author  blanchet 
Fri, 21 Sep 2012 15:53:29 +0200  
changeset 49501  acc9635a644a 
parent 49498  acc583e14167 
child 49502  92a7c1842c78 
permissions  rwrr 
49112  1 
(* 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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49389  5 
Sugared datatype and codatatype constructions. 
49112  6 
*) 
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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; 
25 

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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 
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open BNF_FP_Sugar_Tactics 
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49300  35 
val simp_attrs = @{attributes [simp]}; 
36 

49438  37 
fun split_list8 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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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); 
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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs)); 
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49200  50 
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 = 
49200  53 
mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss); 
54 

49498  55 
fun tick u f = Term.lambda u (HOLogic.mk_prod (u, f $ u)); 
49233  56 

49498  57 
fun tack z_name (c, u) f = 
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let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in 

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Term.lambda z (mk_sum_case (Term.lambda u u, Term.lambda c (f $ c)) $ z) 

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end; 
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49124  62 
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; 
49119  63 

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fun merge_type_arg T T' = if T = T' then T else cannot_merge_types (); 
49119  65 

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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  68 

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fun is_triv_implies thm = 
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op aconv (Logic.dest_implies (Thm.prop_of thm)) 
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handle TERM _ => false; 
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49121  73 
fun type_args_constrained_of (((cAs, _), _), _) = cAs; 
49336  74 
fun type_binding_of (((_, b), _), _) = b; 
49181  75 
fun mixfix_of ((_, mx), _) = mx; 
49121  76 
fun ctr_specs_of (_, ctr_specs) = ctr_specs; 
49119  77 

49286  78 
fun disc_of ((((disc, _), _), _), _) = disc; 
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fun ctr_of ((((_, ctr), _), _), _) = ctr; 

80 
fun args_of (((_, args), _), _) = args; 

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

49181  82 
fun ctr_mixfix_of (_, mx) = mx; 
49119  83 

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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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(* TODO: integration with function package ("size") *) 
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49286  90 
val _ = if not lfp andalso no_dests then error "Cannot define destructorless codatatypes" 
49278  91 
else (); 
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49367  93 
val nn = length specs; 
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val fp_bs = map type_binding_of specs; 
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val fp_b_names = map Binding.name_of fp_bs; 
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val fp_common_name = mk_common_name fp_b_names; 

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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; 
49119  106 

49370  107 
val ((Bs, Cs), no_defs_lthy) = 
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no_defs_lthy0 
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> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As 
49367  110 
> mk_TFrees nn 
49370  111 
>> mk_TFrees nn; 
49119  112 

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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  118 
(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; 
49119  120 

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fun mk_fake_T b = 
49121  122 
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), 
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unsorted_As); 
49121  124 

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val fake_Ts = map mk_fake_T fp_bs; 
49121  126 

49181  127 
val mixfixes = map mixfix_of specs; 
49119  128 

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val _ = (case duplicates Binding.eq_name fp_bs of [] => () 
49119  130 
 b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); 
131 

49121  132 
val ctr_specss = map ctr_specs_of specs; 
49119  133 

49336  134 
val disc_bindingss = map (map disc_of) ctr_specss; 
135 
val ctr_bindingss = 

49498  136 
map2 (fn fp_b_name => map (Binding.qualify false fp_b_name o ctr_of)) fp_b_names ctr_specss; 
49121  137 
val ctr_argsss = map (map args_of) ctr_specss; 
49181  138 
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; 
49119  139 

49336  140 
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; 
49286  142 
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  153 
[] => () 
49342  154 
 A' :: _ => error ("Extra type variable on righthand side: " ^ 
49204  155 
quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); 
49165  156 

49204  157 
fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) = 
49146  158 
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ 
159 
quote (Syntax.string_of_typ fake_lthy T))) 

49204  160 
 eq_fpT _ _ = false; 
49146  161 

49204  162 
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  164 
 freeze_fp T = T; 
49121  165 

49297  166 
val ctr_TsssBs = map (map (map freeze_fp)) fake_ctr_Tsss; 
167 
val ctr_sum_prod_TsBs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssBs; 

49119  168 

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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  171 

49501  172 
val (pre_bnfs, ((dtors0, ctors0, fp_iters0, fp_recs0, fp_induct, dtor_ctors, ctor_dtors, 
173 
ctor_injects, 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  175 

49363  176 
fun add_nesty_bnf_names Us = 
49226  177 
let 
178 
fun add (Type (s, Ts)) ss = 

179 
let val (needs, ss') = fold_map add Ts ss in 

180 
if exists I needs then (true, insert (op =) s ss') else (false, ss') 

181 
end 

49363  182 
 add T ss = (member (op =) Us T, ss); 
49226  183 
in snd oo add end; 
184 

49363  185 
fun nesty_bnfs Us = 
186 
map_filter (bnf_of lthy) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_TsssBs []); 

187 

188 
val nesting_bnfs = nesty_bnfs As; 

189 
val nested_bnfs = nesty_bnfs Bs; 

49226  190 

49167  191 
val timer = time (Timer.startRealTimer ()); 
192 

49501  193 
fun mk_ctor_or_dtor get_T Ts t = 
49176  194 
let val Type (_, Ts0) = get_T (fastype_of t) in 
49124  195 
Term.subst_atomic_types (Ts0 ~~ Ts) t 
49121  196 
end; 
49119  197 

