src/HOL/Tools/BNF/bnf_fp_def_sugar.ML
author blanchet
Mon Mar 03 12:48:20 2014 +0100 (2014-03-03)
changeset 55856 bddaada24074
parent 55803 74d3fe9031d8
child 55858 693ddbbab913
permissions -rw-r--r--
got rid of automatically generated fold constant and theorems (to reduce overhead)
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(*  Title:      HOL/Tools/BNF/bnf_fp_def_sugar.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012, 2013
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Sugared datatype and codatatype constructions.
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*)
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signature BNF_FP_DEF_SUGAR =
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sig
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  type fp_sugar =
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    {T: typ,
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     X: typ,
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     fp: BNF_Util.fp_kind,
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     fp_res_index: int,
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     fp_res: BNF_FP_Util.fp_result,
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     pre_bnf: BNF_Def.bnf,
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     absT_info: BNF_Comp.absT_info,
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     nested_bnfs: BNF_Def.bnf list,
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     nesting_bnfs: BNF_Def.bnf list,
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     ctrXs_Tss: typ list list,
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     ctr_defs: thm list,
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     ctr_sugar: Ctr_Sugar.ctr_sugar,
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     co_iters: term list,
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     maps: thm list,
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     common_co_inducts: thm list,
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     co_inducts: thm list,
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     co_iter_thmss: thm list list,
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     disc_co_iterss: thm list list,
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     sel_co_itersss: thm list list list};
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  val morph_fp_sugar: morphism -> fp_sugar -> fp_sugar
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  val transfer_fp_sugar: Proof.context -> fp_sugar -> fp_sugar
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  val fp_sugar_of: Proof.context -> string -> fp_sugar option
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  val fp_sugars_of: Proof.context -> fp_sugar list
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  val co_induct_of: 'a list -> 'a
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  val strong_co_induct_of: 'a list -> 'a
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  val flat_corec_preds_predsss_gettersss: 'a list -> 'a list list list -> 'a list list list ->
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    'a list
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  val nesty_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list
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  type lfp_sugar_thms =
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    (thm list * thm * Args.src list) * (thm list list * Args.src list)
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  val morph_lfp_sugar_thms: morphism -> lfp_sugar_thms -> lfp_sugar_thms
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  val transfer_lfp_sugar_thms: Proof.context -> lfp_sugar_thms -> lfp_sugar_thms
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  type gfp_sugar_thms =
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    ((thm list * thm) list * Args.src list)
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    * (thm list list * Args.src list)
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    * (thm list list * Args.src list)
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    * (thm list list * Args.src list)
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    * (thm list list list * Args.src list)
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  val morph_gfp_sugar_thms: morphism -> gfp_sugar_thms -> gfp_sugar_thms
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  val transfer_gfp_sugar_thms: Proof.context -> gfp_sugar_thms -> gfp_sugar_thms
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  val mk_co_iters_prelims: BNF_Util.fp_kind -> typ list list list -> typ list -> typ list ->
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    typ list -> typ list -> int list -> int list list -> term list list -> Proof.context ->
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    (term list list
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     * (typ list list * typ list list list list * term list list
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        * term list list list list) list option
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     * (string * term list * term list list
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        * ((term list list * term list list list) * typ list) list) option)
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    * Proof.context
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  val repair_nullary_single_ctr: typ list list -> typ list list
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  val mk_coiter_p_pred_types: typ list -> int list -> typ list list
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  val mk_coiter_fun_arg_types: typ list list list -> typ list -> typ list -> typ list -> int list ->
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    int list list -> term ->
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    typ list list
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    * (typ list list list list * typ list list list * typ list list list list * typ list)
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  val define_iters: string list ->
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    (typ list list * typ list list list list * term list list * term list list list list) list ->
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    (string -> binding) -> typ list -> typ list -> term list -> term list -> Proof.context ->
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    (term list * thm list) * Proof.context
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  val define_coiters: string list -> string * term list * term list list
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    * ((term list list * term list list list) * typ list) list ->
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    (string -> binding) -> typ list -> typ list -> term list -> term list -> Proof.context ->
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    (term list * thm list) * Proof.context
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  val derive_induct_iters_thms_for_types: BNF_Def.bnf list ->
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    (typ list list * typ list list list list * term list list * term list list list list) list ->
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    thm -> thm list list -> BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list ->
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    typ list -> typ list list list -> thm list -> thm list -> thm list -> term list list ->
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    thm list list -> term list list -> thm list list -> local_theory -> lfp_sugar_thms
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  val derive_coinduct_coiters_thms_for_types: BNF_Def.bnf list ->
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    string * term list * term list list * ((term list list * term list list list)
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      * typ list) list ->
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    thm -> thm list -> thm list -> thm list list -> BNF_Def.bnf list -> typ list -> typ list ->
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    typ list -> typ list list list -> int list list -> int list list -> int list -> thm list ->
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    thm list -> (thm -> thm) -> thm list list -> Ctr_Sugar.ctr_sugar list -> term list list ->
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    thm list list -> (thm list -> thm list) -> local_theory -> gfp_sugar_thms
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  type co_datatype_spec =
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    ((((binding option * (typ * sort)) list * binding) * (binding * binding)) * mixfix)
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    * ((binding, binding * typ, term) Ctr_Sugar.ctr_spec * mixfix) list
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  val co_datatypes: BNF_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
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      binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
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      BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory ->
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      BNF_FP_Util.fp_result * local_theory) ->
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    (bool * bool) * co_datatype_spec list ->
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    local_theory -> local_theory
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  val parse_co_datatype_cmd: BNF_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
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      binding list list -> binding list -> (string * sort) list -> typ list * typ list list ->
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      BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory ->
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      BNF_FP_Util.fp_result * local_theory) ->
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    (local_theory -> local_theory) parser
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end;
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structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
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struct
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open Ctr_Sugar
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open BNF_FP_Rec_Sugar_Util
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open BNF_Util
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open BNF_Comp
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open BNF_Def
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open BNF_FP_Util
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open BNF_FP_Def_Sugar_Tactics
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val EqN = "Eq_";
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type fp_sugar =
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  {T: typ,
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   X: typ,
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   fp: fp_kind,
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   fp_res_index: int,
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   fp_res: fp_result,
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   pre_bnf: bnf,
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   absT_info: absT_info,
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   nested_bnfs: bnf list,
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   nesting_bnfs: bnf list,
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   ctrXs_Tss: typ list list,
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   ctr_defs: thm list,
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   ctr_sugar: Ctr_Sugar.ctr_sugar,
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   co_iters: term list,
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   maps: thm list,
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   common_co_inducts: thm list,
