author  blanchet 
Thu, 06 Sep 2012 12:04:40 +0200  
changeset 49182  b8517107ffc5 
parent 49181  64764f0efe80 
child 49183  0cc46e2dee7e 
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. 

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*) 

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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 

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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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49124  24 
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; 
49119  25 

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

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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') 

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 _ => 

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if c = c' then 

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(T, c) 

34 
else 

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error ("Inconsistent sort constraints for type variable " ^ 

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quote (Syntax.string_of_typ ctxt T))) 

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else 

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cannot_merge_types (); 

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fun merge_type_args_constrained ctxt (cAs, cAs') = 

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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  44 
fun type_args_constrained_of (((cAs, _), _), _) = cAs; 
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val type_args_of = map fst o type_args_constrained_of; 

49129  46 
fun type_binder_of (((_, b), _), _) = b; 
49181  47 
fun mixfix_of ((_, mx), _) = mx; 
49121  48 
fun ctr_specs_of (_, ctr_specs) = ctr_specs; 
49119  49 

49121  50 
fun disc_of (((disc, _), _), _) = disc; 
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fun ctr_of (((_, ctr), _), _) = ctr; 

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

49181  53 
fun ctr_mixfix_of (_, mx) = mx; 
49119  54 

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fun prepare_data prepare_typ gfp specs fake_lthy lthy = 
49112  56 
let 
49121  57 
val constrained_As = 
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map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs 

49119  59 
> Library.foldr1 (merge_type_args_constrained lthy); 
49121  60 
val As = map fst constrained_As; 
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val As' = map dest_TFree As; 
49119  62 

49121  63 
val _ = (case duplicates (op =) As of [] => () 
49165  64 
 A :: _ => error ("Duplicate type parameter " ^ quote (Syntax.string_of_typ lthy A))); 
49119  65 

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

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val N = length specs; 

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fun mk_fake_T b = 
49121  71 
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  74 
val bs = map type_binder_of specs; 
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val fake_Ts = map mk_fake_T bs; 
49121  76 

49181  77 
val mixfixes = map mixfix_of specs; 
49119  78 

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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  82 
val ctr_specss = map ctr_specs_of specs; 
49119  83 

49129  84 
val disc_binderss = map (map disc_of) ctr_specss; 
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val ctr_binderss = map (map ctr_of) ctr_specss; 

49121  86 
val ctr_argsss = map (map args_of) ctr_specss; 
49181  87 
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; 
49119  88 

49129  89 
val sel_bindersss = map (map (map fst)) ctr_argsss; 
49121  90 
val ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; 
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49167  92 
val rhs_As' = fold (fold (fold Term.add_tfreesT)) ctr_Tsss []; 
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val _ = (case subtract (op =) As' rhs_As' of 

49165  94 
[] => () 
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 A' :: _ => error ("Extra type variables on rhs: " ^ 

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quote (Syntax.string_of_typ lthy (TFree A')))); 

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49176  98 
val ((Cs, Xs), _) = 
49121  99 
lthy 
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> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs 

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> mk_TFrees N 

49176  102 
>> mk_TFrees N; 
49119  103 

49176  104 
fun is_same_recT (T as Type (s, Us)) (Type (s', Us')) = 
49146  105 
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ 
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quote (Syntax.string_of_typ fake_lthy T))) 

49176  107 
 is_same_recT _ _ = false; 
49146  108 

49176  109 
fun freeze_recXs (T as Type (s, Us)) = 
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(case find_index (is_same_recT T) fake_Ts of 
49176  111 
~1 => Type (s, map freeze_recXs Us) 
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 i => nth Xs i) 

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 freeze_recXs T = T; 

49121  114 

49176  115 
val ctr_TsssXs = map (map (map freeze_recXs)) ctr_Tsss; 
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val sum_prod_TsXs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssXs; 

49119  117 

49176  118 
val eqs = map dest_TFree Xs ~~ sum_prod_TsXs; 
49121  119 

49176  120 
val ((raw_unfs, raw_flds, raw_fp_iters, raw_fp_recs, unf_flds, fld_unfs, fld_injects), lthy') = 
49169  121 
fp_bnf (if gfp then bnf_gfp else bnf_lfp) bs mixfixes As' eqs lthy; 
49121  122 

