author  blanchet 
Sun, 09 Sep 2012 18:55:10 +0200  
changeset 49233  7f412734fbb3 
parent 49232  9ea11f0c53e4 
child 49234  4626ff7cbd2c 
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"; 

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val itersN = "iters"; 
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val recsN = "recs"; 
49129  29 

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fun split_list8 xs = 
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(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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49217  33 
fun strip_map_type (Type (@{type_name fun}, [T as Type _, T'])) = strip_map_type T' >> cons T 
34 
 strip_map_type T = ([], T); 

35 

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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  41 

49199  42 
fun retype_free (Free (s, _)) T = Free (s, T); 
43 

49212  44 
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs)) 
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49200  46 
fun mk_tupled_fun x f xs = HOLogic.tupled_lambda x (Term.list_comb (f, xs)); 
47 
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  49 
mk_tupled_fun (HOLogic.mk_tuple (map HOLogic.mk_tuple xss)) f (flat xss); 
50 

49233  51 
fun tick v f = Term.lambda v (HOLogic.mk_prod (v, f $ v)); 
52 

53 
fun tack z_name (c, v) f = 

54 
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) 

56 
end; 

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49124  58 
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters"; 
49119  59 

60 
fun merge_type_arg_constrained ctxt (T, c) (T', c') = 

61 
if T = T' then 

62 
(case (c, c') of 

63 
(_, NONE) => (T, c) 

64 
 (NONE, _) => (T, c') 

65 
 _ => 

66 
if c = c' then 

67 
(T, c) 

68 
else 

69 
error ("Inconsistent sort constraints for type variable " ^ 

70 
quote (Syntax.string_of_typ ctxt T))) 

71 
else 

72 
cannot_merge_types (); 

73 

74 
fun merge_type_args_constrained ctxt (cAs, cAs') = 

75 
if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs' 

76 
else cannot_merge_types (); 

77 

49121  78 
fun type_args_constrained_of (((cAs, _), _), _) = cAs; 
79 
val type_args_of = map fst o type_args_constrained_of; 

49129  80 
fun type_binder_of (((_, b), _), _) = b; 
49181  81 
fun mixfix_of ((_, mx), _) = mx; 
49121  82 
fun ctr_specs_of (_, ctr_specs) = ctr_specs; 
49119  83 

49121  84 
fun disc_of (((disc, _), _), _) = disc; 
85 
fun ctr_of (((_, ctr), _), _) = ctr; 

86 
fun args_of ((_, args), _) = args; 

49181  87 
fun ctr_mixfix_of (_, mx) = mx; 
49119  88 

49208  89 
fun prepare_datatype prepare_typ lfp specs fake_lthy no_defs_lthy = 
49112  90 
let 
49121  91 
val constrained_As = 
92 
map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs 

49204  93 
> Library.foldr1 (merge_type_args_constrained no_defs_lthy); 
49121  94 
val As = map fst constrained_As; 
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val As' = map dest_TFree As; 
49119  96 

49121  97 
val _ = (case duplicates (op =) As of [] => () 
49204  98 
 A :: _ => error ("Duplicate type parameter " ^ 
99 
quote (Syntax.string_of_typ no_defs_lthy A))); 

49119  100 

101 
(* TODO: use sort constraints on type args *) 

102 

103 
val N = length specs; 

104 

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fun mk_fake_T b = 
49121  106 
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), 
107 
As); 

108 

49129  109 
val bs = map type_binder_of specs; 
49204  110 
val fakeTs = map mk_fake_T bs; 
49121  111 

49181  112 
val mixfixes = map mixfix_of specs; 
49119  113 

114 
val _ = (case duplicates Binding.eq_name bs of [] => () 

115 
 b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); 

116 

49121  117 
val ctr_specss = map ctr_specs_of specs; 
49119  118 

49129  119 
val disc_binderss = map (map disc_of) ctr_specss; 
120 
val ctr_binderss = map (map ctr_of) ctr_specss; 

49121  121 
val ctr_argsss = map (map args_of) ctr_specss; 
49181  122 
val ctr_mixfixess = map (map ctr_mixfix_of) ctr_specss; 
49119  123 

