author  blanchet 
Tue, 11 Sep 2012 13:06:13 +0200  
changeset 49274  ddd606ec45b9 
parent 49273  f839ce127a2e 
child 49275  ce87d6a901eb 
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 
20 
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, 

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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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49234  51 
fun mk_id T = Const (@{const_name id}, T > T); 
52 

49200  53 
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs)); 
54 
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  56 
mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss); 
57 

49233  58 
fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v)); 
59 

60 
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  65 
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; 
49119  66 

67 
fun merge_type_arg_constrained ctxt (T, c) (T', c') = 

68 
if T = T' then 

69 
(case (c, c') of 

70 
(_, NONE) => (T, c) 

71 
 (NONE, _) => (T, c') 

72 
 _ => 

73 
if c = c' then 

74 
(T, c) 

75 
else 

76 
error ("Inconsistent sort constraints for type variable " ^ 

77 
quote (Syntax.string_of_typ ctxt T))) 

78 
else 

79 
cannot_merge_types (); 

80 

81 
fun merge_type_args_constrained ctxt (cAs, cAs') = 

82 
if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs' 

83 
else cannot_merge_types (); 

84 

49121  85 
fun type_args_constrained_of (((cAs, _), _), _) = cAs; 
86 
val type_args_of = map fst o type_args_constrained_of; 

49129  87 
fun type_binder_of (((_, b), _), _) = b; 
49181  88 
fun mixfix_of ((_, mx), _) = mx; 
49121  89 
fun ctr_specs_of (_, ctr_specs) = ctr_specs; 
49119  90 

49121  91 
fun disc_of (((disc, _), _), _) = disc; 
92 
fun ctr_of (((_, ctr), _), _) = ctr; 

93 
fun args_of ((_, args), _) = args; 

49181  94 
fun ctr_mixfix_of (_, mx) = mx; 
49119  95 

49208  96 
fun prepare_datatype prepare_typ lfp specs fake_lthy no_defs_lthy = 
49112  97 
let 
49121  98 
val constrained_As = 
99 
map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs 

49204  100 
> Library.foldr1 (merge_type_args_constrained no_defs_lthy); 
49121  101 
val As = map fst constrained_As; 
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val As' = map dest_TFree As; 
49119  103 

49121  104 
val _ = (case duplicates (op =) As of [] => () 
49204  105 
 A :: _ => error ("Duplicate type parameter " ^ 
106 
quote (Syntax.string_of_typ no_defs_lthy A))); 

49119  107 

108 
(* TODO: use sort constraints on type args *) 

109 

110 
val N = length specs; 

111 

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fun mk_fake_T b = 
49121  113 
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), 
114 
As); 

115 

49129  116 
val bs = map type_binder_of specs; 
49204  117 
val fakeTs = map mk_fake_T bs; 
49121  118 

49181  119 
val mixfixes = map mixfix_of specs; 
49119  120 

121 
val _ = (case duplicates Binding.eq_name bs of [] => () 

122 
 b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); 

123 

49121  124 
val ctr_specss = map ctr_specs_of specs; 
49119  125 

49129  126 
val disc_binderss = map (map disc_of) ctr_specss; 
127 
val ctr_binderss = map (map ctr_of) ctr_specss; 

49121  128 
val ctr_argsss = map (map args_of) ctr_specss; 
49181  129 
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; 
49119  130 

49129  131 
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  133 

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val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; 
49167  135 
val _ = (case subtract (op =) As' rhs_As' of 
49165  136 
[] => () 
137 
 A' :: _ => error ("Extra type variables on rhs: " ^ 

49204  138 
quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); 
49165  139 

49176  140 
val ((Cs, Xs), _) = 
49204  141 
no_defs_lthy 
49121  142 
> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs 
143 
> mk_TFrees N 

49176  144 
>> mk_TFrees N; 
49119  145 

49204  146 
fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) = 
49146  147 
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ 
148 
quote (Syntax.string_of_typ fake_lthy T))) 

49204  149 
 eq_fpT _ _ = false; 
49146  150 

49204  151 
fun freeze_fp (T as Type (s, Us)) = 
152 
(case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us)  j => nth Xs j) 

