author  blanchet 
Sat, 08 Sep 2012 21:04:26 +0200  
changeset 49204  0b735fb2602e 
parent 49203  262ab1ac38b9 
child 49205  674f04c737e0 
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 

4 

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Sugar for constructing LFPs and GFPs. 

6 
*) 

7 

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signature BNF_FP_SUGAR = 

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sig 

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end; 

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structure BNF_FP_Sugar : BNF_FP_SUGAR = 

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struct 

14 

49119  15 
open BNF_Util 
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open BNF_Wrap 

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open BNF_FP_Util 

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open BNF_LFP 

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open BNF_GFP 

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open BNF_FP_Sugar_Tactics 
49119  21 

49129  22 
val caseN = "case"; 
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val itersN = "iters"; 
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val recsN = "recs"; 
49129  25 

49199  26 
fun retype_free (Free (s, _)) T = Free (s, T); 
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fun flat_list_comb (f, xss) = fold (fn xs => fn t => Term.list_comb (t, xs)) xss f 
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49200  30 
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  33 
mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss); 
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49124  35 
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; 
49119  36 

37 
fun merge_type_arg_constrained ctxt (T, c) (T', c') = 

38 
if T = T' then 

39 
(case (c, c') of 

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

41 
 (NONE, _) => (T, c') 

42 
 _ => 

43 
if c = c' then 

44 
(T, c) 

45 
else 

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error ("Inconsistent sort constraints for type variable " ^ 

47 
quote (Syntax.string_of_typ ctxt T))) 

48 
else 

49 
cannot_merge_types (); 

50 

51 
fun merge_type_args_constrained ctxt (cAs, cAs') = 

52 
if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs' 

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else cannot_merge_types (); 

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49121  55 
fun type_args_constrained_of (((cAs, _), _), _) = cAs; 
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val type_args_of = map fst o type_args_constrained_of; 

49129  57 
fun type_binder_of (((_, b), _), _) = b; 
49181  58 
fun mixfix_of ((_, mx), _) = mx; 
49121  59 
fun ctr_specs_of (_, ctr_specs) = ctr_specs; 
49119  60 

49121  61 
fun disc_of (((disc, _), _), _) = disc; 
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fun ctr_of (((_, ctr), _), _) = ctr; 

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

49181  64 
fun ctr_mixfix_of (_, mx) = mx; 
49119  65 

49204  66 
fun prepare_datatype prepare_typ gfp specs fake_lthy no_defs_lthy = 
49112  67 
let 
49121  68 
val constrained_As = 
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map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs 

49204  70 
> Library.foldr1 (merge_type_args_constrained no_defs_lthy); 
49121  71 
val As = map fst constrained_As; 
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val As' = map dest_TFree As; 
49119  73 

49121  74 
val _ = (case duplicates (op =) As of [] => () 
49204  75 
 A :: _ => error ("Duplicate type parameter " ^ 
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quote (Syntax.string_of_typ no_defs_lthy A))); 

49119  77 

78 
(* TODO: use sort constraints on type args *) 

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80 
val N = length specs; 

81 

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fun mk_fake_T b = 
49121  83 
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), 
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As); 

85 

49129  86 
val bs = map type_binder_of specs; 
49204  87 
val fakeTs = map mk_fake_T bs; 
49121  88 

49181  89 
val mixfixes = map mixfix_of specs; 
49119  90 

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

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

93 

49121  94 
val ctr_specss = map ctr_specs_of specs; 
49119  95 

49129  96 
val disc_binderss = map (map disc_of) ctr_specss; 
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val ctr_binderss = map (map ctr_of) ctr_specss; 

49121  98 
val ctr_argsss = map (map args_of) ctr_specss; 
49181  99 
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; 
49119  100 

49129  101 
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  103 

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val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; 
49167  105 
val _ = (case subtract (op =) As' rhs_As' of 
49165  106 
[] => () 
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 A' :: _ => error ("Extra type variables on rhs: " ^ 

49204  108 
quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); 
49165  109 

49176  110 
val ((Cs, Xs), _) = 
49204  111 
no_defs_lthy 
49121  112 
> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs 
113 
> mk_TFrees N 

49176  114 
>> mk_TFrees N; 
49119  115 

49204  116 
fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) = 
49146  117 
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ 
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quote (Syntax.string_of_typ fake_lthy T))) 

49204  119 
 eq_fpT _ _ = false; 
49146  120 

49204  121 
fun freeze_fp (T as Type (s, Us)) = 
122 
(case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us)  j => nth Xs j) 

123 
 freeze_fp T = T; 

49121  124 

49204  125 
val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss; 
49176  126 
val sum_prod_TsXs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssXs; 
49119  127 