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   co_inducts: thm list,
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   co_iter_thmss: thm list list,
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   disc_co_iterss: thm list list,
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   sel_co_itersss: thm list list list};
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fun morph_fp_sugar phi ({T, X, fp, fp_res, fp_res_index, pre_bnf, absT_info, nested_bnfs,
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    nesting_bnfs, ctrXs_Tss, ctr_defs, ctr_sugar, co_iters, maps, common_co_inducts, co_inducts,
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    co_iter_thmss, disc_co_iterss, sel_co_itersss} : fp_sugar) =
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  {T = Morphism.typ phi T,
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   X = Morphism.typ phi X,
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   fp = fp,
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   fp_res = morph_fp_result phi fp_res,
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   fp_res_index = fp_res_index,
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   pre_bnf = morph_bnf phi pre_bnf,
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   absT_info = morph_absT_info phi absT_info,
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   nested_bnfs = map (morph_bnf phi) nested_bnfs,
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   nesting_bnfs = map (morph_bnf phi) nesting_bnfs,
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   ctrXs_Tss = map (map (Morphism.typ phi)) ctrXs_Tss,
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   ctr_defs = map (Morphism.thm phi) ctr_defs,
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   ctr_sugar = morph_ctr_sugar phi ctr_sugar,
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   co_iters = map (Morphism.term phi) co_iters,
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   maps = map (Morphism.thm phi) maps,
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   common_co_inducts = map (Morphism.thm phi) common_co_inducts,
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   co_inducts = map (Morphism.thm phi) co_inducts,
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   co_iter_thmss = map (map (Morphism.thm phi)) co_iter_thmss,
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   disc_co_iterss = map (map (Morphism.thm phi)) disc_co_iterss,
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   sel_co_itersss = map (map (map (Morphism.thm phi))) sel_co_itersss};
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val transfer_fp_sugar =
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  morph_fp_sugar o Morphism.transfer_morphism o Proof_Context.theory_of;
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structure Data = Generic_Data
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(
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  type T = fp_sugar Symtab.table;
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  val empty = Symtab.empty;
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  val extend = I;
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  fun merge data : T = Symtab.merge (K true) data;
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);
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fun fp_sugar_of ctxt =
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  Symtab.lookup (Data.get (Context.Proof ctxt))
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  #> Option.map (transfer_fp_sugar ctxt);
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fun fp_sugars_of ctxt =
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  Symtab.fold (cons o transfer_fp_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
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fun co_induct_of (i :: _) = i;
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fun strong_co_induct_of [_, s] = s;
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(* TODO: register "sum" and "prod" as datatypes to enable N2M reduction for them *)
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fun register_fp_sugar key fp_sugar =
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  Local_Theory.declaration {syntax = false, pervasive = true}
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    (fn phi => Data.map (Symtab.update (key, morph_fp_sugar phi fp_sugar)));
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fun register_fp_sugars Xs fp pre_bnfs absT_infos nested_bnfs nesting_bnfs (fp_res as {Ts, ...})
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    ctrXs_Tsss ctr_defss ctr_sugars co_iterss mapss common_co_inducts co_inductss co_iter_thmsss
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    disc_co_itersss sel_co_iterssss lthy =
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  (0, lthy)
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  |> fold (fn T as Type (s, _) => fn (kk, lthy) => (kk + 1,
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    register_fp_sugar s {T = T, X = nth Xs kk, fp = fp, fp_res = fp_res, fp_res_index = kk,
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        pre_bnf = nth pre_bnfs kk, absT_info = nth absT_infos kk, nested_bnfs = nested_bnfs,
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        nesting_bnfs = nesting_bnfs, ctrXs_Tss = nth ctrXs_Tsss kk, ctr_defs = nth ctr_defss kk,
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        ctr_sugar = nth ctr_sugars kk, co_iters = nth co_iterss kk, maps = nth mapss kk,
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        common_co_inducts = common_co_inducts, co_inducts = nth co_inductss kk,
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        co_iter_thmss = nth co_iter_thmsss kk, disc_co_iterss = nth disc_co_itersss kk,
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        sel_co_itersss = nth sel_co_iterssss kk}
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      lthy)) Ts
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  |> snd;
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(* This function could produce (fairly harmless) clashes in contrived examples (e.g., "x.A",
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   "x.x_A", "y.A"). *)
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fun quasi_unambiguous_case_names names =
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  let
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    val ps = map (`Long_Name.base_name) names;
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    val dups = Library.duplicates (op =) (map fst ps);
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    fun underscore s =
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      let val ss = space_explode Long_Name.separator s in
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        space_implode "_" (drop (length ss - 2) ss)
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      end;
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  in
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    map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
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  end;
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val id_def = @{thm id_def};
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val mp_conj = @{thm mp_conj};
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val fundefcong_attrs = @{attributes [fundef_cong]};
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val nitpicksimp_attrs = @{attributes [nitpick_simp]};
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val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs;
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val simp_attrs = @{attributes [simp]};
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val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
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fun flat_corec_predss_getterss qss fss = maps (op @) (qss ~~ fss);
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fun flat_corec_preds_predsss_gettersss [] [qss] [fss] = flat_corec_predss_getterss qss fss
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  | flat_corec_preds_predsss_gettersss (p :: ps) (qss :: qsss) (fss :: fsss) =
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    p :: flat_corec_predss_getterss qss fss @ flat_corec_preds_predsss_gettersss ps qsss fsss;
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fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) =
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  Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1));
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fun flip_rels lthy n thm =
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  let
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    val Rs = Term.add_vars (prop_of thm) [];
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    val Rs' = rev (drop (length Rs - n) Rs);
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    val cRs = map (fn f => (certify lthy (Var f), certify lthy (mk_flip f))) Rs';
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  in
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    Drule.cterm_instantiate cRs thm
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  end;
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fun mk_ctor_or_dtor get_T Ts t =
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  let val Type (_, Ts0) = get_T (fastype_of t) in
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    Term.subst_atomic_types (Ts0 ~~ Ts) t
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  end;
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val mk_ctor = mk_ctor_or_dtor range_type;
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val mk_dtor = mk_ctor_or_dtor domain_type;
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fun mk_co_iters thy fp fpTs Cs ts0 =
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  let
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    val nn = length fpTs;
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    val (fpTs0, Cs0) =
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      map ((fp = Greatest_FP ? swap) o dest_funT o snd o strip_typeN nn o fastype_of) ts0
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      |> split_list;
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    val rho = tvar_subst thy (fpTs0 @ Cs0) (fpTs @ Cs);
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  in
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    map (Term.subst_TVars rho) ts0
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  end;
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fun unzip_recT (Type (@{type_name prod}, _)) T = [T]
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  | unzip_recT _ (Type (@{type_name prod}, Ts)) = Ts
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  | unzip_recT _ T = [T];
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fun unzip_corecT (Type (@{type_name sum}, _)) T = [T]
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  | unzip_corecT _ (Type (@{type_name sum}, Ts)) = Ts
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  | unzip_corecT _ T = [T];
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fun liveness_of_fp_bnf n bnf =
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  (case T_of_bnf bnf of
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    Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
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  | _ => replicate n false);
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   285
fun cannot_merge_types fp =
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   286
  error ("Mutually " ^ co_prefix fp ^ "recursive types must have the same type parameters");
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   287
blanchet@55700
   288
fun merge_type_arg fp T T' = if T = T' then T else cannot_merge_types fp;
blanchet@52347
   289
blanchet@55700
   290
fun merge_type_args fp (As, As') =
