src/HOL/Tools/Lifting/lifting_def.ML
author kuncar
Thu Apr 10 17:48:14 2014 +0200 (2014-04-10)
changeset 56518 beb3b6851665
parent 56245 84fc7dfa3cd4
child 56519 c1048f5bbb45
permissions -rw-r--r--
left_total and left_unique rules are now transfer rules (cleaner solution, reflexvity_rule attribute not needed anymore)
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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 list -> 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) list -> 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 mono_eq_prover ctxt prop =
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  let
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    val refl_rules = Lifting_Info.get_reflexivity_rules ctxt
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    val transfer_rules = Transfer.get_transfer_raw ctxt
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    fun main_tac (t, i) =
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      case HOLogic.dest_Trueprop t of 
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        Const (@{const_name "less_eq"}, _) $ _ $ _ => REPEAT_ALL_NEW (resolve_tac refl_rules) i
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        |  _ => REPEAT_ALL_NEW (resolve_tac transfer_rules) i
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  in
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    SOME (Goal.prove ctxt [] [] prop (K (SUBGOAL main_tac 1)))
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      handle ERROR _ => NONE
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  end
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fun try_prove_reflexivity ctxt prop =
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  let
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    val thy = Proof_Context.theory_of ctxt
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    val cprop = cterm_of thy prop
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    val rule = @{thm ge_eq_refl}
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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, cprop)
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    val rule = Drule.instantiate_normalize insts rule
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    val prop = hd (prems_of rule)
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  in
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    case mono_eq_prover ctxt prop of
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      SOME thm => SOME (thm RS rule)
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      | NONE => NONE
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  end
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(* 
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  Generates a parametrized transfer rule.
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  transfer_rule - of the form T t f
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  parametric_transfer_rule - of the form par_R t' t
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  Result: par_T t' f, after substituing op= for relations in par_R that relate
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    a type constructor to the same type constructor, it is a merge of (par_R' OO T) t' f
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    using Lifting_Term.merge_transfer_relations
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*)
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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 ctxt 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 =
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      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 (prems, ctxt) = fold_map Thm.assume_hyps assms ctxt
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    val ctxt = Context.proof_map (fold add_transfer_rule prems) 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 map_ter _ x [] = x
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    | map_ter f _ xs = map f xs
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fun generate_transfer_rules lthy quot_thm rsp_thm def_thm par_thms =
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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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    (map_ter (generate_parametric_transfer_rule lthy transfer_rule) [transfer_rule] par_thms
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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 "rel_fun"}, _) $ _ $ 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 "rel_fun"}, _) $ _ $ 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_rep_eq ctxt def_thm rsp_thm (rty, qty) =
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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 unabs_def = unabs_all_def ctxt unfolded_def
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  in  
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    if body_type rty = body_type qty then 
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      SOME (simplify_code_eq ctxt (unabs_def RS @{thm meta_eq_to_obj_eq}))
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    else 
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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 rel_fun = prove_rel ctxt rsp_thm (rty, qty)
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        val rep_abs_thm = [quot_thm, rel_fun] MRSL @{thm Quotient_rep_abs_eq}
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      in
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        case mono_eq_prover ctxt (hd(prems_of rep_abs_thm)) of
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          SOME mono_eq_thm =>
