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

533 
end; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

534 

1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

535 
val setss_nested = map mk_sets_nested nested_bnfs; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

536 

49337  537 
val (induct_thms, induct_thm) = 
538 
let 

49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

539 
val ((phis, phis'), names_lthy) = 
49361
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

540 
lthy 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

541 
> mk_Frees' "P" (map mk_predT fpTs); 
49342  542 

49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

543 
fun mk_set Ts t = 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

544 
let val Type (_, Ts0) = domain_type (fastype_of t) in 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

545 
Term.subst_atomic_types (Ts0 ~~ Ts) t 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

546 
end; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

547 

1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

548 
fun mk_prem_prems names_lthy (x as Free (s, T as Type (T_name, Ts0))) = 
49361
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

549 
(case find_index (curry (op =) T) fpTs of 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

550 
~1 => 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

551 
(case AList.lookup (op =) setss_nested T_name of 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

552 
NONE => [] 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

553 
 SOME raw_sets0 => 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

554 
let 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

555 
val (Ts, raw_sets) = 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

556 
split_list (filter (exists_fp_subtype o fst) (Ts0 ~~ raw_sets0)); 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

557 
val sets = map (mk_set Ts0) raw_sets; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

558 
val (ys, names_lthy') = names_lthy > mk_Frees s Ts; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

559 
val heads = 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

560 
map2 (fn y => fn set => HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x))) 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

561 
ys sets; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

562 
val bodies = flat (map (mk_prem_prems names_lthy') ys); 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

563 
in 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

564 
map2 (curry Logic.mk_implies) heads bodies 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

565 
end) 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

566 
 i => [HOLogic.mk_Trueprop (nth phis i $ x)]) 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

567 
 mk_prem_prems _ _ = []; 
49342  568 

49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

569 
fun close_prem_prem (Free x') t = 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

570 
fold_rev Logic.all (map Free (drop (N + 1) (rev (Term.add_frees t (x' :: phis'))))) t; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

571 

1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

572 
fun mk_prem phi ctr ctr_Ts = 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

573 
let 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

574 
val (xs, names_lthy') = names_lthy > mk_Frees "x" ctr_Ts; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

575 
val prem_prems = 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

576 
maps (fn x => map (close_prem_prem x) (mk_prem_prems names_lthy' x)) xs; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

577 
in 
49361
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

578 
fold_rev Logic.all xs 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

579 
(Logic.list_implies (prem_prems, 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

580 
HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs)))) 
49361
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

581 
end; 
49342  582 

49361
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

583 
val goal = 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

584 
fold_rev (fold_rev Logic.all) [phis, vs] 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

585 
(Library.foldr Logic.list_implies (map3 (map2 o mk_prem) phis ctrss ctr_Tsss, 
49361
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

586 
HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

587 
(map2 (curry (op $)) phis vs)))); 
49342  588 

589 
val induct_thm = 

49361
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

590 
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

591 
mk_induct_tac ctxt); 
49337  592 
in 
593 
`(conj_dests N) induct_thm 

594 
end; 

49201  595 

49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

596 
val (iter_thmss, rec_thmss) = 
49207  597 
let 
49337  598 
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; 
599 
val giters = map (lists_bmoc gss) iters; 

600 
val hrecs = map (lists_bmoc hss) recs; 

601 

49212  602 
fun mk_goal_iter_like fss fiter_like xctr f xs fxs = 
49207  603 
fold_rev (fold_rev Logic.all) (xs :: fss) 
49212  604 
(mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs))); 
49204  605 

49234  606 
fun build_call fiter_likes maybe_tick (T, U) = 
607 
if T = U then 

608 
mk_id T 

609 
else 

610 
(case find_index (curry (op =) T) fpTs of 

611 
~1 => build_map (build_call fiter_likes maybe_tick) T U 

612 
 j => maybe_tick (nth vs j) (nth fiter_likes j)); 

49233  613 

49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

614 
fun mk_U maybe_mk_prodT = 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

615 
typ_subst (map2 (fn fpT => fn C => (fpT, maybe_mk_prodT fpT C)) fpTs Cs); 
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

616 

49342  617 
fun intr_calls fiter_likes maybe_cons maybe_tick maybe_mk_prodT (x as Free (_, T)) = 
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

618 
if member (op =) fpTs T then 
49233  619 
maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x] 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

620 
else if exists_fp_subtype T then 
49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

621 
[build_call fiter_likes maybe_tick (T, mk_U maybe_mk_prodT T) $ x] 
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

622 
else 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

623 
[x]; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

624 

49342  625 
val gxsss = map (map (maps (intr_calls giters (K I) (K I) (K I)))) xsss; 
626 
val hxsss = map (map (maps (intr_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss; 

49204  627 

49212  628 
val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss; 
629 
val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss; 

49204  630 

49203  631 
val iter_tacss = 
49363  632 
map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids iter_defs) fp_iter_thms 
633 
ctr_defss; 

