--- a/src/HOL/Tools/Quotient/quotient_def.ML Fri Mar 23 12:03:59 2012 +0100
+++ b/src/HOL/Tools/Quotient/quotient_def.ML Fri Mar 23 14:03:58 2012 +0100
@@ -6,13 +6,17 @@
signature QUOTIENT_DEF =
sig
+ val add_quotient_def:
+ ((binding * mixfix) * Attrib.binding) * (term * term) -> thm ->
+ local_theory -> Quotient_Info.quotconsts * local_theory
+
val quotient_def:
(binding * typ option * mixfix) option * (Attrib.binding * (term * term)) ->
- local_theory -> Quotient_Info.quotconsts * local_theory
+ local_theory -> Proof.state
val quotient_def_cmd:
(binding * string option * mixfix) option * (Attrib.binding * (string * string)) ->
- local_theory -> Quotient_Info.quotconsts * local_theory
+ local_theory -> Proof.state
val lift_raw_const: typ list -> (string * term * mixfix) -> local_theory ->
Quotient_Info.quotconsts * local_theory
@@ -30,6 +34,7 @@
- attributes
- the new constant as term
- the rhs of the definition as term
+ - respectfulness theorem for the rhs
It stores the qconst_info in the quotconsts data slot.
@@ -45,7 +50,77 @@
quote str ^ " differs from declaration " ^ name ^ pos)
end
-fun gen_quotient_def prep_vars prep_term (raw_var, ((name, atts), (lhs_raw, rhs_raw))) lthy =
+fun add_quotient_def ((var, (name, atts)), (lhs, rhs)) rsp_thm lthy =
+ let
+ val absrep_trm =
+ Quotient_Term.absrep_fun lthy Quotient_Term.AbsF (fastype_of rhs, fastype_of lhs) $ rhs
+ val prop = Syntax.check_term lthy (Logic.mk_equals (lhs, absrep_trm))
+ val (_, prop') = Local_Defs.cert_def lthy prop
+ val (_, newrhs) = Local_Defs.abs_def prop'
+
+ val ((trm, (_ , thm)), lthy') =
+ Local_Theory.define (var, ((Thm.def_binding_optional (#1 var) name, atts), newrhs)) lthy
+
+ (* data storage *)
+ val qconst_data = {qconst = trm, rconst = rhs, def = thm}
+ fun get_rsp_thm_name (lhs_name, _) = Binding.suffix_name "_rsp" lhs_name
+
+ val lthy'' = lthy'
+ |> Local_Theory.declaration {syntax = false, pervasive = true}
+ (fn phi =>
+ (case Quotient_Info.transform_quotconsts phi qconst_data of
+ qcinfo as {qconst = Const (c, _), ...} =>
+ Quotient_Info.update_quotconsts c qcinfo
+ | _ => I))
+ |> (snd oo Local_Theory.note)
+ ((get_rsp_thm_name var, [Attrib.internal (K Quotient_Info.rsp_rules_add)]),
+ [rsp_thm])
+
+ in
+ (qconst_data, lthy'')
+ end
+
+fun mk_readable_rsp_thm_eq tm lthy =
+ let
+ val ctm = cterm_of (Proof_Context.theory_of lthy) tm
+
+ fun norm_fun_eq ctm =
+ let
+ fun abs_conv2 cv = Conv.abs_conv (K (Conv.abs_conv (K cv) lthy)) lthy
+ fun erase_quants ctm' =
+ case (Thm.term_of ctm') of
+ Const ("HOL.eq", _) $ _ $ _ => Conv.all_conv ctm'
+ | _ => (Conv.binder_conv (K erase_quants) lthy then_conv
+ Conv.rewr_conv @{thm fun_eq_iff[symmetric, THEN eq_reflection]}) ctm'
+ in
+ (abs_conv2 erase_quants then_conv Thm.eta_conversion) ctm
+ end
+
+ fun simp_arrows_conv ctm =
+ let
+ val unfold_conv = Conv.rewrs_conv
+ [@{thm fun_rel_eq_rel[THEN eq_reflection]}, @{thm fun_rel_def[THEN eq_reflection]}]
+ val left_conv = simp_arrows_conv then_conv Conv.try_conv norm_fun_eq
+ fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
+ in
+ case (Thm.term_of ctm) of
+ Const (@{const_name "fun_rel"}, _) $ _ $ _ =>
+ (binop_conv2 left_conv simp_arrows_conv then_conv unfold_conv) ctm
+ | _ => Conv.all_conv ctm
+ end
+
+ val simp_conv = Conv.arg_conv (Conv.fun2_conv simp_arrows_conv)
+ val univq_conv = Conv.rewr_conv @{thm HOL.all_simps(6)[symmetric, THEN eq_reflection]}
+ val univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) lthy
+ val eq_thm =
+ (simp_conv then_conv univq_prenex_conv then_conv Thm.beta_conversion true) ctm
