store explicitly quotient types with no_code => more precise registration of code equations
1 (* Title: HOL/Tools/Lifting/lifting_def.ML
4 Definitions for constants on quotient types.
7 signature LIFTING_DEF =
9 val generate_parametric_transfer_rule:
10 Proof.context -> thm -> thm -> thm
13 (binding * mixfix) -> typ -> term -> thm -> thm list -> local_theory -> local_theory
16 (binding * string option * mixfix) * string * (Facts.ref * Args.src list) list -> local_theory -> Proof.state
18 val can_generate_code_cert: thm -> bool
21 structure Lifting_Def: LIFTING_DEF =
28 (* Reflexivity prover *)
30 fun mono_eq_prover ctxt prop =
32 val refl_rules = Lifting_Info.get_reflexivity_rules ctxt
33 val transfer_rules = Transfer.get_transfer_raw ctxt
35 fun main_tac i = (REPEAT_ALL_NEW (DETERM o resolve_tac refl_rules) THEN_ALL_NEW
36 (REPEAT_ALL_NEW (DETERM o resolve_tac transfer_rules))) i
38 SOME (Goal.prove ctxt [] [] prop (K (main_tac 1)))
39 handle ERROR _ => NONE
42 fun try_prove_refl_rel ctxt rel =
48 Const (@{const_name "less_eq"}, T --> T --> HOLogic.boolT) $
49 (Const (@{const_name HOL.eq}, T)) $ x
51 val goal = HOLogic.mk_Trueprop (mk_ge_eq rel);
53 mono_eq_prover ctxt goal
56 fun try_prove_reflexivity ctxt prop =
58 val thy = Proof_Context.theory_of ctxt
59 val cprop = cterm_of thy prop
60 val rule = @{thm ge_eq_refl}
61 val concl_pat = Drule.strip_imp_concl (cprop_of rule)
62 val insts = Thm.first_order_match (concl_pat, cprop)
63 val rule = Drule.instantiate_normalize insts rule
64 val prop = hd (prems_of rule)
66 case mono_eq_prover ctxt prop of
67 SOME thm => SOME (thm RS rule)
72 Generates a parametrized transfer rule.
73 transfer_rule - of the form T t f
74 parametric_transfer_rule - of the form par_R t' t
76 Result: par_T t' f, after substituing op= for relations in par_R that relate
77 a type constructor to the same type constructor, it is a merge of (par_R' OO T) t' f
78 using Lifting_Term.merge_transfer_relations
81 fun generate_parametric_transfer_rule ctxt transfer_rule parametric_transfer_rule =
83 fun preprocess ctxt thm =
85 val tm = (strip_args 2 o HOLogic.dest_Trueprop o concl_of) thm;
86 val param_rel = (snd o dest_comb o fst o dest_comb) tm;
87 val thy = Proof_Context.theory_of ctxt;
88 val free_vars = Term.add_vars param_rel [];
90 fun make_subst (var as (_, typ)) subst =
92 val [rty, rty'] = binder_types typ
94 if (Term.is_TVar rty andalso is_Type rty') then
95 (Var var, HOLogic.eq_const rty')::subst
100 val subst = fold make_subst free_vars [];
101 val csubst = map (pairself (cterm_of thy)) subst;
102 val inst_thm = Drule.cterm_instantiate csubst thm;
105 ((Conv.concl_conv (nprems_of inst_thm) o HOLogic.Trueprop_conv o Conv.fun2_conv o Conv.arg1_conv)
