src/HOL/Tools/BNF/bnf_fp_def_sugar.ML
author traytel
Tue Feb 25 18:14:26 2014 +0100 (2014-02-25)
changeset 55803 74d3fe9031d8
parent 55772 367ec44763fd
child 55856 bddaada24074
permissions -rw-r--r--
joint work with blanchet: intermediate typedef for the input to fp-operations
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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 * 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 * thm list list * Args.src list)
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    * (thm list list * thm list list * Args.src list)
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    * (thm list list * thm list list * Args.src list)
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    * (thm list list list * 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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   284
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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
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   288
fun merge_type_arg fp T T' = if T = T' then T else cannot_merge_types fp;
blanchet@52347
   289
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   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;
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   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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  ((((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
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   308
fun add_nesty_bnf_names Us =
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   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;
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   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 []);
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   319
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   320
fun indexify proj xs f p = f (find_index (curry (op =) (proj p)) xs) p;
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   321
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   322
type lfp_sugar_thms =
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   323
  (thm list * thm * Args.src list) * (thm list list * thm list list * Args.src list)
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   324
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   325
fun morph_lfp_sugar_thms phi ((inducts, induct, induct_attrs), (foldss, 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)) foldss, map (map (Morphism.thm phi)) recss, iter_attrs))
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   328
  : lfp_sugar_thms;
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   329
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   330
val transfer_lfp_sugar_thms =
wenzelm@54740
   331
  morph_lfp_sugar_thms o Morphism.transfer_morphism o Proof_Context.theory_of;
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   332
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   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 * thm list list * Args.src list)
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   336
  * (thm list list * thm list list * Args.src list)
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   337
  * (thm list list * thm list list * Args.src list)
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   338
  * (thm list list list * thm list list list * Args.src list);
blanchet@53746
   339
blanchet@54256
   340
fun morph_gfp_sugar_thms phi ((coinducts_pairs, coinduct_attrs),
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   341
    (unfoldss, corecss, coiter_attrs), (disc_unfoldss, disc_corecss, disc_iter_attrs),
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   342
    (disc_unfold_iffss, disc_corec_iffss, disc_iter_iff_attrs),
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   343
    (sel_unfoldsss, sel_corecsss, sel_iter_attrs)) =
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   344
  ((map (apfst (map (Morphism.thm phi)) o apsnd (Morphism.thm phi)) coinducts_pairs,
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   345
    coinduct_attrs),
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   346
   (map (map (Morphism.thm phi)) unfoldss, map (map (Morphism.thm phi)) corecss, coiter_attrs),
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   347
   (map (map (Morphism.thm phi)) disc_unfoldss, map (map (Morphism.thm phi)) disc_corecss,
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   348
    disc_iter_attrs),
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   349
   (map (map (Morphism.thm phi)) disc_unfold_iffss, map (map (Morphism.thm phi)) disc_corec_iffss,
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   350
    disc_iter_iff_attrs),
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   351
   (map (map (map (Morphism.thm phi))) sel_unfoldsss,
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   352
    map (map (map (Morphism.thm phi))) sel_corecsss, sel_iter_attrs)) : gfp_sugar_thms;
blanchet@54256
   353
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   354
val transfer_gfp_sugar_thms =
wenzelm@54740
   355
  morph_gfp_sugar_thms o Morphism.transfer_morphism o Proof_Context.theory_of;
blanchet@54256
   356
traytel@55803
   357
fun mk_iters_args_types ctr_Tsss Cs absTs repTs ns mss ctor_iter_fun_Tss lthy =
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   358
  let
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   359
    val Css = map2 replicate ns Cs;
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   360
    val y_Tsss = map5 (fn absT => fn repT => fn n => fn ms =>
traytel@55803
   361
        dest_absumprodT absT repT n ms o domain_type)
traytel@55803
   362
      absTs repTs ns mss (map un_fold_of ctor_iter_fun_Tss);
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   363
    val g_Tss = map2 (fn C => map (fn y_Ts => y_Ts ---> C)) Cs y_Tsss;
blanchet@51832
   364
blanchet@51832
   365
    val ((gss, ysss), lthy) =
blanchet@51832
   366
      lthy
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   367
      |> mk_Freess "f" g_Tss
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   368
      ||>> mk_Freesss "x" y_Tsss;
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   369
blanchet@52301
   370
    val y_Tssss = map (map (map single)) y_Tsss;
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   371
    val yssss = map (map (map single)) ysss;
blanchet@52214
   372
blanchet@52214
   373
    val z_Tssss =
traytel@55803
   374
      map6 (fn absT => fn repT => fn n => fn ms => fn ctr_Tss => fn ctor_iter_fun_Ts =>
traytel@55803
   375
          map2 (map2 unzip_recT)
traytel@55803
   376
            ctr_Tss (dest_absumprodT absT repT n ms (domain_type (co_rec_of ctor_iter_fun_Ts))))
traytel@55803
   377
        absTs repTs ns mss ctr_Tsss ctor_iter_fun_Tss;
blanchet@51832
   378
blanchet@52868
   379
    val z_Tsss' = map (map flat_rec_arg_args) z_Tssss;
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   380
    val h_Tss = map2 (map2 (curry (op --->))) z_Tsss' Css;
blanchet@51832
   381
blanchet@51832
   382
    val hss = map2 (map2 retype_free) h_Tss gss;
blanchet@52214
   383
    val zssss_hd = map2 (map2 (map2 (retype_free o hd))) z_Tssss ysss;
blanchet@52214
   384
    val (zssss_tl, lthy) =
blanchet@52214
   385
      lthy
blanchet@52214
   386
      |> mk_Freessss "y" (map (map (map tl)) z_Tssss);
blanchet@52214
   387
    val zssss = map2 (map2 (map2 cons)) zssss_hd zssss_tl;
blanchet@51832
   388
  in
blanchet@52315
   389
    ([(g_Tss, y_Tssss, gss, yssss), (h_Tss, z_Tssss, hss, zssss)], lthy)
blanchet@51832
   390
  end;
blanchet@51832
   391
blanchet@55772
   392
(*avoid "'a itself" arguments in coiterators*)
blanchet@55772
   393
fun repair_nullary_single_ctr [[]] = [[@{typ unit}]]
blanchet@55772
   394
  | repair_nullary_single_ctr Tss = Tss;
blanchet@55772
   395
traytel@55803
   396
fun mk_coiter_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss fun_Ts =
blanchet@51829
   397
  let
blanchet@55772
   398
    val ctr_Tsss' = map repair_nullary_single_ctr ctr_Tsss;
traytel@55803
   399
    val f_absTs = map range_type fun_Ts;
traytel@55803
   400
    val f_Tsss = map repair_nullary_single_ctr (map5 dest_absumprodT absTs repTs ns mss f_absTs);
blanchet@54237
   401
    val f_Tssss = map3 (fn C => map2 (map2 (map (curry (op -->) C) oo unzip_corecT)))
blanchet@53591
   402
      Cs ctr_Tsss' f_Tsss;
blanchet@52871
   403
    val q_Tssss = map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) f_Tssss;
blanchet@52870
   404
  in
traytel@55803
   405
    (q_Tssss, f_Tsss, f_Tssss, f_absTs)
blanchet@52870
   406
  end;
blanchet@51829
   407
blanchet@52898
