author  blanchet 
Sat, 08 Sep 2012 21:04:26 +0200  
changeset 49205  674f04c737e0 
parent 49204  0b735fb2602e 
child 49207  4634c217b77b 
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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Sugar for constructing LFPs and GFPs. 

6 
*) 

7 

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signature BNF_FP_SUGAR = 

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sig 

49205  10 
(* TODO: programmatic interface *) 
49112  11 
end; 
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structure BNF_FP_Sugar : BNF_FP_SUGAR = 

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struct 

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49119  16 
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  22 

49129  23 
val caseN = "case"; 
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val itersN = "iters"; 
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val recsN = "recs"; 
49129  26 

49205  27 
fun split_list7 xs = (map #1 xs, map #2 xs, map #3 xs, map #4 xs, map #5 xs, map #6 xs, map #7 xs); 
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49199  29 
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  33 
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  36 
mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss); 
37 

49124  38 
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; 
49119  39 

40 
fun merge_type_arg_constrained ctxt (T, c) (T', c') = 

41 
if T = T' then 

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(case (c, c') of 

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

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

45 
 _ => 

46 
if c = c' then 

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(T, c) 

48 
else 

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error ("Inconsistent sort constraints for type variable " ^ 

50 
quote (Syntax.string_of_typ ctxt T))) 

51 
else 

52 
cannot_merge_types (); 

53 

54 
fun merge_type_args_constrained ctxt (cAs, cAs') = 

55 
if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs' 

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else cannot_merge_types (); 

57 

49121  58 
fun type_args_constrained_of (((cAs, _), _), _) = cAs; 
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val type_args_of = map fst o type_args_constrained_of; 

49129  60 
fun type_binder_of (((_, b), _), _) = b; 
49181  61 
fun mixfix_of ((_, mx), _) = mx; 
49121  62 
fun ctr_specs_of (_, ctr_specs) = ctr_specs; 
49119  63 

49121  64 
fun disc_of (((disc, _), _), _) = disc; 
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fun ctr_of (((_, ctr), _), _) = ctr; 

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

49181  67 
fun ctr_mixfix_of (_, mx) = mx; 
49119  68 

49204  69 
fun prepare_datatype prepare_typ gfp specs fake_lthy no_defs_lthy = 
49112  70 
let 
49121  71 
val constrained_As = 
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map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs 

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> Library.foldr1 (merge_type_args_constrained no_defs_lthy); 
49121  74 
val As = map fst constrained_As; 
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val As' = map dest_TFree As; 
49119  76 

49121  77 
val _ = (case duplicates (op =) As of [] => () 
49204  78 
 A :: _ => error ("Duplicate type parameter " ^ 
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quote (Syntax.string_of_typ no_defs_lthy A))); 

49119  80 

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

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val N = length specs; 

84 

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

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49129  89 
val bs = map type_binder_of specs; 
49204  90 
val fakeTs = map mk_fake_T bs; 
49121  91 

49181  92 
val mixfixes = map mixfix_of specs; 
49119  93 

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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))); 

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49121  97 
val ctr_specss = map ctr_specs_of specs; 
49119  98 

49129  99 
val disc_binderss = map (map disc_of) ctr_specss; 
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val ctr_binderss = map (map ctr_of) ctr_specss; 

49121  101 
val ctr_argsss = map (map args_of) ctr_specss; 
49181  102 
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; 
49119  103 

49129  104 
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  106 

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val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; 
49167  108 
val _ = (case subtract (op =) As' rhs_As' of 
49165  109 
[] => () 
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 A' :: _ => error ("Extra type variables on rhs: " ^ 

49204  111 
quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); 
49165  112 

49176  113 
val ((Cs, Xs), _) = 
49204  114 
no_defs_lthy 
49121  115 
> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs 
116 
> mk_TFrees N 

49176  117 
>> mk_TFrees N; 
49119  118 

49204  119 
fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) = 
49146  120 
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  122 
 eq_fpT _ _ = false; 
49146  123 

49204  124 
fun freeze_fp (T as Type (s, Us)) = 
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(case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us)  j => nth Xs j) 

126 
 freeze_fp T = T; 