49501  198 
val mk_ctor = mk_ctor_or_dtor range_type; 
199 
val mk_dtor = mk_ctor_or_dtor domain_type; 

49121  200 

49501  201 
val ctors = map (mk_ctor As) ctors0; 
202 
val dtors = map (mk_dtor As) dtors0; 

49124  203 

49501  204 
val fpTs = map (domain_type o fastype_of) dtors; 
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val exists_fp_subtype = exists_subtype (member (op =) fpTs); 
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49297  208 
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Bs ~~ fpTs)))) ctr_TsssBs; 
49203  209 
val ns = map length ctr_Tsss; 
49212  210 
val kss = map (fn n => 1 upto n) ns; 
49203  211 
val mss = map (map length) ctr_Tsss; 
212 
val Css = map2 replicate ns Cs; 

213 

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fun mk_iter_like Ts Us t = 
49121  215 
let 
49336  216 
val (bindings, body) = strip_type (fastype_of t); 
217 
val (f_Us, prebody) = split_last bindings; 

49210  218 
val Type (_, Ts0) = if lfp then prebody else body; 
219 
val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us); 

49176  220 
in 
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Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
49176  222 
end; 
223 

49210  224 
val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0; 
225 
val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0; 

226 

49212  227 
val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1))); 
228 
val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1))); 

49204  229 

49484  230 
val (((iter_only as (gss, _, _), rec_only as (hss, _, _)), 
231 
(zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))), 

232 
names_lthy) = 

49208  233 
if lfp then 
234 
let 

235 
val y_Tsss = 

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map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN_balanced n o domain_type) 
49212  237 
ns mss fp_iter_fun_Ts; 
49208  238 
val g_Tss = map2 (map2 (curry (op >))) y_Tsss Css; 
239 

49484  240 
val ((gss, ysss), lthy) = 
49208  241 
lthy 
242 
> mk_Freess "f" g_Tss 

243 
>> mk_Freesss "x" y_Tsss; 

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244 
val yssss = map (map (map single)) ysss; 
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245 

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246 
fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) = 
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247 
if member (op =) Cs U then Us else [T] 
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248 
 dest_rec_prodT T = [T]; 
49204  249 

49208  250 
val z_Tssss = 
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251 
map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o 
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252 
dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts; 
49208  253 
val h_Tss = map2 (map2 (fold_rev (curry (op >)))) z_Tssss Css; 
49204  254 

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255 
val hss = map2 (map2 retype_free) h_Tss gss; 
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256 
val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss; 
49484  257 
val (zssss_tl, lthy) = 
49208  258 
lthy 
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259 
> mk_Freessss "y" (map (map (map tl)) z_Tssss); 
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260 
val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl; 
49210  261 
in 
49484  262 
((((gss, g_Tss, yssss), (hss, h_Tss, zssss)), 
263 
([], [], [], (([], []), ([], [])), (([], []), ([], [])))), lthy) 

49210  264 
end 
49208  265 
else 
49210  266 
let 
49221
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267 
(*avoid "'a itself" arguments in coiterators and corecursors*) 
6d8d5fe9f3a2
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268 
val mss' = map (fn [0] => [1]  ms => ms) mss; 
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269 

49463  270 
val p_Tss = map2 (fn n => replicate (Int.max (0, n  1)) o mk_pred1T) ns Cs; 
49275  271 

49276  272 
fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss); 
49211  273 

49276  274 
fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss 
275 
 zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) = 

276 
p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss; 

49274
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277 

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278 
fun mk_types maybe_dest_sumT fun_Ts = 
49212  279 
let 
280 
val f_sum_prod_Ts = map range_type fun_Ts; 

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281 
val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts; 
49275  282 
val f_Tssss = 
283 
map3 (fn C => map2 (map (map (curry (op >) C) o maybe_dest_sumT) oo dest_tupleT)) 

284 
Cs mss' f_prod_Tss; 

285 
val q_Tssss = 

49463  286 
map (map (map (fn [_] => []  [_, C] => [mk_pred1T (domain_type C)]))) f_Tssss; 
49276  287 
val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss; 
49275  288 
in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end; 
49176  289 

49275  290 
val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts; 
49211  291 

49484  292 
val ((((Free (z, _), cs), pss), gssss), lthy) = 
49210  293 
lthy 
49233  294 
> yield_singleton (mk_Frees "z") dummyT 
295 
>> mk_Frees "a" Cs 

49211  296 
>> mk_Freess "p" p_Tss 
49275  297 
>> mk_Freessss "g" g_Tssss; 
298 
val rssss = map (map (map (fn [] => []))) r_Tssss; 

49274
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299 

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300 
fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) = 
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301 
if member (op =) Cs U then Us else [T] 
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302 
 dest_corec_sumT T = [T]; 
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303 

49275  304 
val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts; 
49210  305 

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306 
val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss; 
49484  307 
val ((sssss, hssss_tl), lthy) = 
49275  308 
lthy 
309 
> mk_Freessss "q" s_Tssss 

310 
>> mk_Freessss "h" (map (map (map tl)) h_Tssss); 

311 
val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl; 

49211  312 

49212  313 
val cpss = map2 (fn c => map (fn p => p $ c)) cs pss; 
314 

49276  315 
fun mk_preds_getters_join [] [cf] = cf 
316 
 mk_preds_getters_join [cq] [cf, cf'] = 

317 
mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf'); 