49129  124 
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  126 

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val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; 
49167  128 
val _ = (case subtract (op =) As' rhs_As' of 
49165  129 
[] => () 
130 
 A' :: _ => error ("Extra type variables on rhs: " ^ 

49204  131 
quote (Syntax.string_of_typ no_defs_lthy (TFree A')))); 
49165  132 

49176  133 
val ((Cs, Xs), _) = 
49204  134 
no_defs_lthy 
49121  135 
> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs 
136 
> mk_TFrees N 

49176  137 
>> mk_TFrees N; 
49119  138 

49204  139 
fun eq_fpT (T as Type (s, Us)) (Type (s', Us')) = 
49146  140 
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ 
141 
quote (Syntax.string_of_typ fake_lthy T))) 

49204  142 
 eq_fpT _ _ = false; 
49146  143 

49204  144 
fun freeze_fp (T as Type (s, Us)) = 
145 
(case find_index (eq_fpT T) fakeTs of ~1 => Type (s, map freeze_fp Us)  j => nth Xs j) 

146 
 freeze_fp T = T; 

49121  147 

49204  148 
val ctr_TsssXs = map (map (map freeze_fp)) fake_ctr_Tsss; 
49176  149 
val sum_prod_TsXs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssXs; 
49119  150 

49176  151 
val eqs = map dest_TFree Xs ~~ sum_prod_TsXs; 
49121  152 

49226  153 
val (pre_bnfs, ((unfs0, flds0, fp_iters0, fp_recs0, unf_flds, fld_unfs, fld_injects, 
49207  154 
fp_iter_thms, fp_rec_thms), lthy)) = 
49208  155 
fp_bnf (if lfp then bnf_lfp else bnf_gfp) bs mixfixes As' eqs no_defs_lthy; 
49121  156 

49226  157 
val add_nested_bnf_names = 
158 
let 

159 
fun add (Type (s, Ts)) ss = 

160 
let val (needs, ss') = fold_map add Ts ss in 

161 
if exists I needs then (true, insert (op =) s ss') else (false, ss') 

162 
end 

163 
 add T ss = (member (op =) As T, ss); 

164 
in snd oo add end; 

165 

166 
val nested_bnfs = 

167 
map_filter (bnf_of lthy o Long_Name.base_name) 

168 
(fold (fold (fold add_nested_bnf_names)) ctr_TsssXs []); 

169 

49167  170 
val timer = time (Timer.startRealTimer ()); 
171 

49176  172 
fun mk_unf_or_fld get_T Ts t = 
173 
let val Type (_, Ts0) = get_T (fastype_of t) in 

49124  174 
Term.subst_atomic_types (Ts0 ~~ Ts) t 
49121  175 
end; 
49119  176 

49126  177 
val mk_unf = mk_unf_or_fld domain_type; 
178 
val mk_fld = mk_unf_or_fld range_type; 

49121  179 

49203  180 
val unfs = map (mk_unf As) unfs0; 
181 
val flds = map (mk_fld As) flds0; 

49124  182 

49201  183 
val fpTs = map (domain_type o fastype_of) unfs; 
49204  184 

49201  185 
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctr_TsssXs; 
49203  186 
val ns = map length ctr_Tsss; 
49212  187 
val kss = map (fn n => 1 upto n) ns; 
49203  188 
val mss = map (map length) ctr_Tsss; 
189 
val Css = map2 replicate ns Cs; 

190 

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fun mk_iter_like Ts Us t = 
49121  192 
let 
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val (binders, body) = strip_type (fastype_of t); 
49210  194 
val (f_Us, prebody) = split_last binders; 
195 
val Type (_, Ts0) = if lfp then prebody else body; 

196 
val Us0 = distinct (op =) (map (if lfp then body_type else domain_type) f_Us); 

49176  197 
in 
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Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
49176  199 
end; 
200 

49210  201 
val fp_iters as fp_iter1 :: _ = map (mk_iter_like As Cs) fp_iters0; 
202 
val fp_recs as fp_rec1 :: _ = map (mk_iter_like As Cs) fp_recs0; 