49121  127 

49204  128 
val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss; 
49176  129 
val sum_prod_TsXs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssXs; 
49119  130 

49176  131 
val eqs = map dest_TFree Xs ~~ sum_prod_TsXs; 
49121  132 

49205  133 
val ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects, fp_iter_thms, 
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fp_rec_thms), lthy) = 

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fp_bnf (if gfp then bnf_gfp else bnf_lfp) bs mixfixes As' eqs no_defs_lthy; 
49121  136 

49167  137 
val timer = time (Timer.startRealTimer ()); 
138 

49176  139 
fun mk_unf_or_fld get_T Ts t = 
140 
let val Type (_, Ts0) = get_T (fastype_of t) in 

49124  141 
Term.subst_atomic_types (Ts0 ~~ Ts) t 
49121  142 
end; 
49119  143 

49126  144 
val mk_unf = mk_unf_or_fld domain_type; 
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val mk_fld = mk_unf_or_fld range_type; 

49121  146 

49203  147 
val unfs = map (mk_unf As) unfs0; 
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val flds = map (mk_fld As) flds0; 

49124  149 

49201  150 
val fpTs = map (domain_type o fastype_of) unfs; 
49204  151 
val is_fpT = member (op =) fpTs; 
152 

49201  153 
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs; 
49203  154 
val ns = map length ctr_Tsss; 
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val mss = map (map length) ctr_Tsss; 

156 
val Css = map2 replicate ns Cs; 

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val Cs' = flat Css; 

158 

159 
fun mk_iter_or_rec Ts Us c = 

49121  160 
let 
49201  161 
val (binders, body) = strip_type (fastype_of c); 
49203  162 
val (fst_binders, last_binder) = split_last binders; 
163 
val Type (_, Ts0) = if gfp then body else last_binder; 

164 
val Us0 = map (if gfp then domain_type else body_type) fst_binders; 

49176  165 
in 
49201  166 
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) c 
49176  167 
end; 
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49204  169 
val fp_iters as fp_iter1 :: _ = map (mk_iter_or_rec As Cs) fp_iters0; 
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val fp_recs as fp_rec1 :: _ = map (mk_iter_or_rec As Cs) fp_recs0; 

171 

172 
val fp_y_Ts = map domain_type (fst (split_last (binder_types (fastype_of fp_iter1)))); 

173 
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; 

175 

176 
fun dest_rec_pair (T as Type (@{type_name prod}, Us as [_, U])) = 

177 
if member (op =) Cs U then Us else [T] 

178 
 dest_rec_pair T = [T]; 

179 

180 
val fp_z_Ts = map domain_type (fst (split_last (binder_types (fastype_of fp_rec1)))); 

181 
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; 

184 

185 
val ((gss, ysss), _) = 

186 
lthy 

187 
> mk_Freess "f" g_Tss 

188 
>> mk_Freesss "x" y_Tsss; 

189 

190 
val hss = map2 (map2 retype_free) gss h_Tss; 

191 
val (zssss, _) = 

192 
lthy 

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> mk_Freessss "x" z_Tssss; 

49176  194 

49201  195 
fun pour_sugar_on_type ((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec), fld_unf), 
49176  196 
unf_fld), fld_inject), ctr_binders), ctr_mixfixes), ctr_Tss), disc_binders), sel_binderss) 
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no_defs_lthy = 

198 
let 

199 
val n = length ctr_Tss; 

49121  200 
val ks = 1 upto n; 
201 
val ms = map length ctr_Tss; 

202 

49201  203 
val unfT = domain_type (fastype_of fld); 
49121  204 
val prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
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val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  206 

49176  207 
val ((((u, v), fs), xss), _) = 
49204  208 
no_defs_lthy 
49201  209 
> yield_singleton (mk_Frees "u") unfT 
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>> yield_singleton (mk_Frees "v") fpT 

49176  211 
>> mk_Frees "f" case_Ts 
49124  212 
>> mk_Freess "x" ctr_Tss; 
49121  213 

49129  214 
val ctr_rhss = 
49121  215 
map2 (fn k => fn xs => 
216 
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  219 