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   291
  if length As = length As' then map2 (merge_type_arg fp) As As' else cannot_merge_types fp;
blanchet@52347
   292
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   293
fun reassoc_conjs thm =
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   294
  reassoc_conjs (thm RS @{thm conj_assoc[THEN iffD1]})
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   295
  handle THM _ => thm;
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   296
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   297
type co_datatype_spec =
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   298
  ((((binding option * (typ * sort)) list * binding) * (binding * binding)) * mixfix)
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   299
  * ((binding, binding * typ, term) ctr_spec * mixfix) list;
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   300
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   301
fun type_args_named_constrained_of_spec ((((ncAs, _), _), _), _) = ncAs;
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   302
fun type_binding_of_spec ((((_, b), _), _), _) = b;
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   303
fun map_binding_of_spec (((_, (b, _)), _), _) = b;
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   304
fun rel_binding_of_spec (((_, (_, b)), _), _) = b;
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   305
fun mixfix_of_spec ((_, mx), _) = mx;
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   306
fun mixfixed_ctr_specs_of_spec (_, mx_ctr_specs) = mx_ctr_specs;
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   307
blanchet@52347
   308
fun add_nesty_bnf_names Us =
blanchet@52347
   309
  let
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   310
    fun add (Type (s, Ts)) ss =
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   311
        let val (needs, ss') = fold_map add Ts ss in
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   312
          if exists I needs then (true, insert (op =) s ss') else (false, ss')
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   313
        end
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   314
      | add T ss = (member (op =) Us T, ss);
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   315
  in snd oo add end;
blanchet@52347
   316
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   317
fun nesty_bnfs ctxt ctr_Tsss Us =
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   318
  map_filter (bnf_of ctxt) (fold (fold (fold (add_nesty_bnf_names Us))) ctr_Tsss []);
blanchet@52347
   319
blanchet@54237
   320
fun indexify proj xs f p = f (find_index (curry (op =) (proj p)) xs) p;
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   321
blanchet@53746
   322
type lfp_sugar_thms =
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   323
  (thm list * thm * Args.src list) * (thm list list * Args.src list);
blanchet@53746
   324
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   325
fun morph_lfp_sugar_thms phi ((inducts, induct, induct_attrs), (recss, iter_attrs)) =
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   326
  ((map (Morphism.thm phi) inducts, Morphism.thm phi induct, induct_attrs),
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   327
   (map (map (Morphism.thm phi)) recss, iter_attrs))
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   328
  : lfp_sugar_thms;
blanchet@54256
   329
blanchet@54256
   330
val transfer_lfp_sugar_thms =
wenzelm@54740
   331
  morph_lfp_sugar_thms o Morphism.transfer_morphism o Proof_Context.theory_of;
blanchet@54256
   332
blanchet@53746
   333
type gfp_sugar_thms =
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   334
  ((thm list * thm) list * Args.src list)
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   335
  * (thm list list * Args.src list)
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   336
  * (thm list list * Args.src list)
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   337
  * (thm list list * Args.src list)
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   338
  * (thm list list list * Args.src list);
blanchet@53746
   339
blanchet@54256
   340
fun morph_gfp_sugar_thms phi ((coinducts_pairs, coinduct_attrs),
blanchet@55856
   341
    (corecss, coiter_attrs), (disc_corecss, disc_iter_attrs),
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   342
    (disc_corec_iffss, disc_iter_iff_attrs), (sel_corecsss, sel_iter_attrs)) =
blanchet@54256
   343
  ((map (apfst (map (Morphism.thm phi)) o apsnd (Morphism.thm phi)) coinducts_pairs,
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   344
    coinduct_attrs),
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   345
   (map (map (Morphism.thm phi)) corecss, coiter_attrs),
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   346
   (map (map (Morphism.thm phi)) disc_corecss, disc_iter_attrs),
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   347
   (map (map (Morphism.thm phi)) disc_corec_iffss, disc_iter_iff_attrs),
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   348
   (map (map (map (Morphism.thm phi))) sel_corecsss, sel_iter_attrs)) : gfp_sugar_thms;
blanchet@54256
   349
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   350
val transfer_gfp_sugar_thms =
wenzelm@54740
   351
  morph_gfp_sugar_thms o Morphism.transfer_morphism o Proof_Context.theory_of;
blanchet@54256
   352
traytel@55803
   353
fun mk_iters_args_types ctr_Tsss Cs absTs repTs ns mss ctor_iter_fun_Tss lthy =
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   354
  let
blanchet@52214
   355
    val Css = map2 replicate ns Cs;
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   356
    val y_Tsss = map5 (fn absT => fn repT => fn n => fn ms =>
traytel@55803
   357
        dest_absumprodT absT repT n ms o domain_type)
traytel@55803
   358
      absTs repTs ns mss (map un_fold_of ctor_iter_fun_Tss);
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   359
    val g_Tss = map2 (fn C => map (fn y_Ts => y_Ts ---> C)) Cs y_Tsss;
blanchet@51832
   360
blanchet@51832
   361
    val ((gss, ysss), lthy) =
blanchet@51832
   362
      lthy
blanchet@51832
   363
      |> mk_Freess "f" g_Tss
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   364
      ||>> mk_Freesss "x" y_Tsss;
blanchet@52301
   365
blanchet@52301
   366
    val y_Tssss = map (map (map single)) y_Tsss;
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   367
    val yssss = map (map (map single)) ysss;
blanchet@52214
   368
blanchet@52214
   369
    val z_Tssss =
traytel@55803
   370
      map6 (fn absT => fn repT => fn n => fn ms => fn ctr_Tss => fn ctor_iter_fun_Ts =>
traytel@55803
   371
          map2 (map2 unzip_recT)
traytel@55803
   372
            ctr_Tss (dest_absumprodT absT repT n ms (domain_type (co_rec_of ctor_iter_fun_Ts))))
traytel@55803
   373
        absTs repTs ns mss ctr_Tsss ctor_iter_fun_Tss;
blanchet@51832
   374
blanchet@52868
   375
    val z_Tsss' = map (map flat_rec_arg_args) z_Tssss;
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   376
    val h_Tss = map2 (map2 (curry (op --->))) z_Tsss' Css;
blanchet@51832
   377
blanchet@51832
   378
    val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@52214
   379
    val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
blanchet@52214
   380
    val (zssss_tl, lthy) =
blanchet@52214
   381
      lthy
blanchet@52214
   382
      |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
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   383
    val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
blanchet@51832
   384
  in
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   385
    ([(h_Tss, z_Tssss, hss, zssss)], lthy)
blanchet@51832
   386
  end;
blanchet@51832
   387
blanchet@55772
   388
(*avoid "'a itself" arguments in coiterators*)
blanchet@55772
   389
fun repair_nullary_single_ctr [[]] = [[@{typ unit}]]
blanchet@55772
   390
  | repair_nullary_single_ctr Tss = Tss;
blanchet@55772
   391
traytel@55803
   392
fun mk_coiter_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss fun_Ts =
blanchet@51829
   393
  let
blanchet@55772
   394
    val ctr_Tsss' = map repair_nullary_single_ctr ctr_Tsss;
traytel@55803
   395
    val f_absTs = map range_type fun_Ts;
traytel@55803
   396
    val f_Tsss = map repair_nullary_single_ctr (map5 dest_absumprodT absTs repTs ns mss f_absTs);
blanchet@54237
   397
    val f_Tssss = map3 (fn C => map2 (map2 (map (curry (op -->) C) oo unzip_corecT)))
blanchet@53591
   398
      Cs ctr_Tsss' f_Tsss;
blanchet@52871
   399
    val q_Tssss = map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss;
blanchet@52870
   400
  in
traytel@55803
   401
    (q_Tssss, f_Tsss, f_Tssss, f_absTs)
blanchet@52870
   402
  end;
blanchet@51829
   403
blanchet@52898
   404
fun mk_coiter_p_pred_types Cs ns = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@52898
   405
traytel@55803
   406
fun mk_coiter_fun_arg_types ctr_Tsss Cs absTs repTs ns mss dtor_coiter =
traytel@55803
   407
  (mk_coiter_p_pred_types Cs ns,
traytel@55803
   408
   mk_coiter_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss
traytel@55803
   409
     (binder_fun_types (fastype_of dtor_coiter)));
traytel@55803
   410
traytel@55803
   411
fun mk_coiters_args_types ctr_Tsss Cs absTs repTs ns mss dtor_coiter_fun_Tss lthy =
blanchet@52870
   412
  let
blanchet@52898
   413
    val p_Tss = mk_coiter_p_pred_types Cs ns;
blanchet@51829
   414
blanchet@52871
   415
    fun mk_types get_Ts =
blanchet@51829
   416
      let
blanchet@52335
   417
        val fun_Ts = map get_Ts dtor_coiter_fun_Tss;
traytel@55803
   418
        val (q_Tssss, f_Tsss, f_Tssss, f_repTs) =
traytel@55803
   419
          mk_coiter_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss fun_Ts;
blanchet@52870
   420
      in
traytel@55803
   421
        (q_Tssss, f_Tsss, f_Tssss, f_repTs)
blanchet@52870
   422
      end;
blanchet@51829
   423
blanchet@52871
   424
    val (s_Tssss, h_Tsss, h_Tssss, corec_types) = mk_types co_rec_of;
blanchet@51831
   425
blanchet@55856
   426
    val ((((((Free (z, _), cs), pss), sssss), hssss_hd), hssss_tl), lthy) =
blanchet@51829
   427
      lthy
blanchet@52347
   428
      |> yield_singleton (mk_Frees "z") dummyT
blanchet@52347
   429
      ||>> mk_Frees "a" Cs
blanchet@51829
   430
      ||>> mk_Freess "p" p_Tss
blanchet@55856
   431
      ||>> mk_Freessss "q" s_Tssss
blanchet@55856
   432
      ||>> mk_Freessss "g" h_Tssss
blanchet@51829
   433
      ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@55856
   434
    val hssss = map2 (map2 (map2 append)) hssss_hd hssss_tl;
blanchet@51831
   435
blanchet@51831
   436
    val cpss = map2 (map o rapp) cs pss;
blanchet@51829
   437
blanchet@52347
   438
    fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
blanchet@52347
   439
blanchet@52347
   440
    fun build_dtor_coiter_arg _ [] [cf] = cf
blanchet@52347
   441
      | build_dtor_coiter_arg T [cq] [cf, cf'] =
blanchet@52347
   442
        mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@52347
   443
          (build_sum_inj Inr_const (fastype_of cf', T) $ cf');
blanchet@52347
   444
blanchet@52349
   445
    fun mk_args qssss fssss f_Tsss =
blanchet@51831
   446
      let
blanchet@52868
   447
        val pfss = map3 flat_corec_preds_predsss_gettersss pss qssss fssss;
blanchet@51831
   448
        val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@51831
   449
        val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@52347
   450
        val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss;
blanchet@52347
   451
      in (pfss, cqfsss) end;
blanchet@51831
   452
blanchet@52349
   453
    val corec_args = mk_args sssss hssss h_Tsss;
blanchet@51831
   454
  in
blanchet@55856
   455
    ((z, cs, cpss, [(corec_args, corec_types)]), lthy)
blanchet@51831
   456
  end;
blanchet@51829
   457
traytel@55803
   458
fun mk_co_iters_prelims fp ctr_Tsss fpTs Cs absTs repTs ns mss xtor_co_iterss0 lthy =
blanchet@51903
   459
  let
blanchet@52169
   460
    val thy = Proof_Context.theory_of lthy;
blanchet@52169
   461
blanchet@52335
   462
    val (xtor_co_iter_fun_Tss, xtor_co_iterss) =
blanchet@55570
   463
      map (mk_co_iters thy fp fpTs Cs #> `(binder_fun_types o fastype_of o hd))