318 

49275  319 
fun mk_terms qssss fssss = 
49212  320 
let 
49276  321 
val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss; 
49275  322 
val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss; 
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323 
val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss; 
49276  324 
val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss; 
325 
in (pfss, cqfsss) end; 

49210  326 
in 
49484  327 
(((([], [], []), ([], [], [])), 
328 
([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)), 

329 
(mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss)))), lthy) 

49210  330 
end; 
331 

49501  332 
fun define_ctrs_case_for_type ((((((((((((((((((fp_b, fpT), C), ctor), dtor), fp_iter), fp_rec), 
333 
ctor_dtor), dtor_ctor), ctor_inject), n), ks), ms), ctr_bindings), ctr_mixfixes), ctr_Tss), 

49370  334 
disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy = 
49176  335 
let 
49498  336 
val fp_b_name = Binding.name_of fp_b; 
337 

49501  338 
val dtorT = domain_type (fastype_of ctor); 
49210  339 
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
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340 
val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts; 
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341 
val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  342 

49498  343 
val ((((w, fs), xss), u'), _) = 
49204  344 
no_defs_lthy 
49501  345 
> yield_singleton (mk_Frees "w") dtorT 
49176  346 
>> mk_Frees "f" case_Ts 
49370  347 
>> mk_Freess "x" ctr_Tss 
49498  348 
>> yield_singleton Variable.variant_fixes fp_b_name; 
49370  349 

49498  350 
val u = Free (u', fpT); 
49121  351 

49129  352 
val ctr_rhss = 
49501  353 
map2 (fn k => fn xs => fold_rev Term.lambda xs (ctor $ 
49256  354 
mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss; 
49121  355 

49336  356 
val case_binding = Binding.suffix_name ("_" ^ caseN) fp_b; 
49129  357 

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358 
val case_rhs = 
49498  359 
fold_rev Term.lambda (fs @ [u]) 
49501  360 
(mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (dtor $ u)); 
49129  361 

49201  362 
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy 
49169  363 
> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => 
49302
f5bd87aac224
added optional qualifiers for constructors and destructors, similarly to the old package
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parents:
49300
diff
changeset

364 
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 
49336  365 
(case_binding :: ctr_bindings) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) 
49121  366 
> `Local_Theory.restore; 
367 

368 
val phi = Proof_Context.export_morphism lthy lthy'; 

369 

370 
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; 

49130
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49129
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changeset

371 
val case_def = Morphism.thm phi raw_case_def; 
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changeset

372 

49203  373 
val ctrs0 = map (Morphism.term phi) raw_ctrs; 
374 
val casex0 = Morphism.term phi raw_case; 

375 

376 
val ctrs = map (mk_ctr As) ctrs0; 

49121  377 

49135  378 
fun exhaust_tac {context = ctxt, ...} = 
49123
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49121
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379 
let 
49501  380 
val ctor_iff_dtor_thm = 
49135  381 
let 
382 
val goal = 

49498  383 
fold_rev Logic.all [w, u] 
49501  384 
(mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w))); 
49135  385 
in 
386 
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => 

49501  387 
mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [dtorT, fpT]) 
388 
(certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor) 

49135  389 
> Thm.close_derivation 
390 
> Morphism.thm phi 

391 
end; 

392 

393 
val sumEN_thm' = 

49463  394 
unfold_defs lthy @{thms all_unit_eq} 
49255
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changeset

395 
(Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) [] 
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changeset

396 
(mk_sumEN_balanced n)) 
49135  397 
> Morphism.thm phi; 
49123
263b0e330d8b
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49121
diff
changeset

398 
in 
49501  399 
mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm' 
49123
263b0e330d8b
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49121
diff
changeset

400 
end; 
49121  401 

49126  402 
val inject_tacss = 
49205  403 
map2 (fn 0 => K []  _ => fn ctr_def => [fn {context = ctxt, ...} => 
49501  404 
mk_inject_tac ctxt ctr_def ctor_inject]) ms ctr_defs; 
49126  405 

49127  406 
val half_distinct_tacss = 
407 
map (map (fn (def, def') => fn {context = ctxt, ...} => 

49501  408 
mk_half_distinct_tac ctxt ctor_inject [def, def'])) (mk_half_pairss ctr_defs); 
49127  409 

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

410 
val case_tacs = 
3c26e17b2849
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blanchet
parents:
49129
diff
changeset

411 
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => 
49501  412 
mk_case_tac ctxt n k m case_def ctr_def dtor_ctor) ks ms ctr_defs; 
49121  413 

414 
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; 

49134
846264f80f16
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49130
diff
changeset

415 

49438  416 
fun define_iter_rec (wrap_res, no_defs_lthy) = 
49134
846264f80f16
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49130
diff
changeset

417 
let 
49208  418 
val fpT_to_C = fpT > C; 
49199  419 

49215  420 
fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) = 
421 
let 

422 
val res_T = fold_rev (curry (op >)) f_Tss fpT_to_C; 

49336  423 
val binding = Binding.suffix_name ("_" ^ suf) fp_b; 
49215  424 
val spec = 
49336  425 
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binding, res_T)), 
49215  426 
Term.list_comb (fp_iter_like, 
49255
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49254
diff
changeset

427 
map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss)); 
49336  428 
in (binding, spec) end; 
49199  429 

49300  430 
val iter_like_infos = 
49215  431 
[(iterN, fp_iter, iter_only), 
432 
(recN, fp_rec, rec_only)]; 

