author  wenzelm 
Fri, 19 Jan 2007 22:08:08 +0100  
changeset 22101  6d13239d5f52 
parent 21350  6e58289b6685 
child 22578  b0eb5652f210 
permissions  rwrr 
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(* Title: ZF/Tools/datatype_package.ML 
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ID: $Id$ 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 

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Copyright 1994 University of Cambridge 

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Datatype/Codatatype Definitions 
6052  7 

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The functor will be instantiated for normal sums/products (datatype defs) 

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and nonstandard sums/products (codatatype defs) 

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Sums are used only for mutual recursion; 

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Products are used only to derive "streamlined" induction rules for relations 

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*) 

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type datatype_result = 

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{con_defs : thm list, (*definitions made in thy*) 

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case_eqns : thm list, (*equations for case operator*) 

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recursor_eqns : thm list, (*equations for the recursor*) 

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free_iffs : thm list, (*freeness rewrite rules*) 

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free_SEs : thm list, (*freeness destruct rules*) 

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mk_free : string > thm}; (*function to make freeness theorems*) 
6052  22 

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signature DATATYPE_ARG = 

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sig 
6052  25 
val intrs : thm list 
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val elims : thm list 

12183  27 
end; 
6052  28 

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signature DATATYPE_PACKAGE = 

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sig 
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(*Insert definitions for the recursive sets, which 
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must *already* be declared as constants in parent theory!*) 

12183  33 
val add_datatype_i: term * term list > Ind_Syntax.constructor_spec list list > 
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thm list * thm list * thm list > theory > theory * inductive_result * datatype_result 

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val add_datatype: string * string list > (string * string list * mixfix) list list > 

15703  36 
(thmref * Attrib.src list) list * (thmref * Attrib.src list) list * 
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(thmref * Attrib.src list) list > theory > theory * inductive_result * datatype_result 

12131  38 
end; 
6052  39 

12131  40 
functor Add_datatype_def_Fun 
12183  41 
(structure Fp: FP and Pr : PR and CP: CARTPROD and Su : SU 
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and Ind_Package : INDUCTIVE_PACKAGE 

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and Datatype_Arg : DATATYPE_ARG 

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val coind : bool): DATATYPE_PACKAGE = 

6052  45 
struct 
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12183  47 
(*con_ty_lists specifies the constructors in the form (name, prems, mixfix) *) 
6052  48 

12183  49 
fun add_datatype_i (dom_sum, rec_tms) con_ty_lists (monos, type_intrs, type_elims) thy = 
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let 
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val dummy = (*has essential ancestors?*) 

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Theory.requires thy "Datatype" "(co)datatype definitions"; 

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val rec_hds = map head_of rec_tms; 
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val dummy = assert_all is_Const rec_hds 
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(fn t => "Datatype set not previously declared as constant: " ^ 
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Sign.string_of_term (sign_of thy) t); 
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val rec_names = map (#1 o dest_Const) rec_hds 
6052  61 
val rec_base_names = map Sign.base_name rec_names 
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val big_rec_base_name = space_implode "_" rec_base_names 

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val thy_path = thy > Theory.add_path big_rec_base_name 

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val sign = sign_of thy_path 

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val big_rec_name = Sign.intern_const sign big_rec_base_name; 

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val intr_tms = Ind_Syntax.mk_all_intr_tms sign (rec_tms, con_ty_lists); 
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12131  71 
val dummy = 
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writeln ((if coind then "Codatatype" else "Datatype") ^ " definition " ^ quote big_rec_name); 
6052  73 

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val case_varname = "f"; (*name for case variables*) 

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(** Define the constructors **) 

77 

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(*The empty tuple is 0*) 

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fun mk_tuple [] = Const("0",iT) 

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 mk_tuple args = foldr1 (fn (t1, t2) => Pr.pair $ t1 $ t2) args; 
6052  81 

7696  82 
fun mk_inject n k u = access_bal (fn t => Su.inl $ t, fn t => Su.inr $ t, u) n k; 
6052  83 

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val npart = length rec_names; (*number of mutually recursive parts*) 

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86 

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val full_name = Sign.full_name sign; 

88 

12131  89 
(*Make constructor definition; 
6052  90 
kpart is the number of this mutually recursive part*) 
12131  91 
fun mk_con_defs (kpart, con_ty_list) = 
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let val ncon = length con_ty_list (*number of constructors*) 
12131  93 
fun mk_def (((id,T,syn), name, args, prems), kcon) = 
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(*kcon is index of constructor*) 

