author  blanchet 
Thu, 06 Sep 2012 12:14:40 +0200  
changeset 49183  0cc46e2dee7e 
parent 49182  b8517107ffc5 
child 49184  83fdea0c4779 
permissions  rwrr 
49112  1 
(* Title: HOL/Codatatype/Tools/bnf_fp_sugar.ML 
2 
Author: Jasmin Blanchette, TU Muenchen 

3 
Copyright 2012 

4 

5 
Sugar for constructing LFPs and GFPs. 

6 
*) 

7 

8 
signature BNF_FP_SUGAR = 

9 
sig 

10 
end; 

11 

12 
structure BNF_FP_Sugar : BNF_FP_SUGAR = 

13 
struct 

14 

49119  15 
open BNF_Util 
16 
open BNF_Wrap 

17 
open BNF_FP_Util 

18 
open BNF_LFP 

19 
open BNF_GFP 

49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset

20 
open BNF_FP_Sugar_Tactics 
49119  21 

49129  22 
val caseN = "case"; 
23 

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

26 
fun merge_type_arg_constrained ctxt (T, c) (T', c') = 

27 
if T = T' then 

28 
(case (c, c') of 

29 
(_, NONE) => (T, c) 

30 
 (NONE, _) => (T, c') 

31 
 _ => 

32 
if c = c' then 

33 
(T, c) 

34 
else 

35 
error ("Inconsistent sort constraints for type variable " ^ 

36 
quote (Syntax.string_of_typ ctxt T))) 

37 
else 

38 
cannot_merge_types (); 

39 

40 
fun merge_type_args_constrained ctxt (cAs, cAs') = 

41 
if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs' 

42 
else cannot_merge_types (); 

43 

49121  44 
fun type_args_constrained_of (((cAs, _), _), _) = cAs; 
45 
val type_args_of = map fst o type_args_constrained_of; 

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

49121  50 
fun disc_of (((disc, _), _), _) = disc; 
51 
fun ctr_of (((_, ctr), _), _) = ctr; 

52 
fun args_of ((_, args), _) = args; 

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

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

55 
fun prepare_data prepare_typ gfp specs fake_lthy lthy = 
49112  56 
let 
49121  57 
val constrained_As = 
58 
map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs 

49119  59 
> Library.foldr1 (merge_type_args_constrained lthy); 
49121  60 
val As = map fst constrained_As; 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

61 
val As' = map dest_TFree As; 
49119  62 

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

66 
(* TODO: use sort constraints on type args *) 

67 

68 
val N = length specs; 

69 

49182
b8517107ffc5
read the real types off the constant types, rather than using the fake parser types (second step of sugar localization)
blanchet
parents:
49181
diff
changeset

70 
fun mk_fake_T b = 
49121  71 
Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))), 
72 
As); 

73 

49129  74 
val bs = map type_binder_of specs; 
49182
b8517107ffc5
read the real types off the constant types, rather than using the fake parser types (second step of sugar localization)
blanchet
parents:
49181
diff
changeset

75 
val fake_Ts = map mk_fake_T bs; 
49121  76 

49181  77 
val mixfixes = map mixfix_of specs; 
49119  78 

79 
val _ = (case duplicates Binding.eq_name bs of [] => () 

80 
 b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b))); 

81 

49121  82 
val ctr_specss = map ctr_specs_of specs; 
49119  83 

49129  84 
val disc_binderss = map (map disc_of) ctr_specss; 
85 
val ctr_binderss = map (map ctr_of) ctr_specss; 

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

49129  89 
val sel_bindersss = map (map (map fst)) ctr_argsss; 
49183
0cc46e2dee7e
careful about constructor types w.r.t. fake context (third step of localization)
blanchet
parents:
49182
diff
changeset

90 
val fake_ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss; 
49121  91 

49183
0cc46e2dee7e
careful about constructor types w.r.t. fake context (third step of localization)
blanchet
parents:
49182
diff
changeset

92 
val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss []; 
49167  93 
val _ = (case subtract (op =) As' rhs_As' of 
49165  94 
[] => () 
95 
 A' :: _ => error ("Extra type variables on rhs: " ^ 