   408
fun mk_coiter_p_pred_types Cs ns = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
blanchet@52898
   409
traytel@55803
   410
fun mk_coiter_fun_arg_types ctr_Tsss Cs absTs repTs ns mss dtor_coiter =
traytel@55803
   411
  (mk_coiter_p_pred_types Cs ns,
traytel@55803
   412
   mk_coiter_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss
traytel@55803
   413
     (binder_fun_types (fastype_of dtor_coiter)));
traytel@55803
   414
traytel@55803
   415
fun mk_coiters_args_types ctr_Tsss Cs absTs repTs ns mss dtor_coiter_fun_Tss lthy =
blanchet@52870
   416
  let
blanchet@52898
   417
    val p_Tss = mk_coiter_p_pred_types Cs ns;
blanchet@51829
   418
blanchet@52871
   419
    fun mk_types get_Ts =
blanchet@51829
   420
      let
blanchet@52335
   421
        val fun_Ts = map get_Ts dtor_coiter_fun_Tss;
traytel@55803
   422
        val (q_Tssss, f_Tsss, f_Tssss, f_repTs) =
traytel@55803
   423
          mk_coiter_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss fun_Ts;
blanchet@52870
   424
      in
traytel@55803
   425
        (q_Tssss, f_Tsss, f_Tssss, f_repTs)
blanchet@52870
   426
      end;
blanchet@51829
   427
blanchet@52871
   428
    val (r_Tssss, g_Tsss, g_Tssss, unfold_types) = mk_types un_fold_of;
blanchet@52871
   429
    val (s_Tssss, h_Tsss, h_Tssss, corec_types) = mk_types co_rec_of;
blanchet@51831
   430
blanchet@52347
   431
    val ((((Free (z, _), cs), pss), gssss), lthy) =
blanchet@51829
   432
      lthy
blanchet@52347
   433
      |> yield_singleton (mk_Frees "z") dummyT
blanchet@52347
   434
      ||>> mk_Frees "a" Cs
blanchet@51829
   435
      ||>> mk_Freess "p" p_Tss
blanchet@51829
   436
      ||>> mk_Freessss "g" g_Tssss;
blanchet@51829
   437
    val rssss = map (map (map (fn [] => []))) r_Tssss;
blanchet@51829
   438
blanchet@51829
   439
    val hssss_hd = map2 (map2 (map2 (fn T :: _ => fn [g] => retype_free T g))) h_Tssss gssss;
blanchet@51829
   440
    val ((sssss, hssss_tl), lthy) =
blanchet@51829
   441
      lthy
blanchet@51829
   442
      |> mk_Freessss "q" s_Tssss
blanchet@51829
   443
      ||>> mk_Freessss "h" (map (map (map tl)) h_Tssss);
blanchet@51829
   444
    val hssss = map2 (map2 (map2 cons)) hssss_hd hssss_tl;
blanchet@51831
   445
blanchet@51831
   446
    val cpss = map2 (map o rapp) cs pss;
blanchet@51829
   447
blanchet@52347
   448
    fun build_sum_inj mk_inj = build_map lthy (uncurry mk_inj o dest_sumT o snd);
blanchet@52347
   449
blanchet@52347
   450
    fun build_dtor_coiter_arg _ [] [cf] = cf
blanchet@52347
   451
      | build_dtor_coiter_arg T [cq] [cf, cf'] =
blanchet@52347
   452
        mk_If cq (build_sum_inj Inl_const (fastype_of cf, T) $ cf)
blanchet@52347
   453
          (build_sum_inj Inr_const (fastype_of cf', T) $ cf');
blanchet@52347
   454
blanchet@52349
   455
    fun mk_args qssss fssss f_Tsss =
blanchet@51831
   456
      let
blanchet@52868
   457
        val pfss = map3 flat_corec_preds_predsss_gettersss pss qssss fssss;
blanchet@51831
   458
        val cqssss = map2 (map o map o map o rapp) cs qssss;
blanchet@51831
   459
        val cfssss = map2 (map o map o map o rapp) cs fssss;
blanchet@52347
   460
        val cqfsss = map3 (map3 (map3 build_dtor_coiter_arg)) f_Tsss cqssss cfssss;
blanchet@52347
   461
      in (pfss, cqfsss) end;
blanchet@51831
   462
blanchet@52349
   463
    val unfold_args = mk_args rssss gssss g_Tsss;
blanchet@52349
   464
    val corec_args = mk_args sssss hssss h_Tsss;
blanchet@51831
   465
  in
blanchet@52347
   466
    ((z, cs, cpss, [(unfold_args, unfold_types), (corec_args, corec_types)]), lthy)
blanchet@51831
   467
  end;
blanchet@51829
   468
traytel@55803
   469
fun mk_co_iters_prelims fp ctr_Tsss fpTs Cs absTs repTs ns mss xtor_co_iterss0 lthy =
blanchet@51903
   470
  let
blanchet@52169
   471
    val thy = Proof_Context.theory_of lthy;
blanchet@52169
   472
blanchet@52335
   473
    val (xtor_co_iter_fun_Tss, xtor_co_iterss) =
blanchet@55570
   474
      map (mk_co_iters thy fp fpTs Cs #> `(binder_fun_types o fastype_of o hd))
blanchet@55570
   475
        (transpose xtor_co_iterss0)
blanchet@52335
   476
      |> apsnd transpose o apfst transpose o split_list;
blanchet@51903
   477
blanchet@52329
   478
    val ((iters_args_types, coiters_args_types), lthy') =
blanchet@52207
   479
      if fp = Least_FP then
traytel@55803
   480
        mk_iters_args_types ctr_Tsss Cs absTs repTs ns mss xtor_co_iter_fun_Tss lthy
traytel@55803
   481
        |>> (rpair NONE o SOME)
blanchet@51903
   482
      else
traytel@55803
   483
        mk_coiters_args_types ctr_Tsss Cs absTs repTs ns mss xtor_co_iter_fun_Tss lthy
traytel@55803
   484
        |>> (pair NONE o SOME);
blanchet@51903
   485
  in
blanchet@52335
   486
    ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy')
blanchet@51903
   487
  end;
blanchet@51903
   488
traytel@55803
   489
fun mk_preds_getterss_join c cps absT abs cqfss =
traytel@55803
   490
  let
traytel@55803
   491
    val n = length cqfss;
traytel@55803
   492
    val ts = map2 (mk_absumprod absT abs n) (1 upto n) cqfss;
traytel@55803
   493
  in
traytel@55803
   494
    Term.lambda c (mk_IfN absT cps ts)
blanchet@51900
   495
  end;
blanchet@51886
   496
blanchet@52327
   497
fun define_co_iters fp fpT Cs binding_specs lthy0 =
blanchet@51897
   498
  let
blanchet@52170
   499
    val thy = Proof_Context.theory_of lthy0;
blanchet@52170
   500
traytel@53569
   501
    val maybe_conceal_def_binding = Thm.def_binding
traytel@53569
   502
      #> Config.get lthy0 bnf_note_all = false ? Binding.conceal;
traytel@53569
   503
blanchet@52327
   504
    val ((csts, defs), (lthy', lthy)) = lthy0
blanchet@54623
   505
      |> apfst split_list o fold_map (fn (b, rhs) =>
blanchet@54623
   506
        Local_Theory.define ((b, NoSyn), ((maybe_conceal_def_binding b, []), rhs))
blanchet@52327
   507
        #>> apsnd snd) binding_specs
blanchet@52327
   508
      ||> `Local_Theory.restore;
blanchet@52327
   509
blanchet@52327
   510
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52327
   511
blanchet@52327
   512
    val csts' = map (mk_co_iter thy fp fpT Cs o Morphism.term phi) csts;
blanchet@52327
   513
    val defs' = map (Morphism.thm phi) defs;
blanchet@52327
   514
  in
blanchet@52327
   515
    ((csts', defs'), lthy')
blanchet@52327
   516
  end;
blanchet@52327
   517
traytel@55803
   518
fun define_iters iterNs iter_args_typess' mk_binding fpTs Cs reps ctor_iters lthy =
blanchet@52327
   519
  let
blanchet@51899
   520
    val nn = length fpTs;
traytel@55803
   521
    val fpT = domain_type (snd (strip_typeN nn (fastype_of (un_fold_of ctor_iters))));
blanchet@51897
   522
blanchet@54623
   523
    fun generate_iter pre (_, _, fss, xssss) ctor_iter =
traytel@55803
   524
      let val ctor_iter_absTs = map domain_type (fst (strip_typeN nn (fastype_of ctor_iter))) in
traytel@55803
   525
        (mk_binding pre,
traytel@55803
   526
         fold_rev (fold_rev Term.lambda) fss (Term.list_comb (ctor_iter,
traytel@55803
   527
           map4 (fn ctor_iter_absT => fn rep => fn fs => fn xsss =>
traytel@55803
   528
               mk_case_absumprod ctor_iter_absT rep fs
traytel@55803
   529
                 (map (HOLogic.mk_tuple o map HOLogic.mk_tuple) xsss) (map flat_rec_arg_args xsss))
traytel@55803
   530
             ctor_iter_absTs reps fss xssss)))
traytel@55803
   531
      end;
blanchet@51897
   532
  in
blanchet@52327
   533
    define_co_iters Least_FP fpT Cs (map3 generate_iter iterNs iter_args_typess' ctor_iters) lthy
blanchet@51897
   534
  end;
blanchet@51897
   535
traytel@55803
   536
fun define_coiters coiterNs (_, cs, cpss, coiter_args_typess') mk_binding fpTs Cs abss dtor_coiters
blanchet@52347
   537
    lthy =
blanchet@51897
   538
  let
blanchet@51899
   539
    val nn = length fpTs;
blanchet@51899
   540
blanchet@55480
   541
    val Type (_, [_, fpT]) = snd (strip_typeN nn (fastype_of (hd dtor_coiters)));
blanchet@51897
   542
traytel@55803
   543
    fun generate_coiter pre ((pfss, cqfsss), f_absTs) dtor_coiter =
blanchet@54623
   544
      (mk_binding pre,
blanchet@54623
   545
       fold_rev (fold_rev Term.lambda) pfss (Term.list_comb (dtor_coiter,
traytel@55803
   546
         map5 mk_preds_getterss_join cs cpss f_absTs abss cqfsss)));
blanchet@51897
   547
  in
blanchet@52327
   548
    define_co_iters Greatest_FP fpT Cs
blanchet@52327
   549
      (map3 generate_coiter coiterNs coiter_args_typess' dtor_coiters) lthy
blanchet@52320
   550
  end;
blanchet@51897
   551
traytel@53106
   552
fun derive_induct_iters_thms_for_types pre_bnfs [fold_args_types, rec_args_types] ctor_induct
traytel@55803
   553
    ctor_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss fp_abs_inverses
traytel@55803
   554