106 (Raw_Simplifier.rewrite ctxt false (Transfer.get_sym_relator_eq ctxt))) inst_thm
109 fun inst_relcomppI thy ant1 ant2 =
111 val t1 = (HOLogic.dest_Trueprop o concl_of) ant1
112 val t2 = (HOLogic.dest_Trueprop o prop_of) ant2
113 val fun1 = cterm_of thy (strip_args 2 t1)
114 val args1 = map (cterm_of thy) (get_args 2 t1)
115 val fun2 = cterm_of thy (strip_args 2 t2)
116 val args2 = map (cterm_of thy) (get_args 1 t2)
117 val relcomppI = Drule.incr_indexes2 ant1 ant2 @{thm relcomppI}
118 val vars = (rev (Term.add_vars (prop_of relcomppI) []))
119 val subst = map (apfst ((cterm_of thy) o Var)) (vars ~~ ([fun1] @ args1 @ [fun2] @ args2))
121 Drule.cterm_instantiate subst relcomppI
124 fun zip_transfer_rules ctxt thm =
126 val thy = Proof_Context.theory_of ctxt
127 fun mk_POS ty = Const (@{const_name POS}, ty --> ty --> HOLogic.boolT)
128 val rel = (Thm.dest_fun2 o Thm.dest_arg o cprop_of) thm
129 val typ = (typ_of o ctyp_of_term) rel
130 val POS_const = cterm_of thy (mk_POS typ)
131 val var = cterm_of thy (Var (("X", #maxidx (rep_cterm (rel)) + 1), typ))
132 val goal = Thm.apply (cterm_of thy HOLogic.Trueprop) (Thm.apply (Thm.apply POS_const rel) var)
134 [Lifting_Term.merge_transfer_relations ctxt goal, thm] MRSL @{thm POS_apply}
137 val thm = (inst_relcomppI (Proof_Context.theory_of ctxt) parametric_transfer_rule transfer_rule)
138 OF [parametric_transfer_rule, transfer_rule]
139 val preprocessed_thm = preprocess ctxt thm
141 val (fixed_thm, ctxt) = yield_singleton (apfst snd oo Variable.import true) preprocessed_thm ctxt
142 val assms = cprems_of fixed_thm
143 val add_transfer_rule = Thm.attribute_declaration Transfer.transfer_add
144 val (prems, ctxt) = fold_map Thm.assume_hyps assms ctxt
145 val ctxt = Context.proof_map (fold add_transfer_rule prems) ctxt
149 |> zip_transfer_rules ctxt
150 |> implies_intr_list assms
151 |> singleton (Variable.export ctxt orig_ctxt)
156 fun print_generate_transfer_info msg =
158 val error_msg = cat_lines
159 ["Generation of a parametric transfer rule failed.",
160 (Pretty.string_of (Pretty.block
161 [Pretty.str "Reason:", Pretty.brk 2, msg]))]
166 fun map_ter _ x [] = x
167 | map_ter f _ xs = map f xs
169 fun generate_transfer_rules lthy quot_thm rsp_thm def_thm par_thms =
172 ([quot_thm, rsp_thm, def_thm] MRSL @{thm Quotient_to_transfer})
173 |> Lifting_Term.parametrize_transfer_rule lthy
175 (map_ter (generate_parametric_transfer_rule lthy transfer_rule) [transfer_rule] par_thms
176 handle Lifting_Term.MERGE_TRANSFER_REL msg => (print_generate_transfer_info msg; [transfer_rule]))
179 (* Generation of the code certificate from the rsp theorem *)
181 fun get_body_types (Type ("fun", [_, U]), Type ("fun", [_, V])) = get_body_types (U, V)
182 | get_body_types (U, V) = (U, V)
