src/HOL/Tools/Lifting/lifting_def.ML
author wenzelm
Sat Dec 14 17:28:05 2013 +0100 (2013-12-14)
changeset 54742 7a86358a3c0b
parent 54335 03b10317ba78
child 54947 9e632948ed56
permissions -rw-r--r--
proper context for basic Simplifier operations: rewrite_rule, rewrite_goals_rule, rewrite_goals_tac etc.;
clarified tool context in some boundary cases;
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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 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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(* 
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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_T 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 =       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 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 "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
kuncar@47937
   313
        
kuncar@47937
   314
        val rep_abs_folded_unmapped_thm = 
kuncar@47937
   315
          let
kuncar@47937
   316
            val rep_id = [quot_thm, def_thm] MRSL @{thm Quotient_Rep_eq}
kuncar@47937
   317
            val ctm = Thm.dest_equals_lhs (cprop_of rep_id)
kuncar@47937
   318
            val unfolded_maps_eq = unfold_fun_maps ctm
kuncar@47937
   319
            val t1 = [quot_thm, def_thm, rsp_thm] MRSL @{thm Quotient_rep_abs_fold_unmap}
kuncar@47937
   320
            val prems_pat = (hd o Drule.cprems_of) t1
kuncar@47937
   321
            val insts = Thm.first_order_match (prems_pat, cprop_of unfolded_maps_eq)
kuncar@47937
   322
          in
kuncar@47937
   323
            unfolded_maps_eq RS (Drule.instantiate_normalize insts t1)
kuncar@47937
   324
          end
kuncar@47937
   325
      in
kuncar@47937
   326
        rep_abs_folded_unmapped_thm
kuncar@47937
   327
        |> fold (fn _ => fn thm => thm RS @{thm fun_relD2}) ty_args
kuncar@47937
   328
        |> (fn x => x RS (@{thm Quotient_rel_abs2} OF [quot_ret_thm]))
kuncar@47937
   329
      end
kuncar@47937
   330
    
kuncar@47937
   331
    val prems = prems_of abs_eq_with_assms
kuncar@47937
   332
    val indexed_prems = map_index (apfst (fn x => x + 1)) prems
kuncar@51994
   333
    val indexed_assms = map (apsnd (try_prove_reflexivity ctxt)) indexed_prems
kuncar@47937
   334
    val proved_assms = map (apsnd the) (filter (is_some o snd) indexed_assms)
kuncar@47937
   335
    val abs_eq = fold_rev (fn (i, assms) => fn thm => assms RSN (i, thm)) proved_assms abs_eq_with_assms
kuncar@47308
   336
  in
kuncar@47937
   337
    simplify_code_eq ctxt abs_eq
kuncar@47937
   338
  end
kuncar@47937
   339
kuncar@47937
   340
fun define_code_using_abs_eq abs_eq_thm lthy =
kuncar@47937
   341
  if null (Logic.strip_imp_prems(prop_of abs_eq_thm)) then
kuncar@47937
   342
    (snd oo Local_Theory.note) ((Binding.empty, [Code.add_default_eqn_attrib]), [abs_eq_thm]) lthy
kuncar@47937
   343
  else
kuncar@47937
   344
    lthy
kuncar@47937
   345
  
kuncar@51374
   346
fun define_code_using_rep_eq opt_rep_eq_thm lthy = 
kuncar@51374
   347
  case opt_rep_eq_thm of
kuncar@47937
   348
    SOME rep_eq_thm =>   
kuncar@47308
   349
      let
kuncar@47308
   350
        val add_abs_eqn_attribute = 
kuncar@47308
   351
          Thm.declaration_attribute (fn thm => Context.mapping (Code.add_abs_eqn thm) I)
kuncar@47308
   352
        val add_abs_eqn_attrib = Attrib.internal (K add_abs_eqn_attribute);
kuncar@47308
   353
      in
kuncar@47937
   354
        (snd oo Local_Theory.note) ((Binding.empty, [add_abs_eqn_attrib]), [rep_eq_thm]) lthy
kuncar@47308
   355
      end
kuncar@47937
   356
    | NONE => lthy
