src/HOL/Tools/Lifting/lifting_def.ML
author kuncar
Wed May 15 12:10:39 2013 +0200 (2013-05-15)
changeset 51994 82cc2aeb7d13
parent 51957 68c163598f07
child 53205 8d41170242cb
permissions -rw-r--r--
stronger reflexivity prover
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(*  Title:      HOL/Tools/Lifting/lifting_def.ML
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    Author:     Ondrej Kuncar
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Definitions for constants on quotient types.
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*)
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signature LIFTING_DEF =
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sig
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  val generate_parametric_transfer_rule:
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    Proof.context -> thm -> thm -> thm
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  val add_lift_def:
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    (binding * mixfix) -> typ -> term -> thm -> thm option -> local_theory -> local_theory
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  val lift_def_cmd:
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    (binding * string option * mixfix) * string * (Facts.ref * Args.src list) option -> local_theory -> Proof.state
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  val can_generate_code_cert: thm -> bool
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end;
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structure Lifting_Def: LIFTING_DEF =
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struct
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open Lifting_Util
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infix 0 MRSL
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(* Reflexivity prover *)
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fun refl_tac ctxt =
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  let
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    fun intro_reflp_tac (ct, i) = 
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    let
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      val rule = Thm.incr_indexes (#maxidx (rep_cterm ct) + 1) @{thm reflpD}
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      val concl_pat = Drule.strip_imp_concl (cprop_of rule)
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      val insts = Thm.first_order_match (concl_pat, ct)
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    in
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      rtac (Drule.instantiate_normalize insts rule) i
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    end
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    handle Pattern.MATCH => no_tac
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    val rules = @{thm is_equality_eq} ::
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      ((Transfer.get_relator_eq_raw ctxt) @ (Lifting_Info.get_reflexivity_rules ctxt))
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  in
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    EVERY' [CSUBGOAL intro_reflp_tac, 
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            REPEAT_ALL_NEW (resolve_tac rules)]
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  end
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fun try_prove_reflexivity ctxt prop =
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  SOME (Goal.prove ctxt [] [] prop (fn {context, ...} => refl_tac context 1))
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    handle ERROR _ => NONE
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(* Generation of a transfer rule *)
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fun generate_parametric_transfer_rule ctxt transfer_rule parametric_transfer_rule =
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  let
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    fun preprocess ctxt thm =
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      let
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        val tm = (strip_args 2 o HOLogic.dest_Trueprop o concl_of) thm;
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        val param_rel = (snd o dest_comb o fst o dest_comb) tm;
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        val thy = Proof_Context.theory_of ctxt;
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        val free_vars = Term.add_vars param_rel [];
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        fun make_subst (var as (_, typ)) subst = 
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          let
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            val [rty, rty'] = binder_types typ
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          in
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            if (Term.is_TVar rty andalso is_Type rty') then
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              (Var var, HOLogic.eq_const rty')::subst
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            else
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              subst
