author  blanchet 
Tue, 11 Sep 2012 14:51:52 +0200  
changeset 49278  718e4ad1517e 
parent 49277  aee77001243f 
child 49280  52413dc96326 
permissions  rwrr 
49112  1 
(* Title: HOL/Codatatype/Tools/bnf_fp_sugar.ML 
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Author: Jasmin Blanchette, TU Muenchen 

3 
Copyright 2012 

4 

5 
Sugar for constructing LFPs and GFPs. 

6 
*) 

7 

8 
signature BNF_FP_SUGAR = 

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sig 

49205  10 
(* TODO: programmatic interface *) 
49112  11 
end; 
12 

13 
structure BNF_FP_Sugar : BNF_FP_SUGAR = 

14 
struct 

15 

49119  16 
open BNF_Util 
17 
open BNF_Wrap 

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open BNF_Def 
49119  19 
open BNF_FP_Util 
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open BNF_LFP 

21 
open BNF_GFP 

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open BNF_FP_Sugar_Tactics 
49119  23 

49129  24 
val caseN = "case"; 
49213  25 
val coitersN = "coiters"; 
26 
val corecsN = "corecs"; 

49266  27 
val disc_coitersN = "disc_coiters"; 
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val disc_corecsN = "disc_corecs"; 

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val itersN = "iters"; 
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val recsN = "recs"; 
49266  31 
val sel_coitersN = "sel_coiters"; 
32 
val sel_corecsN = "sel_corecs"; 

49129  33 

49266  34 
fun split_list11 xs = 
35 
(map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs, map #8 xs, 

36 
map #9 xs, map #10 xs, map #11 xs); 

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49217  38 
fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' >> cons T 
39 
 strip_map_type T = ([], T); 

40 

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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  46 

49199  47 
fun retype_free (Free (s, _)) T = Free (s, T); 
48 

49212  49 
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs)) 
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49275  51 
fun mk_predT T = T > HOLogic.boolT; 
52 

49234  53 
fun mk_id T = Const (@{const_name id}, T > T); 
54 

49200  55 
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs)); 
56 
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  58 
mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss); 
59 

49233  60 
fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v)); 
61 

62 
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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49124  67 
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; 
49119  68 

69 
fun merge_type_arg_constrained ctxt (T, c) (T', c') = 

70 
if T = T' then 

71 
(case (c, c') of 

72 
(_, NONE) => (T, c) 

73 
 (NONE, _) => (T, c') 

74 
 _ => 

75 
if c = c' then 

76 
(T, c) 

77 
else 

78 
error ("Inconsistent sort constraints for type variable " ^ 

79 
quote (Syntax.string_of_typ ctxt T))) 

80 
else 

81 
cannot_merge_types (); 

82 

83 
fun merge_type_args_constrained ctxt (cAs, cAs') = 

84 
if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs' 

85 
else cannot_merge_types (); 

86 

49121  87 
fun type_args_constrained_of (((cAs, _), _), _) = cAs; 
88 
val type_args_of = map fst o type_args_constrained_of; 

49129  89 
fun type_binder_of (((_, b), _), _) = b; 
49181  90 
fun mixfix_of ((_, mx), _) = mx; 
49121  91 
fun ctr_specs_of (_, ctr_specs) = ctr_specs; 
49119  92 

49121  93 
fun disc_of (((disc, _), _), _) = disc; 
94 
fun ctr_of (((_, ctr), _), _) = ctr; 

95 
fun args_of ((_, args), _) = args; 

49181  96 
fun ctr_mixfix_of (_, mx) = mx; 
49119  97 

49278  98 
fun prepare_datatype prepare_typ lfp (no_dests, specs) fake_lthy no_defs_lthy = 
49112  99 
let 
49278  100 
val _ = if not lfp andalso no_dests then error "Cannot use \"no_dests\" option for codatatypes" 
101 
else (); 

102 

49121  103 
val constrained_As = 
104 
map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs 

49204  105 
> Library.foldr1 (merge_type_args_constrained no_defs_lthy); 
49121  106 
val As = map fst constrained_As; 
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val As' = map dest_TFree As; 
49119  108 