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            let
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              val rep_abs_eq = mono_eq_thm RS rep_abs_thm
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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, rep_abs_eq] MRSL trans
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            in
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              SOME (simplify_code_eq ctxt code_cert)
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            end
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          | NONE => NONE
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      end
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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
kuncar@47937
   314
            val insts = Thm.first_order_match (prems_pat, cprop_of unfolded_maps_eq)
kuncar@47937
   315
          in
kuncar@47937
   316
            unfolded_maps_eq RS (Drule.instantiate_normalize insts t1)
kuncar@47937
   317
          end
kuncar@47937
   318
      in
kuncar@47937
   319
        rep_abs_folded_unmapped_thm
blanchet@55945
   320
        |> fold (fn _ => fn thm => thm RS @{thm rel_funD2}) ty_args
kuncar@47937
   321
        |> (fn x => x RS (@{thm Quotient_rel_abs2} OF [quot_ret_thm]))
kuncar@47937
   322
      end
kuncar@47937
   323
    
kuncar@47937
   324
    val prems = prems_of abs_eq_with_assms
kuncar@47937
   325
    val indexed_prems = map_index (apfst (fn x => x + 1)) prems
kuncar@51994
   326
    val indexed_assms = map (apsnd (try_prove_reflexivity ctxt)) indexed_prems
kuncar@47937
   327
    val proved_assms = map (apsnd the) (filter (is_some o snd) indexed_assms)
kuncar@47937
   328
    val abs_eq = fold_rev (fn (i, assms) => fn thm => assms RSN (i, thm)) proved_assms abs_eq_with_assms
kuncar@47308
   329
  in
kuncar@47937
   330
    simplify_code_eq ctxt abs_eq
kuncar@47937
   331
  end
kuncar@47937
   332
kuncar@47937
   333
kuncar@55724
   334
fun register_code_eq_thy abs_eq_thm opt_rep_eq_thm (rty, qty) thy =
kuncar@47937
   335
  let
kuncar@55724
   336
    fun no_abstr (t $ u) = no_abstr t andalso no_abstr u
kuncar@55724
   337
      | no_abstr (Abs (_, _, t)) = no_abstr t
kuncar@55724
   338
      | no_abstr (Const (name, _)) = not (Code.is_abstr thy name)
kuncar@55724
   339
      | no_abstr _ = true
kuncar@55724
   340
    fun is_valid_eq eqn = can (Code.assert_eqn thy) (mk_meta_eq eqn, true) 
kuncar@55724
   341
      andalso no_abstr (prop_of eqn)
kuncar@55724
   342
    fun is_valid_abs_eq abs_eq = can (Code.assert_abs_eqn thy NONE) (mk_meta_eq abs_eq)
kuncar@47308
   343
kuncar@47308
   344
  in
kuncar@55724
   345
    if is_valid_eq abs_eq_thm then
kuncar@55724
   346
      Code.add_default_eqn abs_eq_thm thy
kuncar@47937
   347
    else
kuncar@55724
   348
      let
kuncar@55724
   349
        val (rty_body, qty_body) = get_body_types (rty, qty)
kuncar@47937
   350
      in
kuncar@55724
   351
        if rty_body = qty_body then
kuncar@55724
   352
         Code.add_default_eqn (the opt_rep_eq_thm) thy
kuncar@47937
   353
        else
kuncar@55724
   354
          if is_some opt_rep_eq_thm andalso is_valid_abs_eq (the opt_rep_eq_thm)
kuncar@55724
   355
          then
kuncar@55724
   356
            Code.add_abs_eqn (the opt_rep_eq_thm) thy
kuncar@55724
   357
          else
kuncar@55724
   358
            thy
kuncar@47937
   359
      end
kuncar@47937
   360
  end
kuncar@47308
   361
kuncar@55724
   362
local
kuncar@55724
   363
  fun encode_code_eq thy abs_eq opt_rep_eq (rty, qty) = 
kuncar@55724
   364
    let
kuncar@55724
   365
      fun mk_type typ = typ |> Logic.mk_type |> cterm_of thy |> Drule.mk_term
kuncar@55724
   366
    in
kuncar@55724
   367
      Conjunction.intr_balanced [abs_eq, (the_default TrueI opt_rep_eq), mk_type rty, mk_type qty]
kuncar@55724
   368
    end
kuncar@55724
   369
  
kuncar@55724
   370
  fun decode_code_eq thm =
kuncar@55724
   371
    let
kuncar@55724
   372
      val [abs_eq, rep_eq, rty, qty] = Conjunction.elim_balanced 4 thm
kuncar@55724
   373
      val opt_rep_eq = if Thm.eq_thm_prop (rep_eq, TrueI) then NONE else SOME rep_eq
kuncar@55724
   374
      fun dest_type typ = typ |> Drule.dest_term |> term_of |> Logic.dest_type
kuncar@55724
   375
    in
kuncar@55724
   376
      (abs_eq, opt_rep_eq, (dest_type rty, dest_type qty)) 
kuncar@55724
   377
    end
kuncar@55724
   378
  
kuncar@55724
   379
  fun register_encoded_code_eq thm thy =
kuncar@55724
   380
    let
kuncar@55724
   381
      val (abs_eq_thm, opt_rep_eq_thm, (rty, qty)) = decode_code_eq thm
kuncar@55724
   382
    in
kuncar@55724
   383
      register_code_eq_thy abs_eq_thm opt_rep_eq_thm (rty, qty) thy
kuncar@55724
   384
    end
kuncar@55724
   385
  
kuncar@55724
   386
  val register_code_eq_attribute = Thm.declaration_attribute
kuncar@55724
   387
    (fn thm => Context.mapping (register_encoded_code_eq thm) I)
kuncar@55724
   388
  val register_code_eq_attrib = Attrib.internal (K register_code_eq_attribute)
kuncar@55724
   389
in
kuncar@55724
   390
kuncar@55724
   391
fun register_code_eq abs_eq_thm opt_rep_eq_thm (rty, qty) lthy =
kuncar@55724
   392
  let
kuncar@55724
   393
    val thy = Proof_Context.theory_of lthy
kuncar@55724
   394
    val encoded_code_eq = encode_code_eq thy abs_eq_thm opt_rep_eq_thm (rty, qty)
kuncar@55724
   395
  in
kuncar@55724
   396
    (snd oo Local_Theory.note) ((Binding.empty, [register_code_eq_attrib]), 
kuncar@55724
   397
      [encoded_code_eq]) lthy
kuncar@55724
   398
  end
kuncar@55724
   399
end
kuncar@55724
   400
            
kuncar@47852
   401
(*
kuncar@47852
   402
  Defines an operation on an abstract type in terms of a corresponding operation 
kuncar@47852
   403
    on a representation type.