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          end;
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        val subst = fold make_subst free_vars [];
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        val csubst = map (pairself (cterm_of thy)) subst;
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        val inst_thm = Drule.cterm_instantiate csubst thm;
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      in
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        Conv.fconv_rule 
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          ((Conv.concl_conv (nprems_of inst_thm) o HOLogic.Trueprop_conv o Conv.fun2_conv o Conv.arg1_conv)
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            (Raw_Simplifier.rewrite false (Transfer.get_sym_relator_eq ctxt))) inst_thm
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      end
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    fun inst_relcomppI thy ant1 ant2 =
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      let
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        val t1 = (HOLogic.dest_Trueprop o concl_of) ant1
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        val t2 = (HOLogic.dest_Trueprop o prop_of) ant2
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        val fun1 = cterm_of thy (strip_args 2 t1)
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        val args1 = map (cterm_of thy) (get_args 2 t1)
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        val fun2 = cterm_of thy (strip_args 2 t2)
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        val args2 = map (cterm_of thy) (get_args 1 t2)
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        val relcomppI = Drule.incr_indexes2 ant1 ant2 @{thm relcomppI}
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        val vars = (rev (Term.add_vars (prop_of relcomppI) []))
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        val subst = map (apfst ((cterm_of thy) o Var)) (vars ~~ ([fun1] @ args1 @ [fun2] @ args2))
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      in
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        Drule.cterm_instantiate subst relcomppI
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      end
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    fun zip_transfer_rules ctxt thm =       let
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        val thy = Proof_Context.theory_of ctxt
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        fun mk_POS ty = Const (@{const_name POS}, ty --> ty --> HOLogic.boolT)
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        val rel = (Thm.dest_fun2 o Thm.dest_arg o cprop_of) thm
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        val typ = (typ_of o ctyp_of_term) rel
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        val POS_const = cterm_of thy (mk_POS typ)
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        val var = cterm_of thy (Var (("X", #maxidx (rep_cterm (rel)) + 1), typ))
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        val goal = Thm.apply (cterm_of thy HOLogic.Trueprop) (Thm.apply (Thm.apply POS_const rel) var)
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      in
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        [Lifting_Term.merge_transfer_relations ctxt goal, thm] MRSL @{thm POS_apply}
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      end
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    val thm = (inst_relcomppI (Proof_Context.theory_of ctxt) parametric_transfer_rule transfer_rule) 
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                OF [parametric_transfer_rule, transfer_rule]
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    val preprocessed_thm = preprocess ctxt thm
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    val orig_ctxt = ctxt
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    val (fixed_thm, ctxt) = yield_singleton (apfst snd oo Variable.import true) preprocessed_thm ctxt
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    val assms = cprems_of fixed_thm
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    val add_transfer_rule = Thm.attribute_declaration Transfer.transfer_add
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    val ctxt = Context.proof_map(fold (add_transfer_rule o Thm.assume) assms) ctxt
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    val zipped_thm =
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      fixed_thm
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      |> undisch_all
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      |> zip_transfer_rules ctxt
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      |> implies_intr_list assms
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      |> singleton (Variable.export ctxt orig_ctxt)
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  in
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    zipped_thm
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  end
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fun print_generate_transfer_info msg = 