    fp_type_definitions abs_inverses ctrss ctr_defss iterss iter_defss lthy =
blanchet@51808
   555
  let
blanchet@52340
   556
    val iterss' = transpose iterss;
blanchet@52340
   557
    val iter_defss' = transpose iter_defss;
blanchet@52340
   558
blanchet@52340
   559
    val [folds, recs] = iterss';
blanchet@52340
   560
    val [fold_defs, rec_defs] = iter_defss';
blanchet@52340
   561
blanchet@51827
   562
    val ctr_Tsss = map (map (binder_types o fastype_of)) ctrss;
blanchet@51827
   563
blanchet@51815
   564
    val nn = length pre_bnfs;
blanchet@51827
   565
    val ns = map length ctr_Tsss;
blanchet@51827
   566
    val mss = map (map length) ctr_Tsss;
blanchet@51815
   567
blanchet@51808
   568
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51808
   569
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@53329
   570
    val nesting_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
blanchet@53329
   571
    val nested_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nested_bnfs;
blanchet@53290
   572
    val nested_set_maps = maps set_map_of_bnf nested_bnfs;
blanchet@51808
   573
blanchet@51816
   574
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   575
blanchet@51832
   576
    val ((((ps, ps'), xsss), us'), names_lthy) =
blanchet@52315
   577
      lthy
blanchet@51808
   578
      |> mk_Frees' "P" (map mk_pred1T fpTs)
blanchet@51827
   579
      ||>> mk_Freesss "x" ctr_Tsss
blanchet@51816
   580
      ||>> Variable.variant_fixes fp_b_names;
blanchet@51808
   581
blanchet@51808
   582
    val us = map2 (curry Free) us' fpTs;
blanchet@51808
   583
blanchet@51808
   584
    fun mk_sets_nested bnf =
blanchet@51808
   585
      let
blanchet@51808
   586
        val Type (T_name, Us) = T_of_bnf bnf;
blanchet@51808
   587
        val lives = lives_of_bnf bnf;
blanchet@51808
   588
        val sets = sets_of_bnf bnf;
blanchet@51808
   589
        fun mk_set U =
blanchet@54237
   590
          (case find_index (curry (op =) U) lives of
blanchet@51808
   591
            ~1 => Term.dummy
blanchet@51808
   592
          | i => nth sets i);
blanchet@51808
   593
      in
blanchet@51808
   594
        (T_name, map mk_set Us)
blanchet@51808
   595
      end;
blanchet@51808
   596
blanchet@51808
   597
    val setss_nested = map mk_sets_nested nested_bnfs;
blanchet@51808
   598
blanchet@51808
   599
    val (induct_thms, induct_thm) =
blanchet@51808
   600
      let
blanchet@51808
   601
        fun mk_set Ts t =
blanchet@51808
   602
          let val Type (_, Ts0) = domain_type (fastype_of t) in
blanchet@51808
   603
            Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@51808
   604
          end;
blanchet@51808
   605
blanchet@52310
   606
        fun mk_raw_prem_prems _ (x as Free (_, Type _)) (X as TFree _) =
blanchet@54237
   607
            [([], (find_index (curry (op =) X) Xs + 1, x))]
blanchet@52310
   608
          | mk_raw_prem_prems names_lthy (x as Free (s, Type (T_name, Ts0))) (Type (_, Xs_Ts0)) =
blanchet@52310
   609
            (case AList.lookup (op =) setss_nested T_name of
blanchet@52310
   610
              NONE => []
blanchet@52310
   611
            | SOME raw_sets0 =>
blanchet@52310
   612
              let
blanchet@52310
   613
                val (Xs_Ts, (Ts, raw_sets)) =
blanchet@52310
   614
                  filter (exists_subtype_in Xs o fst) (Xs_Ts0 ~~ (Ts0 ~~ raw_sets0))
blanchet@52310
   615
                  |> split_list ||> split_list;
blanchet@52310
   616
                val sets = map (mk_set Ts0) raw_sets;
blanchet@52310
   617
                val (ys, names_lthy') = names_lthy |> mk_Frees s Ts;
blanchet@52310
   618
                val xysets = map (pair x) (ys ~~ sets);
blanchet@52310
   619
                val ppremss = map2 (mk_raw_prem_prems names_lthy') ys Xs_Ts;
blanchet@52310
   620
              in
blanchet@52310
   621
                flat (map2 (map o apfst o cons) xysets ppremss)
blanchet@52310
   622
              end)
blanchet@52310
   623
          | mk_raw_prem_prems _ _ _ = [];
blanchet@51808
   624
blanchet@51808
   625
        fun close_prem_prem xs t =
blanchet@51808
   626
          fold_rev Logic.all (map Free (drop (nn + length xs)
blanchet@51808
   627
            (rev (Term.add_frees t (map dest_Free xs @ ps'))))) t;
blanchet@51808
   628
blanchet@51808
   629
        fun mk_prem_prem xs (xysets, (j, x)) =
blanchet@51808
   630
          close_prem_prem xs (Logic.list_implies (map (fn (x', (y, set)) =>
blanchet@51808
   631
              HOLogic.mk_Trueprop (HOLogic.mk_mem (y, set $ x'))) xysets,
blanchet@51808
   632
            HOLogic.mk_Trueprop (nth ps (j - 1) $ x)));
blanchet@51808
   633
blanchet@52310
   634
        fun mk_raw_prem phi ctr ctr_Ts ctrXs_Ts =
blanchet@51808
   635
          let
blanchet@51808
   636
            val (xs, names_lthy') = names_lthy |> mk_Frees "x" ctr_Ts;
blanchet@52310
   637
            val pprems = flat (map2 (mk_raw_prem_prems names_lthy') xs ctrXs_Ts);
blanchet@51808
   638
          in (xs, pprems, HOLogic.mk_Trueprop (phi $ Term.list_comb (ctr, xs))) end;
blanchet@51808
   639
blanchet@51808
   640
        fun mk_prem (xs, raw_pprems, concl) =
blanchet@51808
   641
          fold_rev Logic.all xs (Logic.list_implies (map (mk_prem_prem xs) raw_pprems, concl));
blanchet@51808
   642
blanchet@52310
   643
        val raw_premss = map4 (map3 o mk_raw_prem) ps ctrss ctr_Tsss ctrXs_Tsss;
blanchet@51808
   644
blanchet@51808
   645
        val goal =
blanchet@51808
   646
          Library.foldr (Logic.list_implies o apfst (map mk_prem)) (raw_premss,
blanchet@54237
   647
            HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj (map2 (curry (op $)) ps us)));
blanchet@51808
   648
blanchet@51808
   649
        val kksss = map (map (map (fst o snd) o #2)) raw_premss;
blanchet@51808
   650
traytel@55803
   651
        val ctor_induct' = ctor_induct OF (map2 mk_absumprodE fp_type_definitions mss);
blanchet@51808
   652
blanchet@51808
   653
        val thm =
blanchet@51808
   654
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
   655
            mk_induct_tac ctxt nn ns mss kksss (flat ctr_defss) ctor_induct' fp_abs_inverses
traytel@55803
   656
              abs_inverses nested_set_maps pre_set_defss)
blanchet@51808
   657
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@55409
   658
          (* for "datatype_realizer.ML": *)
blanchet@55409
   659
          |> Thm.name_derivation (fst (dest_Type (hd fpTs)) ^ Long_Name.separator ^
blanchet@55409
   660
            (if nn > 1 then space_implode "_" (tl fp_b_names) ^ Long_Name.separator else "") ^
blanchet@55409
   661
            inductN);
blanchet@51808
   662
      in
blanchet@51808
   663
        `(conj_dests nn) thm
blanchet@51808
   664
      end;
blanchet@51808
   665
blanchet@51808
   666
    val induct_cases = quasi_unambiguous_case_names (maps (map name_of_ctr) ctrss);
blanchet@52305
   667
    val induct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names induct_cases));
blanchet@51808
   668
blanchet@52305
   669
    val xctrss = map2 (map2 (curry Term.list_comb)) ctrss xsss;
blanchet@52305
   670
blanchet@52306
   671
    fun mk_iter_thmss (_, x_Tssss, fss, _) iters iter_defs ctor_iter_thms =
blanchet@51808
   672
      let
blanchet@52305
   673
        val fiters = map (lists_bmoc fss) iters;
blanchet@51808
   674
blanchet@51843
   675
        fun mk_goal fss fiter xctr f xs fxs =
blanchet@51808
   676
          fold_rev (fold_rev Logic.all) (xs :: fss)
blanchet@51843
   677
            (mk_Trueprop_eq (fiter $ xctr, Term.list_comb (f, fxs)));
blanchet@51808
   678
blanchet@52302
   679
        fun maybe_tick (T, U) u f =
blanchet@52302
   680
          if try (fst o HOLogic.dest_prodT) U = SOME T then
blanchet@52302
   681
            Term.lambda u (HOLogic.mk_prod (u, f $ u))
blanchet@52302
   682
          else
blanchet@52302
   683
            f;
blanchet@51808
   684
blanchet@52368
   685
        fun build_iter (x as Free (_, T)) U =
blanchet@52368
   686
          if T = U then
blanchet@52368
   687
            x
blanchet@52368
   688
          else
blanchet@52303
   689
            build_map lthy (indexify (perhaps (try (snd o HOLogic.dest_prodT)) o snd) Cs
blanchet@52368
   690
              (fn kk => fn TU => maybe_tick TU (nth us kk) (nth fiters kk))) (T, U) $ x;
blanchet@52301
   691
blanchet@52868
   692
        val fxsss = map2 (map2 (flat_rec_arg_args oo map2 (map o build_iter))) xsss x_Tssss;
blanchet@51808
   693
blanchet@52306
   694
        val goalss = map5 (map4 o mk_goal fss) fiters xctrss fss xsss fxsss;
blanchet@51808
   695
blanchet@52305
   696
        val tacss =
traytel@55803
   697
          map4 (map ooo mk_iter_tac pre_map_defs (nested_map_idents @ nesting_map_idents) iter_defs)
traytel@55803