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Logic.mk_defpair (list_comb (Const (full_name name, T), args), 

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mk_inject npart kpart 

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(mk_inject ncon kcon (mk_tuple args))) 

6052  98 
in ListPair.map mk_def (con_ty_list, 1 upto ncon) end; 
99 

100 

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(*** Define the case operator ***) 

102 

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(*Combine split terms using case; yields the case operator for one part*) 

12131  104 
fun call_case case_list = 
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let fun call_f (free,[]) = Abs("null", iT, free) 
12131  106 
 call_f (free,args) = 
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CP.ap_split (foldr1 CP.mk_prod (map (#2 o dest_Free) args)) 

108 
Ind_Syntax.iT 

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free 

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in fold_bal (fn (t1, t2) => Su.elim $ t1 $ t2) (map call_f case_list) end; 
6052  111 

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(** Generating function variables for the case definition 

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Nonidentifiers (e.g. infixes) get a name of the form f_op_nnn. **) 

114 

115 
(*The function variable for a single constructor*) 

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fun add_case (((_, T, _), name, args, _), (opno, cases)) = 

117 
if Syntax.is_identifier name then 

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(opno, (Free (case_varname ^ "_" ^ name, T), args) :: cases) 

119 
else 

12131  120 
(opno + 1, (Free (case_varname ^ "_op_" ^ string_of_int opno, T), args) 
6052  121 
:: cases); 
122 

123 
(*Treatment of a list of constructors, for one part 

124 
Result adds a list of terms, each a function variable with arguments*) 

125 
fun add_case_list (con_ty_list, (opno, case_lists)) = 

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let val (opno', case_list) = foldr add_case (opno, []) con_ty_list 
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in (opno', case_list :: case_lists) end; 
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(*Treatment of all parts*) 

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val (_, case_lists) = foldr add_case_list (1,[]) con_ty_lists; 
6052  131 

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(*extract the types of all the variables*) 

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val case_typ = List.concat (map (map (#2 o #1)) con_ty_lists) > (iT>iT); 
6052  134 

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val case_base_name = big_rec_base_name ^ "_case"; 

136 
val case_name = full_name case_base_name; 

137 

138 
(*The list of all the function variables*) 

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val case_args = List.concat (map (map #1) case_lists); 
6052  140 

12131  141 
val case_const = Const (case_name, case_typ); 
6052  142 
val case_tm = list_comb (case_const, case_args); 
143 

144 
val case_def = Logic.mk_defpair 

7696  145 
(case_tm, fold_bal (fn (t1, t2) => Su.elim $ t1 $ t2) (map call_case case_lists)); 
6052  146 

147 

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(** Generating function variables for the recursor definition 

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Nonidentifiers (e.g. infixes) get a name of the form f_op_nnn. **) 

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151 
(*a recursive call for x is the application rec`x *) 

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val rec_call = Ind_Syntax.apply_const $ Free ("rec", iT); 

153 

12131  154 
(*look back down the "case args" (which have been reversed) to 
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determine the de Bruijn index*) 
156 
fun make_rec_call ([], _) arg = error 

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"Internal error in datatype (variable name mismatch)" 
158 
 make_rec_call (a::args, i) arg = 

159 
if a = arg then rec_call $ Bound i 

160 
else make_rec_call (args, i+1) arg; 

6052  161 

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(*creates one case of the "X_case" definition of the recursor*) 

12131  163 
fun call_recursor ((case_var, case_args), (recursor_var, recursor_args)) = 
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let fun add_abs (Free(a,T), u) = Abs(a,T,u) 
12131  165 
val ncase_args = length case_args 
166 
val bound_args = map Bound ((ncase_args  1) downto 0) 

167 
val rec_args = map (make_rec_call (rev case_args,0)) 

168 
(List.drop(recursor_args, ncase_args)) 

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in 
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foldr add_abs 
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(list_comb (recursor_var, 
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bound_args @ rec_args)) case_args 
6052  173 
end 
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175 
(*Find each recursive argument and add a recursive call for it*) 

176 
fun rec_args [] = [] 

177 
 rec_args ((Const("op :",_)$arg$X)::prems) = 

178 
(case head_of X of 

12131  179 
Const(a,_) => (*recursive occurrence?*) 
180 
if a mem_string rec_names 

181 
then arg :: rec_args prems 

182 
else rec_args prems 

183 
 _ => rec_args prems) 

184 
 rec_args (_::prems) = rec_args prems; 

6052  185 

186 
(*Add an argument position for each occurrence of a recursive set. 