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  let
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    val error_msg = cat_lines 
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      ["Generation of a parametric transfer rule failed.",
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      (Pretty.string_of (Pretty.block
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         [Pretty.str "Reason:", Pretty.brk 2, msg]))]
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  in
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    error error_msg
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  end
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fun generate_transfer_rule lthy quot_thm rsp_thm def_thm opt_par_thm =
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  let
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    val transfer_rule =
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      ([quot_thm, rsp_thm, def_thm] MRSL @{thm Quotient_to_transfer})
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      |> Lifting_Term.parametrize_transfer_rule lthy
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  in
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    (option_fold transfer_rule (generate_parametric_transfer_rule lthy transfer_rule) opt_par_thm
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    handle Lifting_Term.MERGE_TRANSFER_REL msg => (print_generate_transfer_info msg; transfer_rule))
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  end
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(* Generation of the code certificate from the rsp theorem *)
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fun get_body_types (Type ("fun", [_, U]), Type ("fun", [_, V])) = get_body_types (U, V)
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  | get_body_types (U, V)  = (U, V)
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fun get_binder_types (Type ("fun", [T, U]), Type ("fun", [V, W])) = (T, V) :: get_binder_types (U, W)
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  | get_binder_types _ = []
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fun get_binder_types_by_rel (Const (@{const_name "fun_rel"}, _) $ _ $ S) (Type ("fun", [T, U]), Type ("fun", [V, W])) = 
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    (T, V) :: get_binder_types_by_rel S (U, W)
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  | get_binder_types_by_rel _ _ = []
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fun get_body_type_by_rel (Const (@{const_name "fun_rel"}, _) $ _ $ S) (Type ("fun", [_, U]), Type ("fun", [_, V])) = 
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    get_body_type_by_rel S (U, V)
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  | get_body_type_by_rel _ (U, V)  = (U, V)
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fun force_rty_type ctxt rty rhs = 
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  let
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    val thy = Proof_Context.theory_of ctxt
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    val rhs_schematic = singleton (Variable.polymorphic ctxt) rhs
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    val rty_schematic = fastype_of rhs_schematic
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    val match = Sign.typ_match thy (rty_schematic, rty) Vartab.empty
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  in
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    Envir.subst_term_types match rhs_schematic
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  end
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fun unabs_def ctxt def = 
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  let
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    val (_, rhs) = Thm.dest_equals (cprop_of def)
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    fun dest_abs (Abs (var_name, T, _)) = (var_name, T)
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      | dest_abs tm = raise TERM("get_abs_var",[tm])
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    val (var_name, T) = dest_abs (term_of rhs)
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    val (new_var_names, ctxt') = Variable.variant_fixes [var_name] ctxt
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    val thy = Proof_Context.theory_of ctxt'
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    val refl_thm = Thm.reflexive (cterm_of thy (Free (hd new_var_names, T)))
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  in
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    Thm.combination def refl_thm |>
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    singleton (Proof_Context.export ctxt' ctxt)
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  end
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fun unabs_all_def ctxt def = 
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  let
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    val (_, rhs) = Thm.dest_equals (cprop_of def)
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    val xs = strip_abs_vars (term_of rhs)
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  in  