203 

49212  204 
val fp_iter_fun_Ts = fst (split_last (binder_types (fastype_of fp_iter1))); 
205 
val fp_rec_fun_Ts = fst (split_last (binder_types (fastype_of fp_rec1))); 

49204  206 

207 
fun dest_rec_pair (T as Type (@{type_name prod}, Us as [_, U])) = 

208 
if member (op =) Cs U then Us else [T] 

209 
 dest_rec_pair T = [T]; 

210 

49215  211 
val ((iter_only as (gss, g_Tss, yssss), rec_only as (hss, h_Tss, zssss)), 
49233  212 
(zs, cs, cpss, p_Tss, coiter_only as ((pgss, cgsss), g_sum_prod_Ts, g_prod_Tss, g_Tsss), 
49215  213 
corec_only as ((phss, chsss), h_sum_prod_Ts, h_prod_Tss, h_Tsss))) = 
49208  214 
if lfp then 
215 
let 

216 
val y_Tsss = 

49210  217 
map3 (fn n => fn ms => map2 dest_tupleT ms o dest_sumTN n o domain_type) 
49212  218 
ns mss fp_iter_fun_Ts; 
49208  219 
val g_Tss = map2 (map2 (curry (op >))) y_Tsss Css; 
220 

221 
val ((gss, ysss), _) = 

222 
lthy 

223 
> mk_Freess "f" g_Tss 

224 
>> mk_Freesss "x" y_Tsss; 

49204  225 

49208  226 
val z_Tssss = 
49210  227 
map3 (fn n => fn ms => map2 (map dest_rec_pair oo dest_tupleT) ms o dest_sumTN n 
49212  228 
o domain_type) ns mss fp_rec_fun_Ts; 
49208  229 
val h_Tss = map2 (map2 (fold_rev (curry (op >)))) z_Tssss Css; 
49204  230 

49208  231 
val hss = map2 (map2 retype_free) gss h_Tss; 
232 
val (zssss, _) = 

233 
lthy 

234 
> mk_Freessss "x" z_Tssss; 

49210  235 
in 
49215  236 
(((gss, g_Tss, map (map (map single)) ysss), (hss, h_Tss, zssss)), 
49233  237 
([], [], [], [], (([], []), [], [], []), (([], []), [], [], []))) 
49210  238 
end 
49208  239 
else 
49210  240 
let 
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241 
(*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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243 

49211  244 
val p_Tss = 
49210  245 
map2 (fn C => fn n => replicate (Int.max (0, n  1)) (C > HOLogic.boolT)) Cs ns; 
49211  246 

49215  247 
fun popescu_zip [] [fs] = fs 
248 
 popescu_zip (p :: ps) (fs :: fss) = p :: fs @ popescu_zip ps fss; 

249 

49212  250 
fun mk_types fun_Ts = 
251 
let 

252 
val f_sum_prod_Ts = map range_type fun_Ts; 

253 
val f_prod_Tss = map2 dest_sumTN ns f_sum_prod_Ts; 

254 
val f_Tsss = 

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255 
map3 (fn C => map2 (map (curry (op >) C) oo dest_tupleT)) Cs mss' f_prod_Tss; 
49212  256 
val pf_Tss = map2 popescu_zip p_Tss f_Tsss 
257 
in (f_sum_prod_Ts, f_prod_Tss, f_Tsss, pf_Tss) end; 

49176  258 

49212  259 
val (g_sum_prod_Ts, g_prod_Tss, g_Tsss, pg_Tss) = mk_types fp_iter_fun_Ts; 
260 
val (h_sum_prod_Ts, h_prod_Tss, h_Tsss, ph_Tss) = mk_types fp_rec_fun_Ts; 

49211  261 

49233  262 
val ((((Free (z, _), cs), pss), gsss), _) = 
49210  263 
lthy 
49233  264 
> yield_singleton (mk_Frees "z") dummyT 
265 
>> mk_Frees "a" Cs 

49211  266 
>> mk_Freess "p" p_Tss 
49210  267 
>> mk_Freesss "g" g_Tsss; 
268 

49211  269 
val hsss = map2 (map2 (map2 retype_free)) gsss h_Tsss; 
270 

49212  271 
val cpss = map2 (fn c => map (fn p => p $ c)) cs pss; 
272 

273 
fun mk_terms fsss = 

274 
let 

275 
val pfss = map2 popescu_zip pss fsss; 