kuncar@47937
   357
kuncar@47937
   358
fun has_constr ctxt quot_thm =
kuncar@47937
   359
  let
kuncar@47937
   360
    val thy = Proof_Context.theory_of ctxt
kuncar@47951
   361
    val abs_fun = quot_thm_abs quot_thm
kuncar@47937
   362
  in
kuncar@47937
   363
    if is_Const abs_fun then
kuncar@47937
   364
      Code.is_constr thy ((fst o dest_Const) abs_fun)
kuncar@47308
   365
    else
kuncar@47937
   366
      false
kuncar@47308
   367
  end
kuncar@47308
   368
kuncar@47937
   369
fun has_abstr ctxt quot_thm =
kuncar@47308
   370
  let
kuncar@47937
   371
    val thy = Proof_Context.theory_of ctxt
kuncar@47951
   372
    val abs_fun = quot_thm_abs quot_thm
kuncar@47308
   373
  in
kuncar@47937
   374
    if is_Const abs_fun then
kuncar@47937
   375
      Code.is_abstr thy ((fst o dest_Const) abs_fun)
kuncar@47937
   376
    else
kuncar@47937
   377
      false
kuncar@47308
   378
  end
kuncar@47308
   379
kuncar@51374
   380
fun define_code abs_eq_thm opt_rep_eq_thm (rty, qty) lthy =
kuncar@47937
   381
  let
kuncar@47937
   382
    val (rty_body, qty_body) = get_body_types (rty, qty)
kuncar@47937
   383
  in
kuncar@47937
   384
    if rty_body = qty_body then
kuncar@47937
   385
      if null (Logic.strip_imp_prems(prop_of abs_eq_thm)) then
kuncar@47937
   386
        (snd oo Local_Theory.note) ((Binding.empty, [Code.add_default_eqn_attrib]), [abs_eq_thm]) lthy
kuncar@47937
   387
      else
kuncar@51374
   388
        (snd oo Local_Theory.note) ((Binding.empty, [Code.add_default_eqn_attrib]), [the opt_rep_eq_thm]) lthy
kuncar@47937
   389
    else
kuncar@47937
   390
      let 
kuncar@47937
   391
        val body_quot_thm = Lifting_Term.prove_quot_thm lthy (rty_body, qty_body)
kuncar@47937
   392
      in
kuncar@47937
   393
        if has_constr lthy body_quot_thm then
kuncar@47937
   394
          define_code_using_abs_eq abs_eq_thm lthy
kuncar@47937
   395
        else if has_abstr lthy body_quot_thm then
kuncar@51374
   396
          define_code_using_rep_eq opt_rep_eq_thm lthy
kuncar@47937
   397
        else
kuncar@47937
   398
          lthy
kuncar@47937
   399
      end
kuncar@47937
   400
  end
kuncar@47308
   401
kuncar@47852
   402
(*
kuncar@47852
   403
  Defines an operation on an abstract type in terms of a corresponding operation 
kuncar@47852
   404
    on a representation type.
kuncar@47852
   405
kuncar@47852
   406
  var - a binding and a mixfix of the new constant being defined
kuncar@47852
   407
  qty - an abstract type of the new constant
kuncar@47852
   408
  rhs - a term representing the new constant on the raw level
kuncar@47937
   409
  rsp_thm - a respectfulness theorem in the internal tagged form (like '(R ===> R ===> R) f f'),
kuncar@47852
   410
    i.e. "(Lifting_Term.equiv_relation (fastype_of rhs, qty)) $ rhs $ rhs"
kuncar@54335
   411
  par_thms - a parametricity theorem for rhs
kuncar@47852
   412
*)
kuncar@47308
   413
kuncar@53951
   414
fun add_lift_def var qty rhs rsp_thm par_thms lthy =
kuncar@47308
   415
  let
kuncar@47308
   416
    val rty = fastype_of rhs
kuncar@47937
   417
    val quot_thm = Lifting_Term.prove_quot_thm lthy (rty, qty)
kuncar@47951
   418
    val absrep_trm =  quot_thm_abs quot_thm
kuncar@47308
   419
    val rty_forced = (domain_type o fastype_of) absrep_trm
kuncar@47308
   420
    val forced_rhs = force_rty_type lthy rty_forced rhs
wenzelm@53207
   421
    val lhs = Free (Binding.name_of (#1 var), qty)
kuncar@47308
   422
    val prop = Logic.mk_equals (lhs, absrep_trm $ forced_rhs)
kuncar@47308
   423
    val (_, prop') = Local_Defs.cert_def lthy prop
kuncar@47308
   424