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    fold (K (unabs_def ctxt)) xs def
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  end
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val map_fun_unfolded = 
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  @{thm map_fun_def[abs_def]} |>
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  unabs_def @{context} |>
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  unabs_def @{context} |>
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  Local_Defs.unfold @{context} [@{thm comp_def}]
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fun unfold_fun_maps ctm =
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  let
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    fun unfold_conv ctm =
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      case (Thm.term_of ctm) of
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        Const (@{const_name "map_fun"}, _) $ _ $ _ => 
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          (Conv.arg_conv unfold_conv then_conv Conv.rewr_conv map_fun_unfolded) ctm
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        | _ => Conv.all_conv ctm
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  in
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    (Conv.fun_conv unfold_conv) ctm
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  end
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fun unfold_fun_maps_beta ctm =
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  let val try_beta_conv = Conv.try_conv (Thm.beta_conversion false)
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  in 
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    (unfold_fun_maps then_conv try_beta_conv) ctm 
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  end
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fun prove_rel ctxt rsp_thm (rty, qty) =
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  let
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    val ty_args = get_binder_types (rty, qty)
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    fun disch_arg args_ty thm = 
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      let
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        val quot_thm = Lifting_Term.prove_quot_thm ctxt args_ty
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      in
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        [quot_thm, thm] MRSL @{thm apply_rsp''}
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      end
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  in
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    fold disch_arg ty_args rsp_thm
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  end
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exception CODE_CERT_GEN of string
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fun simplify_code_eq ctxt def_thm = 
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  Local_Defs.unfold ctxt [@{thm o_apply}, @{thm map_fun_def}, @{thm id_apply}] def_thm
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(*
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  quot_thm - quotient theorem (Quotient R Abs Rep T).
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  returns: whether the Lifting package is capable to generate code for the abstract type
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    represented by quot_thm
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*)
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fun can_generate_code_cert quot_thm  =
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  case quot_thm_rel quot_thm of
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    Const (@{const_name HOL.eq}, _) => true
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    | Const (@{const_name invariant}, _) $ _  => true
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    | _ => false
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fun generate_code_cert ctxt def_thm rsp_thm (rty, qty) =
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  let
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    val thy = Proof_Context.theory_of ctxt
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    val quot_thm = Lifting_Term.prove_quot_thm ctxt (get_body_types (rty, qty))
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    val fun_rel = prove_rel ctxt rsp_thm (rty, qty)
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    val abs_rep_thm = [quot_thm, fun_rel] MRSL @{thm Quotient_rep_abs}
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    val abs_rep_eq = 
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      case (HOLogic.dest_Trueprop o prop_of) fun_rel of
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        Const (@{const_name HOL.eq}, _) $ _ $ _ => abs_rep_thm
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        | Const (@{const_name invariant}, _) $ _ $ _ $ _ => abs_rep_thm RS @{thm invariant_to_eq}
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        | _ => raise CODE_CERT_GEN "relation is neither equality nor invariant"