184 fun get_binder_types (Type ("fun", [T, U]), Type ("fun", [V, W])) = (T, V) :: get_binder_types (U, W)
185 | get_binder_types _ = []
187 fun get_binder_types_by_rel (Const (@{const_name "rel_fun"}, _) $ _ $ S) (Type ("fun", [T, U]), Type ("fun", [V, W])) =
188 (T, V) :: get_binder_types_by_rel S (U, W)
189 | get_binder_types_by_rel _ _ = []
191 fun get_body_type_by_rel (Const (@{const_name "rel_fun"}, _) $ _ $ S) (Type ("fun", [_, U]), Type ("fun", [_, V])) =
192 get_body_type_by_rel S (U, V)
193 | get_body_type_by_rel _ (U, V) = (U, V)
195 fun get_binder_rels (Const (@{const_name "rel_fun"}, _) $ R $ S) = R :: get_binder_rels S
196 | get_binder_rels _ = []
198 fun force_rty_type ctxt rty rhs =
200 val thy = Proof_Context.theory_of ctxt
201 val rhs_schematic = singleton (Variable.polymorphic ctxt) rhs
202 val rty_schematic = fastype_of rhs_schematic
203 val match = Sign.typ_match thy (rty_schematic, rty) Vartab.empty
205 Envir.subst_term_types match rhs_schematic
208 fun unabs_def ctxt def =
210 val (_, rhs) = Thm.dest_equals (cprop_of def)
211 fun dest_abs (Abs (var_name, T, _)) = (var_name, T)
212 | dest_abs tm = raise TERM("get_abs_var",[tm])
213 val (var_name, T) = dest_abs (term_of rhs)
214 val (new_var_names, ctxt') = Variable.variant_fixes [var_name] ctxt
215 val thy = Proof_Context.theory_of ctxt'
216 val refl_thm = Thm.reflexive (cterm_of thy (Free (hd new_var_names, T)))
218 Thm.combination def refl_thm |>
219 singleton (Proof_Context.export ctxt' ctxt)
222 fun unabs_all_def ctxt def =
224 val (_, rhs) = Thm.dest_equals (cprop_of def)
225 val xs = strip_abs_vars (term_of rhs)
227 fold (K (unabs_def ctxt)) xs def
230 val map_fun_unfolded =
231 @{thm map_fun_def[abs_def]} |>
232 unabs_def @{context} |>
233 unabs_def @{context} |>
234 Local_Defs.unfold @{context} [@{thm comp_def}]
236 fun unfold_fun_maps ctm =
238 fun unfold_conv ctm =
239 case (Thm.term_of ctm) of
240 Const (@{const_name "map_fun"}, _) $ _ $ _ =>
241 (Conv.arg_conv unfold_conv then_conv Conv.rewr_conv map_fun_unfolded) ctm
242 | _ => Conv.all_conv ctm
244 (Conv.fun_conv unfold_conv) ctm
247 fun unfold_fun_maps_beta ctm =
248 let val try_beta_conv = Conv.try_conv (Thm.beta_conversion false)
250 (unfold_fun_maps then_conv try_beta_conv) ctm
253 fun prove_rel ctxt rsp_thm (rty, qty) =
255 val ty_args = get_binder_types (rty, qty)
256 fun disch_arg args_ty thm =
258 val quot_thm = Lifting_Term.prove_quot_thm ctxt args_ty
260 [quot_thm, thm] MRSL @{thm apply_rsp''}
263 fold disch_arg ty_args rsp_thm
266 exception CODE_CERT_GEN of string
268 fun simplify_code_eq ctxt def_thm =
269 Local_Defs.unfold ctxt [@{thm o_apply}, @{thm map_fun_def}, @{thm id_apply}] def_thm
272 quot_thm - quotient theorem (Quotient R Abs Rep T).