276 
val cfsss = map2 (fn c => map (map (fn f => f $ c))) cs fsss 

277 
in (pfss, cfsss) end; 

49210  278 
in 
49212  279 
((([], [], []), ([], [], [])), 
49233  280 
([z], cs, cpss, p_Tss, (mk_terms gsss, g_sum_prod_Ts, g_prod_Tss, pg_Tss), 
49212  281 
(mk_terms hsss, h_sum_prod_Ts, h_prod_Tss, ph_Tss))) 
49210  282 
end; 
283 

49212  284 
fun pour_some_sugar_on_type (((((((((((((((((b, fpT), C), fld), unf), fp_iter), fp_rec), 
285 
fld_unf), unf_fld), fld_inject), n), ks), ms), ctr_binders), ctr_mixfixes), ctr_Tss), 

286 
disc_binders), sel_binderss) no_defs_lthy = 

49176  287 
let 
49201  288 
val unfT = domain_type (fastype_of fld); 
49210  289 
val ctr_prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
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290 
val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  291 

49176  292 
val ((((u, v), fs), xss), _) = 
49204  293 
no_defs_lthy 
49201  294 
> yield_singleton (mk_Frees "u") unfT 
295 
>> yield_singleton (mk_Frees "v") fpT 

49176  296 
>> mk_Frees "f" case_Ts 
49124  297 
>> mk_Freess "x" ctr_Tss; 
49121  298 

49129  299 
val ctr_rhss = 
49121  300 
map2 (fn k => fn xs => 
49210  301 
fold_rev Term.lambda xs (fld $ mk_InN ctr_prod_Ts (HOLogic.mk_tuple xs) k)) ks xss; 
49121  302 

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val case_binder = Binding.suffix_name ("_" ^ caseN) b; 
49129  304 

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305 
val case_rhs = 
49176  306 
fold_rev Term.lambda (fs @ [v]) (mk_sum_caseN (map2 mk_uncurried_fun fs xss) $ (unf $ v)); 
49129  307 

49201  308 
val ((raw_case :: raw_ctrs, raw_case_def :: raw_ctr_defs), (lthy', lthy)) = no_defs_lthy 
49169  309 
> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => 
310 
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 

49201  311 
(case_binder :: ctr_binders) (NoSyn :: ctr_mixfixes) (case_rhs :: ctr_rhss) 
49121  312 
> `Local_Theory.restore; 
313 

314 
(*transforms defined frees into consts (and more)*) 

315 
val phi = Proof_Context.export_morphism lthy lthy'; 

316 

317 
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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319 

49203  320 
val ctrs0 = map (Morphism.term phi) raw_ctrs; 
321 
val casex0 = Morphism.term phi raw_case; 

322 

323 
val ctrs = map (mk_ctr As) ctrs0; 

49121  324 

49135  325 
fun exhaust_tac {context = ctxt, ...} = 
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326 
let 
49135  327 
val fld_iff_unf_thm = 
328 
let 

329 
val goal = 

330 
fold_rev Logic.all [u, v] 

331 
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u))); 

332 
in 

333 
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => 

49201  334 
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unfT, fpT]) 
49176  335 
(certify lthy fld) (certify lthy unf) fld_unf unf_fld) 
49135  336 
> Thm.close_derivation 
337 
> Morphism.thm phi 

338 
end; 

339 

340 
val sumEN_thm' = 

341 
Local_Defs.unfold lthy @{thms all_unit_eq} 

49210  342 
(Drule.instantiate' (map (SOME o certifyT lthy) ctr_prod_Ts) [] (mk_sumEN n)) 
49135  343 
> Morphism.thm phi; 
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344 
in 
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changeset

345 
mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm' 
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
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parents:
49121
diff
changeset

346 
end; 
49121  347 

49126  348 
val inject_tacss = 
49205  349 
map2 (fn 0 => K []  _ => fn ctr_def => [fn {context = ctxt, ...} => 
350 
mk_inject_tac ctxt ctr_def fld_inject]) ms ctr_defs; 