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    val unfolded_def = Conv.fconv_rule (Conv.arg_conv unfold_fun_maps_beta) def_thm
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    val unabs_def = unabs_all_def ctxt unfolded_def
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    val rep = (cterm_of thy o quot_thm_rep) quot_thm
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    val rep_refl = Thm.reflexive rep RS @{thm meta_eq_to_obj_eq}
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    val repped_eq = [rep_refl, unabs_def RS @{thm meta_eq_to_obj_eq}] MRSL @{thm cong}
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    val code_cert = [repped_eq, abs_rep_eq] MRSL @{thm trans}
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  in
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    simplify_code_eq ctxt code_cert
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  end
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fun generate_trivial_rep_eq ctxt def_thm =
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  let
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    val unfolded_def = Conv.fconv_rule (Conv.arg_conv unfold_fun_maps_beta) def_thm
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    val code_eq = unabs_all_def ctxt unfolded_def
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    val simp_code_eq = simplify_code_eq ctxt code_eq
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  in
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    simp_code_eq
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  end
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fun generate_rep_eq ctxt def_thm rsp_thm (rty, qty) =
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  if body_type rty = body_type qty then 
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    SOME (generate_trivial_rep_eq ctxt def_thm)
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  else 
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    let
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      val (rty_body, qty_body) = get_body_types (rty, qty)
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      val quot_thm = Lifting_Term.prove_quot_thm ctxt (rty_body, qty_body)
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    in
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      if can_generate_code_cert quot_thm then
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        SOME (generate_code_cert ctxt def_thm rsp_thm (rty, qty))
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      else 
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        NONE
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    end
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fun generate_abs_eq ctxt def_thm rsp_thm quot_thm =
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  let
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    val abs_eq_with_assms =
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      let
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        val (rty, qty) = quot_thm_rty_qty quot_thm
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        val rel = quot_thm_rel quot_thm
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        val ty_args = get_binder_types_by_rel rel (rty, qty)
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        val body_type = get_body_type_by_rel rel (rty, qty)
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        val quot_ret_thm = Lifting_Term.prove_quot_thm ctxt body_type
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        val rep_abs_folded_unmapped_thm = 
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          let
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            val rep_id = [quot_thm, def_thm] MRSL @{thm Quotient_Rep_eq}
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            val ctm = Thm.dest_equals_lhs (cprop_of rep_id)
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            val unfolded_maps_eq = unfold_fun_maps ctm
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            val t1 = [quot_thm, def_thm, rsp_thm] MRSL @{thm Quotient_rep_abs_fold_unmap}
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            val prems_pat = (hd o Drule.cprems_of) t1
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            val insts = Thm.first_order_match (prems_pat, cprop_of unfolded_maps_eq)
kuncar@47937
   311
          in
kuncar@47937
   312
            unfolded_maps_eq RS (Drule.instantiate_normalize insts t1)
kuncar@47937
   313
          end
kuncar@47937
   314
      in
kuncar@47937
   315
        rep_abs_folded_unmapped_thm
kuncar@47937
   316
        |> fold (fn _ => fn thm => thm RS @{thm fun_relD2}) ty_args
kuncar@47937
   317
        |> (fn x => x RS (@{thm Quotient_rel_abs2} OF [quot_ret_thm]))
kuncar@47937
   318
      end
kuncar@47937
   319
    
kuncar@47937
   320
    val prems = prems_of abs_eq_with_assms
kuncar@47937
   321
    val indexed_prems = map_index (apfst (fn x => x + 1)) prems
kuncar@51994
   322
    val indexed_assms = map (apsnd (try_prove_reflexivity ctxt)) indexed_prems
kuncar@47937
   323