433 

49336  434 
val (bindings, specs) = map generate_iter_like iter_like_infos > split_list; 
49215  435 

436 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49201  437 
> apfst split_list o fold_map2 (fn b => fn spec => 
49199  438 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 
49336  439 
#>> apsnd snd) bindings specs 
49199  440 
> `Local_Theory.restore; 
49201  441 

442 
val phi = Proof_Context.export_morphism lthy lthy'; 

443 

49215  444 
val [iter_def, rec_def] = map (Morphism.thm phi) defs; 
49201  445 

49215  446 
val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts; 
49134
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49130
diff
changeset

447 
in 
49438  448 
((wrap_res, ctrs, iter, recx, xss, ctr_defs, iter_def, rec_def), lthy) 
49134
846264f80f16
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diff
changeset

449 
end; 
846264f80f16
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parents:
49130
diff
changeset

450 

49438  451 
fun define_coiter_corec (wrap_res, no_defs_lthy) = 
49210  452 
let 
453 
val B_to_fpT = C > fpT; 

49211  454 

49276  455 
fun mk_preds_getterss_join c n cps sum_prod_T cqfss = 
456 
Term.lambda c (mk_IfN sum_prod_T cps 

457 
(map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n))); 

49275  458 

49276  459 
fun generate_coiter_like (suf, fp_iter_like, ((pfss, cqfsss), (f_sum_prod_Ts, 
49274
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49273
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changeset

460 
pf_Tss))) = 
49211  461 
let 
462 
val res_T = fold_rev (curry (op >)) pf_Tss B_to_fpT; 

49336  463 
val binding = Binding.suffix_name ("_" ^ suf) fp_b; 
49211  464 
val spec = 
49336  465 
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binding, res_T)), 
49211  466 
Term.list_comb (fp_iter_like, 
49276  467 
map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss)); 
49336  468 
in (binding, spec) end; 
49210  469 

49300  470 
val coiter_like_infos = 
49215  471 
[(coiterN, fp_iter, coiter_only), 
472 
(corecN, fp_rec, corec_only)]; 

49212  473 

49336  474 
val (bindings, specs) = map generate_coiter_like coiter_like_infos > split_list; 
49211  475 

476 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49210  477 
> apfst split_list o fold_map2 (fn b => fn spec => 
478 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 

49336  479 
#>> apsnd snd) bindings specs 
49210  480 
> `Local_Theory.restore; 
481 

482 
val phi = Proof_Context.export_morphism lthy lthy'; 

483 

49211  484 
val [coiter_def, corec_def] = map (Morphism.thm phi) defs; 
49210  485 

49211  486 
val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts; 
49210  487 
in 
49438  488 
((wrap_res, ctrs, coiter, corec, xss, ctr_defs, coiter_def, corec_def), lthy) 
49210  489 
end; 
49286  490 

49287
ebe2a5cec4bf
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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
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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; 
49368  504 
val nested_set_natural's = maps set_natural'_of_bnf nested_bnfs; 
49363  505 
val nesting_map_ids = map map_id_of_bnf nesting_bnfs; 
49226  506 

49393  507 
fun mk_map live Ts Us t = 
49426  508 
let 
509 
val (Type (_, Ts0), Type (_, Us0)) = strip_typeN (live + 1) (fastype_of t) >> List.last 

510 
in 

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

511 
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

512 
end; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

513 

49437  514 
fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) = 
49234  515 
let 
49392  516 
val bnf = the (bnf_of lthy s); 
49393  517 
val live = live_of_bnf bnf; 
518 
val mapx = mk_map live Ts Us (map_of_bnf bnf); 

519 
val TUs = map dest_funT (fst (strip_typeN live (fastype_of mapx))); 

49234  520 
val args = map build_arg TUs; 
521 
in Term.list_comb (mapx, args) end; 

522 

49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

523 
val mk_simp_thmss = 
49484  524 
map3 (fn (_, _, injects, distincts, cases, _, _, _) => fn rec_likes => fn iter_likes => 
49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

525 
injects @ distincts @ cases @ rec_likes @ iter_likes); 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

526 

49438  527 
fun derive_induct_iter_rec_thms_for_types ((wrap_ress, ctrss, iters, recs, xsss, ctr_defss, 
49337  528 
iter_defs, rec_defs), lthy) = 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

529 
let 
49498  530 
val (((phis, phis'), us'), names_lthy) = 
49370  531 
lthy 
49463  532 
> mk_Frees' "P" (map mk_pred1T fpTs) 
49498  533 
>> Variable.variant_fixes fp_b_names; 
49370  534 

49498  535 
val us = map2 (curry Free) us' fpTs; 
49370  536 

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

537 
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

538 
let 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

539 
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
blanchet
parents:
49361
diff
changeset

540 
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

541 
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

542 
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

543 
(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

544 
~1 => Term.dummy 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

545 
 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

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

547 
(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

548 
end; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

549 

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

550 
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

551 

49337  552 
val (induct_thms, induct_thm) = 
553 
let 

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

554 
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

555 
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

556 
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

557 
end; 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

558 

49375
993677c1cf2a
tuned code before fixing "mk_induct_discharge_prem_prems_tac"
blanchet
parents:
49372
diff
changeset