blanchet@55570
   464
        (transpose xtor_co_iterss0)
blanchet@52335
   465
      |> apsnd transpose o apfst transpose o split_list;
blanchet@51903
   466
blanchet@52329
   467
    val ((iters_args_types, coiters_args_types), lthy') =
blanchet@52207
   468
      if fp = Least_FP then
traytel@55803
   469
        mk_iters_args_types ctr_Tsss Cs absTs repTs ns mss xtor_co_iter_fun_Tss lthy
traytel@55803
   470
        |>> (rpair NONE o SOME)
blanchet@51903
   471
      else
traytel@55803
   472
        mk_coiters_args_types ctr_Tsss Cs absTs repTs ns mss xtor_co_iter_fun_Tss lthy
traytel@55803
   473
        |>> (pair NONE o SOME);
blanchet@51903
   474
  in
blanchet@52335
   475
    ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy')
blanchet@51903
   476
  end;
blanchet@51903
   477
traytel@55803
   478
fun mk_preds_getterss_join c cps absT abs cqfss =
traytel@55803
   479
  let
traytel@55803
   480
    val n = length cqfss;
traytel@55803
   481
    val ts = map2 (mk_absumprod absT abs n) (1 upto n) cqfss;
traytel@55803
   482
  in
traytel@55803
   483
    Term.lambda c (mk_IfN absT cps ts)
blanchet@51900
   484
  end;
blanchet@51886
   485
blanchet@52327
   486
fun define_co_iters fp fpT Cs binding_specs lthy0 =
blanchet@51897
   487
  let
blanchet@52170
   488
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   489
traytel@53569
   490
    val maybe_conceal_def_binding = Thm.def_binding
traytel@53569
   491
      #> Config.get lthy0 bnf_note_all = false ? Binding.conceal;
traytel@53569
   492
blanchet@52327
   493
    val ((csts, defs), (lthy', lthy)) = lthy0
blanchet@54623
   494
      |> apfst split_list o fold_map (fn (b, rhs) =>
blanchet@54623
   495
        Local_Theory.define ((b, NoSyn), ((maybe_conceal_def_binding b, []), rhs))
blanchet@52327
   496
        #>> apsnd snd) binding_specs
blanchet@52327
   497
      ||> `Local_Theory.restore;
blanchet@52327
   498
blanchet@52327
   499
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52327
   500
blanchet@52327
   501
    val csts' = map (mk_co_iter thy fp fpT Cs o Morphism.term phi) csts;
blanchet@52327
   502
    val defs' = map (Morphism.thm phi) defs;
blanchet@52327
   503
  in
blanchet@52327
   504
    ((csts', defs'), lthy')
blanchet@52327
   505
  end;
blanchet@52327
   506
traytel@55803
   507
fun define_iters iterNs iter_args_typess' mk_binding fpTs Cs reps ctor_iters lthy =
blanchet@52327
   508
  let
blanchet@51899
   509
    val nn = length fpTs;
blanchet@55856
   510
    val fpT = domain_type (snd (strip_typeN nn (fastype_of (co_rec_of ctor_iters))));
blanchet@51897
   511
blanchet@54623
   512
    fun generate_iter pre (_, _, fss, xssss) ctor_iter =
traytel@55803
   513
      let val ctor_iter_absTs = map domain_type (fst (strip_typeN nn (fastype_of ctor_iter))) in
traytel@55803
   514
        (mk_binding pre,
traytel@55803
   515
         fold_rev (fold_rev Term.lambda) fss (Term.list_comb (ctor_iter,
traytel@55803
   516
           map4 (fn ctor_iter_absT => fn rep => fn fs => fn xsss =>
traytel@55803
   517
               mk_case_absumprod ctor_iter_absT rep fs
traytel@55803
   518
                 (map (HOLogic.mk_tuple o map HOLogic.mk_tuple) xsss) (map flat_rec_arg_args xsss))
traytel@55803
   519
             ctor_iter_absTs reps fss xssss)))
traytel@55803
   520
      end;
blanchet@51897
   521
  in
blanchet@52327
   522
    define_co_iters Least_FP fpT Cs (map3 generate_iter iterNs iter_args_typess' ctor_iters) lthy
blanchet@51897
   523
  end;
blanchet@51897
   524
traytel@55803
   525
fun define_coiters coiterNs (_, cs, cpss, coiter_args_typess') mk_binding fpTs Cs abss dtor_coiters
blanchet@52347
   526
    lthy =
blanchet@51897
   527
  let
blanchet@51899
   528
    val nn = length fpTs;
blanchet@51899
   529
blanchet@55480
   530
    val Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of (hd dtor_coiters)));
blanchet@51897
   531
traytel@55803
   532
    fun generate_coiter pre ((pfss, cqfsss), f_absTs) dtor_coiter =
blanchet@54623
   533
      (mk_binding pre,
blanchet@54623
   534
       fold_rev (fold_rev Term.lambda) pfss (Term.list_comb (dtor_coiter,
traytel@55803
   535
         map5 mk_preds_getterss_join cs cpss f_absTs abss cqfsss)));
blanchet@51897
   536
  in
blanchet@52327
   537
    define_co_iters Greatest_FP fpT Cs
blanchet@52327
   538
      (map3 generate_coiter coiterNs coiter_args_typess' dtor_coiters) lthy
blanchet@52320
   539
  end;
blanchet@51897
   540
blanchet@55856
   541
fun derive_induct_iters_thms_for_types pre_bnfs [rec_args_types] ctor_induct ctor_iter_thmss
blanchet@55856
   542
    nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss fp_abs_inverses fp_type_definitions abs_inverses
blanchet@55856
   543
    ctrss ctr_defss iterss iter_defss lthy =
blanchet@51808
   544
  let
blanchet@52340
   545
    val iterss' = transpose iterss;
blanchet@52340
   546
    val iter_defss' = transpose iter_defss;
blanchet@52340
   547
blanchet@55856
   548
    val [recs] = iterss';
blanchet@55856
   549
    val [rec_defs] = iter_defss';
blanchet@52340
   550
blanchet@51827
   551
    val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
blanchet@51827
   552
blanchet@51815
   553
    val nn = length pre_bnfs;
blanchet@51827
   554
    val ns = map length ctr_Tsss;
blanchet@51827
   555
    val mss = map (map length) ctr_Tsss;
blanchet@51815
   556
blanchet@51808
   557
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51808
   558
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@53329
   559
    val nesting_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
blanchet@53329
   560
    val nested_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nested_bnfs;
blanchet@53290
   561
    val nested_set_maps = maps set_map_of_bnf nested_bnfs;
blanchet@51808
   562
blanchet@51816
   563
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   564
blanchet@51832
   565
    val ((((ps, ps'), xsss), us'), names_lthy) =
blanchet@52315
   566
      lthy
blanchet@51808
   567
      |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@51827
   568
      ||>> mk_Freesss "x" ctr_Tsss
blanchet@51816
   569
      ||>> Variable.variant_fixes fp_b_names;
blanchet@51808
   570
blanchet@51808
   571
    val us = map2 (curry Free) us' fpTs;
blanchet@51808
   572
blanchet@51808
   573
    fun mk_sets_nested bnf =
blanchet@51808
   574
      let
blanchet@51808
   575
        val Type (T_name, Us) = T_of_bnf bnf;
blanchet@51808
   576
        val lives = lives_of_bnf bnf;
blanchet@51808
   577
        val sets = sets_of_bnf bnf;
blanchet@51808
   578
        fun mk_set U =
blanchet@54237
   579
          (case find_index (curry (op =) U) lives of
blanchet@51808
   580
            ~1 => Term.dummy
blanchet@51808
   581
          | i => nth sets i);
blanchet@51808
   582
      in
blanchet@51808
   583
        (T_name, map mk_set Us)
blanchet@51808
   584
      end;
blanchet@51808
   585
blanchet@51808
   586
    val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@51808
   587
blanchet@51808
   588
    val (induct_thms, induct_thm) =
blanchet@51808
   589
      let
blanchet@51808
   590
        fun mk_set Ts t =
blanchet@51808
   591
          let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@51808
   592
            Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@51808
   593
          end;
blanchet@51808
   594
blanchet@52310
   595
        fun mk_raw_prem_prems _ (x as Free (_, Type _)) (X as TFree _) =
blanchet@54237
   596
            [([], (find_index (curry (op =) X) Xs + 1, x))]
blanchet@52310
   597
          | mk_raw_prem_prems names_lthy (x as Free (s, Type (T_name, Ts0))) (Type (_, Xs_Ts0)) =
blanchet@52310
   598
            (case AList.lookup (op =) setss_nested T_name of
blanchet@52310
   599
              NONE => []
blanchet@52310
   600
            | SOME raw_sets0 =>
blanchet@52310
   601
              let
blanchet@52310
   602
                val (Xs_Ts, (Ts, raw_sets)) =
blanchet@52310
   603
                  filter (exists_subtype_in Xs o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0))
blanchet@52310
   604
                  |> split_list ||> split_list;
blanchet@52310
   605
                val sets = map (mk_set Ts0) raw_sets;
blanchet@52310
   606
                val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@52310
   607
                val xysets = map (pair x) (ys ~~ sets);
blanchet@52310
   608
                val ppremss = map2 (mk_raw_prem_prems names_lthy') ys Xs_Ts;
blanchet@52310
   609
              in
blanchet@52310
   610
                flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@52310
   611
              end)
blanchet@52310
   612
          | mk_raw_prem_prems _ _ _ = [];
blanchet@51808
   613
blanchet@51808
   614
        fun close_prem_prem xs t =
blanchet@51808
   615
          fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@51808
   616
            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@51808
   617
blanchet@51808
   618
        fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@51808
   619
          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@51808
   620
              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@51808
   621
            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@51808
   622
blanchet@52310
   623
        fun mk_raw_prem phi ctr ctr_Ts ctrXs_Ts =
blanchet@51808
   624
          let
blanchet@51808
   625
            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@52310
   626
            val pprems = flat (map2 (mk_raw_prem_prems names_lthy') xs ctrXs_Ts);
blanchet@51808
   627
          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@51808
   628
blanchet@51808
   629
        fun mk_prem (xs, raw_pprems, concl) =
blanchet@51808
   630
          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@51808
   631
blanchet@52310
   632
        val raw_premss = map4 (map3 o mk_raw_prem) ps ctrss ctr_Tsss ctrXs_Tsss;
blanchet@51808
   633
blanchet@51808
   634
        val goal =
blanchet@51808
   635
          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@54237
   636
            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@51808
   637
blanchet@51808
   638
        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@51808
   639
traytel@55803
   640
        val ctor_induct' = ctor_induct OF (map2 mk_absumprodE fp_type_definitions mss);
blanchet@51808
   641
blanchet@51808
   642
        val thm =
blanchet@51808
   643
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
   644
            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' fp_abs_inverses
traytel@55803
   645
              abs_inverses nested_set_maps pre_set_defss)
blanchet@51808
   646
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@55409
   647
          (* for "datatype_realizer.ML": *)
blanchet@55409
   648
          |> Thm.name_derivation (fst (dest_Type (hd fpTs)) ^ Long_Name.separator ^
blanchet@55409
   649
            (if nn > 1 then space_implode "_" (tl fp_b_names) ^ Long_Name.separator else "") ^
blanchet@55409
   650
            inductN);
blanchet@51808
   651
      in
blanchet@51808
   652
        `(conj_dests nn) thm
blanchet@51808
   653
      end;
blanchet@51808
   654
blanchet@51808
   655
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@52305
   656
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@51808
   657
blanchet@52305
   658
    val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@52305
   659
blanchet@52306
   660
    fun mk_iter_thmss (_, x_Tssss, fss, _) iters iter_defs ctor_iter_thms =
blanchet@51808
   661
      let
blanchet@52305
   662
        val fiters = map (lists_bmoc fss) iters;
blanchet@51808
   663
blanchet@51843
   664
        fun mk_goal fss fiter xctr f xs fxs =
blanchet@51808
   665
          fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@51843
   666
            (mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs)));
blanchet@51808
   667
blanchet@52302
   668
        fun maybe_tick (T, U) u f =
blanchet@52302
   669
          if try (fst o HOLogic.dest_prodT) U = SOME T then
blanchet@52302
   670
            Term.lambda u (HOLogic.mk_prod (u, f $ u))
blanchet@52302
   671
          else
blanchet@52302