153 
 freeze_fp T = T; 

49121  154 

49204  155 
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  157 

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val eqs = map dest_TFree Xs ~~ ctr_sum_prod_TsXs; 
49121  159 

49226  160 
val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects, 
49207  161 
fp_iter_thms, fp_rec_thms), lthy)) = 
49208  162 
fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy; 
49121  163 

49226  164 
val add_nested_bnf_names = 
165 
let 

166 
fun add (Type (s, Ts)) ss = 

167 
let val (needs, ss') = fold_map add Ts ss in 

168 
if exists I needs then (true, insert (op =) s ss') else (false, ss') 

169 
end 

170 
 add T ss = (member (op =) As T, ss); 

171 
in snd oo add end; 

172 

173 
val nested_bnfs = 

49236  174 
map_filter (bnf_of lthy) (fold (fold (fold add_nested_bnf_names)) ctr_TsssXs []); 
49226  175 

49167  176 
val timer = time (Timer.startRealTimer ()); 
177 

49176  178 
fun mk_unf_or_fld get_T Ts t = 
179 
let val Type (_, Ts0) = get_T (fastype_of t) in 

49124  180 
Term.subst_atomic_types (Ts0 ~~ Ts) t 
49121  181 
end; 
49119  182 

49126  183 
val mk_unf = mk_unf_or_fld domain_type; 
184 
val mk_fld = mk_unf_or_fld range_type; 

49121  185 

49203  186 
val unfs = map (mk_unf As) unfs0; 
187 
val flds = map (mk_fld As) flds0; 

49124  188 

49201  189 
val fpTs = map (domain_type o fastype_of) unfs; 
49204  190 

49201  191 
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs; 
49203  192 
val ns = map length ctr_Tsss; 
49212  193 
val kss = map (fn n => 1 upto n) ns; 
49203  194 
val mss = map (map length) ctr_Tsss; 
195 
val Css = map2 replicate ns Cs; 

196 

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fun mk_iter_like Ts Us t = 
49121  198 
let 
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val (binders, body) = strip_type (fastype_of t); 
49210  200 
val (f_Us, prebody) = split_last binders; 
201 
val Type (_, Ts0) = if lfp then prebody else body; 

202 
val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us); 

49176  203 
in 
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Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
49176  205 
end; 
206 

49210  207 
val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0; 
208 
val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0; 

209 

49212  210 
val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1))); 
211 
val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1))); 

49204  212 

49256  213 
val ((iter_only as (gss, _, _), rec_only as (hss, _, _)), 
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(zs, cs, cpss, coiter_only as ((pgss, cgssss), _), corec_only as ((phss, chssss), _))) = 
49208  215 
if lfp then 
216 
let 

217 
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  219 
ns mss fp_iter_fun_Ts; 
49208  220 
val g_Tss = map2 (map2 (curry (op >))) y_Tsss Css; 
221 

222 
val ((gss, ysss), _) = 

223 
lthy 

224 
> mk_Freess "f" g_Tss 

225 
>> 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  231 

49208  232 
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  235 
val h_Tss = map2 (map2 (fold_rev (curry (op >)))) z_Tssss Css; 
49204  236 

49208  237 
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  240 
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  243 
in 
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(((gss, g_Tss, yssss), (hss, h_Tss, zssss)), 
49256  245 
([], [], [], (([], []), ([], [])), (([], []), ([], [])))) 
49210  246 
end 
49208  247 
else 
49210  248 
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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251 

49211  252 
val p_Tss = 
49210  253 
map2 (fn C => fn n => replicate (Int.max (0, n  1)) (C > HOLogic.boolT)) Cs ns; 
49211  254 

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fun zip_getters fss = flat fss; 
49215  256 

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fun zip_preds_getters [] [fss] = zip_getters fss 
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 zip_preds_getters (p :: ps) (fss :: fsss) = 
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p :: zip_getters fss @ zip_preds_getters ps fsss; 
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fun mk_types maybe_dest_sumT fun_Ts = 
49212  262 
let 
263 
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; 
49212  265 
val f_Tsss = 
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map3 (fn C => map2 (map (curry (op >) C) oo dest_tupleT)) Cs mss' f_prod_Tss; 
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val f_Tssss = map (map (map maybe_dest_sumT)) f_Tsss; 
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val pf_Tss = map2 zip_preds_getters p_Tss f_Tssss; 
49256  269 
in (f_sum_prod_Ts, f_Tsss, pf_Tss) end; 
49176  270 