   698
            ctor_iter_thms fp_abs_inverses abs_inverses ctr_defss;
blanchet@51808
   699
blanchet@51808
   700
        fun prove goal tac =
blanchet@51808
   701
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51808
   702
          |> Thm.close_derivation;
blanchet@51808
   703
      in
blanchet@52305
   704
        map2 (map2 prove) goalss tacss
blanchet@51808
   705
      end;
blanchet@51808
   706
blanchet@52340
   707
    val fold_thmss = mk_iter_thmss fold_args_types folds fold_defs (map un_fold_of ctor_iter_thmss);
blanchet@52340
   708
    val rec_thmss = mk_iter_thmss rec_args_types recs rec_defs (map co_rec_of ctor_iter_thmss);
blanchet@51808
   709
  in
blanchet@52345
   710
    ((induct_thms, induct_thm, [induct_case_names_attr]),
blanchet@54145
   711
     (fold_thmss, rec_thmss, code_nitpicksimp_attrs @ simp_attrs))
blanchet@51808
   712
  end;
blanchet@51808
   713
blanchet@52347
   714
fun derive_coinduct_coiters_thms_for_types pre_bnfs (z, cs, cpss,
blanchet@52869
   715
      coiters_args_types as [((pgss, crgsss), _), ((phss, cshsss), _)])
blanchet@54235
   716
    dtor_coinduct dtor_injects dtor_ctors dtor_coiter_thmss nesting_bnfs fpTs Cs Xs ctrXs_Tsss kss
traytel@55803
   717
    mss ns fp_abs_inverses abs_inverses mk_vimage2p ctr_defss (ctr_sugars : ctr_sugar list)
traytel@55803
   718
    coiterss coiter_defss export_args lthy =
blanchet@51810
   719
  let
traytel@53203
   720
    fun mk_ctor_dtor_coiter_thm dtor_inject dtor_ctor coiter =
traytel@53203
   721
      iffD1 OF [dtor_inject, trans OF [coiter, dtor_ctor RS sym]];
traytel@53203
   722
traytel@53203
   723
    val ctor_dtor_coiter_thmss =
traytel@53203
   724
      map3 (map oo mk_ctor_dtor_coiter_thm) dtor_injects dtor_ctors dtor_coiter_thmss;
traytel@53203
   725
blanchet@52339
   726
    val coiterss' = transpose coiterss;
blanchet@52339
   727
    val coiter_defss' = transpose coiter_defss;
blanchet@52339
   728
blanchet@52339
   729
    val [unfold_defs, corec_defs] = coiter_defss';
blanchet@52338
   730
blanchet@51815
   731
    val nn = length pre_bnfs;
blanchet@51815
   732
blanchet@51810
   733
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@51810
   734
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@53329
   735
    val nesting_map_idents = map (unfold_thms lthy [id_def] o map_id0_of_bnf) nesting_bnfs;
blanchet@51830
   736
    val nesting_rel_eqs = map rel_eq_of_bnf nesting_bnfs;
blanchet@51810
   737
blanchet@51816
   738
    val fp_b_names = map base_name_of_typ fpTs;
blanchet@51811
   739
blanchet@53210
   740
    val ctrss = map #ctrs ctr_sugars;
blanchet@53210
   741
    val discss = map #discs ctr_sugars;
blanchet@53210
   742
    val selsss = map #selss ctr_sugars;
blanchet@51840
   743
    val exhausts = map #exhaust ctr_sugars;
blanchet@51840
   744
    val disc_thmsss = map #disc_thmss ctr_sugars;
blanchet@51840
   745
    val discIss = map #discIs ctr_sugars;
blanchet@51840
   746
    val sel_thmsss = map #sel_thmss ctr_sugars;
blanchet@51810
   747
blanchet@51810
   748
    val (((rs, us'), vs'), names_lthy) =
blanchet@52341
   749
      lthy
blanchet@51810
   750
      |> mk_Frees "R" (map (fn T => mk_pred2T T T) fpTs)
blanchet@51816
   751
      ||>> Variable.variant_fixes fp_b_names
blanchet@51816
   752
      ||>> Variable.variant_fixes (map (suffix "'") fp_b_names);
blanchet@51810
   753
blanchet@51810
   754
    val us = map2 (curry Free) us' fpTs;
blanchet@51810
   755
    val udiscss = map2 (map o rapp) us discss;
blanchet@51810
   756
    val uselsss = map2 (map o map o rapp) us selsss;
blanchet@51810
   757
blanchet@51810
   758
    val vs = map2 (curry Free) vs' fpTs;
blanchet@51810
   759
    val vdiscss = map2 (map o rapp) vs discss;
blanchet@51810
   760
    val vselsss = map2 (map o map o rapp) vs selsss;
blanchet@51810
   761
blanchet@52345
   762
    val coinduct_thms_pairs =
blanchet@51810
   763
      let
blanchet@51810
   764
        val uvrs = map3 (fn r => fn u => fn v => r $ u $ v) rs us vs;
blanchet@51810
   765
        val uv_eqs = map2 (curry HOLogic.mk_eq) us vs;
blanchet@51810
   766
        val strong_rs =
blanchet@51810
   767
          map4 (fn u => fn v => fn uvr => fn uv_eq =>
blanchet@51810
   768
            fold_rev Term.lambda [u, v] (HOLogic.mk_disj (uvr, uv_eq))) us vs uvrs uv_eqs;
blanchet@51810
   769
blanchet@54237
   770
        fun build_the_rel rs' T Xs_T =
blanchet@54237
   771
          build_rel lthy (fn (_, X) => nth rs' (find_index (curry (op =) X) Xs)) (T, Xs_T)
blanchet@54237
   772
          |> Term.subst_atomic_types (Xs ~~ fpTs);
blanchet@51810
   773
blanchet@54237
   774
        fun build_rel_app rs' usel vsel Xs_T =
blanchet@54237
   775
          fold rapp [usel, vsel] (build_the_rel rs' (fastype_of usel) Xs_T);
blanchet@51810
   776
blanchet@54237
   777
        fun mk_prem_ctr_concls rs' n k udisc usels vdisc vsels ctrXs_Ts =
blanchet@51810
   778
          (if k = n then [] else [HOLogic.mk_eq (udisc, vdisc)]) @
blanchet@51810
   779
          (if null usels then
blanchet@51810
   780
             []
blanchet@51810
   781
           else
blanchet@51810
   782
             [Library.foldr HOLogic.mk_imp (if n = 1 then [] else [udisc, vdisc],
blanchet@54237
   783
                Library.foldr1 HOLogic.mk_conj (map3 (build_rel_app rs') usels vsels ctrXs_Ts))]);
blanchet@51810
   784
blanchet@54237
   785
        fun mk_prem_concl rs' n udiscs uselss vdiscs vselss ctrXs_Tss =
blanchet@54237
   786
          Library.foldr1 HOLogic.mk_conj (flat (map6 (mk_prem_ctr_concls rs' n)
blanchet@54237
   787
            (1 upto n) udiscs uselss vdiscs vselss ctrXs_Tss))
blanchet@51810
   788
          handle List.Empty => @{term True};
blanchet@51810
   789
blanchet@54237
   790
        fun mk_prem rs' uvr u v n udiscs uselss vdiscs vselss ctrXs_Tss =
blanchet@51810
   791
          fold_rev Logic.all [u, v] (Logic.mk_implies (HOLogic.mk_Trueprop uvr,
blanchet@54237
   792
            HOLogic.mk_Trueprop (mk_prem_concl rs' n udiscs uselss vdiscs vselss ctrXs_Tss)));
blanchet@51810
   793
blanchet@51810
   794
        val concl =
blanchet@51810
   795
          HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@51810
   796
            (map3 (fn uvr => fn u => fn v => HOLogic.mk_imp (uvr, HOLogic.mk_eq (u, v)))
blanchet@51810
   797
               uvrs us vs));
blanchet@51810
   798
blanchet@51810
   799
        fun mk_goal rs' =
blanchet@54237
   800
          Logic.list_implies (map9 (mk_prem rs') uvrs us vs ns udiscss uselsss vdiscss vselsss
blanchet@54237
   801
            ctrXs_Tsss, concl);
blanchet@51810
   802
blanchet@52345
   803
        val goals = map mk_goal [rs, strong_rs];
blanchet@51810
   804
blanchet@51810
   805
        fun prove dtor_coinduct' goal =
blanchet@51810
   806
          Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
   807
            mk_coinduct_tac ctxt nesting_rel_eqs nn ns dtor_coinduct' pre_rel_defs fp_abs_inverses
traytel@55803
   808
              abs_inverses dtor_ctors exhausts ctr_defss disc_thmsss sel_thmsss)
blanchet@51810
   809
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   810
          |> Thm.close_derivation;
blanchet@51810
   811
blanchet@51810
   812
        fun postproc nn thm =
blanchet@51810
   813
          Thm.permute_prems 0 nn
blanchet@51828
   814
            (if nn = 1 then thm RS mp else funpow nn (fn thm => reassoc_conjs (thm RS mp_conj)) thm)
blanchet@51810
   815
          |> Drule.zero_var_indexes
blanchet@51810
   816
          |> `(conj_dests nn);
traytel@53106
   817
traytel@53106
   818
        val rel_eqs = map rel_eq_of_bnf pre_bnfs;
traytel@53106
   819
        val rel_monos = map rel_mono_of_bnf pre_bnfs;
traytel@53106
   820
        val dtor_coinducts =
traytel@55803
   821
          [dtor_coinduct, mk_strong_coinduct_thm dtor_coinduct rel_eqs rel_monos mk_vimage2p lthy]
blanchet@51810
   822
      in
blanchet@52345
   823
        map2 (postproc nn oo prove) dtor_coinducts goals
blanchet@51810
   824
      end;
blanchet@51810
   825
blanchet@51810
   826
    fun mk_coinduct_concls ms discs ctrs =
blanchet@51810
   827
      let
blanchet@51810
   828
        fun mk_disc_concl disc = [name_of_disc disc];
blanchet@51810
   829
        fun mk_ctr_concl 0 _ = []
blanchet@51810
   830
          | mk_ctr_concl _ ctor = [name_of_ctr ctor];
blanchet@51810
   831
        val disc_concls = map mk_disc_concl (fst (split_last discs)) @ [[]];
blanchet@51810
   832
        val ctr_concls = map2 mk_ctr_concl ms ctrs;
blanchet@51810
   833
      in
blanchet@51810
   834
        flat (map2 append disc_concls ctr_concls)
blanchet@51810
   835
      end;
blanchet@51810
   836
blanchet@51816
   837
    val coinduct_cases = quasi_unambiguous_case_names (map (prefix EqN) fp_b_names);