   672
            f;
blanchet@51808
   673
blanchet@52368
   674
        fun build_iter (x as Free (_, T)) U =
blanchet@52368
   675
          if T = U then
blanchet@52368
   676
            x
blanchet@52368
   677
          else
blanchet@52303
   678
            build_map lthy (indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs
blanchet@52368
   679
              (fn kk => fn TU => maybe_tick TU (nth us kk) (nth fiters kk))) (T, U) $ x;
blanchet@52301
   680
blanchet@52868
   681
        val fxsss = map2 (map2 (flat_rec_arg_args oo map2 (map o build_iter))) xsss x_Tssss;
blanchet@51808
   682
blanchet@52306
   683
        val goalss = map5 (map4 o mk_goal fss) fiters xctrss fss xsss fxsss;
blanchet@51808
   684
blanchet@52305
   685
        val tacss =
traytel@55803
   686
          map4 (map ooo mk_iter_tac pre_map_defs (nested_map_idents @ nesting_map_idents) iter_defs)
traytel@55803
   687
            ctor_iter_thms fp_abs_inverses abs_inverses ctr_defss;
blanchet@51808
   688
blanchet@51808
   689
        fun prove goal tac =
blanchet@51808
   690
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51808
   691
          |> Thm.close_derivation;
blanchet@51808
   692
      in
blanchet@52305
   693
        map2 (map2 prove) goalss tacss
blanchet@51808
   694
      end;
blanchet@51808
   695
blanchet@52340
   696
    val rec_thmss = mk_iter_thmss rec_args_types recs rec_defs (map co_rec_of ctor_iter_thmss);
blanchet@51808
   697
  in
blanchet@52345
   698
    ((induct_thms, induct_thm, [induct_case_names_attr]),
blanchet@55856
   699
     (rec_thmss, code_nitpicksimp_attrs @ simp_attrs))
blanchet@51808
   700
  end;
blanchet@51808
   701
blanchet@52347
   702
fun derive_coinduct_coiters_thms_for_types pre_bnfs (z, cs, cpss,
blanchet@55856
   703
      coiters_args_types as [((phss, cshsss), _)])
blanchet@54235
   704
    dtor_coinduct dtor_injects dtor_ctors dtor_coiter_thmss nesting_bnfs fpTs Cs Xs ctrXs_Tsss kss
traytel@55803
   705
    mss ns fp_abs_inverses abs_inverses mk_vimage2p ctr_defss (ctr_sugars : ctr_sugar list)
traytel@55803
   706
    coiterss coiter_defss export_args lthy =
blanchet@51810
   707
  let
traytel@53203
   708
    fun mk_ctor_dtor_coiter_thm dtor_inject dtor_ctor coiter =
traytel@53203
   709
      iffD1 OF [dtor_inject, trans OF [coiter, dtor_ctor RS sym]];
traytel@53203
   710
traytel@53203
   711
    val ctor_dtor_coiter_thmss =
traytel@53203
   712
      map3 (map oo mk_ctor_dtor_coiter_thm) dtor_injects dtor_ctors dtor_coiter_thmss;
traytel@53203
   713
blanchet@52339
   714
    val coiterss' = transpose coiterss;
blanchet@52339
   715
    val coiter_defss' = transpose coiter_defss;
blanchet@52339
   716
blanchet@55856
   717
    val [corec_defs] = coiter_defss';
blanchet@52338
   718
blanchet@51815
   719
    val nn = length pre_bnfs;
blanchet@51815
   720
blanchet@51810
   721
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51810
   722
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@53329
   723
    val nesting_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
blanchet@51830
   724
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@51810
   725
blanchet@51816
   726
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   727
blanchet@53210
   728
    val ctrss = map #ctrs ctr_sugars;
blanchet@53210
   729
    val discss = map #discs ctr_sugars;
blanchet@53210
   730
    val selsss = map #selss ctr_sugars;
blanchet@51840
   731
    val exhausts = map #exhaust ctr_sugars;
blanchet@51840
   732
    val disc_thmsss = map #disc_thmss ctr_sugars;
blanchet@51840
   733
    val discIss = map #discIs ctr_sugars;
blanchet@51840
   734
    val sel_thmsss = map #sel_thmss ctr_sugars;
blanchet@51810
   735
blanchet@51810
   736
    val (((rs, us'), vs'), names_lthy) =
blanchet@52341
   737
      lthy
blanchet@51810
   738
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@51816
   739
      ||>> Variable.variant_fixes fp_b_names
blanchet@51816
   740
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   741
blanchet@51810
   742
    val us = map2 (curry Free) us' fpTs;
blanchet@51810
   743
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   744
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   745
blanchet@51810
   746
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   747
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   748
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   749
blanchet@52345
   750
    val coinduct_thms_pairs =
blanchet@51810
   751
      let
blanchet@51810
   752
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   753
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   754
        val strong_rs =
blanchet@51810
   755
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   756
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   757
blanchet@54237
   758
        fun build_the_rel rs' T Xs_T =
blanchet@54237
   759
          build_rel lthy (fn (_, X) => nth rs' (find_index (curry (op =) X) Xs)) (T, Xs_T)
blanchet@54237
   760
          |> Term.subst_atomic_types (Xs ~~ fpTs);
blanchet@51810
   761
blanchet@54237
   762
        fun build_rel_app rs' usel vsel Xs_T =
blanchet@54237
   763
          fold rapp [usel, vsel] (build_the_rel rs' (fastype_of usel) Xs_T);
blanchet@51810
   764
blanchet@54237
   765
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels ctrXs_Ts =
blanchet@51810
   766
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   767
          (if null usels then
blanchet@51810
   768
             []
blanchet@51810
   769
           else
blanchet@51810
   770
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@54237
   771
                Library.foldr1 HOLogic.mk_conj (map3 (build_rel_app rs') usels vsels ctrXs_Ts))]);
blanchet@51810
   772
blanchet@54237
   773
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss ctrXs_Tss =
blanchet@54237
   774
          Library.foldr1 HOLogic.mk_conj (flat (map6 (mk_prem_ctr_concls rs' n)
blanchet@54237
   775
            (1 upto n) udiscs uselss vdiscs vselss ctrXs_Tss))
blanchet@51810
   776
          handle List.Empty => @{term True};
blanchet@51810
   777
blanchet@54237
   778
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss ctrXs_Tss =
blanchet@51810
   779
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@54237
   780
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss ctrXs_Tss)));
blanchet@51810
   781
blanchet@51810
   782
        val concl =
blanchet@51810
   783
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   784
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   785
               uvrs us vs));
blanchet@51810
   786
blanchet@51810
   787
        fun mk_goal rs' =
blanchet@54237
   788
          Logic.list_implies (map9 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss
blanchet@54237
   789
            ctrXs_Tsss, concl);
blanchet@51810
   790
blanchet@52345
   791
        val goals = map mk_goal [rs, strong_rs];
blanchet@51810
   792
blanchet@51810
   793
        fun prove dtor_coinduct' goal =
blanchet@51810
   794
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
   795
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs fp_abs_inverses
traytel@55803
   796
              abs_inverses dtor_ctors exhausts ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   797
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   798
          |> Thm.close_derivation;
blanchet@51810
   799
blanchet@51810
   800
        fun postproc nn thm =
blanchet@51810
   801
          Thm.permute_prems 0 nn
blanchet@51828
   802
            (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   803
          |> Drule.zero_var_indexes
blanchet@51810
   804
          |> `(conj_dests nn);
traytel@53106
   805
traytel@53106
   806
        val rel_eqs = map rel_eq_of_bnf pre_bnfs;
traytel@53106
   807
        val rel_monos = map rel_mono_of_bnf pre_bnfs;
traytel@53106
   808
        val dtor_coinducts =
traytel@55803
   809
          [dtor_coinduct, mk_strong_coinduct_thm dtor_coinduct rel_eqs rel_monos mk_vimage2p lthy]
blanchet@51810
   810
      in
blanchet@52345
   811
        map2 (postproc nn oo prove) dtor_coinducts goals
blanchet@51810
   812
      end;
blanchet@51810
   813
blanchet@51810
   814
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   815
      let
blanchet@51810
   816
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   817
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   818
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   819
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   820
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   821
      in
blanchet@51810
   822
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   823
      end;
blanchet@51810
   824
blanchet@51816
   825
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   826
    val coinduct_conclss =
blanchet@51810
   827
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   828
blanchet@51810
   829
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   830
blanchet@55856
   831
    val fcoiterss' as [hcorecs] =
blanchet@52869
   832
      map2 (fn (pfss, _) => map (lists_bmoc pfss)) (map fst coiters_args_types) coiterss';
blanchet@51810
   833
blanchet@55856
   834
    val corec_thmss =
blanchet@51810
   835
      let
blanchet@51843
   836
        fun mk_goal pfss c cps fcoiter n k ctr m cfs' =
blanchet@51810
   837
          fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@51810
   838
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@51843
   839
               mk_Trueprop_eq (fcoiter $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   840
blanchet@52347
   841
        fun mk_U maybe_mk_sumT =
blanchet@52347
   842
          typ_subst_nonatomic (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@52347
   843
blanchet@52347
   844
        fun tack z_name (c, u) f =
blanchet@52347
   845
          let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in
blanchet@55414
   846
            Term.lambda z (mk_case_sum (Term.lambda u u, Term.lambda c (f $ c)) $ z)
blanchet@52347
   847
          end;
blanchet@51810
   848
blanchet@52368
   849
        fun build_coiter fcoiters maybe_mk_sumT maybe_tack cqf =
blanchet@52347
   850
          let val T = fastype_of cqf in
blanchet@52347
   851
            if exists_subtype_in Cs T then
blanchet@52368
   852
              let val U = mk_U maybe_mk_sumT T in
blanchet@55483
   853
                build_map lthy (indexify fst (map2 maybe_mk_sumT fpTs Cs) (fn kk => fn _ =>
blanchet@52368
   854
                  maybe_tack (nth cs kk, nth us kk) (nth fcoiters kk))) (T, U) $ cqf
blanchet@52368
   855
              end
blanchet@52347
   856
            else
blanchet@52347
   857
              cqf
blanchet@52347
   858
          end;
blanchet@51810
   859
blanchet@52368
   860
        val cshsss' = map (map (map (build_coiter (co_rec_of fcoiterss') (curry mk_sumT) (tack z))))
blanchet@52351
   861
          cshsss;
blanchet@51810
   862
blanchet@55856
   863
        val goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@51810
   864
blanchet@55856
   865
        val tacss =
traytel@55803
   866
          map4 (map ooo mk_coiter_tac corec_defs nesting_map_idents)
traytel@55803
   867
            (map co_rec_of ctor_dtor_coiter_thmss) pre_map_defs abs_inverses ctr_defss;
blanchet@51810
   868
blanchet@51810
   869
        fun prove goal tac =
blanchet@51815
   870
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   871
          |> Thm.close_derivation;
blanchet@51810
   872
      in
blanchet@55856
   873
        map2 (map2 prove) goalss tacss
blanchet@55856
   874
        |> map (map (unfold_thms lthy @{thms case_sum_if}))
blanchet@51810
   875
      end;
blanchet@51810
   876
blanchet@55856
   877
    val disc_corec_iff_thmss =
blanchet@51810
   878
      let
blanchet@51843
   879
        fun mk_goal c cps fcoiter n k disc =
blanchet@51843
   880
          mk_Trueprop_eq (disc $ (fcoiter $ c),
blanchet@51810
   881
            if n = 1 then @{const True}
blanchet@51810
   882
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   883
blanchet@55856
   884
        val goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@51810
   885
blanchet@51828
   886
        fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   887