    val proved_assms = map (apsnd the) (filter (is_some o snd) indexed_assms)
kuncar@47937
   324
    val abs_eq = fold_rev (fn (i, assms) => fn thm => assms RSN (i, thm)) proved_assms abs_eq_with_assms
kuncar@47308
   325
  in
kuncar@47937
   326
    simplify_code_eq ctxt abs_eq
kuncar@47937
   327
  end
kuncar@47937
   328
kuncar@47937
   329
fun define_code_using_abs_eq abs_eq_thm lthy =
kuncar@47937
   330
  if null (Logic.strip_imp_prems(prop_of abs_eq_thm)) then
kuncar@47937
   331
    (snd oo Local_Theory.note) ((Binding.empty, [Code.add_default_eqn_attrib]), [abs_eq_thm]) lthy
kuncar@47937
   332
  else
kuncar@47937
   333
    lthy
kuncar@47937
   334
  
kuncar@51374
   335
fun define_code_using_rep_eq opt_rep_eq_thm lthy = 
kuncar@51374
   336
  case opt_rep_eq_thm of
kuncar@47937
   337
    SOME rep_eq_thm =>   
kuncar@47308
   338
      let
kuncar@47308
   339
        val add_abs_eqn_attribute = 
kuncar@47308
   340
          Thm.declaration_attribute (fn thm => Context.mapping (Code.add_abs_eqn thm) I)
kuncar@47308
   341
        val add_abs_eqn_attrib = Attrib.internal (K add_abs_eqn_attribute);
kuncar@47308
   342
      in
kuncar@47937
   343
        (snd oo Local_Theory.note) ((Binding.empty, [add_abs_eqn_attrib]), [rep_eq_thm]) lthy
kuncar@47308
   344
      end
kuncar@47937
   345
    | NONE => lthy
kuncar@47937
   346
kuncar@47937
   347
fun has_constr ctxt quot_thm =
kuncar@47937
   348
  let
kuncar@47937
   349
    val thy = Proof_Context.theory_of ctxt
kuncar@47951
   350
    val abs_fun = quot_thm_abs quot_thm
kuncar@47937
   351
  in
kuncar@47937
   352
    if is_Const abs_fun then
kuncar@47937
   353
      Code.is_constr thy ((fst o dest_Const) abs_fun)
kuncar@47308
   354
    else
kuncar@47937
   355
      false
kuncar@47308
   356
  end
kuncar@47308
   357
kuncar@47937
   358
fun has_abstr ctxt quot_thm =
kuncar@47308
   359
  let
kuncar@47937
   360
    val thy = Proof_Context.theory_of ctxt
kuncar@47951
   361
    val abs_fun = quot_thm_abs quot_thm
kuncar@47308
   362
  in
kuncar@47937
   363
    if is_Const abs_fun then
kuncar@47937
   364
      Code.is_abstr thy ((fst o dest_Const) abs_fun)
kuncar@47937
   365
    else
kuncar@47937
   366
      false
kuncar@47308
   367
  end
kuncar@47308
   368
kuncar@51374
   369
fun define_code abs_eq_thm opt_rep_eq_thm (rty, qty) lthy =
kuncar@47937
   370
  let
kuncar@47937
   371
    val (rty_body, qty_body) = get_body_types (rty, qty)
kuncar@47937
   372
  in
kuncar@47937
   373
    if rty_body = qty_body then
kuncar@47937
   374
      if null (Logic.strip_imp_prems(prop_of abs_eq_thm)) then
kuncar@47937
   375
        (snd oo Local_Theory.note) ((Binding.empty, [Code.add_default_eqn_attrib]), [abs_eq_thm]) lthy
kuncar@47937
   376
      else
kuncar@51374
   377
        (snd oo Local_Theory.note) ((Binding.empty, [Code.add_default_eqn_attrib]), [the opt_rep_eq_thm]) lthy
kuncar@47937
   378
    else
kuncar@47937
   379
      let 
kuncar@47937
   380
        val body_quot_thm = Lifting_Term.prove_quot_thm lthy (rty_body, qty_body)
kuncar@47937
   381
      in
kuncar@47937
   382
        if has_constr lthy body_quot_thm then
kuncar@47937
   383
          define_code_using_abs_eq abs_eq_thm lthy
kuncar@47937
   384
        else if has_abstr lthy body_quot_thm then
kuncar@51374
   385
          define_code_using_rep_eq opt_rep_eq_thm lthy
kuncar@47937
   386
        else
kuncar@47937
   387
          lthy
kuncar@47937
   388
      end
kuncar@47937
   389
  end
kuncar@47308
   390
kuncar@47852
   391
(*
kuncar@47852
   392
  Defines an operation on an abstract type in terms of a corresponding operation 
kuncar@47852
   393
    on a representation type.
kuncar@47852
   394
kuncar@47852
   395
  var - a binding and a mixfix of the new constant being defined
kuncar@47852
   396
  qty - an abstract type of the new constant
kuncar@47852
   397
  rhs - a term representing the new constant on the raw level
kuncar@47937
   398
  rsp_thm - a respectfulness theorem in the internal tagged form (like '(R ===> R ===> R) f f'),
kuncar@47852
   399
    i.e. "(Lifting_Term.equiv_relation (fastype_of rhs, qty)) $ rhs $ rhs"
kuncar@47852
   400
*)
kuncar@47308
   401
kuncar@51374
   402
fun add_lift_def var qty rhs rsp_thm opt_par_thm lthy =
kuncar@47308
   403
  let
kuncar@47308
   404
    val rty = fastype_of rhs
kuncar@47937
   405
    val quot_thm = Lifting_Term.prove_quot_thm lthy (rty, qty)
kuncar@47951
   406
    val absrep_trm =  quot_thm_abs quot_thm
kuncar@47308
   407
    val rty_forced = (domain_type o fastype_of) absrep_trm
kuncar@47308
   408
    val forced_rhs = force_rty_type lthy rty_forced rhs
kuncar@47308
   409
    val lhs = Free (Binding.print (#1 var), qty)
kuncar@47308
   410
    val prop = Logic.mk_equals (lhs, absrep_trm $ forced_rhs)
kuncar@47308
   411
    val (_, prop') = Local_Defs.cert_def lthy prop
kuncar@47308
   412
    val (_, newrhs) = Local_Defs.abs_def prop'
kuncar@47308
   413
kuncar@47308
   414
    val ((_, (_ , def_thm)), lthy') = 
kuncar@47308
   415
      Local_Theory.define (var, ((Thm.def_binding (#1 var), []), newrhs)) lthy
kuncar@47308
   416
kuncar@51374
   417
    val transfer_rule = generate_transfer_rule lthy quot_thm rsp_thm def_thm opt_par_thm