49167  123 
val timer = time (Timer.startRealTimer ()); 
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49176  125 
fun mk_unf_or_fld get_T Ts t = 
126 
let val Type (_, Ts0) = get_T (fastype_of t) in 

49124  127 
Term.subst_atomic_types (Ts0 ~~ Ts) t 
49121  128 
end; 
49119  129 

49126  130 
val mk_unf = mk_unf_or_fld domain_type; 
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val mk_fld = mk_unf_or_fld range_type; 

49121  132 

49126  133 
val unfs = map (mk_unf As) raw_unfs; 
49124  134 
val flds = map (mk_fld As) raw_flds; 
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val fp_Ts = map (domain_type o fastype_of) unfs; 
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49176  138 
fun mk_fp_iter_or_rec Ts Us t = 
49121  139 
let 
49176  140 
val (binders, body) = strip_type (fastype_of t); 
141 
val Type (_, Ts0) = if gfp then body else List.last binders; 

142 
val Us0 = map (if gfp then domain_type else body_type) (fst (split_last binders)); 

143 
in 

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Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 

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end; 

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val fp_iters = map (mk_fp_iter_or_rec As Cs) raw_fp_iters; 

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val fp_recs = map (mk_fp_iter_or_rec As Cs) raw_fp_recs; 

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150 
fun pour_sugar_on_type ((((((((((((((b, fp_T), C), fld), unf), fp_iter), fp_rec), fld_unf), 

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unf_fld), fld_inject), ctr_binders), ctr_mixfixes), ctr_Tss), disc_binders), sel_binderss) 

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no_defs_lthy = 

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let 

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val n = length ctr_Tss; 

49121  155 
val ks = 1 upto n; 
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val ms = map length ctr_Tss; 

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49124  158 
val unf_T = domain_type (fastype_of fld); 
49121  159 
val prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
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val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  161 

49176  162 
val ((((u, v), fs), xss), _) = 
49124  163 
lthy 
49176  164 
> yield_singleton (mk_Frees "u") unf_T 
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>> yield_singleton (mk_Frees "v") fp_T 

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>> mk_Frees "f" case_Ts 

49124  167 
>> mk_Freess "x" ctr_Tss; 
49121  168 

49129  169 
val ctr_rhss = 
49121  170 
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  174 

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val case_rhs = 
49176  176 
fold_rev Term.lambda (fs @ [v]) (mk_sum_caseN (map2 mk_uncurried_fun fs xss) $ (unf $ v)); 
49129  177 

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val (((raw_ctrs, raw_ctr_defs), (raw_case, raw_case_def)), (lthy', lthy)) = no_defs_lthy 
49169  179 
> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => 
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Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 

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ctr_binders ctr_mixfixes ctr_rhss 

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>> (Local_Theory.define ((case_binder, NoSyn), ((Thm.def_binding case_binder, []), 
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case_rhs)) #>> apsnd snd) 
49121  184 
> `Local_Theory.restore; 
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186 
(*transforms defined frees into consts (and more)*) 

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val phi = Proof_Context.export_morphism lthy lthy'; 

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189 
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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val ctrs = map (Morphism.term phi) raw_ctrs; 
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val casex = Morphism.term phi raw_case; 
49121  194 

49135  195 
fun exhaust_tac {context = ctxt, ...} = 
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let 
49135  197 
val fld_iff_unf_thm = 
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let 

199 
val goal = 

200 
fold_rev Logic.all [u, v] 

201 
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u))); 

202 
in 

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

49176  204 
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unf_T, fp_T]) 
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(certify lthy fld) (certify lthy unf) fld_unf unf_fld) 

49135  206 
> Thm.close_derivation 
207 
> Morphism.thm phi 

208 
end; 

209 

210 
val sumEN_thm' = 

211 
Local_Defs.unfold lthy @{thms all_unit_eq} 

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

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> 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  217 