blanchet@51810
   838
    val coinduct_conclss =
blanchet@51810
   839
      map3 (quasi_unambiguous_case_names ooo mk_coinduct_concls) mss discss ctrss;
blanchet@51810
   840
blanchet@51810
   841
    fun mk_maybe_not pos = not pos ? HOLogic.mk_not;
blanchet@51810
   842
blanchet@52339
   843
    val fcoiterss' as [gunfolds, hcorecs] =
blanchet@52869
   844
      map2 (fn (pfss, _) => map (lists_bmoc pfss)) (map fst coiters_args_types) coiterss';
blanchet@51810
   845
blanchet@54030
   846
    val (unfold_thmss, corec_thmss) =
blanchet@51810
   847
      let
blanchet@51843
   848
        fun mk_goal pfss c cps fcoiter n k ctr m cfs' =
blanchet@51810
   849
          fold_rev (fold_rev Logic.all) ([c] :: pfss)
blanchet@51810
   850
            (Logic.list_implies (seq_conds (HOLogic.mk_Trueprop oo mk_maybe_not) n k cps,
blanchet@51843
   851
               mk_Trueprop_eq (fcoiter $ c, Term.list_comb (ctr, take m cfs'))));
blanchet@51810
   852
blanchet@52347
   853
        fun mk_U maybe_mk_sumT =
blanchet@52347
   854
          typ_subst_nonatomic (map2 (fn C => fn fpT => (maybe_mk_sumT fpT C, fpT)) Cs fpTs);
blanchet@52347
   855
blanchet@52347
   856
        fun tack z_name (c, u) f =
blanchet@52347
   857
          let val z = Free (z_name, mk_sumT (fastype_of u, fastype_of c)) in
blanchet@55414
   858
            Term.lambda z (mk_case_sum (Term.lambda u u, Term.lambda c (f $ c)) $ z)
blanchet@52347
   859
          end;
blanchet@51810
   860
blanchet@52368
   861
        fun build_coiter fcoiters maybe_mk_sumT maybe_tack cqf =
blanchet@52347
   862
          let val T = fastype_of cqf in
blanchet@52347
   863
            if exists_subtype_in Cs T then
blanchet@52368
   864
              let val U = mk_U maybe_mk_sumT T in
blanchet@55483
   865
                build_map lthy (indexify fst (map2 maybe_mk_sumT fpTs Cs) (fn kk => fn _ =>
blanchet@52368
   866
                  maybe_tack (nth cs kk, nth us kk) (nth fcoiters kk))) (T, U) $ cqf
blanchet@52368
   867
              end
blanchet@52347
   868
            else
blanchet@52347
   869
              cqf
blanchet@52347
   870
          end;
blanchet@51810
   871
blanchet@52368
   872
        val crgsss' = map (map (map (build_coiter (un_fold_of fcoiterss') (K I) (K I)))) crgsss;
blanchet@52368
   873
        val cshsss' = map (map (map (build_coiter (co_rec_of fcoiterss') (curry mk_sumT) (tack z))))
blanchet@52351
   874
          cshsss;
blanchet@51810
   875
blanchet@52347
   876
        val unfold_goalss = map8 (map4 oooo mk_goal pgss) cs cpss gunfolds ns kss ctrss mss crgsss';
blanchet@52347
   877
        val corec_goalss = map8 (map4 oooo mk_goal phss) cs cpss hcorecs ns kss ctrss mss cshsss';
blanchet@51810
   878
blanchet@51810
   879
        val unfold_tacss =
traytel@55803
   880
          map4 (map ooo mk_coiter_tac unfold_defs nesting_map_idents)
traytel@55803
   881
            (map un_fold_of ctor_dtor_coiter_thmss) pre_map_defs abs_inverses ctr_defss;
blanchet@51810
   882
        val corec_tacss =
traytel@55803
   883
          map4 (map ooo mk_coiter_tac corec_defs nesting_map_idents)
traytel@55803
   884
            (map co_rec_of ctor_dtor_coiter_thmss) pre_map_defs abs_inverses ctr_defss;
blanchet@51810
   885
blanchet@51810
   886
        fun prove goal tac =
blanchet@51815
   887
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@51815
   888
          |> Thm.close_derivation;
blanchet@51810
   889
blanchet@51810
   890
        val unfold_thmss = map2 (map2 prove) unfold_goalss unfold_tacss;
blanchet@52347
   891
        val corec_thmss =
blanchet@52347
   892
          map2 (map2 prove) corec_goalss corec_tacss
blanchet@55414
   893
          |> map (map (unfold_thms lthy @{thms case_sum_if}));
blanchet@51810
   894
      in
blanchet@54030
   895
        (unfold_thmss, corec_thmss)
blanchet@51810
   896
      end;
blanchet@51810
   897
blanchet@51810
   898
    val (disc_unfold_iff_thmss, disc_corec_iff_thmss) =
blanchet@51810
   899
      let
blanchet@51843
   900
        fun mk_goal c cps fcoiter n k disc =
blanchet@51843
   901
          mk_Trueprop_eq (disc $ (fcoiter $ c),
blanchet@51810
   902
            if n = 1 then @{const True}
blanchet@51810
   903
            else Library.foldr1 HOLogic.mk_conj (seq_conds mk_maybe_not n k cps));
blanchet@51810
   904
blanchet@51810
   905
        val unfold_goalss = map6 (map2 oooo mk_goal) cs cpss gunfolds ns kss discss;
blanchet@51810
   906
        val corec_goalss = map6 (map2 oooo mk_goal) cs cpss hcorecs ns kss discss;
blanchet@51810
   907
blanchet@51828
   908
        fun mk_case_split' cp = Drule.instantiate' [] [SOME (certify lthy cp)] @{thm case_split};
blanchet@51810
   909
blanchet@51810
   910
        val case_splitss' = map (map mk_case_split') cpss;
blanchet@51810
   911
blanchet@51810
   912
        val unfold_tacss =
blanchet@51843
   913
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' unfold_thmss disc_thmsss;
blanchet@51810
   914
        val corec_tacss =
blanchet@51843
   915
          map3 (map oo mk_disc_coiter_iff_tac) case_splitss' corec_thmss disc_thmsss;
blanchet@51810
   916
blanchet@51810
   917
        fun prove goal tac =
blanchet@51810
   918
          Goal.prove_sorry lthy [] [] goal (tac o #context)
blanchet@52357
   919
          |> singleton export_args
blanchet@51829
   920
          |> singleton (Proof_Context.export names_lthy lthy)
blanchet@51810
   921
          |> Thm.close_derivation;
blanchet@51810
   922
blanchet@51810
   923
        fun proves [_] [_] = []
blanchet@51810
   924
          | proves goals tacs = map2 prove goals tacs;
blanchet@51810
   925
      in
blanchet@51828
   926
        (map2 proves unfold_goalss unfold_tacss, map2 proves corec_goalss corec_tacss)
blanchet@51810
   927
      end;
blanchet@51810
   928
blanchet@53741
   929
    fun mk_disc_coiter_thms coiters discIs = map (op RS) (coiters ~~ discIs);
blanchet@51810
   930
blanchet@51843
   931
    val disc_unfold_thmss = map2 mk_disc_coiter_thms unfold_thmss discIss;
blanchet@51843
   932
    val disc_corec_thmss = map2 mk_disc_coiter_thms corec_thmss discIss;
blanchet@51810
   933
blanchet@51843
   934
    fun mk_sel_coiter_thm coiter_thm sel sel_thm =
blanchet@51810
   935
      let
blanchet@51810
   936
        val (domT, ranT) = dest_funT (fastype_of sel);
blanchet@51810
   937
        val arg_cong' =
blanchet@51810
   938
          Drule.instantiate' (map (SOME o certifyT lthy) [domT, ranT])
blanchet@51810
   939
            [NONE, NONE, SOME (certify lthy sel)] arg_cong
blanchet@51810
   940
          |> Thm.varifyT_global;
blanchet@51810
   941
        val sel_thm' = sel_thm RSN (2, trans);
blanchet@51810
   942
      in
blanchet@51843
   943
        coiter_thm RS arg_cong' RS sel_thm'
blanchet@51810
   944
      end;
blanchet@51810
   945
blanchet@52321
   946
    fun mk_sel_coiter_thms coiter_thmss =
blanchet@53475
   947
      map3 (map3 (map2 o mk_sel_coiter_thm)) coiter_thmss selsss sel_thmsss;
blanchet@51810
   948
blanchet@53475
   949
    val sel_unfold_thmsss = mk_sel_coiter_thms unfold_thmss;
blanchet@53475
   950
    val sel_corec_thmsss = mk_sel_coiter_thms corec_thmss;
blanchet@51810
   951
blanchet@51810
   952
    val coinduct_consumes_attr = Attrib.internal (K (Rule_Cases.consumes nn));
blanchet@51810
   953
    val coinduct_case_names_attr = Attrib.internal (K (Rule_Cases.case_names coinduct_cases));
blanchet@51810
   954
    val coinduct_case_concl_attrs =
blanchet@51810
   955
      map2 (fn casex => fn concls =>
blanchet@51810
   956
          Attrib.internal (K (Rule_Cases.case_conclusion (casex, concls))))
blanchet@51810
   957
        coinduct_cases coinduct_conclss;
blanchet@51810
   958
    val coinduct_case_attrs =
blanchet@51810
   959
      coinduct_consumes_attr :: coinduct_case_names_attr :: coinduct_case_concl_attrs;
blanchet@51810
   960
  in
blanchet@52345
   961
    ((coinduct_thms_pairs, coinduct_case_attrs),
blanchet@54145
   962
     (unfold_thmss, corec_thmss, code_nitpicksimp_attrs),
blanchet@53701
   963
     (disc_unfold_thmss, disc_corec_thmss, []),
blanchet@51810
   964
     (disc_unfold_iff_thmss, disc_corec_iff_thmss, simp_attrs),
blanchet@53475
   965
     (sel_unfold_thmsss, sel_corec_thmsss, simp_attrs))
blanchet@51810
   966
  end;
blanchet@51810
   967
blanchet@52207
   968
fun define_co_datatypes prepare_constraint prepare_typ prepare_term fp construct_fp
blanchet@55410
   969
    (wrap_opts as (no_discs_sels, _), specs) no_defs_lthy0 =
blanchet@49112
   970
  let
blanchet@49298
   971
    (* TODO: sanity checks on arguments *)
blanchet@49298
   972
blanchet@52969
   973
    val _ = if fp = Greatest_FP andalso no_discs_sels then
blanchet@52969
   974