559 
fun mk_raw_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

560 
(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

561 
~1 => 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

562 
(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

563 
NONE => [] 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

564 
 SOME raw_sets0 => 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

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

566 
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

567 
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

568 
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

569 
val (ys, names_lthy') = names_lthy > mk_Frees s Ts; 
49375
993677c1cf2a
tuned code before fixing "mk_induct_discharge_prem_prems_tac"
blanchet
parents:
49372
diff
changeset

570 
val xysets = map (pair x) (ys ~~ sets); 
993677c1cf2a
tuned code before fixing "mk_induct_discharge_prem_prems_tac"
blanchet
parents:
49372
diff
changeset

571 
val ppremss = map (mk_raw_prem_prems names_lthy') ys; 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

572 
in 
49375
993677c1cf2a
tuned code before fixing "mk_induct_discharge_prem_prems_tac"
blanchet
parents:
49372
diff
changeset

573 
flat (map2 (map o apfst o cons) xysets ppremss) 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

574 
end) 
49376
c6366fd0415a
select the right premise in "mk_induct_discharge_prem_prems_tac" instead of relying on backtracking
blanchet
parents:
49375
diff
changeset

575 
 i => [([], (i + 1, x))]) 
49375
993677c1cf2a
tuned code before fixing "mk_induct_discharge_prem_prems_tac"
blanchet
parents:
49372
diff
changeset

576 
 mk_raw_prem_prems _ _ = []; 
49342  577 

49378
19237e465055
fixed issue with bound variables in prem prems + tuning
blanchet
parents:
49377
diff
changeset

578 
fun close_prem_prem xs t = 
19237e465055
fixed issue with bound variables in prem prems + tuning
blanchet
parents:
49377
diff
changeset

579 
fold_rev Logic.all (map Free (drop (nn + length xs) 
19237e465055
fixed issue with bound variables in prem prems + tuning
blanchet
parents:
49377
diff
changeset

580 
(rev (Term.add_frees t (map dest_Free xs @ phis'))))) t; 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

581 

49378
19237e465055
fixed issue with bound variables in prem prems + tuning
blanchet
parents:
49377
diff
changeset

582 
fun mk_prem_prem xs (xysets, (j, x)) = 
19237e465055
fixed issue with bound variables in prem prems + tuning
blanchet
parents:
49377
diff
changeset

583 
close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) => 
49376
c6366fd0415a
select the right premise in "mk_induct_discharge_prem_prems_tac" instead of relying on backtracking
blanchet
parents:
49375
diff
changeset

584 
HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets, 
c6366fd0415a
select the right premise in "mk_induct_discharge_prem_prems_tac" instead of relying on backtracking
blanchet
parents:
49375
diff
changeset

585 
HOLogic.mk_Trueprop (nth phis (j  1) $ x))); 
49375
993677c1cf2a
tuned code before fixing "mk_induct_discharge_prem_prems_tac"
blanchet
parents:
49372
diff
changeset

586 

49372  587 
fun mk_raw_prem phi ctr ctr_Ts = 
49362
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

588 
let 
1271aca16aed
make tactic more robust in the case where "asm_simp_tac" already finishes the job
blanchet
parents:
49361
diff
changeset

589 
val (xs, names_lthy') = names_lthy > mk_Frees "x" ctr_Ts; 
49376
c6366fd0415a
select the right premise in "mk_induct_discharge_prem_prems_tac" instead of relying on backtracking
blanchet
parents:
49375
diff
changeset

590 
val pprems = maps (mk_raw_prem_prems names_lthy') xs; 
49378
19237e465055
fixed issue with bound variables in prem prems + tuning
blanchet
parents:
49377
diff
changeset

591 
in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end; 
49342  592 

49376
c6366fd0415a
select the right premise in "mk_induct_discharge_prem_prems_tac" instead of relying on backtracking
blanchet
parents:
49375
diff
changeset

593 
fun mk_prem (xs, raw_pprems, concl) = 
49378
19237e465055
fixed issue with bound variables in prem prems + tuning
blanchet
parents:
49377
diff
changeset

594 
fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl)); 
49368  595 

49389  596 
val raw_premss = map3 (map2 o mk_raw_prem) phis ctrss ctr_Tsss; 
597 

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

598 
val goal = 
49372  599 
Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss, 
49498  600 
HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) phis us))); 
49368  601 

49429
64ac3471005a
cleaner way of dealing with the set functions of sums and products
blanchet
parents:
49427
diff
changeset

602 
val kksss = map (map (map (fst o snd) o #2)) raw_premss; 
49368  603 

49501  604 
val ctor_induct' = fp_induct OF (map mk_sumEN_tupled_balanced mss); 
49342  605 

606 
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

607 
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => 
49501  608 
mk_induct_tac ctxt ns mss kksss (flat ctr_defss) ctor_induct' 
49389  609 
nested_set_natural's pre_set_defss) 
49368  610 
> singleton (Proof_Context.export names_lthy lthy) 
49337  611 
in 
49367  612 
`(conj_dests nn) induct_thm 
49337  613 
end; 
49201  614 

49438  615 
(* TODO: Generate nicer names in case of clashes *) 
49437  616 
val induct_cases = Datatype_Prop.indexify_names (maps (map base_name_of_ctr) ctrss); 
617 

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

618 
val (iter_thmss, rec_thmss) = 
49207  619 
let 
49337  620 
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; 
621 
val giters = map (lists_bmoc gss) iters; 

622 
val hrecs = map (lists_bmoc hss) recs; 