49121  109 
val _ = (case duplicates (op =) As of [] => () 
49204  110 
 A :: _ => error ("Duplicate type parameter " ^ 
111 
quote (Syntax.string_of_typ no_defs_lthy A))); 

49119  112 

113 
(* TODO: use sort constraints on type args *) 

114 

115 
val N = length specs; 

116 

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fun mk_fake_T b = 
49121  118 
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), 
119 
As); 

120 

49129  121 
val bs = map type_binder_of specs; 
49204  122 
val fakeTs = map mk_fake_T bs; 
49121  123 

49181  124 
val mixfixes = map mixfix_of specs; 
49119  125 

126 
val _ = (case duplicates Binding.eq_name bs of [] => () 

127 
 b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); 

128 

49121  129 
val ctr_specss = map ctr_specs_of specs; 
49119  130 

49129  131 
val disc_binderss = map (map disc_of) ctr_specss; 
132 
val ctr_binderss = map (map ctr_of) ctr_specss; 

49121  133 
val ctr_argsss = map (map args_of) ctr_specss; 
49181  134 
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; 
49119  135 

49129  136 
val sel_bindersss = map (map (map fst)) ctr_argsss; 
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val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; 
49121  138 

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val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; 
49167  140 
val _ = (case subtract (op =) As' rhs_As' of 
49165  141 
[] => () 
142 
 A' :: _ => error ("Extra type variables on rhs: " ^ 

49204  143 
quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); 
49165  144 

49176  145 
val ((Cs, Xs), _) = 
49204  146 
no_defs_lthy 
49121  147 
> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs 
148 
> mk_TFrees N 

49176  149 
>> mk_TFrees N; 
49119  150 

49204  151 
fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) = 
49146  152 
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ 
153 
quote (Syntax.string_of_typ fake_lthy T))) 

49204  154 
 eq_fpT _ _ = false; 
49146  155 

49204  156 
fun freeze_fp (T as Type (s, Us)) = 
157 
(case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us)  j => nth Xs j) 

158 
 freeze_fp T = T; 

49121  159 

49204  160 
val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss; 
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val ctr_sum_prod_TsXs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctr_TsssXs; 
49119  162 

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val eqs = map dest_TFree Xs ~~ ctr_sum_prod_TsXs; 
49121  164 

49226  165 
val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects, 
49207  166 
fp_iter_thms, fp_rec_thms), lthy)) = 
49208  167 
fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy; 
49121  168 

49226  169 
val add_nested_bnf_names = 
170 
let 

171 
fun add (Type (s, Ts)) ss = 

172 
let val (needs, ss') = fold_map add Ts ss in 

173 
if exists I needs then (true, insert (op =) s ss') else (false, ss') 

174 
end 

175 
 add T ss = (member (op =) As T, ss); 

176 
in snd oo add end; 

177 

178 
val nested_bnfs = 

49236  179 
map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssXs []); 
49226  180 

49167  181 
val timer = time (Timer.startRealTimer ()); 
182 

49176  183 
fun mk_unf_or_fld get_T Ts t = 
184 
let val Type (_, Ts0) = get_T (fastype_of t) in 

49124  185 
Term.subst_atomic_types (Ts0 ~~ Ts) t 
49121  186 
end; 
49119  187 

49126  188 
val mk_unf = mk_unf_or_fld domain_type; 
189 
val mk_fld = mk_unf_or_fld range_type; 

49121  190 

49203  191 
val unfs = map (mk_unf As) unfs0; 
192 
val flds = map (mk_fld As) flds0; 

49124  193 

49201  194 
val fpTs = map (domain_type o fastype_of) unfs; 
49204  195 

49201  196 
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs; 
49203  197 
val ns = map length ctr_Tsss; 
49212  198 
val kss = map (fn n => 1 upto n) ns; 
49203  199 
val mss = map (map length) ctr_Tsss; 
200 
val Css = map2 replicate ns Cs; 

201 

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fun mk_iter_like Ts Us t = 
49121  203 
let 
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val (binders, body) = strip_type (fastype_of t); 
49210  205 
val (f_Us, prebody) = split_last binders; 
206 
val Type (_, Ts0) = if lfp then prebody else body; 