blanchet@51810
   888
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   889
blanchet@55856
   890
        val tacss = map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   891
blanchet@51810
   892
        fun prove goal tac =
blanchet@51810
   893
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@52357
   894
          |> singleton export_args
blanchet@51829
   895
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   896
          |> Thm.close_derivation;
blanchet@51810
   897
blanchet@51810
   898
        fun proves [_] [_] = []
blanchet@51810
   899
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   900
      in
blanchet@55856
   901
        map2 proves goalss tacss
blanchet@51810
   902
      end;
blanchet@51810
   903
blanchet@53741
   904
    fun mk_disc_coiter_thms coiters discIs = map (op RS) (coiters ~~ discIs);
blanchet@51810
   905
blanchet@51843
   906
    val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss;
blanchet@51810
   907
blanchet@51843
   908
    fun mk_sel_coiter_thm coiter_thm sel sel_thm =
blanchet@51810
   909
      let
blanchet@51810
   910
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   911
        val arg_cong' =
blanchet@51810
   912
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   913
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   914
          |> Thm.varifyT_global;
blanchet@51810
   915
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   916
      in
blanchet@51843
   917
        coiter_thm RS arg_cong' RS sel_thm'
blanchet@51810
   918
      end;
blanchet@51810
   919
blanchet@52321
   920
    fun mk_sel_coiter_thms coiter_thmss =
blanchet@53475
   921
      map3 (map3 (map2 o mk_sel_coiter_thm)) coiter_thmss selsss sel_thmsss;
blanchet@51810
   922
blanchet@53475
   923
    val sel_corec_thmsss = mk_sel_coiter_thms corec_thmss;
blanchet@51810
   924
blanchet@51810
   925
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   926
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   927
    val coinduct_case_concl_attrs =
blanchet@51810
   928
      map2 (fn casex => fn concls =>
blanchet@51810
   929
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   930
        coinduct_cases coinduct_conclss;
blanchet@51810
   931
    val coinduct_case_attrs =
blanchet@51810
   932
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   933
  in
blanchet@52345
   934
    ((coinduct_thms_pairs, coinduct_case_attrs),
blanchet@55856
   935
     (corec_thmss, code_nitpicksimp_attrs),
blanchet@55856
   936
     (disc_corec_thmss, []),
blanchet@55856
   937
     (disc_corec_iff_thmss, simp_attrs),
blanchet@55856
   938
     (sel_corec_thmsss, simp_attrs))
blanchet@51810
   939
  end;
blanchet@51810
   940
blanchet@52207
   941
fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp
blanchet@55410
   942
    (wrap_opts as (no_discs_sels, _), specs) no_defs_lthy0 =
blanchet@49112
   943
  let
blanchet@49298
   944
    (* TODO: sanity checks on arguments *)
blanchet@49298
   945
blanchet@52969
   946
    val _ = if fp = Greatest_FP andalso no_discs_sels then
blanchet@52969
   947
        error "Cannot define codatatypes without discriminators and selectors"
blanchet@52207
   948
      else
blanchet@52207
   949
        ();
blanchet@49278
   950
blanchet@49367
   951
    val nn = length specs;
blanchet@55469
   952
    val fp_bs = map type_binding_of_spec specs;
blanchet@49498
   953
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
   954
    val fp_common_name = mk_common_name fp_b_names;
blanchet@55469
   955
    val map_bs = map map_binding_of_spec specs;
blanchet@55469
   956
    val rel_bs = map rel_binding_of_spec specs;
blanchet@49298
   957
blanchet@51758
   958
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
   959
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
   960
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
   961
      end;
blanchet@49298
   962
blanchet@55469
   963
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of_spec) specs;
blanchet@49298
   964
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@55700
   965
    val unsorted_As = Library.foldr1 (merge_type_args fp) unsorted_Ass0;
blanchet@53266
   966
    val num_As = length unsorted_As;
blanchet@55699
   967
blanchet@55699
   968
    val set_boss = map (map fst o type_args_named_constrained_of_spec) specs;
blanchet@55699
   969
    val set_bss = map (map (the_default Binding.empty)) set_boss;
blanchet@49119
   970
blanchet@49585
   971
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
   972
      no_defs_lthy0
blanchet@49298
   973
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@53266
   974
      |> mk_TFrees num_As
blanchet@49585
   975
      ||>> mk_TFrees nn
blanchet@51858
   976
      ||>> variant_tfrees fp_b_names;
blanchet@49119
   977
blanchet@55469
   978
    fun add_fake_type spec =
blanchet@55469
   979
      Typedecl.basic_typedecl (type_binding_of_spec spec, num_As, mixfix_of_spec spec);
blanchet@51768
   980
blanchet@53268
   981
    val (fake_T_names, fake_lthy) = fold_map add_fake_type specs no_defs_lthy0;
blanchet@49119
   982
blanchet@53262
   983
    val qsoty = quote o Syntax.string_of_typ fake_lthy;
blanchet@53262
   984
blanchet@54253
   985
    val _ = (case Library.duplicates (op =) unsorted_As of [] => ()
blanchet@53262
   986
      | A :: _ => error ("Duplicate type parameter " ^ qsoty A ^ " in " ^ co_prefix fp ^
blanchet@53262
   987
          "datatype specification"));
blanchet@53262
   988
blanchet@53262
   989
    val bad_args =
blanchet@53262
   990
      map (Logic.type_map (singleton (Variable.polymorphic no_defs_lthy0))) unsorted_As
blanchet@53262
   991
      |> filter_out Term.is_TVar;
blanchet@53262
   992
    val _ = null bad_args orelse
blanchet@53262
   993
      error ("Locally fixed type argument " ^ qsoty (hd bad_args) ^ " in " ^ co_prefix fp ^
blanchet@53262
   994
        "datatype specification");
blanchet@53262
   995
blanchet@55469
   996
    val mixfixes = map mixfix_of_spec specs;
blanchet@49119
   997
blanchet@54253
   998
    val _ = (case Library.duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
   999
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
  1000
blanchet@55469
  1001
    val mx_ctr_specss = map mixfixed_ctr_specs_of_spec specs;
blanchet@55469
  1002
    val ctr_specss = map (map fst) mx_ctr_specss;
blanchet@55469
  1003
    val ctr_mixfixess = map (map snd) mx_ctr_specss;
blanchet@49119
  1004
blanchet@55469
  1005
    val disc_bindingss = map (map disc_of_ctr_spec) ctr_specss;
blanchet@49336
  1006
    val ctr_bindingss =
blanchet@55469
  1007
      map2 (fn fp_b_name => map (Binding.qualify false fp_b_name o ctr_of_ctr_spec)) fp_b_names
blanchet@55469
  1008
        ctr_specss;
blanchet@55469
  1009
    val ctr_argsss = map (map args_of_ctr_spec) ctr_specss;
blanchet@49119
  1010
blanchet@49336
  1011
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
  1012
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@55469
  1013
    val raw_sel_defaultsss = map (map sel_defaults_of_ctr_spec) ctr_specss;
blanchet@49286
  1014
blanchet@49308
  1015
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
  1016
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@53262
  1017
    val As' = map dest_TFree As;
blanchet@49298
  1018
blanchet@49183
  1019
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@53262
  1020
    val _ = (case subtract (op =) As' rhs_As' of [] => ()
blanchet@53262
  1021
      | extras => error ("Extra type variables on right-hand side: " ^
blanchet@53262
  1022
          commas (map (qsoty o TFree) extras)));
blanchet@49165
  1023
blanchet@53268
  1024
    val fake_Ts = map (fn s => Type (s, As)) fake_T_names;
blanchet@53268
  1025
blanchet@53262
  1026
    fun eq_fpT_check (T as Type (s, Ts)) (T' as Type (s', Ts')) =
blanchet@53262
  1027
        s = s' andalso (Ts = Ts' orelse
blanchet@53262
  1028
          error ("Wrong type arguments in " ^ co_prefix fp ^ "recursive type " ^ qsoty T ^
blanchet@53262
  1029
            " (expected " ^ qsoty T' ^ ")"))
blanchet@49591
  1030
      | eq_fpT_check _ _ = false;
blanchet@49146
  1031
blanchet@53222
  1032
    fun freeze_fp (T as Type (s, Ts)) =
blanchet@49591
  1033
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@53222
  1034
          ~1 => Type (s, map freeze_fp Ts)
blanchet@49591
  1035
        | kk => nth Xs kk)
blanchet@49204
  1036
      | freeze_fp T = T;
blanchet@49121
  1037
blanchet@53222
  1038
    val unfreeze_fp = Term.typ_subst_atomic (Xs ~~ fake_Ts);
blanchet@53222
  1039
blanchet@52310
  1040
    val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss;
traytel@55803
  1041
    val ctrXs_repTs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctrXs_Tsss;
blanchet@49119
  1042
blanchet@49298
  1043
    val fp_eqs =
traytel@55803
  1044
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctrXs_repTs;
blanchet@49121
  1045
blanchet@53262
  1046
    val rhsXs_As' = fold (fold (fold Term.add_tfreesT)) ctrXs_Tsss [];
blanchet@53262
  1047
    val _ = (case subtract (op =) rhsXs_As' As' of [] => ()
blanchet@53266
  1048
      | extras => List.app (fn extra => warning ("Unused type variable on right-hand side of " ^
blanchet@53266
  1049
          co_prefix fp ^ "datatype definition: " ^ qsoty (TFree extra))) extras);
blanchet@53262
  1050
blanchet@55701
  1051
    val killed_As =
blanchet@55701
  1052
      map_filter (fn (A, set_bos) => if exists is_none set_bos then SOME A else NONE)
blanchet@55701
  1053
        (unsorted_As ~~ transpose set_boss);
blanchet@55701
  1054
traytel@55803
  1055
    val ((pre_bnfs, absT_infos), (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0,
traytel@55803
  1056
             dtors = dtors0, xtor_co_iterss = xtor_co_iterss0, xtor_co_induct, dtor_ctors,
traytel@55803
  1057
             ctor_dtors, ctor_injects, dtor_injects, xtor_map_thms, xtor_set_thmss, xtor_rel_thms,
traytel@55803
  1058
             xtor_co_iter_thmss, ...},
traytel@53203
  1059
           lthy)) =
blanchet@55701
  1060
      fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As)
blanchet@55701
  1061
        (map dest_TFree killed_As) fp_eqs no_defs_lthy0
blanchet@53222
  1062
      handle BAD_DEAD (X, X_backdrop) =>
blanchet@53222
  1063
        (case X_backdrop of
blanchet@53222
  1064
          Type (bad_tc, _) =>
blanchet@53222
  1065
          let
blanchet@53222
  1066
            val fake_T = qsoty (unfreeze_fp X);
blanchet@53222
  1067
            val fake_T_backdrop = qsoty (unfreeze_fp X_backdrop);
blanchet@53222
  1068
            fun register_hint () =
blanchet@53222
  1069
              "\nUse the " ^ quote (fst (fst @{command_spec "bnf"})) ^ " command to register " ^
blanchet@53222
  1070
              quote bad_tc ^ " as a bounded natural functor to allow nested (co)recursion through \
blanchet@53222
  1071
              \it";
blanchet@53222
  1072
          in
blanchet@53222
  1073
            if is_some (bnf_of no_defs_lthy bad_tc) orelse
blanchet@53222
  1074
               is_some (fp_sugar_of no_defs_lthy bad_tc) then
blanchet@53256
  1075
              error ("Inadmissible " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53256
  1076
                " in type expression " ^ fake_T_backdrop)
blanchet@53222
  1077
            else if is_some (Datatype_Data.get_info (Proof_Context.theory_of no_defs_lthy)
blanchet@53222
  1078
                bad_tc) then
blanchet@53222
  1079
              error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53222
  1080
                " via the old-style datatype " ^ quote bad_tc ^ " in type expression " ^
blanchet@53222
  1081
                fake_T_backdrop ^ register_hint ())
blanchet@53222
  1082
            else
blanchet@53222
  1083
              error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53222
  1084
                " via type constructor " ^ quote bad_tc ^ " in type expression " ^ fake_T_backdrop ^
blanchet@53222
  1085
                register_hint ())
blanchet@53222
  1086
          end);
blanchet@49585
  1087
traytel@55803
  1088
    val abss = map #abs absT_infos;
traytel@55803
  1089
    val reps = map #rep absT_infos;
traytel@55803
  1090
    val absTs = map #absT absT_infos;
traytel@55803
  1091