273 returns: whether the Lifting package is capable to generate code for the abstract type
274 represented by quot_thm
277 fun can_generate_code_cert quot_thm =
278 case quot_thm_rel quot_thm of
279 Const (@{const_name HOL.eq}, _) => true
280 | Const (@{const_name eq_onp}, _) $ _ => true
283 fun generate_rep_eq ctxt def_thm rsp_thm (rty, qty) =
285 val unfolded_def = Conv.fconv_rule (Conv.arg_conv unfold_fun_maps_beta) def_thm
286 val unabs_def = unabs_all_def ctxt unfolded_def
288 if body_type rty = body_type qty then
289 SOME (simplify_code_eq ctxt (unabs_def RS @{thm meta_eq_to_obj_eq}))
292 val thy = Proof_Context.theory_of ctxt
293 val quot_thm = Lifting_Term.prove_quot_thm ctxt (get_body_types (rty, qty))
294 val rel_fun = prove_rel ctxt rsp_thm (rty, qty)
295 val rep_abs_thm = [quot_thm, rel_fun] MRSL @{thm Quotient_rep_abs_eq}
297 case mono_eq_prover ctxt (hd(prems_of rep_abs_thm)) of
300 val rep_abs_eq = mono_eq_thm RS rep_abs_thm
301 val rep = (cterm_of thy o quot_thm_rep) quot_thm
302 val rep_refl = Thm.reflexive rep RS @{thm meta_eq_to_obj_eq}
303 val repped_eq = [rep_refl, unabs_def RS @{thm meta_eq_to_obj_eq}] MRSL @{thm cong}
304 val code_cert = [repped_eq, rep_abs_eq] MRSL trans
306 SOME (simplify_code_eq ctxt code_cert)
312 fun generate_abs_eq ctxt def_thm rsp_thm quot_thm =
314 val abs_eq_with_assms =
316 val (rty, qty) = quot_thm_rty_qty quot_thm
317 val rel = quot_thm_rel quot_thm
318 val ty_args = get_binder_types_by_rel rel (rty, qty)
319 val body_type = get_body_type_by_rel rel (rty, qty)
320 val quot_ret_thm = Lifting_Term.prove_quot_thm ctxt body_type
322 val rep_abs_folded_unmapped_thm =
324 val rep_id = [quot_thm, def_thm] MRSL @{thm Quotient_Rep_eq}
325 val ctm = Thm.dest_equals_lhs (cprop_of rep_id)
326 val unfolded_maps_eq = unfold_fun_maps ctm
327 val t1 = [quot_thm, def_thm, rsp_thm] MRSL @{thm Quotient_rep_abs_fold_unmap}
328 val prems_pat = (hd o Drule.cprems_of) t1
329 val insts = Thm.first_order_match (prems_pat, cprop_of unfolded_maps_eq)
331 unfolded_maps_eq RS (Drule.instantiate_normalize insts t1)
334 rep_abs_folded_unmapped_thm
335 |> fold (fn _ => fn thm => thm RS @{thm rel_funD2}) ty_args
336 |> (fn x => x RS (@{thm Quotient_rel_abs2} OF [quot_ret_thm]))
339 val prem_rels = get_binder_rels (quot_thm_rel quot_thm);
340 val proved_assms = prem_rels |> map (try_prove_refl_rel ctxt)
341 |> map_index (apfst (fn x => x + 1)) |> filter (is_some o snd) |> map (apsnd the)
342 |> map (apsnd (fn assm => assm RS @{thm ge_eq_refl}))
343 val abs_eq = fold_rev (fn (i, assm) => fn thm => assm RSN (i, thm)) proved_assms abs_eq_with_assms
345 simplify_code_eq ctxt abs_eq
349 fun register_code_eq_thy abs_eq_thm opt_rep_eq_thm (rty, qty) thy =
351 fun no_abstr (t $ u) = no_abstr t andalso no_abstr u
352 | no_abstr (Abs (_, _, t)) = no_abstr t
353 | no_abstr (Const (name, _)) = not (Code.is_abstr thy name)