623 

49484  624 
fun mk_goal fss fiter_like xctr f xs fxs = 
49207  625 
fold_rev (fold_rev Logic.all) (xs :: fss) 
49212  626 
(mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs))); 
49204  627 

49234  628 
fun build_call fiter_likes maybe_tick (T, U) = 
629 
if T = U then 

49368  630 
id_const T 
49234  631 
else 
632 
(case find_index (curry (op =) T) fpTs of 

633 
~1 => build_map (build_call fiter_likes maybe_tick) T U 

49498  634 
 j => maybe_tick (nth us j) (nth fiter_likes j)); 
49233  635 

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

636 
fun mk_U maybe_mk_prodT = 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

637 
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

638 

49342  639 
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

640 
if member (op =) fpTs T then 
49233  641 
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

642 
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

643 
[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

644 
else 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

645 
[x]; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

646 

49342  647 
val gxsss = map (map (maps (intr_calls giters (K I) (K I) (K I)))) xsss; 
648 
val hxsss = map (map (maps (intr_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss; 

49204  649 

49484  650 
val iter_goalss = map5 (map4 o mk_goal gss) giters xctrss gss xsss gxsss; 
651 
val rec_goalss = map5 (map4 o mk_goal hss) hrecs xctrss hss xsss hxsss; 

49204  652 

49203  653 
val iter_tacss = 
49363  654 
map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids iter_defs) fp_iter_thms 
655 
ctr_defss; 

49203  656 
val rec_tacss = 
49363  657 
map2 (map o mk_iter_like_tac pre_map_defs nesting_map_ids rec_defs) fp_rec_thms 
658 
ctr_defss; 

49484  659 

660 
fun prove goal tac = Skip_Proof.prove lthy [] [] goal (tac o #context); 

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

661 
in 
49484  662 
(map2 (map2 prove) iter_goalss iter_tacss, 
663 
map2 (map2 prove) rec_goalss rec_tacss) 

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

664 
end; 
49201  665 

49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

666 
val simp_thmss = mk_simp_thmss wrap_ress rec_thmss iter_thmss; 
49438  667 

49437  668 
val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases)); 
669 
fun induct_type_attr T_name = Attrib.internal (K (Induct.induct_type T_name)); 

670 

49450  671 
(* TODO: Also note "recs", "simps", and "splits" if "nn > 1" (for compatibility with the 
49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

672 
old package)? And for codatatypes as well? *) 
49337  673 
val common_notes = 
49437  674 
(if nn > 1 then [(inductN, [induct_thm], [induct_case_names_attr])] else []) 
49337  675 
> map (fn (thmN, thms, attrs) => 
49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

676 
((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])])); 
49337  677 

49226  678 
val notes = 
49437  679 
[(inductN, map single induct_thms, 
680 
fn T_name => [induct_case_names_attr, induct_type_attr T_name]), 

49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

681 
(itersN, iter_thmss, K (Code.add_default_eqn_attrib :: simp_attrs)), 
49438  682 
(recsN, rec_thmss, K (Code.add_default_eqn_attrib :: simp_attrs)), 
683 
(simpsN, simp_thmss, K [])] 

49300  684 
> maps (fn (thmN, thmss, attrs) => 
49437  685 
map3 (fn b => fn Type (T_name, _) => fn thms => 
686 
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), attrs T_name), 

687 
[(thms, [])])) fp_bs fpTs thmss); 

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

688 
in 
49337  689 
lthy > Local_Theory.notes (common_notes @ notes) > snd 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

690 
end; 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

691 

49438  692 
fun derive_coinduct_coiter_corec_thms_for_types ((wrap_ress, ctrss, coiters, corecs, _, 
693 
ctr_defss, coiter_defs, corec_defs), lthy) = 

49212  694 
let 
49484  695 
val discss = map (map (mk_disc_or_sel As) o #1) wrap_ress; 
696 
val selsss = map #2 wrap_ress; 

697 
val disc_thmsss = map #6 wrap_ress; 

698 
val discIss = map #7 wrap_ress; 

699 
val sel_thmsss = map #8 wrap_ress; 

49438  700 

49498  701 
val (us', _) = 
49370  702 
lthy 
49498  703 
> Variable.variant_fixes fp_b_names; 
49370  704 

49498  705 
val us = map2 (curry Free) us' fpTs; 
49370  706 

49337  707 
val (coinduct_thms, coinduct_thm) = 
708 
let 

709 
val coinduct_thm = fp_induct; 

710 
in 

49367  711 
`(conj_dests nn) coinduct_thm 
49337  712 
end; 
49212  713 

49484  714 
fun mk_maybe_not pos = not pos ? HOLogic.mk_not; 
715 

716 
val z = the_single zs; 

717 
val gcoiters = map (lists_bmoc pgss) coiters; 

718 
val hcorecs = map (lists_bmoc phss) corecs; 

719 

49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

720 
val (coiter_thmss, corec_thmss, safe_coiter_thmss, safe_corec_thmss) = 
49212  721 
let 
49484  722 
fun mk_goal pfss c cps fcoiter_like n k ctr m cfs' = 
49212  723 
fold_rev (fold_rev Logic.all) ([c] :: pfss) 
49484  724 
(Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps, 
49276  725 
mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs')))); 
49212  726 

49234  727 
fun build_call fiter_likes maybe_tack (T, U) = 
728 
if T = U then 

49368  729 
id_const T 
49234  730 
else 
731 
(case find_index (curry (op =) U) fpTs of 