49176  128 
val eqs = map dest_TFree Xs ~~ sum_prod_TsXs; 
49121  129 

49204  130 
val ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects), lthy) = 
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fp_bnf (if gfp then bnf_gfp else bnf_lfp) bs mixfixes As' eqs no_defs_lthy; 

49121  132 

49167  133 
val timer = time (Timer.startRealTimer ()); 
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49176  135 
fun mk_unf_or_fld get_T Ts t = 
136 
let val Type (_, Ts0) = get_T (fastype_of t) in 

49124  137 
Term.subst_atomic_types (Ts0 ~~ Ts) t 
49121  138 
end; 
49119  139 

49126  140 
val mk_unf = mk_unf_or_fld domain_type; 
141 
val mk_fld = mk_unf_or_fld range_type; 

49121  142 

49203  143 
val unfs = map (mk_unf As) unfs0; 
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val flds = map (mk_fld As) flds0; 

49124  145 

49201  146 
val fpTs = map (domain_type o fastype_of) unfs; 
49204  147 
val is_fpT = member (op =) fpTs; 
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49201  149 
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs; 
49203  150 
val ns = map length ctr_Tsss; 
151 
val mss = map (map length) ctr_Tsss; 

152 
val Css = map2 replicate ns Cs; 

153 
val Cs' = flat Css; 

154 

155 
fun mk_iter_or_rec Ts Us c = 

49121  156 
let 
49201  157 
val (binders, body) = strip_type (fastype_of c); 
49203  158 
val (fst_binders, last_binder) = split_last binders; 
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val Type (_, Ts0) = if gfp then body else last_binder; 

160 
val Us0 = map (if gfp then domain_type else body_type) fst_binders; 

49176  161 
in 
49201  162 
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) c 
49176  163 
end; 
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49204  165 
val fp_iters as fp_iter1 :: _ = map (mk_iter_or_rec As Cs) fp_iters0; 
166 
val fp_recs as fp_rec1 :: _ = map (mk_iter_or_rec As Cs) fp_recs0; 

167 

168 
val fp_y_Ts = map domain_type (fst (split_last (binder_types (fastype_of fp_iter1)))); 

169 
val y_Tsss = map3 (fn ms => map2 dest_tupleT ms oo dest_sumTN) mss ns fp_y_Ts; 

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val g_Tss = map2 (map2 (curry (op >))) y_Tsss Css; 

171 

172 
fun dest_rec_pair (T as Type (@{type_name prod}, Us as [_, U])) = 

173 
if member (op =) Cs U then Us else [T] 

174 
 dest_rec_pair T = [T]; 

175 

176 
val fp_z_Ts = map domain_type (fst (split_last (binder_types (fastype_of fp_rec1)))); 

177 
val z_Tssss = 

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map3 (fn ms => map2 (map dest_rec_pair oo dest_tupleT) ms oo dest_sumTN) mss ns fp_z_Ts; 

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val h_Tss = map2 (map2 (fold_rev (curry (op >)))) z_Tssss Css; 

180 

181 
val ((gss, ysss), _) = 

182 
lthy 

183 
> mk_Freess "f" g_Tss 

184 
>> mk_Freesss "x" y_Tsss; 

185 

186 
val hss = map2 (map2 retype_free) gss h_Tss; 

187 
val (zssss, _) = 

188 
lthy 

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> mk_Freessss "x" z_Tssss; 

49176  190 

49201  191 
fun pour_sugar_on_type ((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec), fld_unf), 
49176  192 
unf_fld), fld_inject), ctr_binders), ctr_mixfixes), ctr_Tss), disc_binders), sel_binderss) 
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no_defs_lthy = 

194 
let 

195 
val n = length ctr_Tss; 

49121  196 
val ks = 1 upto n; 
197 
val ms = map length ctr_Tss; 

198 

49201  199 
val unfT = domain_type (fastype_of fld); 
49121  200 
val prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
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val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  202 

49176  203 
val ((((u, v), fs), xss), _) = 
49204  204 
no_defs_lthy 
49201  205 
> yield_singleton (mk_Frees "u") unfT 
206 
>> yield_singleton (mk_Frees "v") fpT 

49176  207 
>> mk_Frees "f" case_Ts 
49124  208 
>> mk_Freess "x" ctr_Tss; 
49121  209 

49129  210 
val ctr_rhss = 
49121  211 
map2 (fn k => fn xs => 
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fold_rev Term.lambda xs (fld $ mk_InN prod_Ts (HOLogic.mk_tuple xs) k)) ks xss; 

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val case_binder = Binding.suffix_name ("_" ^ caseN) b; 
49129  215 