355 fun is_valid_eq eqn = can (Code.assert_eqn thy) (mk_meta_eq eqn, true)
356 andalso no_abstr (prop_of eqn)
357 fun is_valid_abs_eq abs_eq = can (Code.assert_abs_eqn thy NONE) (mk_meta_eq abs_eq)
360 if is_valid_eq abs_eq_thm then
361 Code.add_default_eqn abs_eq_thm thy
364 val (rty_body, qty_body) = get_body_types (rty, qty)
366 if rty_body = qty_body then
367 Code.add_default_eqn (the opt_rep_eq_thm) thy
369 if is_some opt_rep_eq_thm andalso is_valid_abs_eq (the opt_rep_eq_thm)
371 Code.add_abs_eqn (the opt_rep_eq_thm) thy
378 fun encode_code_eq thy abs_eq opt_rep_eq (rty, qty) =
380 fun mk_type typ = typ |> Logic.mk_type |> cterm_of thy |> Drule.mk_term
382 Conjunction.intr_balanced [abs_eq, (the_default TrueI opt_rep_eq), mk_type rty, mk_type qty]
385 fun decode_code_eq thm =
387 val [abs_eq, rep_eq, rty, qty] = Conjunction.elim_balanced 4 thm
388 val opt_rep_eq = if Thm.eq_thm_prop (rep_eq, TrueI) then NONE else SOME rep_eq
389 fun dest_type typ = typ |> Drule.dest_term |> term_of |> Logic.dest_type
391 (abs_eq, opt_rep_eq, (dest_type rty, dest_type qty))
394 fun register_encoded_code_eq thm thy =
396 val (abs_eq_thm, opt_rep_eq_thm, (rty, qty)) = decode_code_eq thm
398 register_code_eq_thy abs_eq_thm opt_rep_eq_thm (rty, qty) thy
401 val register_code_eq_attribute = Thm.declaration_attribute
402 (fn thm => Context.mapping (register_encoded_code_eq thm) I)
403 val register_code_eq_attrib = Attrib.internal (K register_code_eq_attribute)
405 fun no_no_code ctxt (rty, qty) =
406 if same_type_constrs (rty, qty) then
407 forall (no_no_code ctxt) (Targs rty ~~ Targs qty)
410 if Lifting_Info.is_no_code_type ctxt (Tname qty) then false
413 val (rty', rtyq) = Lifting_Term.instantiate_rtys ctxt (rty, qty)
414 val (rty's, rtyqs) = (Targs rty', Targs rtyq)
416 forall (no_no_code ctxt) (rty's ~~ rtyqs)
422 fun register_code_eq abs_eq_thm opt_rep_eq_thm (rty, qty) lthy =
424 val thy = Proof_Context.theory_of lthy
425 val encoded_code_eq = encode_code_eq thy abs_eq_thm opt_rep_eq_thm (rty, qty)
427 if no_no_code lthy (rty, qty) then
428 (snd oo Local_Theory.note) ((Binding.empty, [register_code_eq_attrib]), [encoded_code_eq]) lthy
435 Defines an operation on an abstract type in terms of a corresponding operation
436 on a representation type.
438 var - a binding and a mixfix of the new constant being defined
439 qty - an abstract type of the new constant
440 rhs - a term representing the new constant on the raw level
441 rsp_thm - a respectfulness theorem in the internal tagged form (like '(R ===> R ===> R) f f'),
442 i.e. "(Lifting_Term.equiv_relation (fastype_of rhs, qty)) $ rhs $ rhs"
443 par_thms - a parametricity theorem for rhs
446 fun add_lift_def var qty rhs rsp_thm par_thms lthy =
448 val rty = fastype_of rhs
449 val quot_thm = Lifting_Term.prove_quot_thm lthy (rty, qty)
450 val absrep_trm = quot_thm_abs quot_thm
451 val rty_forced = (domain_type o fastype_of) absrep_trm