kuncar@47852
   404
kuncar@47852
   405
  var - a binding and a mixfix of the new constant being defined
kuncar@47852
   406
  qty - an abstract type of the new constant
kuncar@47852
   407
  rhs - a term representing the new constant on the raw level
kuncar@47937
   408
  rsp_thm - a respectfulness theorem in the internal tagged form (like '(R ===> R ===> R) f f'),
kuncar@47852
   409
    i.e. "(Lifting_Term.equiv_relation (fastype_of rhs, qty)) $ rhs $ rhs"
kuncar@54335
   410
  par_thms - a parametricity theorem for rhs
kuncar@47852
   411
*)
kuncar@47308
   412
kuncar@53951
   413
fun add_lift_def var qty rhs rsp_thm par_thms lthy =
kuncar@47308
   414
  let
kuncar@47308
   415
    val rty = fastype_of rhs
kuncar@47937
   416
    val quot_thm = Lifting_Term.prove_quot_thm lthy (rty, qty)
kuncar@47951
   417
    val absrep_trm =  quot_thm_abs quot_thm
kuncar@47308
   418
    val rty_forced = (domain_type o fastype_of) absrep_trm
kuncar@47308
   419
    val forced_rhs = force_rty_type lthy rty_forced rhs
wenzelm@53207
   420
    val lhs = Free (Binding.name_of (#1 var), qty)
kuncar@47308
   421
    val prop = Logic.mk_equals (lhs, absrep_trm $ forced_rhs)
kuncar@47308
   422
    val (_, prop') = Local_Defs.cert_def lthy prop
kuncar@47308
   423
    val (_, newrhs) = Local_Defs.abs_def prop'
kuncar@47308
   424
kuncar@47308
   425
    val ((_, (_ , def_thm)), lthy') = 
kuncar@47308
   426
      Local_Theory.define (var, ((Thm.def_binding (#1 var), []), newrhs)) lthy
kuncar@47308
   427
kuncar@53951
   428
    val transfer_rules = generate_transfer_rules lthy' quot_thm rsp_thm def_thm par_thms
huffman@49975
   429
kuncar@47937
   430
    val abs_eq_thm = generate_abs_eq lthy' def_thm rsp_thm quot_thm
kuncar@51374
   431
    val opt_rep_eq_thm = generate_rep_eq lthy' def_thm rsp_thm (rty_forced, qty)
huffman@47351
   432
kuncar@47545
   433
    fun qualify defname suffix = Binding.qualified true suffix defname
kuncar@47308
   434
kuncar@47545
   435
    val lhs_name = (#1 var)
kuncar@47308
   436
    val rsp_thm_name = qualify lhs_name "rsp"
kuncar@47937
   437
    val abs_eq_thm_name = qualify lhs_name "abs_eq"
kuncar@47937
   438
    val rep_eq_thm_name = qualify lhs_name "rep_eq"
kuncar@51374
   439
    val transfer_rule_name = qualify lhs_name "transfer"
huffman@47373
   440
    val transfer_attr = Attrib.internal (K Transfer.transfer_add)
kuncar@47308
   441
  in
kuncar@47308
   442
    lthy'
kuncar@47308
   443
      |> (snd oo Local_Theory.note) ((rsp_thm_name, []), [rsp_thm])
kuncar@53951
   444
      |> (snd oo Local_Theory.note) ((transfer_rule_name, [transfer_attr]), transfer_rules)
kuncar@47937
   445
      |> (snd oo Local_Theory.note) ((abs_eq_thm_name, []), [abs_eq_thm])
kuncar@51374
   446
      |> (case opt_rep_eq_thm of 
kuncar@47937
   447
            SOME rep_eq_thm => (snd oo Local_Theory.note) ((rep_eq_thm_name, []), [rep_eq_thm])
kuncar@47937
   448
            | NONE => I)
kuncar@55724
   449
      |> register_code_eq abs_eq_thm opt_rep_eq_thm (rty_forced, qty)
kuncar@47308
   450
  end
kuncar@47308
   451
kuncar@55731
   452
local
kuncar@55731
   453
  val invariant_assms_tac_fixed_rules = map (Transfer.prep_transfer_domain_thm @{context})
kuncar@55731
   454
    [@{thm pcr_Domainp_total}, @{thm pcr_Domainp_par_left_total}, @{thm pcr_Domainp_par}, 