        error "Cannot define codatatypes without discriminators and selectors"
blanchet@52207
   975
      else
blanchet@52207
   976
        ();
blanchet@49278
   977
blanchet@49367
   978
    val nn = length specs;
blanchet@55469
   979
    val fp_bs = map type_binding_of_spec specs;
blanchet@49498
   980
    val fp_b_names = map Binding.name_of fp_bs;
blanchet@49498
   981
    val fp_common_name = mk_common_name fp_b_names;
blanchet@55469
   982
    val map_bs = map map_binding_of_spec specs;
blanchet@55469
   983
    val rel_bs = map rel_binding_of_spec specs;
blanchet@49298
   984
blanchet@51758
   985
    fun prepare_type_arg (_, (ty, c)) =
blanchet@49298
   986
      let val TFree (s, _) = prepare_typ no_defs_lthy0 ty in
blanchet@49298
   987
        TFree (s, prepare_constraint no_defs_lthy0 c)
blanchet@49298
   988
      end;
blanchet@49298
   989
blanchet@55469
   990
    val Ass0 = map (map prepare_type_arg o type_args_named_constrained_of_spec) specs;
blanchet@49298
   991
    val unsorted_Ass0 = map (map (resort_tfree HOLogic.typeS)) Ass0;
blanchet@55700
   992
    val unsorted_As = Library.foldr1 (merge_type_args fp) unsorted_Ass0;
blanchet@53266
   993
    val num_As = length unsorted_As;
blanchet@55699
   994
blanchet@55699
   995
    val set_boss = map (map fst o type_args_named_constrained_of_spec) specs;
blanchet@55699
   996
    val set_bss = map (map (the_default Binding.empty)) set_boss;
blanchet@49119
   997
blanchet@49585
   998
    val (((Bs0, Cs), Xs), no_defs_lthy) =
blanchet@49298
   999
      no_defs_lthy0
blanchet@49298
  1000
      |> fold (Variable.declare_typ o resort_tfree dummyS) unsorted_As
blanchet@53266
  1001
      |> mk_TFrees num_As
blanchet@49585
  1002
      ||>> mk_TFrees nn
blanchet@51858
  1003
      ||>> variant_tfrees fp_b_names;
blanchet@49119
  1004
blanchet@55469
  1005
    fun add_fake_type spec =
blanchet@55469
  1006
      Typedecl.basic_typedecl (type_binding_of_spec spec, num_As, mixfix_of_spec spec);
blanchet@51768
  1007
blanchet@53268
  1008
    val (fake_T_names, fake_lthy) = fold_map add_fake_type specs no_defs_lthy0;
blanchet@49119
  1009
blanchet@53262
  1010
    val qsoty = quote o Syntax.string_of_typ fake_lthy;
blanchet@53262
  1011
blanchet@54253
  1012
    val _ = (case Library.duplicates (op =) unsorted_As of [] => ()
blanchet@53262
  1013
      | A :: _ => error ("Duplicate type parameter " ^ qsoty A ^ " in " ^ co_prefix fp ^
blanchet@53262
  1014
          "datatype specification"));
blanchet@53262
  1015
blanchet@53262
  1016
    val bad_args =
blanchet@53262
  1017
      map (Logic.type_map (singleton (Variable.polymorphic no_defs_lthy0))) unsorted_As
blanchet@53262
  1018
      |> filter_out Term.is_TVar;
blanchet@53262
  1019
    val _ = null bad_args orelse
blanchet@53262
  1020
      error ("Locally fixed type argument " ^ qsoty (hd bad_args) ^ " in " ^ co_prefix fp ^
blanchet@53262
  1021
        "datatype specification");
blanchet@53262
  1022
blanchet@55469
  1023
    val mixfixes = map mixfix_of_spec specs;
blanchet@49119
  1024
blanchet@54253
  1025
    val _ = (case Library.duplicates Binding.eq_name fp_bs of [] => ()
blanchet@49119
  1026
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
  1027
blanchet@55469
  1028
    val mx_ctr_specss = map mixfixed_ctr_specs_of_spec specs;
blanchet@55469
  1029
    val ctr_specss = map (map fst) mx_ctr_specss;
blanchet@55469
  1030
    val ctr_mixfixess = map (map snd) mx_ctr_specss;
blanchet@49119
  1031
blanchet@55469
  1032
    val disc_bindingss = map (map disc_of_ctr_spec) ctr_specss;
blanchet@49336
  1033
    val ctr_bindingss =
blanchet@55469
  1034
      map2 (fn fp_b_name => map (Binding.qualify false fp_b_name o ctr_of_ctr_spec)) fp_b_names
blanchet@55469
  1035
        ctr_specss;
blanchet@55469
  1036
    val ctr_argsss = map (map args_of_ctr_spec) ctr_specss;
blanchet@49119
  1037
blanchet@49336
  1038
    val sel_bindingsss = map (map (map fst)) ctr_argsss;
blanchet@49298
  1039
    val fake_ctr_Tsss0 = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@55469
  1040
    val raw_sel_defaultsss = map (map sel_defaults_of_ctr_spec) ctr_specss;
blanchet@49286
  1041
blanchet@49308
  1042
    val (As :: _) :: fake_ctr_Tsss =
blanchet@49298
  1043
      burrow (burrow (Syntax.check_typs fake_lthy)) (Ass0 :: fake_ctr_Tsss0);
blanchet@53262
  1044
    val As' = map dest_TFree As;
blanchet@49298
  1045
blanchet@49183
  1046
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) fake_ctr_Tsss [];
blanchet@53262
  1047
    val _ = (case subtract (op =) As' rhs_As' of [] => ()
blanchet@53262
  1048
      | extras => error ("Extra type variables on right-hand side: " ^
blanchet@53262
  1049
          commas (map (qsoty o TFree) extras)));
blanchet@49165
  1050
blanchet@53268
  1051
    val fake_Ts = map (fn s => Type (s, As)) fake_T_names;
blanchet@53268
  1052
blanchet@53262
  1053
    fun eq_fpT_check (T as Type (s, Ts)) (T' as Type (s', Ts')) =
blanchet@53262
  1054
        s = s' andalso (Ts = Ts' orelse
blanchet@53262
  1055
          error ("Wrong type arguments in " ^ co_prefix fp ^ "recursive type " ^ qsoty T ^
blanchet@53262
  1056
            " (expected " ^ qsoty T' ^ ")"))
blanchet@49591
  1057
      | eq_fpT_check _ _ = false;
blanchet@49146
  1058
blanchet@53222
  1059
    fun freeze_fp (T as Type (s, Ts)) =
blanchet@49591
  1060
        (case find_index (eq_fpT_check T) fake_Ts of
blanchet@53222
  1061
          ~1 => Type (s, map freeze_fp Ts)
blanchet@49591
  1062
        | kk => nth Xs kk)
blanchet@49204
  1063
      | freeze_fp T = T;
blanchet@49121
  1064
blanchet@53222
  1065
    val unfreeze_fp = Term.typ_subst_atomic (Xs ~~ fake_Ts);
blanchet@53222
  1066
blanchet@52310
  1067
    val ctrXs_Tsss = map (map (map freeze_fp)) fake_ctr_Tsss;
traytel@55803
  1068
    val ctrXs_repTs = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctrXs_Tsss;
blanchet@49119
  1069
blanchet@49298
  1070
    val fp_eqs =
traytel@55803
  1071
      map dest_TFree Xs ~~ map (Term.typ_subst_atomic (As ~~ unsorted_As)) ctrXs_repTs;
blanchet@49121
  1072
blanchet@53262
  1073
    val rhsXs_As' = fold (fold (fold Term.add_tfreesT)) ctrXs_Tsss [];
blanchet@53262
  1074
    val _ = (case subtract (op =) rhsXs_As' As' of [] => ()
blanchet@53266
  1075
      | extras => List.app (fn extra => warning ("Unused type variable on right-hand side of " ^
blanchet@53266
  1076
          co_prefix fp ^ "datatype definition: " ^ qsoty (TFree extra))) extras);
blanchet@53262
  1077
blanchet@55701
  1078
    val killed_As =
blanchet@55701
  1079
      map_filter (fn (A, set_bos) => if exists is_none set_bos then SOME A else NONE)
blanchet@55701
  1080
        (unsorted_As ~~ transpose set_boss);
blanchet@55701
  1081
traytel@55803
  1082
    val ((pre_bnfs, absT_infos), (fp_res as {bnfs = fp_bnfs as any_fp_bnf :: _, ctors = ctors0,
traytel@55803
  1083
             dtors = dtors0, xtor_co_iterss = xtor_co_iterss0, xtor_co_induct, dtor_ctors,
traytel@55803
  1084
             ctor_dtors, ctor_injects, dtor_injects, xtor_map_thms, xtor_set_thmss, xtor_rel_thms,
traytel@55803
  1085
             xtor_co_iter_thmss, ...},
traytel@53203
  1086
           lthy)) =
blanchet@55701
  1087
      fp_bnf (construct_fp mixfixes map_bs rel_bs set_bss) fp_bs (map dest_TFree unsorted_As)
blanchet@55701
  1088
        (map dest_TFree killed_As) fp_eqs no_defs_lthy0
blanchet@53222
  1089
      handle BAD_DEAD (X, X_backdrop) =>
blanchet@53222
  1090
        (case X_backdrop of
blanchet@53222
  1091
          Type (bad_tc, _) =>
blanchet@53222
  1092
          let
blanchet@53222
  1093
            val fake_T = qsoty (unfreeze_fp X);
blanchet@53222
  1094
            val fake_T_backdrop = qsoty (unfreeze_fp X_backdrop);
blanchet@53222
  1095
            fun register_hint () =
blanchet@53222
  1096
              "\nUse the " ^ quote (fst (fst @{command_spec "bnf"})) ^ " command to register " ^
blanchet@53222
  1097
              quote bad_tc ^ " as a bounded natural functor to allow nested (co)recursion through \
blanchet@53222
  1098
              \it";
blanchet@53222
  1099
          in
blanchet@53222
  1100
            if is_some (bnf_of no_defs_lthy bad_tc) orelse
blanchet@53222
  1101
               is_some (fp_sugar_of no_defs_lthy bad_tc) then
blanchet@53256
  1102
              error ("Inadmissible " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53256
  1103
                " in type expression " ^ fake_T_backdrop)
blanchet@53222
  1104
            else if is_some (Datatype_Data.get_info (Proof_Context.theory_of no_defs_lthy)
blanchet@53222
  1105
                bad_tc) then
blanchet@53222
  1106
              error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53222
  1107
                " via the old-style datatype " ^ quote bad_tc ^ " in type expression " ^