187 
Strictly speaking, the recursive arguments are the LAST of the function 

188 
variable, but they all have type "i" anyway*) 

189 
fun add_rec_args args' T = (map (fn _ => iT) args') > T 

190 

191 
(*Plug in the function variable type needed for the recursor 

192 
as well as the new arguments (recursive calls)*) 

193 
fun rec_ty_elem ((id, T, syn), name, args, prems) = 

12131  194 
let val args' = rec_args prems 
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in ((id, add_rec_args args' T, syn), 

196 
name, args @ args', prems) 

6052  197 
end; 
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12131  199 
val rec_ty_lists = (map (map rec_ty_elem) con_ty_lists); 
6052  200 

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(*Treatment of all parts*) 

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val (_, recursor_lists) = foldr add_case_list (1,[]) rec_ty_lists; 
6052  203 

204 
(*extract the types of all the variables*) 

15570  205 
val recursor_typ = List.concat (map (map (#2 o #1)) rec_ty_lists) 
12131  206 
> (iT>iT); 
6052  207 

208 
val recursor_base_name = big_rec_base_name ^ "_rec"; 

209 
val recursor_name = full_name recursor_base_name; 

210 

211 
(*The list of all the function variables*) 

15570  212 
val recursor_args = List.concat (map (map #1) recursor_lists); 
6052  213 

214 
val recursor_tm = 

12131  215 
list_comb (Const (recursor_name, recursor_typ), recursor_args); 
6052  216 

12131  217 
val recursor_cases = map call_recursor 
15570  218 
(List.concat case_lists ~~ List.concat recursor_lists) 
6052  219 

12131  220 
val recursor_def = 
6052  221 
Logic.mk_defpair 
12131  222 
(recursor_tm, 
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Ind_Syntax.Vrecursor_const $ 

224 
absfree ("rec", iT, list_comb (case_const, recursor_cases))); 

6052  225 

226 
(* Build the new theory *) 

227 

12183  228 
val need_recursor = (not coind andalso recursor_typ <> case_typ); 
6052  229 

12131  230 
fun add_recursor thy = 
6052  231 
if need_recursor then 
12131  232 
thy > Theory.add_consts_i 
233 
[(recursor_base_name, recursor_typ, NoSyn)] 

18358  234 
> (snd o PureThy.add_defs_i false [Thm.no_attributes recursor_def]) 
6052  235 
else thy; 
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18358  237 
val (con_defs, thy0) = thy_path 
12131  238 
> Theory.add_consts_i 
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((case_base_name, case_typ, NoSyn) :: 

15570  240 
map #1 (List.concat con_ty_lists)) 
12131  241 
> PureThy.add_defs_i false 
242 
(map Thm.no_attributes 

243 
(case_def :: 

15570  244 
List.concat (ListPair.map mk_con_defs 
12131  245 
(1 upto npart, con_ty_lists)))) 
18358  246 
> add_recursor 
247 
> Theory.parent_path 

6052  248 

15570  249 
val intr_names = map #2 (List.concat con_ty_lists); 
12131  250 
val (thy1, ind_result) = 
12187  251 
thy0 > Ind_Package.add_inductive_i 
252 
false (rec_tms, dom_sum) (map Thm.no_attributes (intr_names ~~ intr_tms)) 

253 
(monos, con_defs, type_intrs @ Datatype_Arg.intrs, type_elims @ Datatype_Arg.elims); 

6052  254 

255 
(**** Now prove the datatype theorems in this theory ****) 

256 

257 

258 
(*** Prove the case theorems ***) 

259 

12131  260 
(*Each equation has the form 
6052  261 
case(f_con1,...,f_conn)(coni(args)) = f_coni(args) *) 
12131  262 
fun mk_case_eqn (((_,T,_), name, args, _), case_free) = 
6052  263 
FOLogic.mk_Trueprop 
264 
(FOLogic.mk_eq 

265 
(case_tm $ 

12131  266 
(list_comb (Const (Sign.intern_const (sign_of thy1) name,T), 
267 
args)), 

268 
list_comb (case_free, args))); 

6052  269 

270 
val case_trans = hd con_defs RS Ind_Syntax.def_trans 

271 
and split_trans = Pr.split_eq RS meta_eq_to_obj_eq RS trans; 