452 val forced_rhs = force_rty_type lthy rty_forced rhs
453 val lhs = Free (Binding.name_of (#1 var), qty)
454 val prop = Logic.mk_equals (lhs, absrep_trm $ forced_rhs)
455 val (_, prop') = Local_Defs.cert_def lthy prop
456 val (_, newrhs) = Local_Defs.abs_def prop'
458 val ((_, (_ , def_thm)), lthy') =
459 Local_Theory.define (var, ((Thm.def_binding (#1 var), []), newrhs)) lthy
461 val transfer_rules = generate_transfer_rules lthy' quot_thm rsp_thm def_thm par_thms
463 val abs_eq_thm = generate_abs_eq lthy' def_thm rsp_thm quot_thm
464 val opt_rep_eq_thm = generate_rep_eq lthy' def_thm rsp_thm (rty_forced, qty)
466 fun qualify defname suffix = Binding.qualified true suffix defname
468 val lhs_name = (#1 var)
469 val rsp_thm_name = qualify lhs_name "rsp"
470 val abs_eq_thm_name = qualify lhs_name "abs_eq"
471 val rep_eq_thm_name = qualify lhs_name "rep_eq"
472 val transfer_rule_name = qualify lhs_name "transfer"
473 val transfer_attr = Attrib.internal (K Transfer.transfer_add)
476 |> (snd oo Local_Theory.note) ((rsp_thm_name, []), [rsp_thm])
477 |> (snd oo Local_Theory.note) ((transfer_rule_name, [transfer_attr]), transfer_rules)
478 |> (snd oo Local_Theory.note) ((abs_eq_thm_name, []), [abs_eq_thm])
479 |> (case opt_rep_eq_thm of
480 SOME rep_eq_thm => (snd oo Local_Theory.note) ((rep_eq_thm_name, []), [rep_eq_thm])
482 |> register_code_eq abs_eq_thm opt_rep_eq_thm (rty_forced, qty)
486 val eq_onp_assms_tac_fixed_rules = map (Transfer.prep_transfer_domain_thm @{context})
487 [@{thm pcr_Domainp_total}, @{thm pcr_Domainp_par_left_total}, @{thm pcr_Domainp_par},
490 fun mk_readable_rsp_thm_eq tm lthy =
492 val ctm = cterm_of (Proof_Context.theory_of lthy) tm
494 fun assms_rewr_conv tactic rule ct =
496 fun prove_extra_assms thm =
498 val assms = cprems_of thm
499 fun finish thm = if Thm.no_prems thm then SOME (Goal.conclude thm) else NONE
500 fun prove ctm = Option.mapPartial finish (SINGLE tactic (Goal.init ctm))
502 map_interrupt prove assms
505 fun cconl_of thm = Drule.strip_imp_concl (cprop_of thm)
506 fun lhs_of thm = fst (Thm.dest_equals (cconl_of thm))
507 fun rhs_of thm = snd (Thm.dest_equals (cconl_of thm))
508 val rule1 = Thm.incr_indexes (#maxidx (Thm.rep_cterm ct) + 1) rule;
509 val lhs = lhs_of rule1;
510 val rule2 = Thm.rename_boundvars (Thm.term_of lhs) (Thm.term_of ct) rule1;
512 Thm.instantiate (Thm.match (lhs, ct)) rule2
513 handle Pattern.MATCH => raise CTERM ("assms_rewr_conv", [lhs, ct]);
514 val proved_assms = prove_extra_assms rule3
519 val rule3 = proved_assms MRSL rule3
521 if lhs_of rule3 aconvc ct then rule3
523 let val ceq = Thm.dest_fun2 (Thm.cprop_of rule3)
524 in rule3 COMP Thm.trivial (Thm.mk_binop ceq ct (rhs_of rule3)) end
525 in Thm.transitive rule4 (Thm.beta_conversion true (rhs_of rule4)) end
526 | NONE => Conv.no_conv ct
529 fun assms_rewrs_conv tactic rules = Conv.first_conv (map (assms_rewr_conv tactic) rules)
531 fun simp_arrows_conv ctm =