49126  351 

49127  352 
val half_distinct_tacss = 
353 
map (map (fn (def, def') => fn {context = ctxt, ...} => 

354 
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs); 

355 

49130
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
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parents:
49129
diff
changeset

356 
val case_tacs = 
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
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parents:
49129
diff
changeset

357 
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => 
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
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parents:
49129
diff
changeset

358 
mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs; 
49121  359 

360 
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; 

49134
846264f80f16
optionally provide extra dead variables to the FP constructions
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parents:
49130
diff
changeset

361 

49210  362 
fun some_lfp_sugar no_defs_lthy = 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
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parents:
49130
diff
changeset

363 
let 
49208  364 
val fpT_to_C = fpT > C; 
49199  365 

49215  366 
fun generate_iter_like (suf, fp_iter_like, (fss, f_Tss, xssss)) = 
367 
let 

368 
val res_T = fold_rev (curry (op >)) f_Tss fpT_to_C; 

369 

370 
val binder = Binding.suffix_name ("_" ^ suf) b; 

49199  371 

49215  372 
val spec = 
373 
mk_Trueprop_eq (lists_bmoc fss (Free (Binding.name_of binder, res_T)), 

374 
Term.list_comb (fp_iter_like, 

375 
map2 (mk_sum_caseN oo map2 mk_uncurried2_fun) fss xssss)); 

376 
in (binder, spec) end; 

49199  377 

49215  378 
val iter_likes = 
379 
[(iterN, fp_iter, iter_only), 

380 
(recN, fp_rec, rec_only)]; 

381 

382 
val (binders, specs) = map generate_iter_like iter_likes > split_list; 

383 

384 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49201  385 
> apfst split_list o fold_map2 (fn b => fn spec => 
49199  386 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 
49215  387 
#>> apsnd snd) binders specs 
49199  388 
> `Local_Theory.restore; 
49201  389 

390 
(*transforms defined frees into consts (and more)*) 

391 
val phi = Proof_Context.export_morphism lthy lthy'; 

392 

49215  393 
val [iter_def, rec_def] = map (Morphism.thm phi) defs; 
49201  394 

49215  395 
val [iter, recx] = map (mk_iter_like As Cs o Morphism.term phi) csts; 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
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parents:
49130
diff
changeset

396 
in 
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
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parents:
49213
diff
changeset

397 
((ctrs, iter, recx, v, xss, ctr_defs, iter_def, rec_def), lthy) 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
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parents:
49130
diff
changeset

398 
end; 
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

399 

49210  400 
fun some_gfp_sugar no_defs_lthy = 
401 
let 

402 
val B_to_fpT = C > fpT; 

49211  403 

49212  404 
fun generate_coiter_like (suf, fp_iter_like, ((pfss, cfsss), f_sum_prod_Ts, f_prod_Tss, 
405 
pf_Tss)) = 

49211  406 
let 
407 
val res_T = fold_rev (curry (op >)) pf_Tss B_to_fpT; 

49210  408 

49211  409 
val binder = Binding.suffix_name ("_" ^ suf) b; 
49210  410 

49215  411 
fun mk_popescu_join c n cps sum_prod_T prod_Ts cfss = 
49211  412 
Term.lambda c (mk_IfN sum_prod_T cps 
413 
(map2 (mk_InN prod_Ts) (map HOLogic.mk_tuple cfss) (1 upto n))); 

49210  414 

49211  415 
val spec = 
49212  416 
mk_Trueprop_eq (lists_bmoc pfss (Free (Binding.name_of binder, res_T)), 
49211  417 
Term.list_comb (fp_iter_like, 
49215  418 
map6 mk_popescu_join cs ns cpss f_sum_prod_Ts f_prod_Tss cfsss)); 
49211  419 
in (binder, spec) end; 
49210  420 

49212  421 
val coiter_likes = 
49215  422 
[(coiterN, fp_iter, coiter_only), 
423 
(corecN, fp_rec, corec_only)]; 

49212  424 

49211  425 
val (binders, specs) = map generate_coiter_like coiter_likes > split_list; 
426 