207 
val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us); 

49176  208 
in 
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Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
49176  210 
end; 
211 

49210  212 
val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0; 
213 
val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0; 

214 

49212  215 
val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1))); 
216 
val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1))); 

49204  217 

49256  218 
val ((iter_only as (gss, _, _), rec_only as (hss, _, _)), 
49276  219 
(zs, cs, cpss, coiter_only as ((pgss, crgsss), _), corec_only as ((phss, cshsss), _))) = 
49208  220 
if lfp then 
221 
let 

222 
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  224 
ns mss fp_iter_fun_Ts; 
49208  225 
val g_Tss = map2 (map2 (curry (op >))) y_Tsss Css; 
226 

227 
val ((gss, ysss), _) = 

228 
lthy 

229 
> mk_Freess "f" g_Tss 

230 
>> mk_Freesss "x" y_Tsss; 

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val yssss = map (map (map single)) ysss; 
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fun dest_rec_prodT (T as Type (@{type_name prod}, Us as [_, U])) = 
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if member (op =) Cs U then Us else [T] 
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 dest_rec_prodT T = [T]; 
49204  236 

49208  237 
val z_Tssss = 
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map3 (fn n => fn ms => map2 (map dest_rec_prodT oo dest_tupleT) ms o 
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dest_sumTN_balanced n o domain_type) ns mss fp_rec_fun_Ts; 
49208  240 
val h_Tss = map2 (map2 (fold_rev (curry (op >)))) z_Tssss Css; 
49204  241 

49208  242 
val hss = map2 (map2 retype_free) gss h_Tss; 
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val zssss_hd = map2 (map2 (map2 (fn y => fn T :: _ => retype_free y T))) ysss z_Tssss; 
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val (zssss_tl, _) = 
49208  245 
lthy 
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> mk_Freessss "y" (map (map (map tl)) z_Tssss); 
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val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl; 
49210  248 
in 
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(((gss, g_Tss, yssss), (hss, h_Tss, zssss)), 
49276  250 
([], [], [], (([], []), ([], [])), (([], []), ([], [])))) 
49210  251 
end 
49208  252 
else 
49210  253 
let 
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(*avoid "'a itself" arguments in coiterators and corecursors*) 
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val mss' = map (fn [0] => [1]  ms => ms) mss; 
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256 

49275  257 
val p_Tss = map2 (fn n => replicate (Int.max (0, n  1)) o mk_predT) ns Cs; 
258 

49276  259 
fun zip_predss_getterss qss fss = maps (op @) (qss ~~ fss); 
49211  260 

49276  261 
fun zip_preds_predsss_gettersss [] [qss] [fss] = zip_predss_getterss qss fss 
262 
 zip_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) = 

263 
p :: zip_predss_getterss qss fss @ zip_preds_predsss_gettersss ps qsss fsss; 

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fun mk_types maybe_dest_sumT fun_Ts = 
49212  266 
let 
267 
val f_sum_prod_Ts = map range_type fun_Ts; 

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val f_prod_Tss = map2 dest_sumTN_balanced ns f_sum_prod_Ts; 
49275  269 
val f_Tssss = 
270 
map3 (fn C => map2 (map (map (curry (op >) C) o maybe_dest_sumT) oo dest_tupleT)) 

271 
Cs mss' f_prod_Tss; 

272 
val q_Tssss = 

273 
map (map (map (fn [_] => []  [_, C] => [mk_predT (domain_type C)]))) f_Tssss; 

49276  274 
val pf_Tss = map3 zip_preds_predsss_gettersss p_Tss q_Tssss f_Tssss; 
49275  275 
in (q_Tssss, f_sum_prod_Ts, f_Tssss, pf_Tss) end; 
49176  276 

49275  277 
val (r_Tssss, g_sum_prod_Ts, g_Tssss, pg_Tss) = mk_types single fp_iter_fun_Ts; 
49211  278 

49275  279 
val ((((Free (z, _), cs), pss), gssss), _) = 
49210  280 
lthy 
49233  281 
> yield_singleton (mk_Frees "z") dummyT 
282 
>> mk_Frees "a" Cs 