533 val unfold_conv = Conv.rewrs_conv
534 [@{thm rel_fun_eq_eq_onp[THEN eq_reflection]},
535 @{thm rel_fun_eq_onp_rel[THEN eq_reflection]},
536 @{thm rel_fun_eq[THEN eq_reflection]},
537 @{thm rel_fun_eq_rel[THEN eq_reflection]},
538 @{thm rel_fun_def[THEN eq_reflection]}]
539 fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
540 val eq_onp_assms_tac_rules = @{thm left_unique_OO} ::
541 eq_onp_assms_tac_fixed_rules @ (Transfer.get_transfer_raw lthy)
542 val eq_onp_assms_tac = (TRY o REPEAT_ALL_NEW (resolve_tac eq_onp_assms_tac_rules)
543 THEN_ALL_NEW (DETERM o Transfer.eq_tac lthy)) 1
544 val relator_eq_onp_conv = Conv.bottom_conv
545 (K (Conv.try_conv (assms_rewrs_conv eq_onp_assms_tac
546 (Lifting_Info.get_relator_eq_onp_rules lthy)))) lthy
547 val relator_eq_conv = Conv.bottom_conv
548 (K (Conv.try_conv (Conv.rewrs_conv (Transfer.get_relator_eq lthy)))) lthy
550 case (Thm.term_of ctm) of
551 Const (@{const_name "rel_fun"}, _) $ _ $ _ =>
552 (binop_conv2 simp_arrows_conv simp_arrows_conv then_conv unfold_conv) ctm
553 | _ => (relator_eq_onp_conv then_conv relator_eq_conv) ctm
556 val unfold_ret_val_invs = Conv.bottom_conv
557 (K (Conv.try_conv (Conv.rewr_conv @{thm eq_onp_same_args[THEN eq_reflection]}))) lthy
558 val unfold_inv_conv =
559 Conv.top_sweep_conv (K (Conv.rewr_conv @{thm eq_onp_def[THEN eq_reflection]})) lthy
560 val simp_conv = HOLogic.Trueprop_conv (Conv.fun2_conv simp_arrows_conv)
561 val univq_conv = Conv.rewr_conv @{thm HOL.all_simps(6)[symmetric, THEN eq_reflection]}
562 val univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) lthy
563 val beta_conv = Thm.beta_conversion true
565 (simp_conv then_conv univq_prenex_conv then_conv beta_conv then_conv unfold_ret_val_invs
566 then_conv unfold_inv_conv) ctm
568 Object_Logic.rulify lthy (eq_thm RS Drule.equal_elim_rule2)
572 fun rename_to_tnames ctxt term =
574 fun all_typs (Const (@{const_name Pure.all}, _) $ Abs (_, T, t)) = T :: all_typs t
577 fun rename (Const (@{const_name Pure.all}, T1) $ Abs (_, T2, t)) (new_name :: names) =
578 (Const (@{const_name Pure.all}, T1) $ Abs (new_name, T2, rename t names))
581 val (fixed_def_t, _) = yield_singleton (Variable.importT_terms) term ctxt
582 val new_names = Datatype_Prop.make_tnames (all_typs fixed_def_t)
584 rename term new_names
587 (* This is not very cheap way of getting the rules but we have only few active
588 liftings in the current setting *)
589 fun get_cr_pcr_eqs ctxt =
591 fun collect (data : Lifting_Info.quotient) l =
592 if is_some (#pcr_info data)
593 then ((Thm.symmetric o safe_mk_meta_eq o #pcr_cr_eq o the o #pcr_info) data :: l)
595 val table = Lifting_Info.get_quotients ctxt
597 Symtab.fold (fn (_, data) => fn l => collect data l) table []
602 lifting_definition command. It opens a proof of a corresponding respectfulness
603 theorem in a user-friendly, readable form. Then add_lift_def is called internally.