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val case_rhs = 
49176  221 
fold_rev Term.lambda (fs @ [v]) (mk_sum_caseN (map2 mk_uncurried_fun fs xss) $ (unf $ v)); 
49129  222 

49201  223 
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy 
49169  224 
> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => 
225 
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 

49201  226 
(case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) 
49121  227 
> `Local_Theory.restore; 
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229 
(*transforms defined frees into consts (and more)*) 

230 
val phi = Proof_Context.export_morphism lthy lthy'; 

231 

232 
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  235 
val ctrs0 = map (Morphism.term phi) raw_ctrs; 
236 
val casex0 = Morphism.term phi raw_case; 

237 

238 
val ctrs = map (mk_ctr As) ctrs0; 

49121  239 

49135  240 
fun exhaust_tac {context = ctxt, ...} = 
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let 
49135  242 
val fld_iff_unf_thm = 
243 
let 

244 
val goal = 

245 
fold_rev Logic.all [u, v] 

246 
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u))); 

247 
in 

248 
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => 

49201  249 
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT]) 
49176  250 
(certify lthy fld) (certify lthy unf) fld_unf unf_fld) 
49135  251 
> Thm.close_derivation 
252 
> Morphism.thm phi 

253 
end; 

254 

255 
val sumEN_thm' = 

256 
Local_Defs.unfold lthy @{thms all_unit_eq} 

257 
(Drule.instantiate' (map (SOME o certifyT lthy) prod_Ts) [] (mk_sumEN n)) 

258 
> 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  262 

49126  263 
val inject_tacss = 
49205  264 
map2 (fn 0 => K []  _ => fn ctr_def => [fn {context = ctxt, ...} => 
265 
mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs; 

49126  266 

49127  267 
val half_distinct_tacss = 
268 
map (map (fn (def, def') => fn {context = ctxt, ...} => 

269 
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs); 

270 

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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  274 

275 
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; 

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49199  277 
fun sugar_datatype no_defs_lthy = 
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let 
49201  279 
val iter_T = flat g_Tss > fpT > C; 
280 
val rec_T = flat h_Tss > fpT > C; 

49199  281 

282 
val iter_binder = Binding.suffix_name ("_" ^ iterN) b; 

283 
val rec_binder = Binding.suffix_name ("_" ^ recN) b; 

284 

285 
val iter_free = Free (Binding.name_of iter_binder, iter_T); 

286 
val rec_free = Free (Binding.name_of rec_binder, rec_T); 

287 

288 
val iter_spec = 

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mk_Trueprop_eq (flat_list_comb (iter_free, gss), 
49199  290 
Term.list_comb (fp_iter, map2 (mk_sum_caseN oo map2 mk_uncurried_fun) gss ysss)); 
291 
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  294 

295 
val (([raw_iter, raw_rec], [raw_iter_def, raw_rec_def]), (lthy', lthy)) = no_defs_lthy 

49201  296 
> apfst split_list o fold_map2 (fn b => fn spec => 
49199  297 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 
49201  298 
#>> apsnd snd) [iter_binder, rec_binder] [iter_spec, rec_spec] 
49199  299 
> `Local_Theory.restore; 
49201  300 

301 
(*transforms defined frees into consts (and more)*) 

302 
val phi = Proof_Context.export_morphism lthy lthy'; 

303 

304 
val iter_def = Morphism.thm phi raw_iter_def; 

305 
val rec_def = Morphism.thm phi raw_rec_def; 

306 

49203  307 
val iter0 = Morphism.term phi raw_iter; 
308 
val rec0 = Morphism.term phi raw_rec; 

309 

310 
val iter = mk_iter_or_rec As Cs' iter0; 

311 
val recx = mk_iter_or_rec As Cs' rec0; 

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in 
49205  313 
((ctrs, iter, recx, xss, ctr_defs, iter_def, rec_def), lthy) 
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end; 
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49205  316 
fun sugar_codatatype no_defs_lthy = 
317 
(([], @{term True}, @{term True}, [], [], TrueI, TrueI), no_defs_lthy); 

49119  318 
in 
49203  319 
wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy' 
49199  320 
> (if gfp then sugar_codatatype else sugar_datatype) 
49119  321 
end; 
49167  322 