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val (g_sum_prod_Ts, g_Tsss, pg_Tss) = mk_types single fp_iter_fun_Ts; 
49211  272 

49233  273 
val ((((Free (z, _), cs), pss), gsss), _) = 
49210  274 
lthy 
49233  275 
> yield_singleton (mk_Frees "z") dummyT 
276 
>> mk_Frees "a" Cs 

49211  277 
>> mk_Freess "p" p_Tss 
49210  278 
>> mk_Freesss "g" g_Tsss; 
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val gssss = map (map (map single)) gsss; 
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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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284 

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285 
val (h_sum_prod_Ts, h_Tsss, ph_Tss) = mk_types dest_corec_sumT fp_rec_fun_Ts; 
49210  286 

49211  287 
val hsss = map2 (map2 (map2 retype_free)) gsss h_Tsss; 
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288 
val hssss = map (map (map single)) hsss; (*###*) 
49211  289 

49212  290 
val cpss = map2 (fn c => map (fn p => p $ c)) cs pss; 
291 

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292 
fun mk_terms fssss = 
49212  293 
let 
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294 
val pfss = map2 zip_preds_getters pss fssss; 
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295 
val cfssss = map2 (fn c => map (map (map (fn f => f $ c)))) cs fssss; 
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296 
in (pfss, cfssss) end; 
49210  297 
in 
49212  298 
((([], [], []), ([], [], [])), 
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299 
([z], cs, cpss, (mk_terms gssss, (g_sum_prod_Ts, pg_Tss)), 
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300 
(mk_terms hssss, (h_sum_prod_Ts, ph_Tss)))) 
49210  301 
end; 
302 

49212  303 
fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec), 
304 
fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss), 

305 
disc_binders), sel_binderss) no_defs_lthy = 

49176  306 
let 
49201  307 
val unfT = domain_type (fastype_of fld); 
49210  308 
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
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309 
val ctr_sum_prod_T = mk_sumTN_balanced ctr_prod_Ts; 
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310 
val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  311 

49176  312 
val ((((u, v), fs), xss), _) = 
49204  313 
no_defs_lthy 
49201  314 
> yield_singleton (mk_Frees "u") unfT 
315 
>> yield_singleton (mk_Frees "v") fpT 

49176  316 
>> mk_Frees "f" case_Ts 
49124  317 
>> mk_Freess "x" ctr_Tss; 
49121  318 

49129  319 
val ctr_rhss = 
49256  320 
map2 (fn k => fn xs => fold_rev Term.lambda xs (fld $ 
321 
mk_InN_balanced ctr_sum_prod_T n (HOLogic.mk_tuple xs) k)) ks xss; 

49121  322 

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323 
val case_binder = Binding.suffix_name ("_" ^ caseN) b; 
49129  324 

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325 
val case_rhs = 
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326 
fold_rev Term.lambda (fs @ [v]) 
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327 
(mk_sum_caseN_balanced (map2 mk_uncurried_fun fs xss) $ (unf $ v)); 
49129  328 

49201  329 
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy 
49169  330 
> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => 
331 
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 

49201  332 
(case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) 
49121  333 
> `Local_Theory.restore; 
334 

335 
(*transforms defined frees into consts (and more)*) 

336 
val phi = Proof_Context.export_morphism lthy lthy'; 

337 

338 
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; 

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339 
val case_def = Morphism.thm phi raw_case_def; 
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340 

49203  341 
val ctrs0 = map (Morphism.term phi) raw_ctrs; 
342 
val casex0 = Morphism.term phi raw_case; 

343 

344 
val ctrs = map (mk_ctr As) ctrs0; 

49121  345 

49135  346 
fun exhaust_tac {context = ctxt, ...} = 
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347 
let 
49135  348 
val fld_iff_unf_thm = 
349 
let 

350 
val goal = 

351 
fold_rev Logic.all [u, v] 