49211  283 
>> mk_Freess "p" p_Tss 
49275  284 
>> mk_Freessss "g" g_Tssss; 
285 
val rssss = map (map (map (fn [] => []))) r_Tssss; 

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fun dest_corec_sumT (T as Type (@{type_name sum}, Us as [_, U])) = 
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if member (op =) Cs U then Us else [T] 
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 dest_corec_sumT T = [T]; 
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290 

49275  291 
val (s_Tssss, h_sum_prod_Ts, h_Tssss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts; 
49210  292 

49275  293 
val hssss_hd = map2 (map2 (map2 (fn [g] => fn T :: _ => retype_free g T))) gssss h_Tssss; 
294 
val ((sssss, hssss_tl), _) = 

295 
lthy 

296 
> mk_Freessss "q" s_Tssss 

297 
>> mk_Freessss "h" (map (map (map tl)) h_Tssss); 

298 
val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl; 

49211  299 

49212  300 
val cpss = map2 (fn c => map (fn p => p $ c)) cs pss; 
301 

49276  302 
fun mk_preds_getters_join [] [cf] = cf 
303 
 mk_preds_getters_join [cq] [cf, cf'] = 

304 
mk_If cq (mk_Inl (fastype_of cf') cf) (mk_Inr (fastype_of cf) cf'); 

305 

49275  306 
fun mk_terms qssss fssss = 
49212  307 
let 
49276  308 
val pfss = map3 zip_preds_predsss_gettersss pss qssss fssss; 
49275  309 
val cqssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs qssss; 
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310 
val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss; 
49276  311 
val cqfsss = map2 (map2 (map2 mk_preds_getters_join)) cqssss cfssss; 
312 
in (pfss, cqfsss) end; 

49210  313 
in 
49212  314 
((([], [], []), ([], [], [])), 
49275  315 
([z], cs, cpss, (mk_terms rssss gssss, (g_sum_prod_Ts, pg_Tss)), 
316 
(mk_terms sssss hssss, (h_sum_prod_Ts, ph_Tss)))) 

49210  317 
end; 
318 

49212  319 
fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec), 
320 
fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss), 

321 
disc_binders), sel_binderss) no_defs_lthy = 

49176  322 
let 
49201  323 
val unfT = domain_type (fastype_of fld); 
49210  324 
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
49255
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325 
val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts; 
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326 
val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  327 

49176  328 
val ((((u, v), fs), xss), _) = 
49204  329 
no_defs_lthy 
49201  330 
> yield_singleton (mk_Frees "u") unfT 
331 
>> yield_singleton (mk_Frees "v") fpT 

49176  332 
>> mk_Frees "f" case_Ts 
49124  333 
>> mk_Freess "x" ctr_Tss; 
49121  334 

49129  335 
val ctr_rhss = 
49256  336 
map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $ 
337 
mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss; 

49121  338 

49130
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49129
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changeset

339 
val case_binder = Binding.suffix_name ("_" ^ caseN) b; 
49129  340 

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341 
val case_rhs = 
49255
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342 
fold_rev Term.lambda (fs @ [v]) 
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343 
(mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v)); 
49129  344 

49201  345 
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy 
49169  346 
> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => 
347 
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 

49201  348 
(case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) 
49121  349 
> `Local_Theory.restore; 
350 

351 
(*transforms defined frees into consts (and more)*) 

352 
val phi = Proof_Context.export_morphism lthy lthy'; 

353 

354 
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; 

49130
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49129
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changeset

355 
val case_def = Morphism.thm phi raw_case_def; 
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parents:
49129
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changeset

356 

49203  357 
val ctrs0 = map (Morphism.term phi) raw_ctrs; 
358 
val casex0 = Morphism.term phi raw_case; 

359 

360 
val ctrs = map (mk_ctr As) ctrs0; 

49121  361 

49135  362 
fun exhaust_tac {context = ctxt, ...} = 
49123
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changeset

363 
let 
49135  364 
val fld_iff_unf_thm = 
365 
let 

366 
val goal = 

367 
fold_rev Logic.all [u, v] 