49205  323 
fun pour_more_sugar_on_datatypes ((ctrss, iters, recs, xsss, ctr_defss, iter_defs, rec_defs), 
324 
lthy) = 

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let 
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val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; 
49204  327 
val giters = map (fn iter => flat_list_comb (iter, gss)) iters; 
328 
val hrecs = map (fn recx => flat_list_comb (recx, hss)) recs; 

49201  329 

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val (iter_thmss, rec_thmss) = 
49205  331 
if true then 
332 
`I (map (map (K TrueI)) ctr_defss) 

333 
else let 

49204  334 
fun mk_goal_iter_or_rec fss fc xctr f xs xs' = 
335 
mk_Trueprop_eq (fc $ xctr, Term.list_comb (f, xs')); 

336 

337 
fun fix_iter_free (x as Free (_, T)) = 

338 
(case find_index (eq_fpT T) fpTs of ~1 => x  j => nth giters j $ x); 

339 
fun fix_rec_free (x as Free (_, T)) = 

340 
(case find_index (eq_fpT T) fpTs of ~1 => [x]  j => [x, nth hrecs j $ x]); 

49201  341 

49204  342 
val iter_xsss = map (map (map fix_iter_free)) xsss; 
343 
val rec_xsss = map (map (maps fix_rec_free)) xsss; 

344 

345 
val goal_iterss = 

346 
map5 (map4 o mk_goal_iter_or_rec gss) giters xctrss gss xsss iter_xsss; 

347 
val goal_recss = 

348 
map5 (map4 o mk_goal_iter_or_rec hss) hrecs xctrss hss xsss rec_xsss; 

349 

49203  350 
val iter_tacss = 
49205  351 
map2 (map o mk_iter_or_rec_tac bnf_map_defs iter_defs) fp_iter_thms ctr_defss; 
49203  352 
val rec_tacss = 
49205  353 
map2 (map o mk_iter_or_rec_tac bnf_map_defs rec_defs) fp_rec_thms ctr_defss; 
49202
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in 
49205  355 
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 
356 
goal_iterss iter_tacss, 

357 
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 

358 
goal_recss rec_tacss) 

49202
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end; 
49201  360 

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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49204  372 
val lthy' = lthy 
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> fold_map pour_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~ fp_recs ~~ 
49176  374 
fld_unfs ~~ unf_flds ~~ fld_injects ~~ ctr_binderss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ 
49202
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disc_binderss ~~ sel_bindersss) 
49205  376 
>> split_list7 
377 
> (if gfp then snd else pour_more_sugar_on_datatypes); 

49167  378 

379 
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ 

380 
(if gfp then "co" else "") ^ "datatype")); 

49112  381 
in 
49204  382 
(timer; lthy') 
49112  383 
end; 
384 

49199  385 
fun datatype_cmd info specs lthy = 
49121  386 
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  393 
in 
49199  394 
prepare_datatype Syntax.read_typ info specs fake_lthy lthy 
49121  395 
end; 
49119  396 

49129  397 
val parse_opt_binding_colon = Scan.optional (Parse.binding  Parse.$$$ ":") no_binder 
49119  398 

49112  399 
val parse_ctr_arg = 
49119  400 
Parse.$$$ "("  parse_opt_binding_colon  Parse.typ  Parse.$$$ ")"  
49129  401 
(Parse.typ >> pair no_binder); 
49112  402 

403 
val parse_single_spec = 

404 
Parse.type_args_constrained  Parse.binding  Parse.opt_mixfix  

49119  405 
(@{keyword "="}  Parse.enum1 "" (parse_opt_binding_colon  Parse.binding  
406 
Scan.repeat parse_ctr_arg  Parse.opt_mixfix)); 

49112  407 

408 
val _ = 

409 
Outer_Syntax.local_theory @{command_spec "data"} "define BNFbased inductive datatypes" 

49199  410 
(Parse.and_list1 parse_single_spec >> datatype_cmd false); 
49112  411 

412 
val _ = 

413 
Outer_Syntax.local_theory @{command_spec "codata"} "define BNFbased coinductive datatypes" 

49199  414 
(Parse.and_list1 parse_single_spec >> datatype_cmd true); 
49112  415 

416 
end; 