427 
val ((csts, defs), (lthy', lthy)) = no_defs_lthy 

49210  428 
> apfst split_list o fold_map2 (fn b => fn spec => 
429 
Specification.definition (SOME (b, NONE, NoSyn), ((Thm.def_binding b, []), spec)) 

49211  430 
#>> apsnd snd) binders specs 
49210  431 
> `Local_Theory.restore; 
432 

433 
(*transforms defined frees into consts (and more)*) 

434 
val phi = Proof_Context.export_morphism lthy lthy'; 

435 

49211  436 
val [coiter_def, corec_def] = map (Morphism.thm phi) defs; 
49210  437 

49211  438 
val [coiter, corec] = map (mk_iter_like As Cs o Morphism.term phi) csts; 
49210  439 
in 
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

440 
((ctrs, coiter, corec, v, xss, ctr_defs, coiter_def, corec_def), lthy) 
49210  441 
end; 
49119  442 
in 
49203  443 
wrap_datatype tacss ((ctrs0, casex0), (disc_binders, sel_binderss)) lthy' 
49210  444 
> (if lfp then some_lfp_sugar else some_gfp_sugar) 
49119  445 
end; 
49167  446 

49226  447 
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

448 
val map_ids = map map_id_of_bnf nested_bnfs; 
49226  449 

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

450 
fun mk_map Ts Us t = 
49217  451 
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
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parents:
49213
diff
changeset

452 
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

453 
end; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

454 

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

455 
fun pour_more_sugar_on_lfps ((ctrss, iters, recs, vs, xsss, ctr_defss, iter_defs, rec_defs), 
49205  456 
lthy) = 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

457 
let 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

458 
val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss; 
49212  459 
val giters = map (lists_bmoc gss) iters; 
460 
val hrecs = map (lists_bmoc hss) recs; 

49201  461 

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

462 
val (iter_thmss, rec_thmss) = 
49207  463 
let 
49212  464 
fun mk_goal_iter_like fss fiter_like xctr f xs fxs = 
49207  465 
fold_rev (fold_rev Logic.all) (xs :: fss) 
49212  466 
(mk_Trueprop_eq (fiter_like $ xctr, Term.list_comb (f, fxs))); 
49204  467 

49233  468 
fun build_call fiter_likes maybe_tick = 
469 
let 

470 
fun build (T, U) = 

471 
if T = U then 

472 
Const (@{const_name id}, T > T) 

473 
else 

474 
(case (find_index (curry (op =) T) fpTs, (T, U)) of 

475 
(~1, (Type (s, Ts), Type (_, Us))) => 

476 
let 

477 
val map0 = map_of_bnf (the (bnf_of lthy (Long_Name.base_name s))); 

478 
val mapx = mk_map Ts Us map0; 

479 
val TUs = 

480 
map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx))))); 

481 
val args = map build TUs; 

482 
in Term.list_comb (mapx, args) end 

483 
 (j, _) => maybe_tick (nth vs j) (nth fiter_likes j)) 

484 
in build end; 

485 

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

486 
fun mk_U maybe_prodT = 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

487 
typ_subst (map2 (fn fpT => fn C => (fpT, maybe_prodT fpT C)) fpTs Cs); 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

488 

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

489 
fun repair_calls fiter_likes maybe_cons maybe_tick maybe_prodT (x as Free (_, T)) = 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

490 
if member (op =) fpTs T then 
49233  491 
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

492 
else if exists_subtype (member (op =) fpTs) T then 
49233  493 
[build_call fiter_likes maybe_tick (T, mk_U maybe_prodT T) $ x] 
49214
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

494 
else 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

495 
[x]; 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

496 

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

497 
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

498 
val hxsss = 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

499 
map (map (maps (repair_calls hrecs cons tick (curry HOLogic.mk_prodT)))) xsss; 
49204  500 

49212  501 
val goal_iterss = map5 (map4 o mk_goal_iter_like gss) giters xctrss gss xsss gxsss; 
502 
val goal_recss = map5 (map4 o mk_goal_iter_like hss) hrecs xctrss hss xsss hxsss; 