blanchet@53222
  1108
                fake_T_backdrop ^ register_hint ())
blanchet@53222
  1109
            else
blanchet@53222
  1110
              error ("Unsupported " ^ co_prefix fp ^ "recursive occurrence of type " ^ fake_T ^
blanchet@53222
  1111
                " via type constructor " ^ quote bad_tc ^ " in type expression " ^ fake_T_backdrop ^
blanchet@53222
  1112
                register_hint ())
blanchet@53222
  1113
          end);
blanchet@49585
  1114
traytel@55803
  1115
    val abss = map #abs absT_infos;
traytel@55803
  1116
    val reps = map #rep absT_infos;
traytel@55803
  1117
    val absTs = map #absT absT_infos;
traytel@55803
  1118
    val repTs = map #repT absT_infos;
traytel@55803
  1119
    val abs_injects = map #abs_inject absT_infos;
traytel@55803
  1120
    val abs_inverses = map #abs_inverse absT_infos;
traytel@55803
  1121
    val type_definitions = map #type_definition absT_infos;
traytel@55803
  1122
traytel@53143
  1123
    val time = time lthy;
blanchet@49585
  1124
    val timer = time (Timer.startRealTimer ());
blanchet@49121
  1125
blanchet@52310
  1126
    val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
blanchet@52310
  1127
    val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss Xs;
blanchet@49226
  1128
blanchet@49585
  1129
    val pre_map_defs = map map_def_of_bnf pre_bnfs;
blanchet@49585
  1130
    val pre_set_defss = map set_defs_of_bnf pre_bnfs;
blanchet@49585
  1131
    val pre_rel_defs = map rel_def_of_bnf pre_bnfs;
blanchet@53290
  1132
    val nesting_set_maps = maps set_map_of_bnf nesting_bnfs;
blanchet@53290
  1133
    val nested_set_maps = maps set_map_of_bnf nested_bnfs;
blanchet@49585
  1134
blanchet@49585
  1135
    val live = live_of_bnf any_fp_bnf;
blanchet@52961
  1136
    val _ =
blanchet@52961
  1137
      if live = 0 andalso exists (not o Binding.is_empty) (map_bs @ rel_bs) then
blanchet@53266
  1138
        warning "Map function and relator names ignored"
blanchet@52961
  1139
      else
blanchet@52961
  1140
        ();
blanchet@49585
  1141
blanchet@49585
  1142
    val Bs =
blanchet@49585
  1143
      map3 (fn alive => fn A as TFree (_, S) => fn B => if alive then resort_tfree S B else A)
blanchet@53266
  1144
        (liveness_of_fp_bnf num_As any_fp_bnf) As Bs0;
blanchet@49585
  1145
blanchet@49585
  1146
    val B_ify = Term.typ_subst_atomic (As ~~ Bs);
blanchet@49167
  1147
blanchet@49501
  1148
    val ctors = map (mk_ctor As) ctors0;
blanchet@49501
  1149
    val dtors = map (mk_dtor As) dtors0;
blanchet@49124
  1150
blanchet@49501
  1151
    val fpTs = map (domain_type o fastype_of) dtors;
blanchet@49362
  1152
blanchet@51780
  1153
    fun massage_simple_notes base =
blanchet@51780
  1154
      filter_out (null o #2)
blanchet@51780
  1155
      #> map (fn (thmN, thms, attrs) =>
blanchet@55410
  1156
        ((Binding.qualify true base (Binding.name thmN), attrs), [(thms, [])]));
blanchet@51780
  1157
blanchet@51780
  1158
    val massage_multi_notes =
blanchet@51780
  1159
      maps (fn (thmN, thmss, attrs) =>
blanchet@53792
  1160
        map3 (fn fp_b_name => fn Type (T_name, _) => fn thms =>
blanchet@55410
  1161
            ((Binding.qualify true fp_b_name (Binding.name thmN), attrs T_name), [(thms, [])]))
blanchet@53792
  1162
          fp_b_names fpTs thmss)
blanchet@53792
  1163
      #> filter_out (null o fst o hd o snd);
blanchet@51780
  1164
blanchet@52310
  1165
    val ctr_Tsss = map (map (map (Term.typ_subst_atomic (Xs ~~ fpTs)))) ctrXs_Tsss;
blanchet@49203
  1166
    val ns = map length ctr_Tsss;
blanchet@49212
  1167
    val kss = map (fn n => 1 upto n) ns;
blanchet@49203
  1168
    val mss = map (map length) ctr_Tsss;
blanchet@49203
  1169
blanchet@52367
  1170
    val ((xtor_co_iterss, iters_args_types, coiters_args_types), lthy') =
traytel@55803
  1171
      mk_co_iters_prelims fp ctr_Tsss fpTs Cs absTs repTs ns mss xtor_co_iterss0 lthy;
blanchet@49210
  1172
traytel@55803
  1173
    fun define_ctrs_dtrs_for_type (((((((((((((((((((((((((((fp_bnf, fp_b), fpT), ctor), dtor),
traytel@55803
  1174
              xtor_co_iters), ctor_dtor), dtor_ctor), ctor_inject), pre_map_def), pre_set_defs),
traytel@55803
  1175
            pre_rel_def), fp_map_thm), fp_set_thms), fp_rel_thm), n), ks), ms), abs),
traytel@55803
  1176
          abs_inject), abs_inverse), type_definition), ctr_bindings), ctr_mixfixes), ctr_Tss),
traytel@55803
  1177
        disc_bindings), sel_bindingss), raw_sel_defaultss) no_defs_lthy =
blanchet@49176
  1178
      let
blanchet@49498
  1179
        val fp_b_name = Binding.name_of fp_b;
blanchet@49498
  1180
traytel@55803
  1181
        val ctr_absT = domain_type (fastype_of ctor);
blanchet@49119
  1182
blanchet@52968
  1183
        val ((((w, xss), yss), u'), names_lthy) =
blanchet@49204
  1184
          no_defs_lthy
traytel@55803
  1185
          |> yield_singleton (mk_Frees "w") ctr_absT
blanchet@49370
  1186
          ||>> mk_Freess "x" ctr_Tss
blanchet@49585
  1187
          ||>> mk_Freess "y" (map (map B_ify) ctr_Tss)
blanchet@49498
  1188
          ||>> yield_singleton Variable.variant_fixes fp_b_name;
blanchet@49370
  1189
blanchet@49498
  1190
        val u = Free (u', fpT);
blanchet@49121
  1191
blanchet@49129
  1192
        val ctr_rhss =
traytel@55803
  1193
          map2 (fn k => fn xs => fold_rev Term.lambda xs (ctor $ mk_absumprod ctr_absT abs n k xs))
traytel@55803
  1194
            ks xss;
blanchet@49121
  1195
traytel@53569
  1196
        val maybe_conceal_def_binding = Thm.def_binding
traytel@53569
  1197
          #> Config.get no_defs_lthy bnf_note_all = false ? Binding.conceal;
traytel@53569
  1198
blanchet@52968
  1199
        val ((raw_ctrs, raw_ctr_defs), (lthy', lthy)) = no_defs_lthy
blanchet@49169
  1200
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
traytel@53569
  1201
              Local_Theory.define ((b, mx), ((maybe_conceal_def_binding b, []), rhs)) #>> apsnd snd)
blanchet@52968
  1202
            ctr_bindings ctr_mixfixes ctr_rhss
blanchet@49121
  1203
          ||> `Local_Theory.restore;
blanchet@49121
  1204
blanchet@49121
  1205
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
  1206
blanchet@49121
  1207
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49585
  1208
        val ctr_defs' =
blanchet@49585
  1209
          map2 (fn m => fn def => mk_unabs_def m (def RS meta_eq_to_obj_eq)) ms ctr_defs;
blanchet@49130
  1210
blanchet@49203
  1211
        val ctrs0 = map (Morphism.term phi) raw_ctrs;
blanchet@49203
  1212
        val ctrs = map (mk_ctr As) ctrs0;
blanchet@49121
  1213
blanchet@51897
  1214
        fun wrap_ctrs lthy =
blanchet@49123
  1215
          let
traytel@50170
  1216
            fun exhaust_tac {context = ctxt, prems = _} =
blanchet@49135
  1217
              let
blanchet@49585
  1218
                val ctor_iff_dtor_thm =
blanchet@49585
  1219
                  let
blanchet@49585
  1220
                    val goal =
blanchet@49585
  1221
                      fold_rev Logic.all [w, u]
blanchet@49585
  1222
                        (mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
blanchet@49585
  1223
                  in
wenzelm@51551
  1224
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
traytel@55803
  1225
                      mk_ctor_iff_dtor_tac ctxt (map (SOME o certifyT lthy) [ctr_absT, fpT])
blanchet@49585
  1226
                        (certify lthy ctor) (certify lthy dtor) ctor_dtor dtor_ctor)
blanchet@55409
  1227
                    |> Morphism.thm phi
blanchet@49585
  1228
                    |> Thm.close_derivation
blanchet@49585
  1229
                  end;
blanchet@49585
  1230
blanchet@49585
  1231
                val sumEN_thm' =
traytel@55803
  1232
                  unfold_thms lthy @{thms unit_all_eq1} (mk_absumprodE type_definition ms)
blanchet@49585
  1233
                  |> Morphism.thm phi;
blanchet@49135
  1234
              in
blanchet@49585
  1235
                mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm'
blanchet@49135
  1236
              end;
blanchet@49135
  1237
blanchet@49585
  1238
            val inject_tacss =
traytel@55803
  1239
              map2 (fn ctr_def => fn 0 => [] | _ => [fn {context = ctxt, ...} =>
traytel@55803
  1240
                mk_inject_tac ctxt ctr_def ctor_inject abs_inject]) ctr_defs ms;
blanchet@49585
  1241
blanchet@49585
  1242
            val half_distinct_tacss =
blanchet@49585
  1243
              map (map (fn (def, def') => fn {context = ctxt, ...} =>
traytel@55803
  1244
                  mk_half_distinct_tac ctxt ctor_inject abs_inject [def, def']))
traytel@55803
  1245
                (mk_half_pairss (`I ctr_defs));
blanchet@49585
  1246
blanchet@52968
  1247