732 
~1 => build_map (build_call fiter_likes maybe_tack) T U 

49498  733 
 j => maybe_tack (nth cs j, nth us j) (nth fiter_likes j)); 
49233  734 

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

735 
fun mk_U maybe_mk_sumT = 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

736 
typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs); 
49212  737 

49342  738 
fun intr_calls fiter_likes maybe_mk_sumT maybe_tack cqf = 
49276  739 
let val T = fastype_of cqf in 
740 
if exists_subtype (member (op =) Cs) T then 

741 
build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf 

742 
else 

743 
cqf 

744 
end; 

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

745 

49342  746 
val crgsss' = map (map (map (intr_calls gcoiters (K I) (K I)))) crgsss; 
747 
val cshsss' = map (map (map (intr_calls hcorecs (curry mk_sumT) (tack z)))) cshsss; 

49212  748 

49484  749 
val coiter_goalss = 
750 
map8 (map4 oooo mk_goal pgss) cs cpss gcoiters ns kss ctrss mss crgsss'; 

751 
val corec_goalss = 

752 
map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss'; 

49213  753 

754 
val coiter_tacss = 

49363  755 
map3 (map oo mk_coiter_like_tac coiter_defs nesting_map_ids) fp_iter_thms pre_map_defs 
49226  756 
ctr_defss; 
49233  757 
val corec_tacss = 
49363  758 
map3 (map oo mk_coiter_like_tac corec_defs nesting_map_ids) fp_rec_thms pre_map_defs 
49233  759 
ctr_defss; 
49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

760 

49484  761 
fun prove goal tac = 
762 
Skip_Proof.prove lthy [] [] goal (tac o #context) > Thm.close_derivation; 

763 

764 
val coiter_thmss = map2 (map2 prove) coiter_goalss coiter_tacss; 

49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

765 
val corec_thmss = 
49484  766 
map2 (map2 prove) corec_goalss corec_tacss 
767 
> map (map (unfold_defs lthy @{thms sum_case_if})); 

49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

768 

504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

769 
val coiter_safesss = map2 (map2 (map2 (curry (op =)))) crgsss' crgsss; 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

770 
val corec_safesss = map2 (map2 (map2 (curry (op =)))) cshsss' cshsss; 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

771 

504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

772 
val filter_safesss = 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

773 
map2 (map_filter (fn (safes, thm) => if forall I safes then SOME thm else NONE) oo 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

774 
curry (op ~~)); 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

775 

504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

776 
val safe_coiter_thmss = filter_safesss coiter_safesss coiter_thmss; 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

777 
val safe_corec_thmss = filter_safesss corec_safesss corec_thmss; 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

778 
in 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

779 
(coiter_thmss, corec_thmss, safe_coiter_thmss, safe_corec_thmss) 
49212  780 
end; 
781 

49484  782 
val (disc_coiter_iff_thmss, disc_corec_iff_thmss) = 
49482  783 
let 
49484  784 
fun mk_goal c cps fcoiter_like n k disc = 
785 
mk_Trueprop_eq (disc $ (fcoiter_like $ c), 

786 
if n = 1 then @{const True} 

787 
else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps)); 

788 

789 
val coiter_goalss = map6 (map2 oooo mk_goal) cs cpss gcoiters ns kss discss; 

790 
val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss; 

791 

792 
fun mk_case_split' cp = 

793 
Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split}; 

794 

795 
val case_splitss' = map (map mk_case_split') cpss; 

49482  796 

49484  797 
val coiter_tacss = 
798 
map3 (map oo mk_disc_coiter_like_iff_tac) case_splitss' coiter_thmss disc_thmsss; 

799 
val corec_tacss = 

800 
map3 (map oo mk_disc_coiter_like_iff_tac) case_splitss' corec_thmss disc_thmsss; 

801 

802 
fun prove goal tac = 

803 
Skip_Proof.prove lthy [] [] goal (tac o #context) 

804 
> Thm.close_derivation 

805 
> singleton (Proof_Context.export names_lthy no_defs_lthy); 

806 

807 
fun proves [_] [_] = [] 

808 
 proves goals tacs = map2 prove goals tacs; 

49482  809 
in 
49484  810 
(map2 proves coiter_goalss coiter_tacss, 
811 
map2 proves corec_goalss corec_tacss) 

49482  812 
end; 
813 

49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

814 
fun mk_disc_coiter_like_thms coiter_likes discIs = 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

815 
map (op RS) (filter_out (is_triv_implies o snd) (coiter_likes ~~ discIs)); 
49266  816 

817 
val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss; 

818 
val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss; 

819 

49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

820 
fun mk_sel_coiter_like_thm coiter_like_thm sel sel_thm = 
49266  821 
let 
49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

822 
val (domT, ranT) = dest_funT (fastype_of sel); 
49266  823 
val arg_cong' = 
824 
Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT]) 

49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

825 
[NONE, NONE, SOME (certify lthy sel)] arg_cong 
49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

826 
> Thm.varifyT_global; 
49266  827 
val sel_thm' = sel_thm RSN (2, trans); 
828 
in 

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

829 
coiter_like_thm RS arg_cong' RS sel_thm' 
49266  830 
end; 
831 

49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

832 
fun mk_sel_coiter_like_thms coiter_likess = 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

833 
map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_likess selsss sel_thmsss > map flat; 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