49204  503 

49203  504 
val iter_tacss = 
49229
d5717b5e2217
use map_id, not map_id', to allow better composition
blanchet
parents:
49226
diff
changeset

505 
map2 (map o mk_iter_like_tac pre_map_defs map_ids iter_defs) fp_iter_thms ctr_defss; 
49203  506 
val rec_tacss = 
49229
d5717b5e2217
use map_id, not map_id', to allow better composition
blanchet
parents:
49226
diff
changeset

507 
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

508 
in 
49205  509 
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 
510 
goal_iterss iter_tacss, 

511 
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 

512 
goal_recss rec_tacss) 

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

513 
end; 
49201  514 

49226  515 
val notes = 
49202
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

516 
[(itersN, iter_thmss), 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

517 
(recsN, rec_thmss)] 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

518 
> maps (fn (thmN, thmss) => 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

519 
map2 (fn b => fn thms => 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

520 
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

521 
bs thmss); 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

522 
in 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

523 
lthy > Local_Theory.notes notes > snd 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

524 
end; 
f493cd25737f
some work towards iterator and recursor properties
blanchet
parents:
49201
diff
changeset

525 

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

526 
fun pour_more_sugar_on_gfps ((ctrss, coiters, corecs, vs, xsss, ctr_defss, coiter_defs, 
2a3cb4c71b87
construct the right iterator theorem in the recursive case
blanchet
parents:
49213
diff
changeset

527 
corec_defs), lthy) = 
49212  528 
let 
49233  529 
val z = the_single zs; 
530 

49212  531 
val gcoiters = map (lists_bmoc pgss) coiters; 
532 
val hcorecs = map (lists_bmoc phss) corecs; 

533 

534 
val (coiter_thmss, corec_thmss) = 

535 
let 

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

536 
fun mk_goal_cond pos = HOLogic.mk_Trueprop o (not pos ? HOLogic.mk_not); 
49212  537 

538 
fun mk_goal_coiter_like pfss c cps fcoiter_like n k ctr cfs' = 

539 
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

540 
(Logic.list_implies (seq_conds mk_goal_cond n k cps, 
49212  541 
mk_Trueprop_eq (fcoiter_like $ c, Term.list_comb (ctr, cfs')))); 
542 

49233  543 
fun build_call fiter_likes maybe_tack = 
544 
let 

545 
fun build (T, U) = 

546 
if T = U then 

547 
Const (@{const_name id}, T > T) 

548 
else 

549 
(case (find_index (curry (op =) U) fpTs, (T, U)) of 

550 
(~1, (Type (s, Ts), Type (_, Us))) => 

551 
let 

552 
val map0 = map_of_bnf (the (bnf_of lthy (Long_Name.base_name s))); 

553 
val mapx = mk_map Ts Us map0; 

554 
val TUs = 

555 
map dest_funT (fst (split_last (fst (strip_map_type (fastype_of mapx))))); 

556 
val args = map build TUs; 

557 
in Term.list_comb (mapx, args) end 

558 
 (j, _) => maybe_tack (nth cs j, nth vs j) (nth fiter_likes j)) 

559 
in build end; 

560 

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

561 
fun mk_U maybe_sumT = 
49233  562 
typ_subst (map2 (fn C => fn fpT => (maybe_sumT fpT C, fpT)) Cs fpTs); 
49212  563 

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

564 
fun repair_calls fiter_likes maybe_sumT maybe_tack 
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

565 
(cf as Free (_, Type (_, [_, T])) $ _) = 
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

566 
if exists_subtype (member (op =) Cs) T then 
49233  567 
build_call fiter_likes maybe_tack (T, mk_U maybe_sumT T) $ cf 
49232
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

568 
else 
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

569 
cf; 
9ea11f0c53e4
fixed and enabled generation of "coiters" theorems, including the recursive case
blanchet
parents:
49230
diff
changeset

570 

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

571 
val cgsss = map (map (map (repair_calls gcoiters (K I) (K I)))) cgsss; 
49233  572 
val chsss = map (map (map (repair_calls hcorecs (curry mk_sumT) (tack z)))) chsss; 
49212  573 