368 
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u))); 

369 
in 

370 
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => 

49201  371 
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT]) 
49176  372 
(certify lthy fld) (certify lthy unf) fld_unf unf_fld) 
49135  373 
> Thm.close_derivation 
374 
> Morphism.thm phi 

375 
end; 

376 

377 
val sumEN_thm' = 

378 
Local_Defs.unfold lthy @{thms all_unit_eq} 

49255
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changeset

379 
(Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) [] 
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changeset

380 
(mk_sumEN_balanced n)) 
49135  381 
> Morphism.thm phi; 
49123
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parents:
49121
diff
changeset

382 
in 
49161
a8e74375d971
fixed (n + 1)st bug in "mk_exhaust_tac"  arose with uncurried constructors
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parents:
49157
diff
changeset

383 
mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm' 
49123
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parents:
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diff
changeset

384 
end; 
49121  385 

49126  386 
val inject_tacss = 
49205  387 
map2 (fn 0 => K []  _ => fn ctr_def => [fn {context = ctxt, ...} => 
388 
mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs; 

49126  389 

49127  390 
val half_distinct_tacss = 
391 
map (map (fn (def, def') => fn {context = ctxt, ...} => 

392 
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs); 

393 

49130
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parents:
49129
diff
changeset

394 
val case_tacs = 
3c26e17b2849
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parents:
49129
diff
changeset

395 
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => 
3c26e17b2849
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blanchet
parents:
49129
diff
changeset

396 
mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs; 
49121  397 

398 
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; 

49134
846264f80f16
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blanchet
parents:
49130
diff
changeset

399 

49267
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correctly generate sel_coiter and sel_corec theorems
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49266
diff
changeset

400 
fun some_lfp_sugar ((selss0, discIs, sel_thmss), no_defs_lthy) = 
49134
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parents:
49130
diff
changeset

401 
let 
49208  402 
val fpT_to_C = fpT > C; 
49199  403 

49215  404 
fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) = 
405 
let 

406 
val res_T = fold_rev (curry (op >)) f_Tss fpT_to_C; 

407 

408 
val binder = Binding.suffix_name ("_" ^ suf) b; 

49199  409 

49215  410 
val spec = 
411 
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)), 

412 
Term.list_comb (fp_iter_like, 

49255
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parents:
49254
diff
changeset

413 
map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss)); 
49215  414 
in (binder, spec) end; 
49199  415 

49274
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parents:
49273
diff
changeset

416 
val iter_like_bundles = 
49215  417 
[(iterN, fp_iter, iter_only), 
418 
(recN, fp_rec, rec_only)]; 

419 

49274
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parents:
49273
diff
changeset

420 
val (binders, specs) = map generate_iter_like iter_like_bundles > split_list; 
49215  421 

422 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49201  423 
> apfst split_list o fold_map2 (fn b => fn spec => 
49199  424 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 
49215  425 
#>> apsnd snd) binders specs 
49199  426 
> `Local_Theory.restore; 
49201  427 

428 
(*transforms defined frees into consts (and more)*) 

429 
val phi = Proof_Context.export_morphism lthy lthy'; 

430 

49215  431 
val [iter_def, rec_def] = map (Morphism.thm phi) defs; 
49201  432 

49215  433 
val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts; 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

434 
in 
49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

435 
((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def), 
49266  436 
lthy) 
49134
846264f80f16
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blanchet
parents:
49130
diff
changeset

437 
end; 
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

438 

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

439 
fun some_gfp_sugar ((selss0, discIs, sel_thmss), no_defs_lthy) = 
49210  440 
let 
441 
val B_to_fpT = C > fpT; 

49211  442 

49276  443 
fun mk_preds_getterss_join c n cps sum_prod_T cqfss = 
444 
Term.lambda c (mk_IfN sum_prod_T cps 

445 
(map2 (mk_InN_balanced sum_prod_T n) (map HOLogic.mk_tuple cqfss) (1 upto n))); 

49275  446 

49276  447 
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
blanchet
parents:
49273
diff
changeset