834 

504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

835 
val sel_coiter_thmss = mk_sel_coiter_like_thms coiter_thmss; 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

836 
val sel_corec_thmss = mk_sel_coiter_like_thms corec_thmss; 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

837 

504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

838 
fun zip_coiter_like_thms coiter_likes disc_coiter_likes sel_coiter_likes = 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

839 
coiter_likes @ disc_coiter_likes @ sel_coiter_likes; 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

840 

504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

841 
val simp_thmss = 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

842 
mk_simp_thmss wrap_ress 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

843 
(map3 zip_coiter_like_thms safe_corec_thmss disc_corec_thmss sel_corec_thmss) 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

844 
(map3 zip_coiter_like_thms safe_coiter_thmss disc_coiter_thmss sel_coiter_thmss); 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

845 

504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

846 
val anonymous_notes = 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

847 
[(flat safe_coiter_thmss @ flat safe_corec_thmss, simp_attrs)] 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

848 
> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])])); 
49266  849 

49342  850 
val common_notes = 
49367  851 
(if nn > 1 then [(coinductN, [coinduct_thm], [])] (* FIXME: attribs *) else []) 
49342  852 
> map (fn (thmN, thms, attrs) => 
49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

853 
((Binding.qualify true fp_common_name (Binding.name thmN), attrs), [(thms, [])])); 
49342  854 

49212  855 
val notes = 
49342  856 
[(coinductN, map single coinduct_thms, []), (* FIXME: attribs *) 
857 
(coitersN, coiter_thmss, []), 

49482  858 
(corecsN, corec_thmss, []), 
49484  859 
(disc_coiter_iffN, disc_coiter_iff_thmss, simp_attrs), 
49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

860 
(disc_coitersN, disc_coiter_thmss, simp_attrs), 
49484  861 
(disc_corec_iffN, disc_corec_iff_thmss, simp_attrs), 
49482  862 
(disc_corecsN, disc_corec_thmss, simp_attrs), 
49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

863 
(sel_coitersN, sel_coiter_thmss, simp_attrs), 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

864 
(sel_corecsN, sel_corec_thmss, simp_attrs), 
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

865 
(simpsN, simp_thmss, [])] 
49300  866 
> maps (fn (thmN, thmss, attrs) => 
49266  867 
map_filter (fn (_, []) => NONE  (b, thms) => 
49300  868 
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

869 
[(thms, [])])) (fp_bs ~~ thmss)); 
49212  870 
in 
49479
504f0a38f608
added "simp"s to coiter/corec theorems + export under "simps" name
blanchet
parents:
49478
diff
changeset

871 
lthy > Local_Theory.notes (anonymous_notes @ common_notes @ notes) > snd 
49212  872 
end; 
873 

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

874 
fun wrap_types_and_define_iter_likes ((wraps, define_iter_likess), lthy) = 
49438  875 
fold_map2 (curry (op o)) define_iter_likess wraps lthy >> split_list8 
49287
ebe2a5cec4bf
allow defaults for one datatype to involve the constructor of another one in the mutually recursive case
blanchet
parents:
49286
diff
changeset

876 

49204  877 
val lthy' = lthy 
49501  878 
> fold_map define_ctrs_case_for_type (fp_bs ~~ fpTs ~~ Cs ~~ ctors ~~ dtors ~~ fp_iters ~~ 
879 
fp_recs ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ ns ~~ kss ~~ mss ~~ ctr_bindingss ~~ 

49370  880 
ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~ 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

881 
>> split_list > wrap_types_and_define_iter_likes 
49337  882 
> (if lfp then derive_induct_iter_rec_thms_for_types 
883 
else derive_coinduct_coiter_corec_thms_for_types); 

49167  884 

885 
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ 

49208  886 
(if lfp then "" else "co") ^ "datatype")); 
49112  887 
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

888 
timer; lthy' 
49112  889 
end; 
890 

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

891 
val datatyp = define_datatype (K I) (K I) (K I); 
49297  892 

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

893 
val datatype_cmd = define_datatype Typedecl.read_constraint Syntax.parse_typ Syntax.read_term; 
49119  894 

49112  895 
val parse_ctr_arg = 
49329
82452dc63ed5
desambiguate grammar (e.g. for Nil's mixfix ("[]"))
blanchet
parents:
49311
diff
changeset

896 
@{keyword "("}  parse_binding_colon  Parse.typ  @{keyword ")"}  
49434
433dc7e028c8
separated registration of BNFs from bnf_def (BNFs are now stored only for bnf_def and (co)data commands)
traytel
parents:
49429
diff
changeset

897 
(Parse.typ >> pair Binding.empty); 
49112  898 

49286  899 
val parse_defaults = 
900 
@{keyword "("}  @{keyword "defaults"}  Scan.repeat parse_bound_term  @{keyword ")"}; 

901 

49112  902 
val parse_single_spec = 
903 
Parse.type_args_constrained  Parse.binding  Parse.opt_mixfix  

49119  904 
(@{keyword "="}  Parse.enum1 "" (parse_opt_binding_colon  Parse.binding  
49286  905 
Scan.repeat parse_ctr_arg  Scan.optional parse_defaults []  Parse.opt_mixfix)); 
49112  906 

49278  907 
val parse_datatype = parse_wrap_options  Parse.and_list1 parse_single_spec; 
908 

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

909 
fun parse_datatype_cmd lfp construct = parse_datatype >> datatype_cmd lfp construct; 
49112  910 

911 
end; 