diff --git a/src/HOL/Tools/Quotient/quotient_def.ML b/src/HOL/Tools/Quotient/quotient_def.ML --- a/src/HOL/Tools/Quotient/quotient_def.ML +++ b/src/HOL/Tools/Quotient/quotient_def.ML @@ -1,214 +1,210 @@ (* Title: HOL/Tools/Quotient/quotient_def.ML Author: Cezary Kaliszyk and Christian Urban Definitions for constants on quotient types. *) 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 -> Proof.state val quotient_def_cmd: (binding * string option * mixfix) option * (Attrib.binding * (string * string)) -> local_theory -> Proof.state end; structure Quotient_Def: QUOTIENT_DEF = struct (** Interface and Syntax Setup **) (* Generation of the code certificate from the rsp theorem *) open Lifting_Util infix 0 MRSL (* The ML-interface for a quotient definition takes as argument: - an optional binding and mixfix annotation - 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. Restriction: At the moment the left- and right-hand side of the definition must be a constant. *) fun error_msg bind str = let val name = Binding.name_of bind val pos = Position.here (Binding.pos_of bind) in error ("Head of quotient_definition " ^ quote str ^ " differs from declaration " ^ name ^ pos) end fun add_quotient_def ((var, (name, atts)), (lhs, rhs)) rsp_thm lthy = let val rty = fastype_of rhs val qty = fastype_of lhs val absrep_trm = Quotient_Term.absrep_fun lthy Quotient_Term.AbsF (rty, qty) $ rhs val prop = Syntax.check_term lthy (Logic.mk_equals (lhs, absrep_trm)) val (_, prop') = Local_Defs.cert_def lthy (K []) prop val (_, newrhs) = Local_Defs.abs_def prop' val ((qconst, (_ , def)), lthy') = Local_Theory.define (var, ((Thm.def_binding_optional (#1 var) name, atts), newrhs)) lthy fun qconst_data phi = Quotient_Info.transform_quotconsts phi {qconst = qconst, rconst = rhs, def = def} fun qualify defname suffix = Binding.name suffix |> Binding.qualify true defname val lhs_name = Binding.name_of (#1 var) val rsp_thm_name = qualify lhs_name "rsp" val lthy'' = lthy' |> Local_Theory.declaration {syntax = false, pervasive = true} (fn phi => (case qconst_data phi of qcinfo as {qconst = Const (c, _), ...} => Quotient_Info.update_quotconsts (c, qcinfo) | _ => I)) |> (snd oo Local_Theory.note) ((rsp_thm_name, @{attributes [quot_respect]}), [rsp_thm]) in (qconst_data Morphism.identity, lthy'') end -fun mk_readable_rsp_thm_eq tm lthy = +fun mk_readable_rsp_thm_eq tm ctxt = let - val ctm = Thm.cterm_of lthy tm + val ctm = Thm.cterm_of ctxt 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 (\<^const_name>\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 abs_conv2 cv = Conv.abs_conv (Conv.abs_conv (cv o #2) o #2) ctxt + fun erase_quants ctxt' ctm' = + case (Thm.term_of ctm') of + Const (\<^const_name>\HOL.eq\, _) $ _ $ _ => Conv.all_conv ctm' + | _ => (Conv.binder_conv (erase_quants o #2) ctxt' then_conv + Conv.rewr_conv @{thm fun_eq_iff[symmetric, THEN eq_reflection]}) ctm' + val norm_fun_eq = abs_conv2 erase_quants then_conv Thm.eta_conversion fun simp_arrows_conv ctm = let val unfold_conv = Conv.rewrs_conv [@{thm rel_fun_eq_eq_onp[THEN eq_reflection]}, @{thm rel_fun_eq_rel[THEN eq_reflection]}, @{thm rel_fun_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>\rel_fun\, _) $ _ $ _ => (binop_conv2 left_conv simp_arrows_conv then_conv unfold_conv) ctm | _ => Conv.all_conv ctm end val unfold_ret_val_invs = Conv.bottom_conv - (K (Conv.try_conv (Conv.rewr_conv @{thm eq_onp_same_args[THEN eq_reflection]}))) lthy + (K (Conv.try_conv (Conv.rewr_conv @{thm eq_onp_same_args[THEN eq_reflection]}))) ctxt 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 univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) ctxt val beta_conv = Thm.beta_conversion true val eq_thm = (simp_conv then_conv univq_prenex_conv then_conv beta_conv then_conv unfold_ret_val_invs) ctm in - Object_Logic.rulify lthy (eq_thm RS Drule.equal_elim_rule2) + Object_Logic.rulify ctxt (eq_thm RS Drule.equal_elim_rule2) end fun gen_quotient_def prep_var parse_term (raw_var, (attr, (raw_lhs, raw_rhs))) lthy = let val (opt_var, ctxt) = (case raw_var of NONE => (NONE, lthy) | SOME var => prep_var var lthy |>> SOME) val lhs_constraints = (case opt_var of SOME (_, SOME T, _) => [T] | _ => []) fun prep_term Ts = parse_term ctxt #> fold Type.constraint Ts #> Syntax.check_term ctxt; val lhs = prep_term lhs_constraints raw_lhs val rhs = prep_term [] raw_rhs val (lhs_str, lhs_ty) = dest_Free lhs handle TERM _ => error "Constant already defined" val _ = if null (strip_abs_vars rhs) then () else error "The definiens cannot be an abstraction" val _ = if is_Const rhs then () else warning "The definiens is not a constant" val var = (case opt_var of NONE => (Binding.name lhs_str, NoSyn) | SOME (binding, _, mx) => if Variable.check_name binding = lhs_str then (binding, mx) else error_msg binding lhs_str); fun try_to_prove_refl thm = let val lhs_eq = thm |> Thm.prop_of |> Logic.dest_implies |> fst |> strip_all_body |> try HOLogic.dest_Trueprop in case lhs_eq of SOME (Const (\<^const_name>\HOL.eq\, _) $ _ $ _) => SOME (@{thm refl} RS thm) | SOME _ => (case body_type (fastype_of lhs) of Type (typ_name, _) => \<^try>\ #equiv_thm (the (Quotient_Info.lookup_quotients lthy typ_name)) RS @{thm Equiv_Relations.equivp_reflp} RS thm\ | _ => NONE ) | _ => NONE end 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 (Thm.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 _ => resolve_tac ctxt [readable_rsp_thm_eq] 1 THEN Proof_Context.fact_tac ctxt [thm] 1) in snd (add_quotient_def ((var, attr), (lhs, rhs)) internal_rsp_thm lthy) end in case maybe_proven_rsp_thm of SOME _ => Proof.theorem NONE after_qed [] lthy | NONE => Proof.theorem NONE after_qed [[(readable_rsp_tm,[])]] lthy end val quotient_def = gen_quotient_def Proof_Context.cert_var (K I) val quotient_def_cmd = gen_quotient_def Proof_Context.read_var Syntax.parse_term (* command syntax *) val _ = Outer_Syntax.local_theory_to_proof \<^command_keyword>\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))) >> quotient_def_cmd); end;