    val (_, newrhs) = Local_Defs.abs_def prop'
kuncar@47308
   425
kuncar@47308
   426
    val ((_, (_ , def_thm)), lthy') = 
kuncar@47308
   427
      Local_Theory.define (var, ((Thm.def_binding (#1 var), []), newrhs)) lthy
kuncar@47308
   428
kuncar@53951
   429
    val transfer_rules = generate_transfer_rules lthy' quot_thm rsp_thm def_thm par_thms
huffman@49975
   430
kuncar@47937
   431
    val abs_eq_thm = generate_abs_eq lthy' def_thm rsp_thm quot_thm
kuncar@51374
   432
    val opt_rep_eq_thm = generate_rep_eq lthy' def_thm rsp_thm (rty_forced, qty)
huffman@47351
   433
kuncar@47545
   434
    fun qualify defname suffix = Binding.qualified true suffix defname
kuncar@47308
   435
kuncar@47545
   436
    val lhs_name = (#1 var)
kuncar@47308
   437
    val rsp_thm_name = qualify lhs_name "rsp"
kuncar@47937
   438
    val abs_eq_thm_name = qualify lhs_name "abs_eq"
kuncar@47937
   439
    val rep_eq_thm_name = qualify lhs_name "rep_eq"
kuncar@51374
   440
    val transfer_rule_name = qualify lhs_name "transfer"
huffman@47373
   441
    val transfer_attr = Attrib.internal (K Transfer.transfer_add)
kuncar@47308
   442
  in
kuncar@47308
   443
    lthy'
kuncar@47308
   444
      |> (snd oo Local_Theory.note) ((rsp_thm_name, []), [rsp_thm])
kuncar@53951
   445
      |> (snd oo Local_Theory.note) ((transfer_rule_name, [transfer_attr]), transfer_rules)
kuncar@47937
   446
      |> (snd oo Local_Theory.note) ((abs_eq_thm_name, []), [abs_eq_thm])
kuncar@51374
   447
      |> (case opt_rep_eq_thm of 
kuncar@47937
   448
            SOME rep_eq_thm => (snd oo Local_Theory.note) ((rep_eq_thm_name, []), [rep_eq_thm])
kuncar@47937
   449
            | NONE => I)
kuncar@51374
   450
      |> define_code abs_eq_thm opt_rep_eq_thm (rty_forced, qty)
kuncar@47308
   451
  end
kuncar@47308
   452
kuncar@47308
   453
fun mk_readable_rsp_thm_eq tm lthy =
kuncar@47308
   454
  let
kuncar@47308
   455
    val ctm = cterm_of (Proof_Context.theory_of lthy) tm
kuncar@47308
   456
    
kuncar@47308
   457
    fun simp_arrows_conv ctm =
kuncar@47308
   458
      let
kuncar@47308
   459
        val unfold_conv = Conv.rewrs_conv 
kuncar@49626
   460
          [@{thm fun_rel_eq_invariant[THEN eq_reflection]}, 
kuncar@49626
   461
            @{thm fun_rel_eq[THEN eq_reflection]},
kuncar@49626
   462
            @{thm fun_rel_eq_rel[THEN eq_reflection]}, 
kuncar@47308
   463
            @{thm fun_rel_def[THEN eq_reflection]}]
kuncar@47308
   464
        fun binop_conv2 cv1 cv2 = Conv.combination_conv (Conv.arg_conv cv1) cv2
kuncar@47634
   465
        val invariant_commute_conv = Conv.bottom_conv
kuncar@47634
   466
          (K (Conv.try_conv (Conv.rewrs_conv (Lifting_Info.get_invariant_commute_rules lthy)))) lthy
kuncar@49626
   467
        val relator_eq_conv = Conv.bottom_conv
kuncar@49626
   468
          (K (Conv.try_conv (Conv.rewrs_conv (Transfer.get_relator_eq lthy)))) lthy
kuncar@47308
   469
      in
kuncar@47308
   470
        case (Thm.term_of ctm) of
kuncar@47308
   471
          Const (@{const_name "fun_rel"}, _) $ _ $ _ => 
kuncar@49626
   472
            (binop_conv2 simp_arrows_conv simp_arrows_conv then_conv unfold_conv) ctm
kuncar@49626
   473
          | _ => (invariant_commute_conv then_conv relator_eq_conv) ctm
kuncar@47308
   474
      end
kuncar@47937
   475
    
kuncar@47308
   476
    val unfold_ret_val_invs = Conv.bottom_conv 
kuncar@47308
   477
      (K (Conv.try_conv (Conv.rewr_conv @{thm invariant_same_args}))) lthy 
wenzelm@51314
   478
    val simp_conv = HOLogic.Trueprop_conv (Conv.fun2_conv simp_arrows_conv)
kuncar@47308
   479
    val univq_conv = Conv.rewr_conv @{thm HOL.all_simps(6)[symmetric, THEN eq_reflection]}