49203  634 
val rec_tacss = 
49363  635 
map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids rec_defs) fp_rec_thms 
636 
ctr_defss; 

49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

637 
in 
49276  638 
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 
49205  639 
goal_iterss iter_tacss, 
49276  640 
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 
49205  641 
goal_recss rec_tacss) 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

642 
end; 
49201  643 

49337  644 
val common_notes = 
49342  645 
(if N > 1 then [(inductN, [induct_thm], [])] (* FIXME: attribs *) else []) 
49337  646 
> map (fn (thmN, thms, attrs) => 
647 
((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])])); 

648 

49226  649 
val notes = 
49342  650 
[(inductN, map single induct_thms, []), (* FIXME: attribs *) 
651 
(itersN, iter_thmss, simp_attrs), 

49300  652 
(recsN, rec_thmss, Code.add_default_eqn_attrib :: simp_attrs)] 
653 
> maps (fn (thmN, thmss, attrs) => 

49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

654 
map2 (fn b => fn thms => 
49300  655 
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs), 
49302
f5bd87aac224
added optional qualifiers for constructors and destructors, similarly to the old package
blanchet
parents:
49300
diff
changeset

656 
[(thms, [])])) fp_bs thmss); 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

657 
in 
49337  658 
lthy > Local_Theory.notes (common_notes @ notes) > snd 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

659 
end; 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

660 

49337  661 
fun derive_coinduct_coiter_corec_thms_for_types ((ctrss, selsss, coiters, corecs, vs, _, 
662 
ctr_defss, discIss, sel_thmsss, coiter_defs, corec_defs), lthy) = 

49212  663 
let 
49337  664 
val (coinduct_thms, coinduct_thm) = 
665 
let 

666 
val coinduct_thm = fp_induct; 

667 
in 

668 
`(conj_dests N) coinduct_thm 

669 
end; 

49212  670 

671 
val (coiter_thmss, corec_thmss) = 

672 
let 

49337  673 
val z = the_single zs; 
674 
val gcoiters = map (lists_bmoc pgss) coiters; 

675 
val hcorecs = map (lists_bmoc phss) corecs; 

676 

49232
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

677 
fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not); 
49212  678 

49276  679 
fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' = 
49212  680 
fold_rev (fold_rev Logic.all) ([c] :: pfss) 
49232
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

681 
(Logic.list_implies (seq_conds mk_goal_cond n k cps, 
49276  682 
mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs')))); 
49212  683 

49234  684 
fun build_call fiter_likes maybe_tack (T, U) = 
685 
if T = U then 

686 
mk_id T 

687 
else 

688 
(case find_index (curry (op =) U) fpTs of 

689 
~1 => build_map (build_call fiter_likes maybe_tack) T U 

690 
 j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j)); 

49233  691 

49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

692 
fun mk_U maybe_mk_sumT = 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

693 
typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs); 
49212  694 

49342  695 
fun intr_calls fiter_likes maybe_mk_sumT maybe_tack cqf = 
49276  696 
let val T = fastype_of cqf in 
697 
if exists_subtype (member (op =) Cs) T then 

698 
build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf 

699 
else 

700 
cqf 

701 
end; 

49232
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

702 

49342  703 
val crgsss' = map (map (map (intr_calls gcoiters (K I) (K I)))) crgsss; 
704 
val cshsss' = map (map (map (intr_calls hcorecs (curry mk_sumT) (tack z)))) cshsss; 

49212  705 

706 
val goal_coiterss = 

49276  707 
map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss'; 
49233  708 
val goal_corecss = 
49276  709 
map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss'; 
49213  710 

711 
val coiter_tacss = 

49363  712 
map3 (map oo mk_coiter_like_tac coiter_defs nesting_map_ids) fp_iter_thms pre_map_defs 
49226  713 
ctr_defss; 
49233  714 
val corec_tacss = 
49363  715 
map3 (map oo mk_coiter_like_tac corec_defs nesting_map_ids) fp_rec_thms pre_map_defs 
49233  716 
ctr_defss; 
49212  717 
in 
49276  718 
(map2 (map2 (fn goal => fn tac => 
719 
Skip_Proof.prove lthy [] [] goal (tac o #context) > Thm.close_derivation)) 

49213  720 
goal_coiterss coiter_tacss, 
49276  721 
map2 (map2 (fn goal => fn tac => 
722 
Skip_Proof.prove lthy [] [] goal (tac o #context) 

723 
> Local_Defs.unfold lthy @{thms sum_case_if} > Thm.close_derivation)) 

49233  724 
goal_corecss corec_tacss) 
49212  725 
end; 
726 

49266  727 
fun mk_disc_coiter_like_thms [_] = K [] 
728 
 mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms; 

729 

730 
val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss; 

731 
val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss; 

732 

49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

733 
fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm = 
49266  734 
let 
49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