352 
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u))); 

353 
in 

354 
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => 

49201  355 
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT]) 
49176  356 
(certify lthy fld) (certify lthy unf) fld_unf unf_fld) 
49135  357 
> Thm.close_derivation 
358 
> Morphism.thm phi 

359 
end; 

360 

361 
val sumEN_thm' = 

362 
Local_Defs.unfold lthy @{thms all_unit_eq} 

49255
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363 
(Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) [] 
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364 
(mk_sumEN_balanced n)) 
49135  365 
> Morphism.thm phi; 
49123
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changeset

366 
in 
49161
a8e74375d971
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changeset

367 
mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm' 
49123
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368 
end; 
49121  369 

49126  370 
val inject_tacss = 
49205  371 
map2 (fn 0 => K []  _ => fn ctr_def => [fn {context = ctxt, ...} => 
372 
mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs; 

49126  373 

49127  374 
val half_distinct_tacss = 
375 
map (map (fn (def, def') => fn {context = ctxt, ...} => 

376 
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs); 

377 

49130
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49129
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changeset

378 
val case_tacs = 
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changeset

379 
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => 
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49129
diff
changeset

380 
mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs; 
49121  381 

382 
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; 

49134
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changeset

383 

49267
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changeset

384 
fun some_lfp_sugar ((selss0, discIs, sel_thmss), no_defs_lthy) = 
49134
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385 
let 
49208  386 
val fpT_to_C = fpT > C; 
49199  387 

49215  388 
fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) = 
389 
let 

390 
val res_T = fold_rev (curry (op >)) f_Tss fpT_to_C; 

391 

392 
val binder = Binding.suffix_name ("_" ^ suf) b; 

49199  393 

49215  394 
val spec = 
395 
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)), 

396 
Term.list_comb (fp_iter_like, 

49255
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changeset

397 
map2 (mk_sum_caseN_balanced oo map2 mk_uncurried2_fun) fss xssss)); 
49215  398 
in (binder, spec) end; 
49199  399 

49274
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changeset

400 
val iter_like_bundles = 
49215  401 
[(iterN, fp_iter, iter_only), 
402 
(recN, fp_rec, rec_only)]; 

403 

49274
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parents:
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diff
changeset

404 
val (binders, specs) = map generate_iter_like iter_like_bundles > split_list; 
49215  405 

406 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49201  407 
> apfst split_list o fold_map2 (fn b => fn spec => 
49199  408 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 
49215  409 
#>> apsnd snd) binders specs 
49199  410 
> `Local_Theory.restore; 
49201  411 

412 
(*transforms defined frees into consts (and more)*) 

413 
val phi = Proof_Context.export_morphism lthy lthy'; 

414 

49215  415 
val [iter_def, rec_def] = map (Morphism.thm phi) defs; 
49201  416 

49215  417 
val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts; 
49134
846264f80f16
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parents:
49130
diff
changeset

418 
in 
49267
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blanchet
parents:
49266
diff
changeset

419 
((ctrs, selss0, iter, recx, v, xss, ctr_defs, discIs, sel_thmss, iter_def, rec_def), 
49266  420 
lthy) 
49134
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49130
diff
changeset

421 
end; 
846264f80f16
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parents:
49130
diff
changeset

422 

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

423 
fun some_gfp_sugar ((selss0, discIs, sel_thmss), no_defs_lthy) = 
49210  424 
let 
425 
val B_to_fpT = C > fpT; 

49211  426 

49274
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parents:
49273
diff
changeset

427 
fun mk_preds_getters_join c n cps sum_prod_T cfsss = 
ddd606ec45b9
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parents:
49273
diff
changeset

428 
Term.lambda c (mk_IfN sum_prod_T cps 
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diff
changeset

429 
(map2 (mk_InN_balanced sum_prod_T n) (map (HOLogic.mk_tuple o flat) cfsss) (*###*) 
ddd606ec45b9
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parents:
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diff
changeset

430 
(1 upto n))); 
ddd606ec45b9
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blanchet
parents:
49273
diff
changeset

431 

ddd606ec45b9
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diff
changeset

432 
fun generate_coiter_like (suf, fp_iter_like, ((pfss, cfssss), (f_sum_prod_Ts, 
ddd606ec45b9
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parents:
49273
diff
changeset