kuncar@47308
   480
    val univq_prenex_conv = Conv.top_conv (K (Conv.try_conv univq_conv)) lthy
kuncar@47308
   481
    val beta_conv = Thm.beta_conversion true
kuncar@47308
   482
    val eq_thm = 
kuncar@47308
   483
      (simp_conv then_conv univq_prenex_conv then_conv beta_conv then_conv unfold_ret_val_invs) ctm
kuncar@47308
   484
  in
wenzelm@54742
   485
    Object_Logic.rulify lthy (eq_thm RS Drule.equal_elim_rule2)
kuncar@47308
   486
  end
kuncar@47308
   487
kuncar@47607
   488
fun rename_to_tnames ctxt term =
kuncar@47607
   489
  let
kuncar@47607
   490
    fun all_typs (Const ("all", _) $ Abs (_, T, t)) = T :: all_typs t
kuncar@47607
   491
      | all_typs _ = []
kuncar@47308
   492
kuncar@47607
   493
    fun rename (Const ("all", T1) $ Abs (_, T2, t)) (new_name :: names) = 
kuncar@47607
   494
        (Const ("all", T1) $ Abs (new_name, T2, rename t names)) 
kuncar@47607
   495
      | rename t _ = t
kuncar@47607
   496
kuncar@47607
   497
    val (fixed_def_t, _) = yield_singleton (Variable.importT_terms) term ctxt
kuncar@47607
   498
    val new_names = Datatype_Prop.make_tnames (all_typs fixed_def_t)
kuncar@47607
   499
  in
kuncar@47607
   500
    rename term new_names
kuncar@47607
   501
  end
kuncar@47308
   502
kuncar@47852
   503
(*
kuncar@47852
   504
kuncar@47852
   505
  lifting_definition command. It opens a proof of a corresponding respectfulness 
kuncar@47852
   506
  theorem in a user-friendly, readable form. Then add_lift_def is called internally.
kuncar@47852
   507
kuncar@47852
   508
*)
kuncar@47852
   509
kuncar@53951
   510
fun lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy =
kuncar@47308
   511
  let
kuncar@51994
   512
    val ((binding, SOME qty, mx), lthy) = yield_singleton Proof_Context.read_vars raw_var lthy 
kuncar@51994
   513
    val rhs = (Syntax.check_term lthy o Syntax.parse_term lthy) rhs_raw
kuncar@51994
   514
    val rsp_rel = Lifting_Term.equiv_relation lthy (fastype_of rhs, qty)
kuncar@47308
   515
    val rty_forced = (domain_type o fastype_of) rsp_rel;
kuncar@51994
   516
    val forced_rhs = force_rty_type lthy rty_forced rhs;
kuncar@47308
   517
    val internal_rsp_tm = HOLogic.mk_Trueprop (rsp_rel $ forced_rhs $ forced_rhs)
kuncar@51994
   518
    val opt_proven_rsp_thm = try_prove_reflexivity lthy internal_rsp_tm
kuncar@53951
   519
    val par_thms = Attrib.eval_thms lthy par_xthms
kuncar@51994
   520
    
kuncar@51994
   521
    fun after_qed internal_rsp_thm lthy = 
kuncar@53951
   522
      add_lift_def (binding, mx) qty rhs internal_rsp_thm par_thms lthy
kuncar@47308
   523
kuncar@47308
   524
  in
kuncar@51374
   525
    case opt_proven_rsp_thm of
kuncar@51994
   526
      SOME thm => Proof.theorem NONE (K (after_qed thm)) [] lthy
kuncar@51994
   527
      | NONE =>  
kuncar@51994
   528
        let
kuncar@51994
   529
          val readable_rsp_thm_eq = mk_readable_rsp_thm_eq internal_rsp_tm lthy
kuncar@51994
   530
          val (readable_rsp_tm, _) = Logic.dest_implies (prop_of readable_rsp_thm_eq)
kuncar@51994
   531
          val readable_rsp_tm_tnames = rename_to_tnames lthy readable_rsp_tm
kuncar@51994
   532
      
kuncar@51994
   533
          fun after_qed' thm_list lthy = 
kuncar@51994
   534
            let
kuncar@51994
   535
              val internal_rsp_thm = Goal.prove lthy [] [] internal_rsp_tm 
wenzelm@54742
   536
                  (fn {context = ctxt, ...} =>
wenzelm@54742
   537
                    rtac readable_rsp_thm_eq 1 THEN Proof_Context.fact_tac ctxt (hd thm_list) 1)
kuncar@51994
   538
            in
kuncar@51994
   539