448 
pf_Tss))) = 
49211  449 
let 
450 
val res_T = fold_rev (curry (op >)) pf_Tss B_to_fpT; 

49210  451 

49211  452 
val binder = Binding.suffix_name ("_" ^ suf) b; 
49210  453 

49211  454 
val spec = 
49212  455 
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)), 
49211  456 
Term.list_comb (fp_iter_like, 
49276  457 
map5 mk_preds_getterss_join cs ns cpss f_sum_prod_Ts cqfsss)); 
49211  458 
in (binder, spec) end; 
49210  459 

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

460 
val coiter_like_bundles = 
49215  461 
[(coiterN, fp_iter, coiter_only), 
462 
(corecN, fp_rec, corec_only)]; 

49212  463 

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

464 
val (binders, specs) = map generate_coiter_like coiter_like_bundles > split_list; 
49211  465 

466 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49210  467 
> apfst split_list o fold_map2 (fn b => fn spec => 
468 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 

49211  469 
#>> apsnd snd) binders specs 
49210  470 
> `Local_Theory.restore; 
471 

472 
(*transforms defined frees into consts (and more)*) 

473 
val phi = Proof_Context.export_morphism lthy lthy'; 

474 

49211  475 
val [coiter_def, corec_def] = map (Morphism.thm phi) defs; 
49210  476 

49211  477 
val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts; 
49210  478 
in 
49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

479 
((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def, 
49266  480 
corec_def), lthy) 
49210  481 
end; 
49119  482 
in 
49278  483 
wrap_datatype tacss (((no_dests, ctrs0), casex0), (disc_binders, sel_binderss)) lthy' 
49210  484 
> (if lfp then some_lfp_sugar else some_gfp_sugar) 
49119  485 
end; 
49167  486 

49226  487 
val pre_map_defs = map map_def_of_bnf pre_bnfs; 
49229
d5717b5e2217
use map_id, not map_id', to allow better composition
blanchet
parents:
49226
diff
changeset

488 
val map_ids = map map_id_of_bnf nested_bnfs; 
49226  489 

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

490 
fun mk_map Ts Us t = 
49217  491 
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

492 
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

493 
end; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

494 

49234  495 
fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) = 
496 
let 

49236  497 
val map0 = map_of_bnf (the (bnf_of lthy s)); 
49234  498 
val mapx = mk_map Ts Us map0; 
499 
val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx))))); 

500 
val args = map build_arg TUs; 

501 
in Term.list_comb (mapx, args) end; 

502 

49266  503 
fun pour_more_sugar_on_lfps ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, iter_defs, 
504 
rec_defs), lthy) = 

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

505 
let 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

506 
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; 
49212  507 
val giters = map (lists_bmoc gss) iters; 
508 
val hrecs = map (lists_bmoc hss) recs; 

49201  509 

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

510 
val (iter_thmss, rec_thmss) = 
49207  511 
let 
49212  512 
fun mk_goal_iter_like fss fiter_like xctr f xs fxs = 
49207  513 
fold_rev (fold_rev Logic.all) (xs :: fss) 
49212  514 
(mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs))); 
49204  515 

49234  516 
fun build_call fiter_likes maybe_tick (T, U) = 
517 
if T = U then 

518 
mk_id T 

519 
else 

520 
(case find_index (curry (op =) T) fpTs of 

521 
~1 => build_map (build_call fiter_likes maybe_tick) T U 

522 
 j => maybe_tick (nth vs j) (nth fiter_likes j)); 

49233  523 

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

524 
fun mk_U maybe_mk_prodT = 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

525 
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

526 

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

527 
fun repair_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

528 
if member (op =) fpTs T then 
49233  529 
maybe_cons x [build_call fiter_likes (K I) (T, mk_U (K I) T) $ x] 
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

530 
else if exists_subtype (member (op =) fpTs) T then 
49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

531 
[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

532 
else 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

533 
[x]; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

534 

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

535 
val gxsss = map (map (maps (repair_calls giters (K I) (K I) (K I)))) xsss; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

536 
val hxsss = 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

537 
map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss; 
49204  538 

49212  539 
val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss; 
540 
val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss; 