272 

17985  273 
fun prove_case_eqn (arg, con_def) = 
20046  274 
Goal.prove_global thy1 [] [] 
17985  275 
(Ind_Syntax.traceIt "next case equation = " thy1 (mk_case_eqn arg)) 
276 
(*Proves a single case equation. Could use simp_tac, but it's slower!*) 

277 
(fn _ => EVERY 

278 
[rewtac con_def, 

279 
rtac case_trans 1, 

20046  280 
REPEAT (resolve_tac [refl, split_trans, Su.case_inl RS trans, Su.case_inr RS trans] 1)]); 
6052  281 

12187  282 
val free_iffs = map standard (con_defs RL [Ind_Syntax.def_swap_iff]); 
6052  283 

12131  284 
val case_eqns = 
285 
map prove_case_eqn 

15570  286 
(List.concat con_ty_lists ~~ case_args ~~ tl con_defs); 
6052  287 

288 
(*** Prove the recursor theorems ***) 

289 

290 
val recursor_eqns = case try (get_def thy1) recursor_base_name of 

15531  291 
NONE => (writeln " [ No recursion operator ]"; 
12131  292 
[]) 
15531  293 
 SOME recursor_def => 
6052  294 
let 
12131  295 
(*Replace subterms rec`x (where rec is a Free var) by recursor_tm(x) *) 
296 
fun subst_rec (Const("op `",_) $ Free _ $ arg) = recursor_tm $ arg 

297 
 subst_rec tm = 

298 
let val (head, args) = strip_comb tm 

299 
in list_comb (head, map subst_rec args) end; 

6052  300 

12131  301 
(*Each equation has the form 
302 
REC(coni(args)) = f_coni(args, REC(rec_arg), ...) 

303 
where REC = recursor(f_con1,...,f_conn) and rec_arg is a recursive 

304 
constructor argument.*) 

305 
fun mk_recursor_eqn (((_,T,_), name, args, _), recursor_case) = 

306 
FOLogic.mk_Trueprop 

307 
(FOLogic.mk_eq 

308 
(recursor_tm $ 

309 
(list_comb (Const (Sign.intern_const (sign_of thy1) name,T), 

310 
args)), 

18185  311 
subst_rec (Term.betapplys (recursor_case, args)))); 
6052  312 

12131  313 
val recursor_trans = recursor_def RS def_Vrecursor RS trans; 
6052  314 

12131  315 
fun prove_recursor_eqn arg = 
20046  316 
Goal.prove_global thy1 [] [] 
17985  317 
(Ind_Syntax.traceIt "next recursor equation = " thy1 (mk_recursor_eqn arg)) 
318 
(*Proves a single recursor equation.*) 

319 
(fn _ => EVERY 

320 
[rtac recursor_trans 1, 

321 
simp_tac (rank_ss addsimps case_eqns) 1, 

20046  322 
IF_UNSOLVED (simp_tac (rank_ss addsimps tl con_defs) 1)]); 
6052  323 
in 
15570  324 
map prove_recursor_eqn (List.concat con_ty_lists ~~ recursor_cases) 
6052  325 
end 
326 

327 
val constructors = 

328 
map (head_of o #1 o Logic.dest_equals o #prop o rep_thm) (tl con_defs); 

329 

12187  330 
val free_SEs = map standard (Ind_Syntax.mk_free_SEs free_iffs); 
6052  331 

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val {intrs, elim, induct, mutual_induct, ...} = ind_result 
6052  333 

334 
(*Typical theorems have the form ~con1=con2, con1=con2==>False, 

335 
con1(x)=con1(y) ==> x=y, con1(x)=con1(y) <> x=y, etc. *) 

336 
fun mk_free s = 

17985  337 
let val thy = theory_of_thm elim in (*Don't use thy1: it will be stale*) 
20046  338 
Goal.prove_global thy [] [] (Sign.read_prop thy s) 
17985  339 
(fn _ => EVERY 
340 
[rewrite_goals_tac con_defs, 

20046  341 
fast_tac (ZF_cs addSEs free_SEs @ Su.free_SEs) 1]) 
17985  342 
end; 
6052  343 

344 
val simps = case_eqns @ recursor_eqns; 

345 

346 
val dt_info = 

12131  347 
{inductive = true, 
348 
constructors = constructors, 

349 
rec_rewrites = recursor_eqns, 

350 
case_rewrites = case_eqns, 

351 
induct = induct, 

352 
mutual_induct = mutual_induct, 

353 
exhaustion = elim}; 