433 
pf_Tss))) = 
49211  434 
let 
435 
val res_T = fold_rev (curry (op >)) pf_Tss B_to_fpT; 

49210  436 

49211  437 
val binder = Binding.suffix_name ("_" ^ suf) b; 
49210  438 

49211  439 
val spec = 
49212  440 
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)), 
49211  441 
Term.list_comb (fp_iter_like, 
49274
ddd606ec45b9
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parents:
49273
diff
changeset

442 
map5 mk_preds_getters_join cs ns cpss f_sum_prod_Ts cfssss)); 
49211  443 
in (binder, spec) end; 
49210  444 

49274
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parents:
49273
diff
changeset

445 
val coiter_like_bundles = 
49215  446 
[(coiterN, fp_iter, coiter_only), 
447 
(corecN, fp_rec, corec_only)]; 

49212  448 

49274
ddd606ec45b9
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blanchet
parents:
49273
diff
changeset

449 
val (binders, specs) = map generate_coiter_like coiter_like_bundles > split_list; 
49211  450 

451 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49210  452 
> apfst split_list o fold_map2 (fn b => fn spec => 
453 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 

49211  454 
#>> apsnd snd) binders specs 
49210  455 
> `Local_Theory.restore; 
456 

457 
(*transforms defined frees into consts (and more)*) 

458 
val phi = Proof_Context.export_morphism lthy lthy'; 

459 

49211  460 
val [coiter_def, corec_def] = map (Morphism.thm phi) defs; 
49210  461 

49211  462 
val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts; 
49210  463 
in 
49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

464 
((ctrs, selss0, coiter, corec, v, xss, ctr_defs, discIs, sel_thmss, coiter_def, 
49266  465 
corec_def), lthy) 
49210  466 
end; 
49119  467 
in 
49203  468 
wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy' 
49210  469 
> (if lfp then some_lfp_sugar else some_gfp_sugar) 
49119  470 
end; 
49167  471 

49226  472 
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

473 
val map_ids = map map_id_of_bnf nested_bnfs; 
49226  474 

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

475 
fun mk_map Ts Us t = 
49217  476 
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

477 
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

478 
end; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

479 

49234  480 
fun build_map build_arg (Type (s, Ts)) (Type (_, Us)) = 
481 
let 

49236  482 
val map0 = map_of_bnf (the (bnf_of lthy s)); 
49234  483 
val mapx = mk_map Ts Us map0; 
484 
val TUs = map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx))))); 

485 
val args = map build_arg TUs; 

486 
in Term.list_comb (mapx, args) end; 

487 

49266  488 
fun pour_more_sugar_on_lfps ((ctrss, _, iters, recs, vs, xsss, ctr_defss, _, _, iter_defs, 
489 
rec_defs), lthy) = 

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

490 
let 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

491 
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; 
49212  492 
val giters = map (lists_bmoc gss) iters; 
493 
val hrecs = map (lists_bmoc hss) recs; 

49201  494 

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

495 
val (iter_thmss, rec_thmss) = 
49207  496 
let 
49212  497 
fun mk_goal_iter_like fss fiter_like xctr f xs fxs = 
49207  498 
fold_rev (fold_rev Logic.all) (xs :: fss) 
49212  499 
(mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs))); 
49204  500 

49234  501 
fun build_call fiter_likes maybe_tick (T, U) = 
502 
if T = U then 

503 
mk_id T 

504 
else 

505 
(case find_index (curry (op =) T) fpTs of 

506 
~1 => build_map (build_call fiter_likes maybe_tick) T U 

507 
 j => maybe_tick (nth vs j) (nth fiter_likes j)); 

49233  508 

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

509 
fun mk_U maybe_mk_prodT = 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

510 
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

511 

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

512 
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

513 
if member (op =) fpTs T then 
49233  514 
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

515 
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

516 
[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

517 
else 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

518 
[x]; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

519 

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

520 
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

521 
val hxsss = 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

522 
map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss; 
49204  523 

49212  524 
val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss; 
525 
val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss; 