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val case_rhs = 
49176  217 
fold_rev Term.lambda (fs @ [v]) (mk_sum_caseN (map2 mk_uncurried_fun fs xss) $ (unf $ v)); 
49129  218 

49201  219 
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy 
49169  220 
> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => 
221 
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 

49201  222 
(case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) 
49121  223 
> `Local_Theory.restore; 
224 

225 
(*transforms defined frees into consts (and more)*) 

226 
val phi = Proof_Context.export_morphism lthy lthy'; 

227 

228 
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; 

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val case_def = Morphism.thm phi raw_case_def; 
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49203  231 
val ctrs0 = map (Morphism.term phi) raw_ctrs; 
232 
val casex0 = Morphism.term phi raw_case; 

233 

234 
val ctrs = map (mk_ctr As) ctrs0; 

49121  235 

49135  236 
fun exhaust_tac {context = ctxt, ...} = 
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let 
49135  238 
val fld_iff_unf_thm = 
239 
let 

240 
val goal = 

241 
fold_rev Logic.all [u, v] 

242 
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u))); 

243 
in 

244 
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => 

49201  245 
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT]) 
49176  246 
(certify lthy fld) (certify lthy unf) fld_unf unf_fld) 
49135  247 
> Thm.close_derivation 
248 
> Morphism.thm phi 

249 
end; 

250 

251 
val sumEN_thm' = 

252 
Local_Defs.unfold lthy @{thms all_unit_eq} 

253 
(Drule.instantiate' (map (SOME o certifyT lthy) prod_Ts) [] (mk_sumEN n)) 

254 
> Morphism.thm phi; 

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in 
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mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm' 
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end; 
49121  258 

49126  259 
val inject_tacss = 
260 
map2 (fn 0 => K [] 

261 
 _ => fn ctr_def => [fn {context = ctxt, ...} => 

262 
mk_inject_tac ctxt ctr_def fld_inject]) 

263 
ms ctr_defs; 

264 

49127  265 
val half_distinct_tacss = 
266 
map (map (fn (def, def') => fn {context = ctxt, ...} => 

267 
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs); 

268 

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val case_tacs = 
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map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => 
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mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs; 
49121  272 

273 
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; 

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49199  275 
fun sugar_datatype no_defs_lthy = 
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let 
49201  277 
val iter_T = flat g_Tss > fpT > C; 
278 
val rec_T = flat h_Tss > fpT > C; 

49199  279 

280 
val iter_binder = Binding.suffix_name ("_" ^ iterN) b; 

281 
val rec_binder = Binding.suffix_name ("_" ^ recN) b; 

282 

283 
val iter_free = Free (Binding.name_of iter_binder, iter_T); 

284 
val rec_free = Free (Binding.name_of rec_binder, rec_T); 

285 

286 
val iter_spec = 

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mk_Trueprop_eq (flat_list_comb (iter_free, gss), 
49199  288 
Term.list_comb (fp_iter, map2 (mk_sum_caseN oo map2 mk_uncurried_fun) gss ysss)); 
289 
val rec_spec = 

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mk_Trueprop_eq (flat_list_comb (rec_free, hss), 
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Term.list_comb (fp_rec, map2 (mk_sum_caseN oo map2 mk_uncurried2_fun) hss zssss)); 
49199  292 

293 
val (([raw_iter, raw_rec], [raw_iter_def, raw_rec_def]), (lthy', lthy)) = no_defs_lthy 

49201  294 
> apfst split_list o fold_map2 (fn b => fn spec => 
49199  295 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 
49201  296 
#>> apsnd snd) [iter_binder, rec_binder] [iter_spec, rec_spec] 
49199  297 
> `Local_Theory.restore; 
49201  298 

299 
(*transforms defined frees into consts (and more)*) 

300 
val phi = Proof_Context.export_morphism lthy lthy'; 

301 

302 
val iter_def = Morphism.thm phi raw_iter_def; 

303 
val rec_def = Morphism.thm phi raw_rec_def; 

304 

49203  305 
val iter0 = Morphism.term phi raw_iter; 
306 
val rec0 = Morphism.term phi raw_rec; 

307 

308 
val iter = mk_iter_or_rec As Cs' iter0; 

309 
val recx = mk_iter_or_rec As Cs' rec0; 

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in 
49204  311 
([[ctrs], [[iter]], [[recx]], xss], lthy) 
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end; 
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fun sugar_codatatype no_defs_lthy = ([], no_defs_lthy); 
49119  315 
in 
49203  316 
wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy' 
49199  317 
> (if gfp then sugar_codatatype else sugar_datatype) 
49119  318 
end; 
49167  319 