kuncar@55731
   455
      @{thm pcr_Domainp}]
kuncar@55731
   456
in
kuncar@47308
   457
fun mk_readable_rsp_thm_eq tm lthy =
kuncar@47308
   458
  let
kuncar@47308
   459
    val ctm = cterm_of (Proof_Context.theory_of lthy) tm
kuncar@47308
   460
    
kuncar@55731
   461
    (* This is not very cheap way of getting the rules but we have only few active
kuncar@55731
   462
      liftings in the current setting *)
kuncar@55731
   463
    fun get_cr_pcr_eqs ctxt =
kuncar@55731
   464
      let
kuncar@55731
   465
        fun collect (data : Lifting_Info.quotient) l =
kuncar@55731
   466
          if is_some (#pcr_info data) 
kuncar@55731
   467
          then ((Thm.symmetric o safe_mk_meta_eq o #pcr_cr_eq o the o #pcr_info) data :: l) 
kuncar@55731
   468
          else l
kuncar@55731
   469
        val table = Lifting_Info.get_quotients ctxt
kuncar@55731
   470
      in
kuncar@55731
   471
        Symtab.fold (fn (_, data) => fn l => collect data l) table []
kuncar@55731
   472
      end
kuncar@55731
   473
kuncar@55731
   474
    fun assms_rewr_conv tactic rule ct =
kuncar@55731
   475
      let
kuncar@55731
   476
        fun prove_extra_assms thm =
kuncar@55731
   477
          let
kuncar@55731
   478
            val assms = cprems_of thm
kuncar@55731
   479
            fun finish thm = if Thm.no_prems thm then SOME (Goal.conclude thm) else NONE
kuncar@55731
   480
            fun prove ctm = Option.mapPartial finish (SINGLE tactic (Goal.init ctm))
kuncar@55731
   481
          in
kuncar@55731
   482
            map_interrupt prove assms
kuncar@55731
   483
          end
kuncar@55731
   484
    
kuncar@55731
   485
        fun cconl_of thm = Drule.strip_imp_concl (cprop_of thm)
kuncar@55731
   486
        fun lhs_of thm = fst (Thm.dest_equals (cconl_of thm))
kuncar@55731
   487
        fun rhs_of thm = snd (Thm.dest_equals (cconl_of thm))
kuncar@55731
   488
        val rule1 = Thm.incr_indexes (#maxidx (Thm.rep_cterm ct) + 1) rule;
kuncar@55731
   489
        val lhs = lhs_of rule1;
kuncar@55731
   490
        val rule2 = Thm.rename_boundvars (Thm.term_of lhs) (Thm.term_of ct) rule1;
kuncar@55731
   491
        val rule3 =
kuncar@55731
   492
          Thm.instantiate (Thm.match (lhs, ct)) rule2
kuncar@55731
   493
            handle Pattern.MATCH => raise CTERM ("assms_rewr_conv", [lhs, ct]);
kuncar@55731
   494
        val proved_assms = prove_extra_assms rule3
kuncar@55731
   495
      in
kuncar@55731
   496
        case proved_assms of
kuncar@55731
   497
          SOME proved_assms =>
kuncar@55731
   498
            let
kuncar@55731
   499
              val rule3 = proved_assms MRSL rule3
kuncar@55731
   500
              val rule4 =
kuncar@55731
   501
                if lhs_of rule3 aconvc ct then rule3
kuncar@55731
   502
                else
kuncar@55731
   503
                  let val ceq = Thm.dest_fun2 (Thm.cprop_of rule3)
kuncar@55731
   504
                  in rule3 COMP Thm.trivial (Thm.mk_binop ceq ct (rhs_of rule3)) end
kuncar@55731
   505
            in Thm.transitive rule4 (Thm.beta_conversion true (rhs_of rule4)) end
kuncar@55731
   506
          | NONE => Conv.no_conv ct
kuncar@55731
   507
      end
kuncar@55731
   508
kuncar@55731
   509
    fun assms_rewrs_conv tactic rules = Conv.first_conv (map (assms_rewr_conv tactic) rules)