49204  526 

49203  527 
val iter_tacss = 
49229
d5717b5e2217
use map_id, not map_id', to allow better composition
blanchet
parents:
49226
diff
changeset

528 
map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss; 
49203  529 
val rec_tacss = 
49229
d5717b5e2217
use map_id, not map_id', to allow better composition
blanchet
parents:
49226
diff
changeset

530 
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

531 
in 
49266  532 
(map2 (map2 (fn goal => fn tac => 
533 
Skip_Proof.prove lthy [] [] goal (tac o #context) > Thm.close_derivation)) 

49205  534 
goal_iterss iter_tacss, 
49266  535 
map2 (map2 (fn goal => fn tac => 
536 
Skip_Proof.prove lthy [] [] goal (tac o #context) > Thm.close_derivation)) 

49205  537 
goal_recss rec_tacss) 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

538 
end; 
49201  539 

49226  540 
val notes = 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

541 
[(itersN, iter_thmss), 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

542 
(recsN, rec_thmss)] 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

543 
> maps (fn (thmN, thmss) => 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

544 
map2 (fn b => fn thms => 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

545 
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

546 
bs thmss); 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

547 
in 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

548 
lthy > Local_Theory.notes notes > snd 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

549 
end; 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

550 

49266  551 
fun pour_more_sugar_on_gfps ((ctrss, selsss, coiters, corecs, vs, _, ctr_defss, discIss, 
552 
sel_thmsss, coiter_defs, corec_defs), lthy) = 

49212  553 
let 
49233  554 
val z = the_single zs; 
555 

49212  556 
val gcoiters = map (lists_bmoc pgss) coiters; 
557 
val hcorecs = map (lists_bmoc phss) corecs; 

558 

559 
val (coiter_thmss, corec_thmss) = 

560 
let 

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

561 
fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not); 
49212  562 

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

563 
fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr m cfss' = 
49212  564 
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

565 
(Logic.list_implies (seq_conds mk_goal_cond n k cps, 
49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

566 
mk_Trueprop_eq (fcoiter_like $ c, lists_bmoc (take m cfss') ctr))); 
49212  567 

49234  568 
fun build_call fiter_likes maybe_tack (T, U) = 
569 
if T = U then 

570 
mk_id T 

571 
else 

572 
(case find_index (curry (op =) U) fpTs of 

573 
~1 => build_map (build_call fiter_likes maybe_tack) T U 

574 
 j => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j)); 

49233  575 

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

576 
fun mk_U maybe_mk_sumT = 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

577 
typ_subst (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs); 
49212  578 

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

579 
fun repair_calls fiter_likes maybe_mk_sumT maybe_tack 
49232
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

580 
(cf as Free (_, Type (_, [_, T])) $ _) = 
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

581 
if exists_subtype (member (op =) Cs) T then 
49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

582 
build_call fiter_likes maybe_tack (T, mk_U maybe_mk_sumT T) $ cf 
49232
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

583 
else 
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

584 
cf; 
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

585 

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

586 
val cgssss' = 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

587 
map (map (map (map (repair_calls gcoiters (K I) (K I))))) cgssss; 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

588 
val chssss' = 
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

589 
map (map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z))))) chssss; 
49212  590 

591 
val goal_coiterss = 

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

592 
map8 (map4 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss mss cgssss'; 
49233  593 
val goal_corecss = 
49274
ddd606ec45b9
first step towards splitting corecursor function arguments into (p, g, h) triples
blanchet
parents:
49273
diff
changeset

594 
map8 (map4 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss mss chssss'; 
49213  595 

596 
val coiter_tacss = 

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

597 
map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs 
49226  598 
ctr_defss; 
49233  599 
val corec_tacss = 
600 
map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs 

601 
ctr_defss; 

49212  602 
in 
49213  603 
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 
604 
goal_coiterss coiter_tacss, 

49233  605 
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 
606 
goal_corecss corec_tacss) 

49212  607 
end; 
608 

49266  609 
fun mk_disc_coiter_like_thms [_] = K [] 
610 
 mk_disc_coiter_like_thms thms = map2 (curry (op RS)) thms; 

611 

612 
val disc_coiter_thmss = map2 mk_disc_coiter_like_thms coiter_thmss discIss; 