96 
quote (Syntax.string_of_typ lthy (TFree A')))); 

97 

49176  98 
val ((Cs, Xs), _) = 
49121  99 
lthy 
100 
> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs 

101 
> mk_TFrees N 

49176  102 
>> mk_TFrees N; 
49119  103 

49176  104 
fun is_same_recT (T as Type (s, Us)) (Type (s', Us')) = 
49146  105 
s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^ 
106 
quote (Syntax.string_of_typ fake_lthy T))) 

49176  107 
 is_same_recT _ _ = false; 
49146  108 

49176  109 
fun freeze_recXs (T as Type (s, Us)) = 
49182
b8517107ffc5
read the real types off the constant types, rather than using the fake parser types (second step of sugar localization)
blanchet
parents:
49181
diff
changeset

110 
(case find_index (is_same_recT T) fake_Ts of 
49176  111 
~1 => Type (s, map freeze_recXs Us) 
112 
 i => nth Xs i) 

113 
 freeze_recXs T = T; 

49121  114 

49183
0cc46e2dee7e
careful about constructor types w.r.t. fake context (third step of localization)
blanchet
parents:
49182
diff
changeset

115 
val ctr_TsssXs = map (map (map freeze_recXs)) fake_ctr_Tsss; 
49176  116 
val sum_prod_TsXs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssXs; 
49119  117 

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

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

49167  123 
val timer = time (Timer.startRealTimer ()); 
124 

49176  125 
fun mk_unf_or_fld get_T Ts t = 
126 
let val Type (_, Ts0) = get_T (fastype_of t) in 

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

49126  130 
val mk_unf = mk_unf_or_fld domain_type; 
131 
val mk_fld = mk_unf_or_fld range_type; 

49121  132 

49126  133 
val unfs = map (mk_unf As) raw_unfs; 
49124  134 
val flds = map (mk_fld As) raw_flds; 
135 

49182
b8517107ffc5
read the real types off the constant types, rather than using the fake parser types (second step of sugar localization)
blanchet
parents:
49181
diff
changeset

136 
val fp_Ts = map (domain_type o fastype_of) unfs; 
49183
0cc46e2dee7e
careful about constructor types w.r.t. fake context (third step of localization)
blanchet
parents:
49182
diff
changeset

137 
val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fp_Ts)))) ctr_TsssXs; 
49182
b8517107ffc5
read the real types off the constant types, rather than using the fake parser types (second step of sugar localization)
blanchet
parents:
49181
diff
changeset

138 

49176  139 
fun mk_fp_iter_or_rec Ts Us t = 
49121  140 
let 
49176  141 
val (binders, body) = strip_type (fastype_of t); 
142 
val Type (_, Ts0) = if gfp then body else List.last binders; 

143 
val Us0 = map (if gfp then domain_type else body_type) (fst (split_last binders)); 

144 
in 

145 
Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t 

146 
end; 

147 

148 
val fp_iters = map (mk_fp_iter_or_rec As Cs) raw_fp_iters; 

149 
val fp_recs = map (mk_fp_iter_or_rec As Cs) raw_fp_recs; 

150 

151 
fun pour_sugar_on_type ((((((((((((((b, fp_T), C), fld), unf), fp_iter), fp_rec), fld_unf), 

152 
unf_fld), fld_inject), ctr_binders), ctr_mixfixes), ctr_Tss), disc_binders), sel_binderss) 

153 
no_defs_lthy = 

154 
let 

155 
val n = length ctr_Tss; 

49121  156 
val ks = 1 upto n; 
157 
val ms = map length ctr_Tss; 

158 

49124  159 
val unf_T = domain_type (fastype_of fld); 
49121  160 
val prod_Ts = map HOLogic.mk_tupleT ctr_Tss; 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

161 
val case_Ts = map (fn Ts => Ts > C) ctr_Tss; 
49119  162 

49176  163 
val ((((u, v), fs), xss), _) = 
49124  164 
lthy 
49176  165 
> yield_singleton (mk_Frees "u") unf_T 
166 
>> yield_singleton (mk_Frees "v") fp_T 