huffman@49975
   418
kuncar@47937
   419
    val abs_eq_thm = generate_abs_eq lthy' def_thm rsp_thm quot_thm
kuncar@51374
   420
    val opt_rep_eq_thm = generate_rep_eq lthy' def_thm rsp_thm (rty_forced, qty)
huffman@47351
   421
kuncar@47545
   422
    fun qualify defname suffix = Binding.qualified true suffix defname
kuncar@47308
   423
kuncar@47545
   424
    val lhs_name = (#1 var)
kuncar@47308
   425
    val rsp_thm_name = qualify lhs_name "rsp"
kuncar@47937
   426
    val abs_eq_thm_name = qualify lhs_name "abs_eq"
kuncar@47937
   427
    val rep_eq_thm_name = qualify lhs_name "rep_eq"
kuncar@51374
   428
    val transfer_rule_name = qualify lhs_name "transfer"
huffman@47373
   429
    val transfer_attr = Attrib.internal (K Transfer.transfer_add)
kuncar@47308
   430
  in
kuncar@47308
   431
    lthy'
kuncar@47308
   432
      |> (snd oo Local_Theory.note) ((rsp_thm_name, []), [rsp_thm])
kuncar@51374
   433
      |> (snd oo Local_Theory.note) ((transfer_rule_name, [transfer_attr]), [transfer_rule])
kuncar@47937
   434
      |> (snd oo Local_Theory.note) ((abs_eq_thm_name, []), [abs_eq_thm])
kuncar@51374
   435
      |> (case opt_rep_eq_thm of 
kuncar@47937
   436
            SOME rep_eq_thm => (snd oo Local_Theory.note) ((rep_eq_thm_name, []), [rep_eq_thm])
kuncar@47937
   437
            | NONE => I)
kuncar@51374
   438
      |> define_code abs_eq_thm opt_rep_eq_thm (rty_forced, qty)
kuncar@47308
   439
  end
kuncar@47308
   440
kuncar@47308
   441
fun mk_readable_rsp_thm_eq tm lthy =
kuncar@47308
   442
  let
kuncar@47308
   443
    val ctm = cterm_of (Proof_Context.theory_of lthy) tm
kuncar@47308
   444
    
kuncar@47308
   445
    fun simp_arrows_conv ctm =
kuncar@47308
   446
      let
kuncar@47308
   447
        val unfold_conv = Conv.rewrs_conv 
kuncar@49626
   448
          [@{thm fun_rel_eq_invariant[THEN eq_reflection]}, 
kuncar@49626
   449
            @{thm fun_rel_eq[THEN eq_reflection]},
kuncar@49626
   450
            @{thm fun_rel_eq_rel[THEN eq_reflection]}, 
kuncar@47308
   451
            @{thm fun_rel_def[THEN eq_reflection]}]
kuncar@47308
   452
        fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
kuncar@47634
   453
        val invariant_commute_conv = Conv.bottom_conv
kuncar@47634
   454
          (K (Conv.try_conv (Conv.rewrs_conv (Lifting_Info.get_invariant_commute_rules lthy)))) lthy
kuncar@49626
   455
        val relator_eq_conv = Conv.bottom_conv
kuncar@49626
   456
          (K (Conv.try_conv (Conv.rewrs_conv (Transfer.get_relator_eq lthy)))) lthy
kuncar@47308
   457
      in
kuncar@47308
   458
        case (Thm.term_of ctm) of
kuncar@47308
   459
          Const (@{const_name "fun_rel"}, _) $ _ $ _ => 
kuncar@49626
   460
            (binop_conv2 simp_arrows_conv simp_arrows_conv then_conv unfold_conv) ctm
kuncar@49626
   461
          | _ => (invariant_commute_conv then_conv relator_eq_conv) ctm
kuncar@47308
   462
      end
kuncar@47937
   463
    
kuncar@47308
   464
    val unfold_ret_val_invs = Conv.bottom_conv 
kuncar@47308
   465
      (K (Conv.try_conv (Conv.rewr_conv @{thm invariant_same_args}))) lthy 
wenzelm@51314
   466
    val simp_conv = HOLogic.Trueprop_conv (Conv.fun2_conv simp_arrows_conv)
kuncar@47308
   467
    val univq_conv = Conv.rewr_conv @{thm HOL.all_simps(6)[symmetric, THEN eq_reflection]}
kuncar@47308
   468
    val univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) lthy
kuncar@47308
   469
    val beta_conv = Thm.beta_conversion true
kuncar@47308
   470
    val eq_thm = 
kuncar@47308
   471
      (simp_conv then_conv univq_prenex_conv then_conv beta_conv then_conv unfold_ret_val_invs) ctm
kuncar@47308
   472
  in
kuncar@47308
   473
    Object_Logic.rulify(eq_thm RS Drule.equal_elim_rule2)
kuncar@47308
   474
  end
kuncar@47308
   475
kuncar@47607
   476
fun rename_to_tnames ctxt term =
kuncar@47607
   477
  let
kuncar@47607
   478
    fun all_typs (Const ("all", _) $ Abs (_, T, t)) = T :: all_typs t
kuncar@47607
   479
      | all_typs _ = []
kuncar@47308
   480
kuncar@47607
   481
    fun rename (Const ("all", T1) $ Abs (_, T2, t)) (new_name :: names) = 
kuncar@47607
   482
        (Const ("all", T1) $ Abs (new_name, T2, rename t names)) 
kuncar@47607
   483
      | rename t _ = t
kuncar@47607
   484
kuncar@47607
   485
    val (fixed_def_t, _) = yield_singleton (Variable.importT_terms) term ctxt
kuncar@47607
   486
    val new_names = Datatype_Prop.make_tnames (all_typs fixed_def_t)
kuncar@47607
   487
  in
kuncar@47607
   488
    rename term new_names
kuncar@47607
   489
  end
kuncar@47308
   490
kuncar@47852
   491
(*
kuncar@47852
   492
kuncar@47852
   493
  lifting_definition command. It opens a proof of a corresponding respectfulness 
kuncar@47852
   494
  theorem in a user-friendly, readable form. Then add_lift_def is called internally.
kuncar@47852
   495
kuncar@47852
   496
*)
kuncar@47852
   497
kuncar@51374
   498
fun lift_def_cmd (raw_var, rhs_raw, opt_par_xthm) lthy =
kuncar@47308
   499
  let
kuncar@51994
   500
    val ((binding, SOME qty, mx), lthy) = yield_singleton Proof_Context.read_vars raw_var lthy 
kuncar@51994
   501
    val rhs = (Syntax.check_term lthy o Syntax.parse_term lthy) rhs_raw
kuncar@51994
   502