kuncar@55731
   510
kuncar@47308
   511
    fun simp_arrows_conv ctm =
kuncar@47308
   512
      let
kuncar@47308
   513
        val unfold_conv = Conv.rewrs_conv 
blanchet@55945
   514
          [@{thm rel_fun_eq_invariant[THEN eq_reflection]}, 
blanchet@55945
   515
            @{thm rel_fun_invariant_rel[THEN eq_reflection]},
blanchet@55945
   516
            @{thm rel_fun_eq[THEN eq_reflection]},
blanchet@55945
   517
            @{thm rel_fun_eq_rel[THEN eq_reflection]}, 
blanchet@55945
   518
            @{thm rel_fun_def[THEN eq_reflection]}]
kuncar@47308
   519
        fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
kuncar@56518
   520
        val invariant_assms_tac_rules = @{thm left_unique_OO} :: 
kuncar@55731
   521
            invariant_assms_tac_fixed_rules @ (Transfer.get_transfer_raw lthy)
kuncar@55731
   522
        val invariant_assms_tac = (TRY o REPEAT_ALL_NEW (resolve_tac invariant_assms_tac_rules) 
kuncar@55731
   523
          THEN_ALL_NEW (DETERM o Transfer.eq_tac lthy)) 1
kuncar@47634
   524
        val invariant_commute_conv = Conv.bottom_conv
kuncar@55731
   525
          (K (Conv.try_conv (assms_rewrs_conv invariant_assms_tac
kuncar@55731
   526
            (Lifting_Info.get_invariant_commute_rules lthy)))) lthy
kuncar@49626
   527
        val relator_eq_conv = Conv.bottom_conv
kuncar@49626
   528
          (K (Conv.try_conv (Conv.rewrs_conv (Transfer.get_relator_eq lthy)))) lthy
kuncar@47308
   529
      in
kuncar@47308
   530
        case (Thm.term_of ctm) of
blanchet@55945
   531
          Const (@{const_name "rel_fun"}, _) $ _ $ _ => 
kuncar@49626
   532
            (binop_conv2 simp_arrows_conv simp_arrows_conv then_conv unfold_conv) ctm
kuncar@49626
   533
          | _ => (invariant_commute_conv then_conv relator_eq_conv) ctm
kuncar@47308
   534
      end
kuncar@47937
   535
    
kuncar@47308
   536
    val unfold_ret_val_invs = Conv.bottom_conv 
kuncar@55731
   537
      (K (Conv.try_conv (Conv.rewr_conv @{thm invariant_same_args}))) lthy
kuncar@55731
   538
    val cr_to_pcr_conv = Raw_Simplifier.rewrite lthy false (get_cr_pcr_eqs lthy)
kuncar@55773
   539
    val unfold_inv_conv = 
kuncar@55773
   540
      Conv.top_sweep_conv (K (Conv.rewr_conv @{thm invariant_def[THEN eq_reflection]})) lthy
kuncar@55773
   541
    val simp_conv = HOLogic.Trueprop_conv (Conv.fun2_conv 
kuncar@55773
   542
      (cr_to_pcr_conv then_conv simp_arrows_conv))
kuncar@47308
   543
    val univq_conv = Conv.rewr_conv @{thm HOL.all_simps(6)[symmetric, THEN eq_reflection]}
kuncar@47308
   544
    val univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) lthy
kuncar@47308
   545
    val beta_conv = Thm.beta_conversion true
kuncar@47308
   546
    val eq_thm = 
kuncar@55773
   547
      (simp_conv then_conv univq_prenex_conv then_conv beta_conv then_conv unfold_ret_val_invs
kuncar@55773
   548
         then_conv unfold_inv_conv) ctm
kuncar@47308
   549
  in
wenzelm@54742
   550
    Object_Logic.rulify lthy (eq_thm RS Drule.equal_elim_rule2)
kuncar@47308
   551
  end
kuncar@55731
   552
end
kuncar@47308
   553
kuncar@47607
   554
fun rename_to_tnames ctxt term =
kuncar@47607
   555
  let
wenzelm@56245
   556
    fun all_typs (Const (@{const_name Pure.all}, _) $ Abs (_, T, t)) = T :: all_typs t
kuncar@47607