735 
val (domT, ranT) = dest_funT (fastype_of sel0); 
49266  736 
val arg_cong' = 
737 
Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT]) 

49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

738 
[NONE, NONE, SOME (certify lthy sel0)] arg_cong 
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

739 
> Thm.varifyT_global; 
49266  740 
val sel_thm' = sel_thm RSN (2, trans); 
741 
in 

49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

742 
coiter_like_thm RS arg_cong' RS sel_thm' 
49266  743 
end; 
744 

745 
val sel_coiter_thmsss = 

746 
map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss; 

747 
val sel_corec_thmsss = 

49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

748 
map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss; 
49266  749 

49342  750 
val common_notes = 
751 
(if N > 1 then [(coinductN, [coinduct_thm], [])] (* FIXME: attribs *) else []) 

752 
> map (fn (thmN, thms, attrs) => 

753 
((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])])); 

754 

49212  755 
val notes = 
49342  756 
[(coinductN, map single coinduct_thms, []), (* FIXME: attribs *) 
757 
(coitersN, coiter_thmss, []), 

49300  758 
(disc_coitersN, disc_coiter_thmss, []), 
759 
(sel_coitersN, map flat sel_coiter_thmsss, []), 

760 
(corecsN, corec_thmss, []), 

761 
(disc_corecsN, disc_corec_thmss, []), 

762 
(sel_corecsN, map flat sel_corec_thmsss, [])] 

763 
> maps (fn (thmN, thmss, attrs) => 

49266  764 
map_filter (fn (_, []) => NONE  (b, thms) => 
49300  765 
SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs), 
49302
f5bd87aac224
added optional qualifiers for constructors and destructors, similarly to the old package
blanchet
parents:
49300
diff
changeset

766 
[(thms, [])])) (fp_bs ~~ thmss)); 
49212  767 
in 
49361
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

768 
lthy > Local_Theory.notes (common_notes @ notes) > snd 
49212  769 
end; 
770 

49287
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

771 
fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) = 
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

772 
fold_map2 (curry (op o)) define_iter_likess wraps lthy >> split_list11 
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

773 

49204  774 
val lthy' = lthy 
49361
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

775 
> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ vs ~~ flds ~~ unfs ~~ 
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

776 
fp_iters ~~ fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ 
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

777 
ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ 
cc1d39529dd1
derive induction via backward proof, to ensure that the premises are in the right order for constructors like "X x y x" where x and y are mutually recursive
blanchet
parents:
49342
diff
changeset

778 
raw_sel_defaultsss) 
49287
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

779 
>> split_list > wrap_types_and_define_iter_likes 
49337  780 
> (if lfp then derive_induct_iter_rec_thms_for_types 
781 
else derive_coinduct_coiter_corec_thms_for_types); 

49167  782 

783 
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ 

49208  784 
(if lfp then "" else "co") ^ "datatype")); 
49112  785 
in 
49308
6190b701e4f4
reorganized dependencies so that the sugar does not depend on GFP  this will be essential for bootstrapping
blanchet
parents:
49302
diff
changeset

786 
timer; lthy' 
49112  787 
end; 
788 

49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

789 
val datatyp = define_datatype (K I) (K I) (K I); 
49297  790 

49298
36e551d3af3b
support for sort constraints in new (co)data commands
blanchet
parents:
49297
diff
changeset

791 
val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term; 
49119  792 

49329
82452dc63ed5
desambiguate grammar (e.g. for Nil's mixfix ("[]"))
blanchet
parents:
49311
diff
changeset

793 
val parse_binding_colon = Parse.binding  @{keyword ":"}; 
49336  794 
val parse_opt_binding_colon = Scan.optional parse_binding_colon no_binding; 
49119  795 

49112  796 
val parse_ctr_arg = 
49329
82452dc63ed5
desambiguate grammar (e.g. for Nil's mixfix ("[]"))
blanchet
parents:
49311
diff
changeset

797 
@{keyword "("}  parse_binding_colon  Parse.typ  @{keyword ")"}  
49336  798 
(Parse.typ >> pair no_binding); 
49112  799 

49286  800 
val parse_defaults = 
801 
@{keyword "("}  @{keyword "defaults"}  Scan.repeat parse_bound_term  @{keyword ")"}; 

802 

49112  803 
val parse_single_spec = 
804 
Parse.type_args_constrained  Parse.binding  Parse.opt_mixfix  

49119  805 
(@{keyword "="}  Parse.enum1 "" (parse_opt_binding_colon  Parse.binding  
49286  806 
Scan.repeat parse_ctr_arg  Scan.optional parse_defaults []  Parse.opt_mixfix)); 
49112  807 

49278  808 
val parse_datatype = parse_wrap_options  Parse.and_list1 parse_single_spec; 
809 

49308
6190b701e4f4
reorganized dependencies so that the sugar does not depend on GFP  this will be essential for bootstrapping
blanchet
parents:
49302
diff
changeset

810 
fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct; 
49112  811 

812 
end; 