    val rsp_rel = Lifting_Term.equiv_relation lthy (fastype_of rhs, qty)
kuncar@47308
   503
    val rty_forced = (domain_type o fastype_of) rsp_rel;
kuncar@51994
   504
    val forced_rhs = force_rty_type lthy rty_forced rhs;
kuncar@47308
   505
    val internal_rsp_tm = HOLogic.mk_Trueprop (rsp_rel $ forced_rhs $ forced_rhs)
kuncar@51994
   506
    val opt_proven_rsp_thm = try_prove_reflexivity lthy internal_rsp_tm
kuncar@51994
   507
    val opt_par_thm = Option.map (singleton (Attrib.eval_thms lthy)) opt_par_xthm
kuncar@51994
   508
    
kuncar@51994
   509
    fun after_qed internal_rsp_thm lthy = 
kuncar@51994
   510
      add_lift_def (binding, mx) qty rhs internal_rsp_thm opt_par_thm lthy
kuncar@47308
   511
kuncar@47308
   512
  in
kuncar@51374
   513
    case opt_proven_rsp_thm of
kuncar@51994
   514
      SOME thm => Proof.theorem NONE (K (after_qed thm)) [] lthy
kuncar@51994
   515
      | NONE =>  
kuncar@51994
   516
        let
kuncar@51994
   517
          val readable_rsp_thm_eq = mk_readable_rsp_thm_eq internal_rsp_tm lthy
kuncar@51994
   518
          val (readable_rsp_tm, _) = Logic.dest_implies (prop_of readable_rsp_thm_eq)
kuncar@51994
   519
          val readable_rsp_tm_tnames = rename_to_tnames lthy readable_rsp_tm
kuncar@51994
   520
      
kuncar@51994
   521
          fun after_qed' thm_list lthy = 
kuncar@51994
   522
            let
kuncar@51994
   523
              val internal_rsp_thm = Goal.prove lthy [] [] internal_rsp_tm 
kuncar@51994
   524
                  (fn _ => rtac readable_rsp_thm_eq 1 THEN Proof_Context.fact_tac (hd thm_list) 1)
kuncar@51994
   525
            in
kuncar@51994
   526
              after_qed internal_rsp_thm lthy
kuncar@51994
   527
            end
kuncar@51994
   528
        in
kuncar@51994
   529
          Proof.theorem NONE after_qed' [[(readable_rsp_tm_tnames,[])]] lthy
kuncar@51994
   530
        end 
kuncar@47308
   531
  end
kuncar@47308
   532
kuncar@47379
   533
fun quot_thm_err ctxt (rty, qty) pretty_msg =
kuncar@47379
   534
  let
kuncar@47379
   535
    val error_msg = cat_lines
kuncar@47379
   536
       ["Lifting failed for the following types:",
kuncar@47379
   537
        Pretty.string_of (Pretty.block
kuncar@47379
   538
         [Pretty.str "Raw type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty]),
kuncar@47379
   539
        Pretty.string_of (Pretty.block
kuncar@47379
   540
         [Pretty.str "Abstract type:", Pretty.brk 2, Syntax.pretty_typ ctxt qty]),
kuncar@47379
   541
        "",
kuncar@47379
   542
        (Pretty.string_of (Pretty.block
kuncar@47379
   543
         [Pretty.str "Reason:", Pretty.brk 2, pretty_msg]))]
kuncar@47379
   544
  in
kuncar@47379
   545
    error error_msg
kuncar@47379
   546
  end
kuncar@47379
   547
kuncar@47504
   548
fun check_rty_err ctxt (rty_schematic, rty_forced) (raw_var, rhs_raw) =
kuncar@47379
   549
  let
kuncar@47504
   550
    val (_, ctxt') = yield_singleton Proof_Context.read_vars raw_var ctxt 
kuncar@47504
   551
    val rhs = (Syntax.check_term ctxt' o Syntax.parse_term ctxt') rhs_raw
kuncar@47379
   552
    val error_msg = cat_lines
kuncar@47379
   553
       ["Lifting failed for the following term:",
kuncar@47379
   554
        Pretty.string_of (Pretty.block
kuncar@47379
   555
         [Pretty.str "Term:", Pretty.brk 2, Syntax.pretty_term ctxt rhs]),
kuncar@47379
   556
        Pretty.string_of (Pretty.block
kuncar@47504
   557
         [Pretty.str "Type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty_schematic]),
kuncar@47379
   558
        "",
kuncar@47379
   559
        (Pretty.string_of (Pretty.block
kuncar@47379
   560
         [Pretty.str "Reason:", 
kuncar@47379
   561
          Pretty.brk 2, 
kuncar@51957
   562
          Pretty.str "The type of the term cannot be instantiated to",
kuncar@47379
   563
          Pretty.brk 1,
kuncar@47504
   564
          Pretty.quote (Syntax.pretty_typ ctxt rty_forced),
kuncar@47379
   565
          Pretty.str "."]))]
kuncar@47379
   566
    in
kuncar@47379
   567
      error error_msg
kuncar@47379
   568
    end
kuncar@47379
   569
kuncar@51374
   570
fun lift_def_cmd_with_err_handling (raw_var, rhs_raw, opt_par_xthm) lthy =
kuncar@51374
   571
  (lift_def_cmd (raw_var, rhs_raw, opt_par_xthm) lthy
kuncar@47379
   572
    handle Lifting_Term.QUOT_THM (rty, qty, msg) => quot_thm_err lthy (rty, qty) msg)
kuncar@47504
   573
    handle Lifting_Term.CHECK_RTY (rty_schematic, rty_forced) => 
kuncar@47504
   574
      check_rty_err lthy (rty_schematic, rty_forced) (raw_var, rhs_raw)
kuncar@47379
   575
kuncar@47308
   576
(* parser and command *)
kuncar@47308
   577
val liftdef_parser =
kuncar@51374
   578
  (((Parse.binding -- (@{keyword "::"} |-- (Parse.typ >> SOME) -- Parse.opt_mixfix')) >> Parse.triple2)
kuncar@51374
   579
    --| @{keyword "is"} -- Parse.term -- Scan.option (@{keyword "parametric"} |-- Parse.!!! Parse_Spec.xthm)) >> Parse.triple1
kuncar@47308
   580
val _ =
kuncar@47308
   581
  Outer_Syntax.local_theory_to_proof @{command_spec "lift_definition"}
kuncar@47308
   582
    "definition for constants over the quotient type"
kuncar@47379
   583
      (liftdef_parser >> lift_def_cmd_with_err_handling)
kuncar@47308
   584
kuncar@47308
   585
kuncar@47308
   586
end; (* structure *)