   557
      | all_typs _ = []
kuncar@47308
   558
wenzelm@56245
   559
    fun rename (Const (@{const_name Pure.all}, T1) $ Abs (_, T2, t)) (new_name :: names) = 
wenzelm@56245
   560
        (Const (@{const_name Pure.all}, T1) $ Abs (new_name, T2, rename t names)) 
kuncar@47607
   561
      | rename t _ = t
kuncar@47607
   562
kuncar@47607
   563
    val (fixed_def_t, _) = yield_singleton (Variable.importT_terms) term ctxt
kuncar@47607
   564
    val new_names = Datatype_Prop.make_tnames (all_typs fixed_def_t)
kuncar@47607
   565
  in
kuncar@47607
   566
    rename term new_names
kuncar@47607
   567
  end
kuncar@47308
   568
kuncar@47852
   569
(*
kuncar@47852
   570
kuncar@47852
   571
  lifting_definition command. It opens a proof of a corresponding respectfulness 
kuncar@47852
   572
  theorem in a user-friendly, readable form. Then add_lift_def is called internally.
kuncar@47852
   573
kuncar@47852
   574
*)
kuncar@47852
   575
kuncar@53951
   576
fun lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy =
kuncar@47308
   577
  let
kuncar@51994
   578
    val ((binding, SOME qty, mx), lthy) = yield_singleton Proof_Context.read_vars raw_var lthy 
kuncar@51994
   579
    val rhs = (Syntax.check_term lthy o Syntax.parse_term lthy) rhs_raw
kuncar@51994
   580
    val rsp_rel = Lifting_Term.equiv_relation lthy (fastype_of rhs, qty)
kuncar@47308
   581
    val rty_forced = (domain_type o fastype_of) rsp_rel;
kuncar@51994
   582
    val forced_rhs = force_rty_type lthy rty_forced rhs;
kuncar@47308
   583
    val internal_rsp_tm = HOLogic.mk_Trueprop (rsp_rel $ forced_rhs $ forced_rhs)
kuncar@51994
   584
    val opt_proven_rsp_thm = try_prove_reflexivity lthy internal_rsp_tm
kuncar@53951
   585
    val par_thms = Attrib.eval_thms lthy par_xthms
kuncar@51994
   586
    
kuncar@51994
   587
    fun after_qed internal_rsp_thm lthy = 
kuncar@53951
   588
      add_lift_def (binding, mx) qty rhs internal_rsp_thm par_thms lthy
kuncar@47308
   589
kuncar@47308
   590
  in
kuncar@51374
   591
    case opt_proven_rsp_thm of
kuncar@51994
   592
      SOME thm => Proof.theorem NONE (K (after_qed thm)) [] lthy
kuncar@51994
   593
      | NONE =>  
kuncar@51994
   594
        let
kuncar@51994
   595
          val readable_rsp_thm_eq = mk_readable_rsp_thm_eq internal_rsp_tm lthy
kuncar@51994
   596
          val (readable_rsp_tm, _) = Logic.dest_implies (prop_of readable_rsp_thm_eq)
kuncar@51994
   597
          val readable_rsp_tm_tnames = rename_to_tnames lthy readable_rsp_tm
kuncar@51994
   598
      
kuncar@51994
   599
          fun after_qed' thm_list lthy = 
kuncar@51994
   600
            let
kuncar@51994
   601
              val internal_rsp_thm = Goal.prove lthy [] [] internal_rsp_tm 
wenzelm@54742
   602
                  (fn {context = ctxt, ...} =>
wenzelm@54742
   603
                    rtac readable_rsp_thm_eq 1 THEN Proof_Context.fact_tac ctxt (hd thm_list) 1)
kuncar@51994
   604
            in
kuncar@51994
   605
              after_qed internal_rsp_thm lthy
kuncar@51994
   606
            end
kuncar@51994
   607
        in
kuncar@51994
   608
          Proof.theorem NONE after_qed' [[(readable_rsp_tm_tnames,[])]] lthy
kuncar@51994
   609
        end 
kuncar@47308
   610
  end
kuncar@47308
   611
kuncar@47379
   612
fun quot_thm_err ctxt (rty, qty) pretty_msg =