574 
val goal_coiterss = 

575 
map7 (map3 oooo mk_goal_coiter_like pgss) cs cpss gcoiters ns kss ctrss cgsss; 

49233  576 
val goal_corecss = 
577 
map7 (map3 oooo mk_goal_coiter_like phss) cs cpss hcorecs ns kss ctrss chsss; 

49213  578 

579 
val coiter_tacss = 

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

580 
map3 (map oo mk_coiter_like_tac coiter_defs map_ids) fp_iter_thms pre_map_defs 
49226  581 
ctr_defss; 
49233  582 
val corec_tacss = 
583 
map3 (map oo mk_coiter_like_tac corec_defs map_ids) fp_rec_thms pre_map_defs 

584 
ctr_defss; 

49212  585 
in 
49213  586 
(map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 
587 
goal_coiterss coiter_tacss, 

49233  588 
map2 (map2 (fn goal => fn tac => Skip_Proof.prove lthy [] [] goal (tac o #context))) 
589 
goal_corecss corec_tacss) 

49212  590 
end; 
591 

592 
val notes = 

49233  593 
[(coitersN, coiter_thmss), 
594 
(corecsN, corec_thmss)] 

49212  595 
> maps (fn (thmN, thmss) => 
596 
map2 (fn b => fn thms => 

597 
((Binding.qualify true (Binding.name_of b) (Binding.name thmN), []), [(thms, [])])) 

598 
bs thmss); 

599 
in 

49230  600 
lthy > Local_Theory.notes notes > snd 
49212  601 
end; 
602 

49204  603 
val lthy' = lthy 
49210  604 
> fold_map pour_some_sugar_on_type (bs ~~ fpTs ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~ 
49212  605 
fp_recs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ns ~~ kss ~~ mss ~~ ctr_binderss ~~ 
606 
ctr_mixfixess ~~ ctr_Tsss ~~ disc_binderss ~~ sel_bindersss) 

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

607 
>> split_list8 
49212  608 
> (if lfp then pour_more_sugar_on_lfps else pour_more_sugar_on_gfps); 
49167  609 

610 
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ 

49208  611 
(if lfp then "" else "co") ^ "datatype")); 
49112  612 
in 
49204  613 
(timer; lthy') 
49112  614 
end; 
615 

49199  616 
fun datatype_cmd info specs lthy = 
49121  617 
let 
49209  618 
(* 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

619 
(*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

620 
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

621 
val fake_thy = Theory.copy 
49184
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset

622 
#> fold (fn spec => perhaps (try (Sign.add_type lthy 
83fdea0c4779
gracefully handle shadowing case (fourth step of sugar localization)
blanchet
parents:
49183
diff
changeset

623 
(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

624 
val fake_lthy = Proof_Context.background_theory fake_thy lthy; 
49121  625 
in 
49199  626 
prepare_datatype Syntax.read_typ info specs fake_lthy lthy 
49121  627 
end; 
49119  628 

49129  629 
val parse_opt_binding_colon = Scan.optional (Parse.binding  Parse.$$$ ":") no_binder 
49119  630 

49112  631 
val parse_ctr_arg = 
49119  632 
Parse.$$$ "("  parse_opt_binding_colon  Parse.typ  Parse.$$$ ")"  
49129  633 
(Parse.typ >> pair no_binder); 
49112  634 

635 
val parse_single_spec = 

636 
Parse.type_args_constrained  Parse.binding  Parse.opt_mixfix  

49119  637 
(@{keyword "="}  Parse.enum1 "" (parse_opt_binding_colon  Parse.binding  
638 
Scan.repeat parse_ctr_arg  Parse.opt_mixfix)); 

49112  639 

640 
val _ = 

641 
Outer_Syntax.local_theory @{command_spec "data"} "define BNFbased inductive datatypes" 

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(Parse.and_list1 parse_single_spec >> datatype_cmd true); 
49112  643 

644 
val _ = 

645 
Outer_Syntax.local_theory @{command_spec "codata"} "define BNFbased coinductive datatypes" 

49208  646 
(Parse.and_list1 parse_single_spec >> datatype_cmd false); 
49112  647 

648 
end; 