49204  320 
fun pour_more_sugar_on_datatypes ([[ctrss], [[iters]], [[recs]], xsss], lthy) = 
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let 
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val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; 
49204  323 
val giters = map (fn iter => flat_list_comb (iter, gss)) iters; 
324 
val hrecs = map (fn recx => flat_list_comb (recx, hss)) recs; 

49201  325 

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val (iter_thmss, rec_thmss) = 
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let 
49204  328 
fun mk_goal_iter_or_rec fss fc xctr f xs xs' = 
329 
mk_Trueprop_eq (fc $ xctr, Term.list_comb (f, xs')); 

330 

331 
fun fix_iter_free (x as Free (_, T)) = 

332 
(case find_index (eq_fpT T) fpTs of ~1 => x  j => nth giters j $ x); 

333 
fun fix_rec_free (x as Free (_, T)) = 

334 
(case find_index (eq_fpT T) fpTs of ~1 => [x]  j => [x, nth hrecs j $ x]); 

49201  335 

49204  336 
val iter_xsss = map (map (map fix_iter_free)) xsss; 
337 
val rec_xsss = map (map (maps fix_rec_free)) xsss; 

338 

339 
val goal_iterss = 

340 
map5 (map4 o mk_goal_iter_or_rec gss) giters xctrss gss xsss iter_xsss; 

341 
val goal_recss = 

342 
map5 (map4 o mk_goal_iter_or_rec hss) hrecs xctrss hss xsss rec_xsss; 

343 

49203  344 
val iter_tacss = 
345 
map (map (K (fn _ => Skip_Proof.cheat_tac (Proof_Context.theory_of lthy)))) goal_iterss; 

346 
(* ### map (map mk_iter_or_rec_tac); (* needs ctr_def, iter_def, fld_iter *) *) 

347 
val rec_tacss = 

348 
map (map (K (fn _ => Skip_Proof.cheat_tac (Proof_Context.theory_of lthy)))) goal_recss; 

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in 
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(map2 (map2 (Skip_Proof.prove lthy [] [])) goal_iterss iter_tacss, 
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map2 (map2 (Skip_Proof.prove lthy [] [])) goal_recss rec_tacss) 
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end; 
49201  353 

49202
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val notes = 
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[(itersN, iter_thmss), 
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(recsN, rec_thmss)] 
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> maps (fn (thmN, thmss) => 
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map2 (fn b => fn thms => 
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((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) 
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bs thmss); 
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in 
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lthy > Local_Theory.notes notes > snd 
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end; 
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364 

49204  365 
val lthy' = lthy 
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> fold_map pour_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~ fp_recs ~~ 
49176  367 
fld_unfs ~~ unf_flds ~~ fld_injects ~~ ctr_binderss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ 
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disc_binderss ~~ sel_bindersss) 
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> (if gfp then snd else pour_more_sugar_on_datatypes o apfst transpose); 
49167  370 

371 
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ 

372 
(if gfp then "co" else "") ^ "datatype")); 

49112  373 
in 
49204  374 
(timer; lthy') 
49112  375 
end; 
376 

49199  377 
fun datatype_cmd info specs lthy = 
49121  378 
let 
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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 = Theory.copy 
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#> fold (fn spec => perhaps (try (Sign.add_type lthy 
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(type_binder_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 lthy; 
49121  385 
in 
49199  386 
prepare_datatype Syntax.read_typ info specs fake_lthy lthy 
49121  387 
end; 
49119  388 

49129  389 
val parse_opt_binding_colon = Scan.optional (Parse.binding  Parse.$$$ ":") no_binder 
49119  390 

49112  391 
val parse_ctr_arg = 
49119  392 
Parse.$$$ "("  parse_opt_binding_colon  Parse.typ  Parse.$$$ ")"  
49129  393 
(Parse.typ >> pair no_binder); 
49112  394 

395 
val parse_single_spec = 

396 
Parse.type_args_constrained  Parse.binding  Parse.opt_mixfix  

49119  397 
(@{keyword "="}  Parse.enum1 "" (parse_opt_binding_colon  Parse.binding  
398 
Scan.repeat parse_ctr_arg  Parse.opt_mixfix)); 

49112  399 

400 
val _ = 

401 
Outer_Syntax.local_theory @{command_spec "data"} "define BNFbased inductive datatypes" 

49199  402 
(Parse.and_list1 parse_single_spec >> datatype_cmd false); 
49112  403 

404 
val _ = 

405 
Outer_Syntax.local_theory @{command_spec "codata"} "define BNFbased coinductive datatypes" 

49199  406 
(Parse.and_list1 parse_single_spec >> datatype_cmd true); 
49112  407 

408 
end; 