613 
val disc_corec_thmss = map2 mk_disc_coiter_like_thms corec_thmss discIss; 

614 

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

615 
fun mk_sel_coiter_like_thm coiter_like_thm sel0 sel_thm = 
49266  616 
let 
49267
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

617 
val (domT, ranT) = dest_funT (fastype_of sel0); 
49266  618 
val arg_cong' = 
619 
Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT]) 

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

620 
[NONE, NONE, SOME (certify lthy sel0)] arg_cong 
c96a07255e10
correctly generate sel_coiter and sel_corec theorems
blanchet
parents:
49266
diff
changeset

621 
> Thm.varifyT_global; 
49266  622 
val sel_thm' = sel_thm RSN (2, trans); 
623 
in 

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

624 
coiter_like_thm RS arg_cong' RS sel_thm' 
49266  625 
end; 
626 

627 
val sel_coiter_thmsss = 

628 
map3 (map3 (map2 o mk_sel_coiter_like_thm)) coiter_thmss selsss sel_thmsss; 

629 
val sel_corec_thmsss = 

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

630 
map3 (map3 (map2 o mk_sel_coiter_like_thm)) corec_thmss selsss sel_thmsss; 
49266  631 

49212  632 
val notes = 
49233  633 
[(coitersN, coiter_thmss), 
49266  634 
(disc_coitersN, disc_coiter_thmss), 
635 
(sel_coitersN, map flat sel_coiter_thmsss), 

636 
(corecsN, corec_thmss), 

637 
(disc_corecsN, disc_corec_thmss), 

638 
(sel_corecsN, map flat sel_corec_thmsss)] 

49212  639 
> maps (fn (thmN, thmss) => 
49266  640 
map_filter (fn (_, []) => NONE  (b, thms) => 
641 
SOME ((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), 

642 
[(thms, [])])) (bs ~~ thmss)); 

49212  643 
in 
49230  644 
lthy > Local_Theory.notes notes > snd 
49212  645 
end; 
646 

49204  647 
val lthy' = lthy 
49210  648 
> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~ 
49212  649 
fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~ 
650 
ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss) 

49266  651 
>> split_list11 
49212  652 
> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps); 
49167  653 

654 
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ 

49208  655 
(if lfp then "" else "co") ^ "datatype")); 
49112  656 
in 
49204  657 
(timer; lthy') 
49112  658 
end; 
659 

49199  660 
fun datatype_cmd info specs lthy = 
49121  661 
let 
49209  662 
(* 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

663 
(*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

664 
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

665 
val fake_thy = Theory.copy 
49184
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset

666 
#> fold (fn spec => perhaps (try (Sign.add_type lthy 
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset

667 
(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

668 
val fake_lthy = Proof_Context.background_theory fake_thy lthy; 
49121  669 
in 
49199  670 
prepare_datatype Syntax.read_typ info specs fake_lthy lthy 
49121  671 
end; 
49119  672 

49129  673 
val parse_opt_binding_colon = Scan.optional (Parse.binding  Parse.$$$ ":") no_binder 
49119  674 

49112  675 
val parse_ctr_arg = 
49119  676 
Parse.$$$ "("  parse_opt_binding_colon  Parse.typ  Parse.$$$ ")"  
49129  677 
(Parse.typ >> pair no_binder); 
49112  678 

679 
val parse_single_spec = 

680 
Parse.type_args_constrained  Parse.binding  Parse.opt_mixfix  

49119  681 
(@{keyword "="}  Parse.enum1 "" (parse_opt_binding_colon  Parse.binding  
682 
Scan.repeat parse_ctr_arg  Parse.opt_mixfix)); 

49112  683 

684 
val _ = 

685 
Outer_Syntax.local_theory @{command_spec "data"} "define BNFbased inductive datatypes" 

49208  686 
(Parse.and_list1 parse_single_spec >> datatype_cmd true); 
49112  687 

688 
val _ = 

689 
Outer_Syntax.local_theory @{command_spec "codata"} "define BNFbased coinductive datatypes" 

49208  690 
(Parse.and_list1 parse_single_spec >> datatype_cmd false); 
49112  691 

692 
end; 