kuncar@47379
   613
  let
kuncar@47379
   614
    val error_msg = cat_lines
kuncar@47379
   615
       ["Lifting failed for the following types:",
kuncar@47379
   616
        Pretty.string_of (Pretty.block
kuncar@47379
   617
         [Pretty.str "Raw type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty]),
kuncar@47379
   618
        Pretty.string_of (Pretty.block
kuncar@47379
   619
         [Pretty.str "Abstract type:", Pretty.brk 2, Syntax.pretty_typ ctxt qty]),
kuncar@47379
   620
        "",
kuncar@47379
   621
        (Pretty.string_of (Pretty.block
kuncar@47379
   622
         [Pretty.str "Reason:", Pretty.brk 2, pretty_msg]))]
kuncar@47379
   623
  in
kuncar@47379
   624
    error error_msg
kuncar@47379
   625
  end
kuncar@47379
   626
kuncar@47504
   627
fun check_rty_err ctxt (rty_schematic, rty_forced) (raw_var, rhs_raw) =
kuncar@47379
   628
  let
kuncar@47504
   629
    val (_, ctxt') = yield_singleton Proof_Context.read_vars raw_var ctxt 
kuncar@47504
   630
    val rhs = (Syntax.check_term ctxt' o Syntax.parse_term ctxt') rhs_raw
kuncar@47379
   631
    val error_msg = cat_lines
kuncar@47379
   632
       ["Lifting failed for the following term:",
kuncar@47379
   633
        Pretty.string_of (Pretty.block
kuncar@47379
   634
         [Pretty.str "Term:", Pretty.brk 2, Syntax.pretty_term ctxt rhs]),
kuncar@47379
   635
        Pretty.string_of (Pretty.block
kuncar@47504
   636
         [Pretty.str "Type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty_schematic]),
kuncar@47379
   637
        "",
kuncar@47379
   638
        (Pretty.string_of (Pretty.block
kuncar@47379
   639
         [Pretty.str "Reason:", 
kuncar@47379
   640
          Pretty.brk 2, 
kuncar@51957
   641
          Pretty.str "The type of the term cannot be instantiated to",
kuncar@47379
   642
          Pretty.brk 1,
kuncar@47504
   643
          Pretty.quote (Syntax.pretty_typ ctxt rty_forced),
kuncar@47379
   644
          Pretty.str "."]))]
kuncar@47379
   645
    in
kuncar@47379
   646
      error error_msg
kuncar@47379
   647
    end
kuncar@47379
   648
kuncar@53951
   649
fun lift_def_cmd_with_err_handling (raw_var, rhs_raw, par_xthms) lthy =
kuncar@53951
   650
  (lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy
kuncar@47379
   651
    handle Lifting_Term.QUOT_THM (rty, qty, msg) => quot_thm_err lthy (rty, qty) msg)
kuncar@47504
   652
    handle Lifting_Term.CHECK_RTY (rty_schematic, rty_forced) => 
kuncar@47504
   653
      check_rty_err lthy (rty_schematic, rty_forced) (raw_var, rhs_raw)
kuncar@47379
   654
kuncar@47308
   655
(* parser and command *)
kuncar@47308
   656
val liftdef_parser =
kuncar@51374
   657
  (((Parse.binding -- (@{keyword "::"} |-- (Parse.typ >> SOME) -- Parse.opt_mixfix')) >> Parse.triple2)
kuncar@53951
   658
    --| @{keyword "is"} -- Parse.term -- 
kuncar@53951
   659
      Scan.optional (@{keyword "parametric"} |-- Parse.!!! Parse_Spec.xthms1) []) >> Parse.triple1
kuncar@47308
   660
val _ =
kuncar@47308
   661
  Outer_Syntax.local_theory_to_proof @{command_spec "lift_definition"}
kuncar@47308
   662
    "definition for constants over the quotient type"
kuncar@47379
   663
      (liftdef_parser >> lift_def_cmd_with_err_handling)
kuncar@47308
   664
kuncar@47308
   665
kuncar@53651
   666
end (* structure *)