              after_qed internal_rsp_thm lthy
kuncar@51994
   540
            end
kuncar@51994
   541
        in
kuncar@51994
   542
          Proof.theorem NONE after_qed' [[(readable_rsp_tm_tnames,[])]] lthy
kuncar@51994
   543
        end 
kuncar@47308
   544
  end
kuncar@47308
   545
kuncar@47379
   546
fun quot_thm_err ctxt (rty, qty) pretty_msg =
kuncar@47379
   547
  let
kuncar@47379
   548
    val error_msg = cat_lines
kuncar@47379
   549
       ["Lifting failed for the following types:",
kuncar@47379
   550
        Pretty.string_of (Pretty.block
kuncar@47379
   551
         [Pretty.str "Raw type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty]),
kuncar@47379
   552
        Pretty.string_of (Pretty.block
kuncar@47379
   553
         [Pretty.str "Abstract type:", Pretty.brk 2, Syntax.pretty_typ ctxt qty]),
kuncar@47379
   554
        "",
kuncar@47379
   555
        (Pretty.string_of (Pretty.block
kuncar@47379
   556
         [Pretty.str "Reason:", Pretty.brk 2, pretty_msg]))]
kuncar@47379
   557
  in
kuncar@47379
   558
    error error_msg
kuncar@47379
   559
  end
kuncar@47379
   560
kuncar@47504
   561
fun check_rty_err ctxt (rty_schematic, rty_forced) (raw_var, rhs_raw) =
kuncar@47379
   562
  let
kuncar@47504
   563
    val (_, ctxt') = yield_singleton Proof_Context.read_vars raw_var ctxt 
kuncar@47504
   564
    val rhs = (Syntax.check_term ctxt' o Syntax.parse_term ctxt') rhs_raw
kuncar@47379
   565
    val error_msg = cat_lines
kuncar@47379
   566
       ["Lifting failed for the following term:",
kuncar@47379
   567
        Pretty.string_of (Pretty.block
kuncar@47379
   568
         [Pretty.str "Term:", Pretty.brk 2, Syntax.pretty_term ctxt rhs]),
kuncar@47379
   569
        Pretty.string_of (Pretty.block
kuncar@47504
   570
         [Pretty.str "Type:", Pretty.brk 2, Syntax.pretty_typ ctxt rty_schematic]),
kuncar@47379
   571
        "",
kuncar@47379
   572
        (Pretty.string_of (Pretty.block
kuncar@47379
   573
         [Pretty.str "Reason:", 
kuncar@47379
   574
          Pretty.brk 2, 
kuncar@51957
   575
          Pretty.str "The type of the term cannot be instantiated to",
kuncar@47379
   576
          Pretty.brk 1,
kuncar@47504
   577
          Pretty.quote (Syntax.pretty_typ ctxt rty_forced),
kuncar@47379
   578
          Pretty.str "."]))]
kuncar@47379
   579
    in
kuncar@47379
   580
      error error_msg
kuncar@47379
   581
    end
kuncar@47379
   582
kuncar@53951
   583
fun lift_def_cmd_with_err_handling (raw_var, rhs_raw, par_xthms) lthy =
kuncar@53951
   584
  (lift_def_cmd (raw_var, rhs_raw, par_xthms) lthy
kuncar@47379
   585
    handle Lifting_Term.QUOT_THM (rty, qty, msg) => quot_thm_err lthy (rty, qty) msg)
kuncar@47504
   586
    handle Lifting_Term.CHECK_RTY (rty_schematic, rty_forced) => 
kuncar@47504
   587
      check_rty_err lthy (rty_schematic, rty_forced) (raw_var, rhs_raw)
kuncar@47379
   588
kuncar@47308
   589
(* parser and command *)
kuncar@47308
   590
val liftdef_parser =
kuncar@51374
   591
  (((Parse.binding -- (@{keyword "::"} |-- (Parse.typ >> SOME) -- Parse.opt_mixfix')) >> Parse.triple2)
kuncar@53951
   592
    --| @{keyword "is"} -- Parse.term -- 
kuncar@53951
   593
      Scan.optional (@{keyword "parametric"} |-- Parse.!!! Parse_Spec.xthms1) []) >> Parse.triple1
kuncar@47308
   594
val _ =
kuncar@47308
   595
  Outer_Syntax.local_theory_to_proof @{command_spec "lift_definition"}
kuncar@47308
   596
    "definition for constants over the quotient type"
kuncar@47379
   597
      (liftdef_parser >> lift_def_cmd_with_err_handling)
kuncar@47308
   598
kuncar@47308
   599
kuncar@53651
   600
end (* structure *)