49204  541 

49203  542 
val iter_tacss = 
49229
d5717b5e2217
use map_id, not map_id', to allow better composition
blanchet
parents:
49226
diff
changeset

543 
map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss; 
49203  544 
val rec_tacss = 
49229
d5717b5e2217
use map_id, not map_id', to allow better composition
blanchet
parents:
49226
diff
changeset

545 
map2 (map o mk_iter_like_tac pre_map_defs map_ids rec_defs) fp_rec_thms ctr_defss; 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

546 
in 
49276  547 
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 
49205  548 
goal_iterss iter_tacss, 
49276  549 
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 
49205  550 
goal_recss rec_tacss) 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

551 
end; 
49201  552 

49226  553 
val notes = 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

554 
[(itersN, iter_thmss), 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

555 
(recsN, rec_thmss)] 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

556 
> maps (fn (thmN, thmss) => 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

557 
map2 (fn b => fn thms => 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

558 
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

559 
bs thmss); 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

560 
in 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

561 
lthy > Local_Theory.notes notes > snd 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

562 
end; 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

563 

49266  564 
fun pour_more_sugar_on_gfps ((ctrss, selsss, coiters, corecs, vs, _, ctr_defss, discIss, 
565 
sel_thmsss, coiter_defs, corec_defs), lthy) = 

49212  566 
let 
49233  567 
val z = the_single zs; 
568 

49212  569 
val gcoiters = map (lists_bmoc pgss) coiters; 
570 
val hcorecs = map (lists_bmoc phss) corecs; 

571 

572 
val (coiter_thmss, corec_thmss) = 

573 
let 

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

574 
fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not); 
49212  575 

49276  576 
fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfs' = 
49212  577 
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

578 
(Logic.list_implies (seq_conds mk_goal_cond n k cps, 
49276  579 
mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, take m cfs')))); 
49212  580 

49234  581 
fun build_call fiter_likes maybe_tack (T, U) = 
582 
if T = U then 

583 
mk_id T 

584 
else 

585 
(case find_index (curry (op =) U) fpTs of 

586 
~1 => build_map (build_call fiter_likes maybe_tack) T U 

587 
 j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j)); 

49233  588 

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

589 
fun mk_U maybe_mk_sumT = 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

590 
typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs); 
49212  591 

49276  592 
fun repair_calls fiter_likes maybe_mk_sumT maybe_tack cqf = 
593 
let val T = fastype_of cqf in 

594 
if exists_subtype (member (op =) Cs) T then 

595 
build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cqf 

596 
else 

597 
cqf 

598 
end; 

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

599 

49276  600 
val crgsss' = map (map (map (repair_calls gcoiters (K I) (K I)))) crgsss; 
601 
val cshsss' = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) cshsss; 

49212  602 

603 
val goal_coiterss = 

49276  604 
map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss crgsss'; 
49233  605 
val goal_corecss = 
49276  606 
map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss cshsss'; 
49213  607 

608 
val coiter_tacss = 

49229
d5717b5e2217
use map_id, not map_id', to allow better composition
blanchet
parents:
49226
diff
changeset

609 
map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs 
49226  610 
ctr_defss; 
49233  611 
val corec_tacss = 
612 
map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs 

613 
ctr_defss; 

49212  614 
in 
49276  615 
(map2 (map2 (fn goal => fn tac => 
616 
Skip_Proof.prove lthy [] [] goal (tac o #context) > Thm.close_derivation)) 

49213  617 
goal_coiterss coiter_tacss, 
49276  618 
map2 (map2 (fn goal => fn tac => 
619 
Skip_Proof.prove lthy [] [] goal (tac o #context) 

620 
> Local_Defs.unfold lthy @{thms sum_case_if} > Thm.close_derivation)) 

49233  621 
goal_corecss corec_tacss) 
49212  622 
end; 
623 

49266  624 
fun mk_disc_coiter_like_thms [_] = K [] 
625 
 mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms; 

626 

627 
val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss; 

628 
val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss; 

629 

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

630 
fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm = 
49266  631 
let 
49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

632 
val (domT, ranT) = dest_funT (fastype_of sel0); 
49266  633 
val arg_cong' = 
634 
Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT]) 