167 
>> mk_Frees "f" case_Ts 

49124  168 
>> mk_Freess "x" ctr_Tss; 
49121  169 

49129  170 
val ctr_rhss = 
49121  171 
map2 (fn k => fn xs => 
172 
fold_rev Term.lambda xs (fld $ mk_InN prod_Ts (HOLogic.mk_tuple xs) k)) ks xss; 

173 

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

174 
val case_binder = Binding.suffix_name ("_" ^ caseN) b; 
49129  175 

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

176 
val case_rhs = 
49176  177 
fold_rev Term.lambda (fs @ [v]) (mk_sum_caseN (map2 mk_uncurried_fun fs xss) $ (unf $ v)); 
49129  178 

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

179 
val (((raw_ctrs, raw_ctr_defs), (raw_case, raw_case_def)), (lthy', lthy)) = no_defs_lthy 
49169  180 
> apfst split_list o fold_map3 (fn b => fn mx => fn rhs => 
181 
Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd) 

182 
ctr_binders ctr_mixfixes ctr_rhss 

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

183 
>> (Local_Theory.define ((case_binder, NoSyn), ((Thm.def_binding case_binder, []), 
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset

184 
case_rhs)) #>> apsnd snd) 
49121  185 
> `Local_Theory.restore; 
186 

187 
(*transforms defined frees into consts (and more)*) 

188 
val phi = Proof_Context.export_morphism lthy lthy'; 

189 

190 
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs; 

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

191 
val case_def = Morphism.thm phi raw_case_def; 
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset

192 

49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset

193 
val ctrs = map (Morphism.term phi) raw_ctrs; 
49130
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset

194 
val casex = Morphism.term phi raw_case; 
49121  195 

49135  196 
fun exhaust_tac {context = ctxt, ...} = 
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset

197 
let 
49135  198 
val fld_iff_unf_thm = 
199 
let 

200 
val goal = 

201 
fold_rev Logic.all [u, v] 

202 
(mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u))); 

203 
in 

204 
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} => 

49176  205 
mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unf_T, fp_T]) 
206 
(certify lthy fld) (certify lthy unf) fld_unf unf_fld) 

49135  207 
> Thm.close_derivation 
208 
> Morphism.thm phi 

209 
end; 

210 

211 
val sumEN_thm' = 

212 
Local_Defs.unfold lthy @{thms all_unit_eq} 

213 
(Drule.instantiate' (map (SOME o certifyT lthy) prod_Ts) [] (mk_sumEN n)) 

214 
> Morphism.thm phi; 

49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset

215 
in 
49161
a8e74375d971
fixed (n + 1)st bug in "mk_exhaust_tac"  arose with uncurried constructors
blanchet
parents:
49157
diff
changeset

216 
mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm' 
49123
263b0e330d8b
more work on sugar + simplify Trueprop + eq idiom everywhere
blanchet
parents:
49121
diff
changeset

217 
end; 
49121  218 

49126  219 
val inject_tacss = 
220 
map2 (fn 0 => K [] 

221 
 _ => fn ctr_def => [fn {context = ctxt, ...} => 

222 
mk_inject_tac ctxt ctr_def fld_inject]) 

223 
ms ctr_defs; 

224 

49127  225 
val half_distinct_tacss = 
226 
map (map (fn (def, def') => fn {context = ctxt, ...} => 

227 
mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs); 

228 

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

229 
val case_tacs = 
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset

230 
map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} => 
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset

231 
mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs; 
49121  232 

233 
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs]; 

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

234 

49176  235 
(* (co)iterators, (co)recursors, (co)induction *) 
236 

237 
val is_recT = member (op =) fp_Ts; 

238 

239 
val ns = map length ctr_Tsss; 

240 
val mss = map (map length) ctr_Tsss; 

241 
val Css = map2 replicate ns Cs; 