607 fun lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy =
609 val ((binding, SOME qty, mx), lthy) = yield_singleton Proof_Context.read_vars raw_var lthy
610 val rhs = (Syntax.check_term lthy o Syntax.parse_term lthy) rhs_raw
611 val rsp_rel = Lifting_Term.equiv_relation lthy (fastype_of rhs, qty)
612 val rty_forced = (domain_type o fastype_of) rsp_rel;
613 val forced_rhs = force_rty_type lthy rty_forced rhs;
614 val cr_to_pcr_conv = HOLogic.Trueprop_conv (Conv.fun2_conv
615 (Raw_Simplifier.rewrite lthy false (get_cr_pcr_eqs lthy)))
616 val (prsp_tm, rsp_prsp_eq) = HOLogic.mk_Trueprop (rsp_rel $ forced_rhs $ forced_rhs)
617 |> cterm_of (Proof_Context.theory_of lthy)
620 |>> Logic.dest_equals
622 val to_rsp = rsp_prsp_eq RS Drule.equal_elim_rule2
623 val opt_proven_rsp_thm = try_prove_reflexivity lthy prsp_tm
624 val par_thms = Attrib.eval_thms lthy par_xthms
626 fun after_qed internal_rsp_thm lthy =
627 add_lift_def (binding, mx) qty rhs (internal_rsp_thm RS to_rsp) par_thms lthy
629 case opt_proven_rsp_thm of
630 SOME thm => Proof.theorem NONE (K (after_qed thm)) [] lthy
633 val readable_rsp_thm_eq = mk_readable_rsp_thm_eq prsp_tm lthy
634 val (readable_rsp_tm, _) = Logic.dest_implies (prop_of readable_rsp_thm_eq)
635 val readable_rsp_tm_tnames = rename_to_tnames lthy readable_rsp_tm
637 fun after_qed' thm_list lthy =
639 val internal_rsp_thm = Goal.prove lthy [] [] prsp_tm
640 (fn {context = ctxt, ...} =>
641 rtac readable_rsp_thm_eq 1 THEN Proof_Context.fact_tac ctxt (hd thm_list) 1)
643 after_qed internal_rsp_thm lthy
646 Proof.theorem NONE after_qed' [[(readable_rsp_tm_tnames,[])]] lthy
650 fun quot_thm_err ctxt (rty, qty) pretty_msg =
652 val error_msg = cat_lines
653 ["Lifting failed for the following types:",
654 Pretty.string_of (Pretty.block
655 [Pretty.str "Raw type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty]),
656 Pretty.string_of (Pretty.block
657 [Pretty.str "Abstract type:", Pretty.brk 2, Syntax.pretty_typ ctxt qty]),
659 (Pretty.string_of (Pretty.block
660 [Pretty.str "Reason:", Pretty.brk 2, pretty_msg]))]
665 fun check_rty_err ctxt (rty_schematic, rty_forced) (raw_var, rhs_raw) =
667 val (_, ctxt') = yield_singleton Proof_Context.read_vars raw_var ctxt
668 val rhs = (Syntax.check_term ctxt' o Syntax.parse_term ctxt') rhs_raw
669 val error_msg = cat_lines
670 ["Lifting failed for the following term:",
671 Pretty.string_of (Pretty.block
672 [Pretty.str "Term:", Pretty.brk 2, Syntax.pretty_term ctxt rhs]),
673 Pretty.string_of (Pretty.block
674 [Pretty.str "Type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty_schematic]),
676 (Pretty.string_of (Pretty.block
677 [Pretty.str "Reason:",
679 Pretty.str "The type of the term cannot be instantiated to",
681 Pretty.quote (Syntax.pretty_typ ctxt rty_forced),
687 fun lift_def_cmd_with_err_handling (raw_var, rhs_raw, par_xthms) lthy =
688 (lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy
689 handle Lifting_Term.QUOT_THM (rty, qty, msg) => quot_thm_err lthy (rty, qty) msg)
690 handle Lifting_Term.CHECK_RTY (rty_schematic, rty_forced) =>
691 check_rty_err lthy (rty_schematic, rty_forced) (raw_var, rhs_raw)
693 (* parser and command *)
695 (((Parse.binding -- (@{keyword "::"} |-- (Parse.typ >> SOME) -- Parse.opt_mixfix')) >> Parse.triple2)
696 --| @{keyword "is"} -- Parse.term --
697 Scan.optional (@{keyword "parametric"} |-- Parse.!!! Parse_Spec.xthms1) []) >> Parse.triple1
699 Outer_Syntax.local_theory_to_proof @{command_spec "lift_definition"}
700 "definition for constants over the quotient type"
701 (liftdef_parser >> lift_def_cmd_with_err_handling)