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

635 
[NONE, NONE, SOME (certify lthy sel0)] arg_cong 
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

636 
> Thm.varifyT_global; 
49266  637 
val sel_thm' = sel_thm RSN (2, trans); 
638 
in 

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

639 
coiter_like_thm RS arg_cong' RS sel_thm' 
49266  640 
end; 
641 

642 
val sel_coiter_thmsss = 

643 
map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss; 

644 
val sel_corec_thmsss = 

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

645 
map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss; 
49266  646 

49212  647 
val notes = 
49233  648 
[(coitersN, coiter_thmss), 
49266  649 
(disc_coitersN, disc_coiter_thmss), 
650 
(sel_coitersN, map flat sel_coiter_thmsss), 

651 
(corecsN, corec_thmss), 

652 
(disc_corecsN, disc_corec_thmss), 

653 
(sel_corecsN, map flat sel_corec_thmsss)] 

49212  654 
> maps (fn (thmN, thmss) => 
49266  655 
map_filter (fn (_, []) => NONE  (b, thms) => 
656 
SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), 

657 
[(thms, [])])) (bs ~~ thmss)); 

49212  658 
in 
49230  659 
lthy > Local_Theory.notes notes > snd 
49212  660 
end; 
661 

49204  662 
val lthy' = lthy 
49210  663 
> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~ 
49212  664 
fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~ 
665 
ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss) 

49266  666 
>> split_list11 
49212  667 
> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps); 
49167  668 

669 
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ 

49208  670 
(if lfp then "" else "co") ^ "datatype")); 
49112  671 
in 
49204  672 
(timer; lthy') 
49112  673 
end; 
674 

49278  675 
fun datatype_cmd lfp (bundle as (_, specs)) lthy = 
49121  676 
let 
49209  677 
(* TODO: cleaner handling of fake contexts, without "background_theory" *) 
49184
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset

678 
(*the "perhaps o try" below helps gracefully handles the case where the new type is defined in a 
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset

679 
locale and shadows an existing global type*) 
49179
f9d48d479c84
don't throw away the context when hacking the theory (first step to localize the sugar code)
blanchet
parents:
49177
diff
changeset

680 
val fake_thy = Theory.copy 
49184
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset

681 
#> fold (fn spec => perhaps (try (Sign.add_type lthy 
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset

682 
(type_binder_of spec, length (type_args_constrained_of spec), mixfix_of spec)))) specs; 
49179
f9d48d479c84
don't throw away the context when hacking the theory (first step to localize the sugar code)
blanchet
parents:
49177
diff
changeset

683 
val fake_lthy = Proof_Context.background_theory fake_thy lthy; 
49121  684 
in 
49278  685 
prepare_datatype Syntax.read_typ lfp bundle fake_lthy lthy 
49121  686 
end; 
49119  687 

49277  688 
val parse_opt_binding_colon = Scan.optional (Parse.binding  @{keyword ":"}) no_binder 
49119  689 

49112  690 
val parse_ctr_arg = 
49277  691 
@{keyword "("}  parse_opt_binding_colon  Parse.typ  @{keyword ")"}  
49129  692 
(Parse.typ >> pair no_binder); 
49112  693 

694 
val parse_single_spec = 

695 
Parse.type_args_constrained  Parse.binding  Parse.opt_mixfix  

49119  696 
(@{keyword "="}  Parse.enum1 "" (parse_opt_binding_colon  Parse.binding  
697 
Scan.repeat parse_ctr_arg  Parse.opt_mixfix)); 

49112  698 

49278  699 
val parse_datatype = parse_wrap_options  Parse.and_list1 parse_single_spec; 
700 

49112  701 
val _ = 
702 
Outer_Syntax.local_theory @{command_spec "data"} "define BNFbased inductive datatypes" 

49278  703 
(parse_datatype >> datatype_cmd true); 
49112  704 

705 
val _ = 

706 
Outer_Syntax.local_theory @{command_spec "codata"} "define BNFbased coinductive datatypes" 

49278  707 
(parse_datatype >> datatype_cmd false); 
49112  708 

709 
end; 