49126  218 
val inject_tacss = 
219 
map2 (fn 0 => K [] 

220 
 _ => fn ctr_def => [fn {context = ctxt, ...} => 

221 
mk_inject_tac ctxt ctr_def fld_inject]) 

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ms ctr_defs; 

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49127  224 
val half_distinct_tacss = 
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map (map (fn (def, def') => fn {context = ctxt, ...} => 

226 
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs); 

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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  231 

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

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49176  234 
(* (co)iterators, (co)recursors, (co)induction *) 
235 

236 
val is_recT = member (op =) fp_Ts; 

237 

238 
val ns = map length ctr_Tsss; 

239 
val mss = map (map length) ctr_Tsss; 

240 
val Css = map2 replicate ns Cs; 

241 

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fun sugar_lfp lthy = 
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let 
49176  244 
val fp_y_Ts = map domain_type (fst (split_last (binder_types (fastype_of fp_iter)))); 
245 
val y_prod_Tss = map2 dest_sumTN ns fp_y_Ts; 

246 
val y_Tsss = map2 (map2 dest_tupleT) mss y_prod_Tss; 

247 
val g_Tss = map2 (map2 (curry (op >))) y_Tsss Css; 

248 
val iter_T = flat g_Tss > fp_T > C; 

49146  249 

49176  250 
val ((gss, ysss), _) = 
251 
lthy 

252 
> mk_Freess "f" g_Tss 

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>> mk_Freesss "x" y_Tsss; 
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49146  255 
val iter_rhs = 
49176  256 
fold_rev (fold_rev Term.lambda) gss 
257 
(Term.list_comb (fp_iter, map2 (mk_sum_caseN oo map2 mk_uncurried_fun) gss ysss)); 

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in 
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lthy 
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end; 
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fun sugar_gfp lthy = lthy; 
49119  263 
in 
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wrap_data tacss ((ctrs, casex), (disc_binders, sel_binderss)) lthy' 
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> (if gfp then sugar_gfp else sugar_lfp) 
49119  266 
end; 
49167  267 

268 
val lthy'' = 

49176  269 
fold pour_sugar_on_type (bs ~~ fp_Ts ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~ fp_recs ~~ 
270 
fld_unfs ~~ unf_flds ~~ fld_injects ~~ ctr_binderss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ 

271 
disc_binderss ~~ sel_bindersss) lthy'; 

49167  272 

273 
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ 

274 
(if gfp then "co" else "") ^ "datatype")); 

49112  275 
in 
49167  276 
(timer; lthy'') 
49112  277 
end; 
278 

49121  279 
fun data_cmd info specs lthy = 
280 
let 

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val fake_thy = Theory.copy 
49180  282 
#> fold (fn spec => Sign.add_type lthy 
49181  283 
(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  285 
in 
286 
prepare_data Syntax.read_typ info specs fake_lthy lthy 

287 
end; 

49119  288 

49129  289 
val parse_opt_binding_colon = Scan.optional (Parse.binding  Parse.$$$ ":") no_binder 
49119  290 

49112  291 
val parse_ctr_arg = 
49119  292 
Parse.$$$ "("  parse_opt_binding_colon  Parse.typ  Parse.$$$ ")"  
49129  293 
(Parse.typ >> pair no_binder); 
49112  294 

295 
val parse_single_spec = 

296 
Parse.type_args_constrained  Parse.binding  Parse.opt_mixfix  

49119  297 
(@{keyword "="}  Parse.enum1 "" (parse_opt_binding_colon  Parse.binding  
298 
Scan.repeat parse_ctr_arg  Parse.opt_mixfix)); 

49112  299 

300 
val _ = 

301 
Outer_Syntax.local_theory @{command_spec "data"} "define BNFbased inductive datatypes" 

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(Parse.and_list1 parse_single_spec >> data_cmd false); 
49112  303 

304 
val _ = 

305 
Outer_Syntax.local_theory @{command_spec "codata"} "define BNFbased coinductive datatypes" 

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(Parse.and_list1 parse_single_spec >> data_cmd true); 
49112  307 

308 
end; 