    val repTs = map #repT absT_infos;
traytel@55803
  1092
    val abs_injects = map #abs_inject absT_infos;
traytel@55803
  1093
    val abs_inverses = map #abs_inverse absT_infos;
traytel@55803
  1094
    val type_definitions = map #type_definition absT_infos;
traytel@55803
  1095
traytel@53143
  1096
    val time = time lthy;
blanchet@49585
  1097
    val timer = time (Timer.startRealTimer ());
blanchet@49121
  1098
blanchet@52310
  1099
    val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
blanchet@52310
  1100
    val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss Xs;
blanchet@49226
  1101
blanchet@49585
  1102
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
  1103
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
  1104
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@53290
  1105
    val nesting_set_maps = maps set_map_of_bnf nesting_bnfs;
blanchet@53290
  1106
    val nested_set_maps = maps set_map_of_bnf nested_bnfs;
blanchet@49585
  1107
blanchet@49585
  1108
    val live = live_of_bnf any_fp_bnf;
blanchet@52961
  1109
    val _ =
blanchet@52961
  1110
      if live = 0 andalso exists (not o Binding.is_empty) (map_bs @ rel_bs) then
blanchet@53266
  1111
        warning "Map function and relator names ignored"
blanchet@52961
  1112
      else
blanchet@52961
  1113
        ();
blanchet@49585
  1114
blanchet@49585
  1115
    val Bs =
blanchet@49585
  1116
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@53266
  1117
        (liveness_of_fp_bnf num_As any_fp_bnf) As Bs0;
blanchet@49585
  1118
blanchet@49585
  1119
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
  1120
blanchet@49501
  1121
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
  1122
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
  1123
blanchet@49501
  1124
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
  1125
blanchet@51780
  1126
    fun massage_simple_notes base =
blanchet@51780
  1127
      filter_out (null o #2)
blanchet@51780
  1128
      #> map (fn (thmN, thms, attrs) =>
blanchet@55410
  1129
        ((Binding.qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
  1130
blanchet@51780
  1131
    val massage_multi_notes =
blanchet@51780
  1132
      maps (fn (thmN, thmss, attrs) =>
blanchet@53792
  1133
        map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@55410
  1134
            ((Binding.qualify true fp_b_name (Binding.name thmN), attrs T_name), [(thms, [])]))
blanchet@53792
  1135
          fp_b_names fpTs thmss)
blanchet@53792
  1136
      #> filter_out (null o fst o hd o snd);
blanchet@51780
  1137
blanchet@52310
  1138
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctrXs_Tsss;
blanchet@49203
  1139
    val ns = map length ctr_Tsss;
blanchet@49212
  1140
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
  1141
    val mss = map (map length) ctr_Tsss;
blanchet@49203
  1142
blanchet@52367
  1143
    val ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy') =
traytel@55803
  1144
      mk_co_iters_prelims fp ctr_Tsss fpTs Cs absTs repTs ns mss xtor_co_iterss0 lthy;
blanchet@49210
  1145
traytel@55803
  1146
    fun define_ctrs_dtrs_for_type (((((((((((((((((((((((((((fp_bnf, fp_b), fpT), ctor), dtor),
traytel@55803
  1147
              xtor_co_iters), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
traytel@55803
  1148
            pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), abs),
traytel@55803
  1149
          abs_inject), abs_inverse), type_definition), ctr_bindings), ctr_mixfixes), ctr_Tss),
traytel@55803
  1150
        disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
  1151
      let
blanchet@49498
  1152
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
  1153
traytel@55803
  1154
        val ctr_absT = domain_type (fastype_of ctor);
blanchet@49119
  1155
blanchet@52968
  1156
        val ((((w, xss), yss), u'), names_lthy) =
blanchet@49204
  1157
          no_defs_lthy
traytel@55803
  1158
          |> yield_singleton (mk_Frees "w") ctr_absT
blanchet@49370
  1159
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
  1160
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
  1161
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
  1162
blanchet@49498
  1163
        val u = Free (u', fpT);
blanchet@49121
  1164
blanchet@49129
  1165
        val ctr_rhss =
traytel@55803
  1166
          map2 (fn k => fn xs => fold_rev Term.lambda xs (ctor $ mk_absumprod ctr_absT abs n k xs))
traytel@55803
  1167
            ks xss;
blanchet@49121
  1168
traytel@53569
  1169
        val maybe_conceal_def_binding = Thm.def_binding
traytel@53569
  1170
          #> Config.get no_defs_lthy bnf_note_all = false ? Binding.conceal;
traytel@53569
  1171
blanchet@52968
  1172
        val ((raw_ctrs, raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
  1173
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
traytel@53569
  1174
              Local_Theory.define ((b, mx), ((maybe_conceal_def_binding b, []), rhs)) #>> apsnd snd)
blanchet@52968
  1175
            ctr_bindings ctr_mixfixes ctr_rhss
blanchet@49121
  1176
          ||> `Local_Theory.restore;
blanchet@49121
  1177
blanchet@49121
  1178
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
  1179
blanchet@49121
  1180
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
  1181
        val ctr_defs' =
blanchet@49585
  1182
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
  1183
blanchet@49203
  1184
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
  1185
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
  1186
blanchet@51897
  1187
        fun wrap_ctrs lthy =
blanchet@49123
  1188
          let
traytel@50170
  1189
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
  1190
              let
blanchet@49585
  1191
                val ctor_iff_dtor_thm =
blanchet@49585
  1192
                  let
blanchet@49585
  1193
                    val goal =
blanchet@49585
  1194
                      fold_rev Logic.all [w, u]
blanchet@49585
  1195
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
  1196
                  in
wenzelm@51551
  1197
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
  1198
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [ctr_absT, fpT])
blanchet@49585
  1199
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@55409
  1200
                    |> Morphism.thm phi
blanchet@49585
  1201
                    |> Thm.close_derivation
blanchet@49585
  1202
                  end;
blanchet@49585
  1203
blanchet@49585
  1204
                val sumEN_thm' =
traytel@55803
  1205
                  unfold_thms lthy @{thms unit_all_eq1} (mk_absumprodE type_definition ms)
blanchet@49585
  1206
                  |> Morphism.thm phi;
blanchet@49135
  1207
              in
blanchet@49585
  1208
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
  1209
              end;
blanchet@49135
  1210
blanchet@49585
  1211
            val inject_tacss =
traytel@55803
  1212
              map2 (fn ctr_def => fn 0 => [] | _ => [fn {context = ctxt, ...} =>
traytel@55803
  1213
                mk_inject_tac ctxt ctr_def ctor_inject abs_inject]) ctr_defs ms;
blanchet@49585
  1214
blanchet@49585
  1215
            val half_distinct_tacss =
blanchet@49585
  1216
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
traytel@55803
  1217
                  mk_half_distinct_tac ctxt ctor_inject abs_inject [def, def']))
traytel@55803
  1218
                (mk_half_pairss (`I ctr_defs));
blanchet@49585
  1219
blanchet@52968
  1220
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss;
blanchet@49585
  1221
blanchet@49585
  1222
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@55469
  1223
blanchet@55469
  1224
            fun ctr_spec_of disc_b ctr0 sel_bs sel_defs = (((disc_b, ctr0), sel_bs), sel_defs);
blanchet@55469
  1225
            val ctr_specs = map4 ctr_spec_of disc_bindings ctrs0 sel_bindingss sel_defaultss;
blanchet@49123
  1226
          in
blanchet@55469
  1227
            free_constructors tacss ((wrap_opts, standard_binding), ctr_specs) lthy
blanchet@49123
  1228
          end;
blanchet@49121
  1229
blanchet@55397
  1230
        fun derive_maps_sets_rels (ctr_sugar as {case_cong, ...} : ctr_sugar, lthy) =
blanchet@51835
  1231
          if live = 0 then
blanchet@51840
  1232
            ((([], [], [], []), ctr_sugar), lthy)
blanchet@51835
  1233
          else
blanchet@51835
  1234
            let
blanchet@51835
  1235
              val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@51835
  1236
              val nones = replicate live NONE;
blanchet@49585
  1237
blanchet@51835
  1238
              val ctor_cong =
blanchet@52207
  1239
                if fp = Least_FP then
blanchet@51835
  1240
                  Drule.dummy_thm
blanchet@51835
  1241
                else
blanchet@51835
  1242
                  let val ctor' = mk_ctor Bs ctor in
blanchet@51835
  1243
                    cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51835
  1244
                  end;
blanchet@49585
  1245
traytel@55803
  1246
              fun mk_cIn ctor k xs =
traytel@55803
  1247
                let val absT = domain_type (fastype_of ctor) in
traytel@55803
  1248
                  mk_absumprod absT abs n k xs
traytel@55803
  1249
                  |> fp = Greatest_FP ? curry (op $) ctor
traytel@55803
  1250
                  |> certify lthy
traytel@55803
  1251
                end;
blanchet@49585
  1252
traytel@55803
  1253
              val cxIns = map2 (mk_cIn ctor) ks xss;
traytel@55803
  1254
              val cyIns = map2 (mk_cIn (map_types B_ify ctor)) ks yss;
blanchet@49585
  1255
blanchet@51835
  1256
              fun mk_map_thm ctr_def' cxIn =
blanchet@51835
  1257
                fold_thms lthy [ctr_def']
traytel@55803
  1258
                  (unfold_thms lthy (o_apply :: pre_map_def ::
traytel@55803
  1259
                       (if fp = Least_FP then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map @
traytel@55803
  1260
                       abs_inverses)
blanchet@51835
  1261
                     (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@52207
  1262
                        (if fp = Least_FP then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@51835
  1263
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1264
blanchet@51835
  1265
              fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@51835
  1266
                fold_thms lthy [ctr_def']
blanchet@53290
  1267
                  (unfold_thms lthy (pre_set_defs @ nested_set_maps @ nesting_set_maps @
traytel@55803
  1268
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_set @
traytel@55803
  1269
                       abs_inverses)
blanchet@51835
  1270
                     (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@51835
  1271
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1272
blanchet@51835
  1273
              fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49127
  1274
blanchet@51835
  1275
              val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@51835
  1276
              val set_thmss = map mk_set_thms fp_set_thms;
blanchet@55463
  1277
              val set_thms = flat set_thmss;
blanchet@51835
  1278
blanchet@51835
  1279
              val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1280
blanchet@51835
  1281
              fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@51835
  1282
                fold_thms lthy ctr_defs'
traytel@55803
  1283
                  (unfold_thms lthy (pre_rel_def :: abs_inverse ::
traytel@55803
  1284
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_rel @
traytel@55803
  1285
                       @{thms vimage2p_def Inl_Inr_False})
blanchet@53266
  1286
                     (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@51835
  1287
                |> postproc
blanchet@51835
  1288
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1289
blanchet@51835
  1290
              fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@51835
  1291
                mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1292
blanchet@51835
  1293
              val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1294
blanchet@51835
  1295
              fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@51835