+ in
+ Object_Logic.rulify(eq_thm RS Drule.equal_elim_rule2)
+ end
+
+
+
+fun gen_quotient_def prep_vars prep_term (raw_var, (attr, (lhs_raw, rhs_raw))) lthy =
let
val (vars, ctxt) = prep_vars (the_list raw_var) lthy
val T_opt = (case vars of [(_, SOME T, _)] => SOME T | _ => NONE)
@@ -63,27 +138,50 @@
if Variable.check_name binding = lhs_str then (binding, mx)
else error_msg binding lhs_str
| _ => raise Match)
-
- val absrep_trm = Quotient_Term.absrep_fun lthy Quotient_Term.AbsF (fastype_of rhs, lhs_ty) $ rhs
- val prop = Syntax.check_term lthy (Logic.mk_equals (lhs, absrep_trm))
- val (_, prop') = Local_Defs.cert_def lthy prop
- val (_, newrhs) = Local_Defs.abs_def prop'
-
- val ((trm, (_ , thm)), lthy') =
- Local_Theory.define (var, ((Thm.def_binding_optional (#1 var) name, atts), newrhs)) lthy
+
+ fun try_to_prove_refl thm =
+ let
+ val lhs_eq =
+ thm
+ |> prop_of
+ |> Logic.dest_implies
+ |> fst
+ |> strip_all_body
+ |> try HOLogic.dest_Trueprop
+ in
+ case lhs_eq of
+ SOME (Const ("HOL.eq", _) $ _ $ _) => SOME (@{thm refl} RS thm)
+ | SOME _ => (case body_type (fastype_of lhs) of
+ Type (typ_name, _) => ( SOME
+ (#equiv_thm (the (Quotient_Info.lookup_quotients lthy typ_name))
+ RS @{thm Equiv_Relations.equivp_reflp} RS thm)
+ handle _ => NONE)
+ | _ => NONE
+ )
+ | _ => NONE
+ end
- (* data storage *)
- val qconst_data = {qconst = trm, rconst = rhs, def = thm}
+ val rsp_rel = Quotient_Term.equiv_relation lthy (fastype_of rhs, lhs_ty)
+ val internal_rsp_tm = HOLogic.mk_Trueprop (Syntax.check_term lthy (rsp_rel $ rhs $ rhs))
+ val readable_rsp_thm_eq = mk_readable_rsp_thm_eq internal_rsp_tm lthy
+ val maybe_proven_rsp_thm = try_to_prove_refl readable_rsp_thm_eq
+ val (readable_rsp_tm, _) = Logic.dest_implies (prop_of readable_rsp_thm_eq)
+
+ fun after_qed thm_list lthy =
+ let
+ val internal_rsp_thm =
+ case thm_list of
+ [] => the maybe_proven_rsp_thm
+ | [[thm]] => Goal.prove ctxt [] [] internal_rsp_tm
+ (fn _ => rtac readable_rsp_thm_eq 1 THEN Proof_Context.fact_tac [thm] 1)
+ in
+ snd (add_quotient_def ((var, attr), (lhs, rhs)) internal_rsp_thm lthy)
+ end
- val lthy'' = lthy'
- |> Local_Theory.declaration {syntax = false, pervasive = true}
- (fn phi =>
- (case Quotient_Info.transform_quotconsts phi qconst_data of
- qcinfo as {qconst = Const (c, _), ...} =>
- Quotient_Info.update_quotconsts c qcinfo
- | _ => I));
in
- (qconst_data, lthy'')
+ case maybe_proven_rsp_thm of
+ SOME _ => Proof.theorem NONE after_qed [] lthy
+ | NONE => Proof.theorem NONE after_qed [[(readable_rsp_tm,[])]] lthy
end
fun check_term' cnstr ctxt =
@@ -103,16 +201,19 @@
val qty = Quotient_Term.derive_qtyp ctxt qtys rty
val lhs = Free (qconst_name, qty)
in
- quotient_def (SOME (Binding.name qconst_name, NONE, mx), (Attrib.empty_binding, (lhs, rconst))) ctxt
+ (*quotient_def (SOME (Binding.name qconst_name, NONE, mx), (Attrib.empty_binding, (lhs, rconst))) ctxt*)
+ ({qconst = lhs, rconst = lhs, def = @{thm refl}}, ctxt)
end
-(* command *)
+(* parser and command *)
+val quotdef_parser =
+ Scan.option Parse_Spec.constdecl --
+ Parse.!!! (Parse_Spec.opt_thm_name ":" -- (Parse.term --| @{keyword "is"} -- Parse.term))
val _ =
- Outer_Syntax.local_theory @{command_spec "quotient_definition"}
+ Outer_Syntax.local_theory_to_proof @{command_spec "quotient_definition"}
"definition for constants over the quotient type"
- (Scan.option Parse_Spec.constdecl --
- Parse.!!! (Parse_Spec.opt_thm_name ":" -- (Parse.term --| @{keyword "is"} -- Parse.term))
- >> (snd oo quotient_def_cmd))
+ (quotdef_parser >> quotient_def_cmd)
+
end; (* structure *)