242 

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

243 
fun sugar_lfp lthy = 
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

244 
let 
49176  245 
val fp_y_Ts = map domain_type (fst (split_last (binder_types (fastype_of fp_iter)))); 
246 
val y_prod_Tss = map2 dest_sumTN ns fp_y_Ts; 

247 
val y_Tsss = map2 (map2 dest_tupleT) mss y_prod_Tss; 

248 
val g_Tss = map2 (map2 (curry (op >))) y_Tsss Css; 

249 
val iter_T = flat g_Tss > fp_T > C; 

49146  250 

49176  251 
val ((gss, ysss), _) = 
252 
lthy 

253 
> mk_Freess "f" g_Tss 

49177
db8ce685073f
introduced and used "mk_Freesss", and simplified "mk_Freess(')"
blanchet
parents:
49176
diff
changeset

254 
>> mk_Freesss "x" y_Tsss; 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

255 

49146  256 
val iter_rhs = 
49176  257 
fold_rev (fold_rev Term.lambda) gss 
258 
(Term.list_comb (fp_iter, map2 (mk_sum_caseN oo map2 mk_uncurried_fun) gss ysss)); 

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

259 
in 
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

260 
lthy 
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

261 
end; 
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

262 

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

263 
fun sugar_gfp lthy = lthy; 
49119  264 
in 
49130
3c26e17b2849
implemented "mk_case_tac"  and got rid of "cheat_tac"
blanchet
parents:
49129
diff
changeset

265 
wrap_data tacss ((ctrs, casex), (disc_binders, sel_binderss)) lthy' 
49134
846264f80f16
optionally provide extra dead variables to the FP constructions
blanchet
parents:
49130
diff
changeset

266 
> (if gfp then sugar_gfp else sugar_lfp) 
49119  267 
end; 
49167  268 

269 
val lthy'' = 

49176  270 
fold pour_sugar_on_type (bs ~~ fp_Ts ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~ fp_recs ~~ 
271 
fld_unfs ~~ unf_flds ~~ fld_injects ~~ ctr_binderss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ 

272 
disc_binderss ~~ sel_bindersss) lthy'; 

49167  273 

274 
val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^ 

275 
(if gfp then "co" else "") ^ "datatype")); 

49112  276 
in 
49167  277 
(timer; lthy'') 
49112  278 
end; 
279 

49121  280 
fun data_cmd info specs lthy = 
281 
let 

49179
f9d48d479c84
don't throw away the context when hacking the theory (first step to localize the sugar code)
blanchet
parents:
49177
diff
changeset

282 
val fake_thy = Theory.copy 
49180  283 
#> fold (fn spec => Sign.add_type lthy 
49181  284 
(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

285 
val fake_lthy = Proof_Context.background_theory fake_thy lthy; 
49121  286 
in 
287 
prepare_data Syntax.read_typ info specs fake_lthy lthy 

288 
end; 

49119  289 

49129  290 
val parse_opt_binding_colon = Scan.optional (Parse.binding  Parse.$$$ ":") no_binder 
49119  291 

49112  292 
val parse_ctr_arg = 
49119  293 
Parse.$$$ "("  parse_opt_binding_colon  Parse.typ  Parse.$$$ ")"  
49129  294 
(Parse.typ >> pair no_binder); 
49112  295 

296 
val parse_single_spec = 

297 
Parse.type_args_constrained  Parse.binding  Parse.opt_mixfix  

49119  298 
(@{keyword "="}  Parse.enum1 "" (parse_opt_binding_colon  Parse.binding  
299 
Scan.repeat parse_ctr_arg  Parse.opt_mixfix)); 

49112  300 

301 
val _ = 

302 
Outer_Syntax.local_theory @{command_spec "data"} "define BNFbased inductive datatypes" 

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

303 
(Parse.and_list1 parse_single_spec >> data_cmd false); 
49112  304 

305 
val _ = 

306 
Outer_Syntax.local_theory @{command_spec "codata"} "define BNFbased coinductive datatypes" 

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

307 
(Parse.and_list1 parse_single_spec >> data_cmd true); 
49112  308 

309 
end; 