6052  354 

355 
val con_info = 

356 
{big_rec_name = big_rec_name, 

12131  357 
constructors = constructors, 
6052  358 
(*let primrec handle definition by cases*) 
12131  359 
free_iffs = free_iffs, 
360 
rec_rewrites = (case recursor_eqns of 

361 
[] => case_eqns  _ => recursor_eqns)}; 

6052  362 

363 
(*associate with each constructor the datatype name and rewrites*) 

364 
val con_pairs = map (fn c => (#1 (dest_Const c), con_info)) constructors 

365 

366 
in 

367 
(*Updating theory components: simprules and datatype info*) 

368 
(thy1 > Theory.add_path big_rec_base_name 

18377  369 
> PureThy.add_thmss 
18728  370 
[(("simps", simps), [Simplifier.simp_add]), 
371 
(("", intrs), [Classical.safe_intro NONE]), 

12187  372 
(("con_defs", con_defs), []), 
373 
(("case_eqns", case_eqns), []), 

374 
(("recursor_eqns", recursor_eqns), []), 

375 
(("free_iffs", free_iffs), []), 

18377  376 
(("free_elims", free_SEs), [])] > snd 
17412  377 
> DatatypesData.map (Symtab.update (big_rec_name, dt_info)) 
378 
> ConstructorsData.map (fold Symtab.update con_pairs) 

12131  379 
> Theory.parent_path, 
6052  380 
ind_result, 
381 
{con_defs = con_defs, 

382 
case_eqns = case_eqns, 

383 
recursor_eqns = recursor_eqns, 

384 
free_iffs = free_iffs, 

385 
free_SEs = free_SEs, 

386 
mk_free = mk_free}) 

387 
end; 

388 

17936  389 
fun add_datatype (sdom, srec_tms) scon_ty_lists (raw_monos, raw_type_intrs, raw_type_elims) thy = 
12183  390 
let 
17936  391 
val read_i = Sign.simple_read_term thy Ind_Syntax.iT; 
12183  392 
val rec_tms = map read_i srec_tms; 
17936  393 
val con_ty_lists = Ind_Syntax.read_constructs thy scon_ty_lists; 
12183  394 
val dom_sum = 
395 
if sdom = "" then Ind_Syntax.data_domain coind (rec_tms, con_ty_lists) 

396 
else read_i sdom; 

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thy 
21350  399 
> IsarCmd.apply_theorems raw_monos 
400 
>> IsarCmd.apply_theorems raw_type_intrs 

401 
>> IsarCmd.apply_theorems raw_type_elims 

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> (fn ((monos, type_intrs), type_elims) => 
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add_datatype_i (dom_sum, rec_tms) con_ty_lists (monos, type_intrs, type_elims)) 
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404 
end; 
12183  405 

406 
(* outer syntax *) 

407 

17057  408 
local structure P = OuterParse and K = OuterKeyword in 
12183  409 

410 
fun mk_datatype ((((dom, dts), monos), type_intrs), type_elims) = 

411 
#1 o add_datatype (dom, map fst dts) (map snd dts) (monos, type_intrs, type_elims); 

412 

413 
val con_decl = 

414 
P.name  Scan.optional (P.$$$ "("  P.list1 P.term  P.$$$ ")") []  P.opt_mixfix 

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>> P.triple1; 
12183  416 

417 
val datatype_decl = 

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(Scan.optional ((P.$$$ "\\<subseteq>"  P.$$$ "<=")  P.!!! P.term) "")  
12183  419 
P.and_list1 (P.term  (P.$$$ "="  P.enum1 "" con_decl))  
22101  420 
Scan.optional (P.$$$ "monos"  P.!!! SpecParse.xthms1) []  
421 
Scan.optional (P.$$$ "type_intros"  P.!!! SpecParse.xthms1) []  

422 
Scan.optional (P.$$$ "type_elims"  P.!!! SpecParse.xthms1) [] 

12183  423 
>> (Toplevel.theory o mk_datatype); 
424 

425 
val coind_prefix = if coind then "co" else ""; 

426 

427 
val inductiveP = OuterSyntax.command (coind_prefix ^ "datatype") 

428 
("define " ^ coind_prefix ^ "datatype") K.thy_decl datatype_decl; 

429 

430 
val _ = OuterSyntax.add_parsers [inductiveP]; 

6052  431 

432 
end; 

12183  433 

434 
end; 

15705  435 