  1296
                mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@51835
  1297
                  cxIn cyIn;
blanchet@49121
  1298
blanchet@51835
  1299
              fun mk_other_half_rel_distinct_thm thm =
blanchet@51835
  1300
                flip_rels lthy live thm
blanchet@51835
  1301
                RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1302
blanchet@51835
  1303
              val half_rel_distinct_thmss =
blanchet@51835
  1304
                map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@51835
  1305
              val other_half_rel_distinct_thmss =
blanchet@51835
  1306
                map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@51835
  1307
              val (rel_distinct_thms, _) =
blanchet@51835
  1308
                join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1309
blanchet@55463
  1310
              val rel_eq_thms =
blanchet@55463
  1311
                map (fn th => th RS @{thm eq_False[THEN iffD2]}) rel_distinct_thms @
blanchet@55463
  1312
                map2 (fn th => fn 0 => th RS @{thm eq_True[THEN iffD2]} | _ => th)
blanchet@55463
  1313
                  rel_inject_thms ms;
blanchet@55463
  1314
blanchet@54145
  1315
              val anonymous_notes =
blanchet@55397
  1316
                [([case_cong], fundefcong_attrs),
blanchet@55463
  1317
                 (rel_eq_thms, code_nitpicksimp_attrs)]
blanchet@54145
  1318
                |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@54145
  1319
blanchet@51835
  1320
              val notes =
blanchet@54145
  1321
                [(mapN, map_thms, code_nitpicksimp_attrs @ simp_attrs),
blanchet@54145
  1322
                 (rel_distinctN, rel_distinct_thms, simp_attrs),
blanchet@54145
  1323
                 (rel_injectN, rel_inject_thms, simp_attrs),
blanchet@55463
  1324
                 (setN, set_thms, code_nitpicksimp_attrs @ simp_attrs)]
blanchet@51835
  1325
                |> massage_simple_notes fp_b_name;
blanchet@51835
  1326
            in
blanchet@51840
  1327
              (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
blanchet@55463
  1328
               lthy
blanchet@55535
  1329
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) map_thms)
blanchet@55535
  1330
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) rel_eq_thms)
blanchet@55535
  1331
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) set_thms)
blanchet@55463
  1332
               |> Local_Theory.notes (anonymous_notes @ notes)
blanchet@55463
  1333
               |> snd)
blanchet@51835
  1334
            end;
blanchet@49585
  1335
blanchet@55410
  1336
        fun mk_binding pre = Binding.qualify false fp_b_name (Binding.prefix_name (pre ^ "_") fp_b);
blanchet@49287
  1337
blanchet@51883
  1338
        fun massage_res (((maps_sets_rels, ctr_sugar), co_iter_res), lthy) =
blanchet@51883
  1339
          (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_iter_res), lthy);
blanchet@49119
  1340
      in
blanchet@51897
  1341
        (wrap_ctrs
blanchet@51835
  1342
         #> derive_maps_sets_rels
blanchet@52313
  1343
         ##>>
blanchet@55856
  1344
           (if fp = Least_FP then define_iters [recN] (the iters_args_types) mk_binding fpTs Cs reps
blanchet@55856
  1345
           else define_coiters [corecN] (the coiters_args_types) mk_binding fpTs Cs abss)
blanchet@55856
  1346
             [co_rec_of xtor_co_iters]
blanchet@51835
  1347
         #> massage_res, lthy')
blanchet@49119
  1348
      end;
blanchet@49167
  1349
blanchet@51835
  1350
    fun wrap_types_etc (wrap_types_etcs, lthy) =
blanchet@51835
  1351
      fold_map I wrap_types_etcs lthy
blanchet@52342
  1352
      |>> apsnd split_list o apfst (apsnd split_list4 o apfst split_list4 o split_list)
blanchet@52342
  1353
        o split_list;
blanchet@49226
  1354
blanchet@55856
  1355
    fun mk_simp_thms ({injects, distincts, case_thms, ...} : ctr_sugar) co_recs mapsx rel_injects
blanchet@55856
  1356
        rel_distincts setss =
blanchet@55856
  1357
      injects @ distincts @ case_thms @ co_recs @ mapsx @ rel_injects @ rel_distincts @ flat setss;
blanchet@49479
  1358
blanchet@53807
  1359
    fun derive_note_induct_iters_thms_for_types
blanchet@53476
  1360
        ((((mapss, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@52342
  1361
          (iterss, iter_defss)), lthy) =
blanchet@49202
  1362
      let
blanchet@55856
  1363
        val ((induct_thms, induct_thm, induct_attrs), (rec_thmss, iter_attrs)) =
traytel@53106
  1364
          derive_induct_iters_thms_for_types pre_bnfs (the iters_args_types) xtor_co_induct
traytel@55803
  1365
            xtor_co_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss abs_inverses
traytel@55803
  1366
            type_definitions abs_inverses ctrss ctr_defss iterss iter_defss lthy;
blanchet@49201
  1367
blanchet@51830
  1368
        val induct_type_attr = Attrib.internal o K o Induct.induct_type;
blanchet@51810
  1369
blanchet@51835
  1370
        val simp_thmss =
blanchet@55856
  1371
          map6 mk_simp_thms ctr_sugars rec_thmss mapss rel_injects rel_distincts setss;
blanchet@49438
  1372
blanchet@49337
  1373
        val common_notes =
blanchet@51808
  1374
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1375
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1376
blanchet@49226
  1377
        val notes =
blanchet@55856
  1378
          [(inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@53808
  1379
           (recN, rec_thmss, K iter_attrs),
blanchet@49585
  1380
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1381
          |> massage_multi_notes;
blanchet@49202
  1382
      in
blanchet@51824
  1383
        lthy
blanchet@55463
  1384
        |> Spec_Rules.add Spec_Rules.Equational (map co_rec_of iterss, flat rec_thmss)
blanchet@51824
  1385
        |> Local_Theory.notes (common_notes @ notes) |> snd
traytel@55803
  1386
        |> register_fp_sugars Xs Least_FP pre_bnfs absT_infos nested_bnfs nesting_bnfs fp_res
traytel@55803
  1387
          ctrXs_Tsss ctr_defss ctr_sugars iterss mapss [induct_thm] (map single induct_thms)
blanchet@55856
  1388
          (map single rec_thmss) (replicate nn []) (replicate nn [])
blanchet@49202
  1389
      end;
blanchet@49202
  1390
blanchet@53807
  1391
    fun derive_note_coinduct_coiters_thms_for_types
blanchet@53476
  1392
        ((((mapss, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
blanchet@52342
  1393
          (coiterss, coiter_defss)), lthy) =
blanchet@49212
  1394
      let
blanchet@52345
  1395
        val (([(coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)],
blanchet@51810
  1396
              coinduct_attrs),
blanchet@55856
  1397
             (corec_thmss, coiter_attrs),
blanchet@55856
  1398
             (disc_corec_thmss, disc_coiter_attrs),
blanchet@55856
  1399
             (disc_corec_iff_thmss, disc_coiter_iff_attrs),
blanchet@55856
  1400
             (sel_corec_thmsss, sel_coiter_attrs)) =
traytel@53106
  1401
          derive_coinduct_coiters_thms_for_types pre_bnfs (the coiters_args_types) xtor_co_induct
blanchet@54235
  1402
            dtor_injects dtor_ctors xtor_co_iter_thmss nesting_bnfs fpTs Cs Xs ctrXs_Tsss kss mss ns
traytel@55803
  1403
            abs_inverses abs_inverses I ctr_defss ctr_sugars coiterss coiter_defss
traytel@55803
  1404
            (Proof_Context.export lthy' no_defs_lthy) lthy;
blanchet@49212
  1405
blanchet@53475
  1406
        val sel_corec_thmss = map flat sel_corec_thmsss;
blanchet@53475
  1407
blanchet@51830
  1408
        val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
blanchet@49479
  1409
blanchet@54030
  1410
        val flat_coiter_thms = append oo append;
blanchet@49479
  1411
blanchet@49479
  1412
        val simp_thmss =
blanchet@55856
  1413
          map6 mk_simp_thms ctr_sugars
blanchet@54030
  1414
            (map3 flat_coiter_thms disc_corec_thmss disc_corec_iff_thmss sel_corec_thmss)
blanchet@53476
  1415
            mapss rel_injects rel_distincts setss;
blanchet@49479
  1416
blanchet@49342
  1417
        val common_notes =
blanchet@49591
  1418
          (if nn > 1 then
blanchet@51810
  1419
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1420
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1421
           else
blanchet@49591
  1422
             [])
blanchet@51780
  1423
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1424
blanchet@49212
  1425
        val notes =
blanchet@51780
  1426
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1427
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@51843
  1428
           (corecN, corec_thmss, K coiter_attrs),
blanchet@51843
  1429
           (disc_corecN, disc_corec_thmss, K disc_coiter_attrs),
blanchet@51843
  1430
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1431
           (sel_corecN, sel_corec_thmss, K sel_coiter_attrs),
blanchet@51780
  1432
           (simpsN, simp_thmss, K []),
blanchet@55856
  1433
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs)]
blanchet@51780
  1434
          |> massage_multi_notes;
blanchet@55463
  1435
blanchet@55463
  1436
        (* TODO: code theorems *)
blanchet@55463
  1437
        fun add_spec_rules coiter_of sel_thmss ctr_thmss =
blanchet@55463
  1438
          fold (curry (Spec_Rules.add Spec_Rules.Equational) (map coiter_of coiterss))
blanchet@55463
  1439
            [flat sel_thmss, flat ctr_thmss]
blanchet@49212
  1440
      in
blanchet@51824
  1441
        lthy
blanchet@55463
  1442
        |> add_spec_rules co_rec_of sel_corec_thmss corec_thmss
blanchet@54030
  1443
        |> Local_Theory.notes (common_notes @ notes) |> snd
traytel@55803
  1444
        |> register_fp_sugars Xs Greatest_FP pre_bnfs absT_infos nested_bnfs nesting_bnfs fp_res
traytel@55803
  1445
          ctrXs_Tsss ctr_defss ctr_sugars coiterss mapss [coinduct_thm, strong_coinduct_thm]
blanchet@55856
  1446
          (transpose [coinduct_thms, strong_coinduct_thms]) (map single corec_thmss)
blanchet@55856
  1447
          (map single disc_corec_thmss) (map single sel_corec_thmsss)
blanchet@49212
  1448
      end;
blanchet@49212
  1449
blanchet@52367
  1450
    val lthy'' = lthy'
blanchet@52968
  1451
      |> fold_map define_ctrs_dtrs_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ ctors ~~ dtors ~~
blanchet@52330
  1452
        xtor_co_iterss ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@52314
  1453
        pre_set_defss ~~ pre_rel_defs ~~ xtor_map_thms ~~ xtor_set_thmss ~~ xtor_rel_thms ~~ ns ~~
traytel@55803
  1454
        kss ~~ mss ~~ abss ~~ abs_injects ~~ abs_inverses ~~ type_definitions ~~
traytel@55803
  1455
        ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
traytel@55803
  1456
        raw_sel_defaultsss)
blanchet@51835
  1457
      |> wrap_types_etc
blanchet@53807
  1458
      |> fp_case fp derive_note_induct_iters_thms_for_types
blanchet@53807
  1459
           derive_note_coinduct_coiters_thms_for_types;
blanchet@49167
  1460
blanchet@49167
  1461
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@52899
  1462
      co_prefix fp ^ "datatype"));
blanchet@49112
  1463
  in
blanchet@52367
  1464
    timer; lthy''
blanchet@49112
  1465
  end;
blanchet@49112
  1466
wenzelm@53974
  1467
fun co_datatypes x = define_co_datatypes (K I) (K I) (K I) x;
blanchet@49297
  1468
wenzelm@53974
  1469
fun co_datatype_cmd x =
wenzelm@53974
  1470
  define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term x;
blanchet@49119
  1471
blanchet@55469
  1472
val parse_ctr_arg =
blanchet@55469
  1473
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
blanchet@55469
  1474
  (Parse.typ >> pair Binding.empty);
blanchet@55469
  1475
blanchet@55469
  1476
val parse_ctr_specs =
blanchet@55469
  1477
  Parse.enum1 "|" (parse_ctr_spec parse_binding parse_ctr_arg -- Parse.opt_mixfix);
blanchet@51767
  1478
blanchet@51767
  1479
val parse_spec =
blanchet@51790
  1480
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@55469
  1481
  Parse.opt_mixfix -- (@{keyword "="} |-- parse_ctr_specs);
blanchet@51767
  1482
blanchet@55469
  1483
val parse_co_datatype = parse_ctr_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1484
blanchet@52207
  1485
fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;
blanchet@49112
  1486
blanchet@49112
  1487
end;