            val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss;
blanchet@49585
  1248
blanchet@49585
  1249
            val sel_defaultss = map (map (apsnd (prepare_term lthy))) raw_sel_defaultss
blanchet@55469
  1250
blanchet@55469
  1251
            fun ctr_spec_of disc_b ctr0 sel_bs sel_defs = (((disc_b, ctr0), sel_bs), sel_defs);
blanchet@55469
  1252
            val ctr_specs = map4 ctr_spec_of disc_bindings ctrs0 sel_bindingss sel_defaultss;
blanchet@49123
  1253
          in
blanchet@55469
  1254
            free_constructors tacss ((wrap_opts, standard_binding), ctr_specs) lthy
blanchet@49123
  1255
          end;
blanchet@49121
  1256
blanchet@55397
  1257
        fun derive_maps_sets_rels (ctr_sugar as {case_cong, ...} : ctr_sugar, lthy) =
blanchet@51835
  1258
          if live = 0 then
blanchet@51840
  1259
            ((([], [], [], []), ctr_sugar), lthy)
blanchet@51835
  1260
          else
blanchet@51835
  1261
            let
blanchet@51835
  1262
              val rel_flip = rel_flip_of_bnf fp_bnf;
blanchet@51835
  1263
              val nones = replicate live NONE;
blanchet@49585
  1264
blanchet@51835
  1265
              val ctor_cong =
blanchet@52207
  1266
                if fp = Least_FP then
blanchet@51835
  1267
                  Drule.dummy_thm
blanchet@51835
  1268
                else
blanchet@51835
  1269
                  let val ctor' = mk_ctor Bs ctor in
blanchet@51835
  1270
                    cterm_instantiate_pos [NONE, NONE, SOME (certify lthy ctor')] arg_cong
blanchet@51835
  1271
                  end;
blanchet@49585
  1272
traytel@55803
  1273
              fun mk_cIn ctor k xs =
traytel@55803
  1274
                let val absT = domain_type (fastype_of ctor) in
traytel@55803
  1275
                  mk_absumprod absT abs n k xs
traytel@55803
  1276
                  |> fp = Greatest_FP ? curry (op $) ctor
traytel@55803
  1277
                  |> certify lthy
traytel@55803
  1278
                end;
blanchet@49585
  1279
traytel@55803
  1280
              val cxIns = map2 (mk_cIn ctor) ks xss;
traytel@55803
  1281
              val cyIns = map2 (mk_cIn (map_types B_ify ctor)) ks yss;
blanchet@49585
  1282
blanchet@51835
  1283
              fun mk_map_thm ctr_def' cxIn =
blanchet@51835
  1284
                fold_thms lthy [ctr_def']
traytel@55803
  1285
                  (unfold_thms lthy (o_apply :: pre_map_def ::
traytel@55803
  1286
                       (if fp = Least_FP then [] else [ctor_dtor, dtor_ctor]) @ sum_prod_thms_map @
traytel@55803
  1287
                       abs_inverses)
blanchet@51835
  1288
                     (cterm_instantiate_pos (nones @ [SOME cxIn])
blanchet@52207
  1289
                        (if fp = Least_FP then fp_map_thm else fp_map_thm RS ctor_cong)))
blanchet@51835
  1290
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1291
blanchet@51835
  1292
              fun mk_set_thm fp_set_thm ctr_def' cxIn =
blanchet@51835
  1293
                fold_thms lthy [ctr_def']
blanchet@53290
  1294
                  (unfold_thms lthy (pre_set_defs @ nested_set_maps @ nesting_set_maps @
traytel@55803
  1295
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_set @
traytel@55803
  1296
                       abs_inverses)
blanchet@51835
  1297
                     (cterm_instantiate_pos [SOME cxIn] fp_set_thm))
blanchet@51835
  1298
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1299
blanchet@51835
  1300
              fun mk_set_thms fp_set_thm = map2 (mk_set_thm fp_set_thm) ctr_defs' cxIns;
blanchet@49127
  1301
blanchet@51835
  1302
              val map_thms = map2 mk_map_thm ctr_defs' cxIns;
blanchet@51835
  1303
              val set_thmss = map mk_set_thms fp_set_thms;
blanchet@55463
  1304
              val set_thms = flat set_thmss;
blanchet@51835
  1305
blanchet@51835
  1306
              val rel_infos = (ctr_defs' ~~ cxIns, ctr_defs' ~~ cyIns);
blanchet@49585
  1307
blanchet@51835
  1308
              fun mk_rel_thm postproc ctr_defs' cxIn cyIn =
blanchet@51835
  1309
                fold_thms lthy ctr_defs'
traytel@55803
  1310
                  (unfold_thms lthy (pre_rel_def :: abs_inverse ::
traytel@55803
  1311
                       (if fp = Least_FP then [] else [dtor_ctor]) @ sum_prod_thms_rel @
traytel@55803
  1312
                       @{thms vimage2p_def Inl_Inr_False})
blanchet@53266
  1313
                     (cterm_instantiate_pos (nones @ [SOME cxIn, SOME cyIn]) fp_rel_thm))
blanchet@51835
  1314
                |> postproc
blanchet@51835
  1315
                |> singleton (Proof_Context.export names_lthy no_defs_lthy);
blanchet@49585
  1316
blanchet@51835
  1317
              fun mk_rel_inject_thm ((ctr_def', cxIn), (_, cyIn)) =
blanchet@51835
  1318
                mk_rel_thm (unfold_thms lthy @{thms eq_sym_Unity_conv}) [ctr_def'] cxIn cyIn;
blanchet@49585
  1319
blanchet@51835
  1320
              val rel_inject_thms = map mk_rel_inject_thm (op ~~ rel_infos);
blanchet@49585
  1321
blanchet@51835
  1322
              fun mk_half_rel_distinct_thm ((xctr_def', cxIn), (yctr_def', cyIn)) =
blanchet@51835
  1323
                mk_rel_thm (fn thm => thm RS @{thm eq_False[THEN iffD1]}) [xctr_def', yctr_def']
blanchet@51835
  1324
                  cxIn cyIn;
blanchet@49121
  1325
blanchet@51835
  1326
              fun mk_other_half_rel_distinct_thm thm =
blanchet@51835
  1327
                flip_rels lthy live thm
blanchet@51835
  1328
                RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
blanchet@49585
  1329
blanchet@51835
  1330
              val half_rel_distinct_thmss =
blanchet@51835
  1331
                map (map mk_half_rel_distinct_thm) (mk_half_pairss rel_infos);
blanchet@51835
  1332
              val other_half_rel_distinct_thmss =
blanchet@51835
  1333
                map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
blanchet@51835
  1334
              val (rel_distinct_thms, _) =
blanchet@51835
  1335
                join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
blanchet@49134
  1336
blanchet@55463
  1337
              val rel_eq_thms =
blanchet@55463
  1338
                map (fn th => th RS @{thm eq_False[THEN iffD2]}) rel_distinct_thms @
blanchet@55463
  1339
                map2 (fn th => fn 0 => th RS @{thm eq_True[THEN iffD2]} | _ => th)
blanchet@55463
  1340
                  rel_inject_thms ms;
blanchet@55463
  1341
blanchet@54145
  1342
              val anonymous_notes =
blanchet@55397
  1343
                [([case_cong], fundefcong_attrs),
blanchet@55463
  1344
                 (rel_eq_thms, code_nitpicksimp_attrs)]
blanchet@54145
  1345
                |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@54145
  1346
blanchet@51835
  1347
              val notes =
blanchet@54145
  1348
                [(mapN, map_thms, code_nitpicksimp_attrs @ simp_attrs),
blanchet@54145
  1349
                 (rel_distinctN, rel_distinct_thms, simp_attrs),
blanchet@54145
  1350
                 (rel_injectN, rel_inject_thms, simp_attrs),
blanchet@55463
  1351
                 (setN, set_thms, code_nitpicksimp_attrs @ simp_attrs)]
blanchet@51835
  1352
                |> massage_simple_notes fp_b_name;
blanchet@51835
  1353
            in
blanchet@51840
  1354
              (((map_thms, rel_inject_thms, rel_distinct_thms, set_thmss), ctr_sugar),
blanchet@55463
  1355
               lthy
blanchet@55535
  1356
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) map_thms)
blanchet@55535
  1357
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) rel_eq_thms)
blanchet@55535
  1358
               |> Spec_Rules.add Spec_Rules.Equational (`(single o lhs_head_of o hd) set_thms)
blanchet@55463
  1359
               |> Local_Theory.notes (anonymous_notes @ notes)
blanchet@55463
  1360
               |> snd)
blanchet@51835
  1361
            end;
blanchet@49585
  1362
blanchet@55410
  1363
        fun mk_binding pre = Binding.qualify false fp_b_name (Binding.prefix_name (pre ^ "_") fp_b);
blanchet@49287
  1364
blanchet@51883
  1365
        fun massage_res (((maps_sets_rels, ctr_sugar), co_iter_res), lthy) =
blanchet@51883
  1366
          (((maps_sets_rels, (ctrs, xss, ctr_defs, ctr_sugar)), co_iter_res), lthy);
blanchet@49119
  1367
      in
blanchet@51897
  1368
        (wrap_ctrs
blanchet@51835
  1369
         #> derive_maps_sets_rels
blanchet@52313
  1370
         ##>>
traytel@55803
  1371
           (if fp = Least_FP then
traytel@55803
  1372
             define_iters [foldN, recN] (the iters_args_types) mk_binding fpTs Cs reps xtor_co_iters
traytel@55803
  1373
           else
traytel@55803
  1374
             define_coiters [unfoldN, corecN] (the coiters_args_types) mk_binding fpTs Cs abss
traytel@55803
  1375
               xtor_co_iters)
blanchet@51835
  1376
         #> massage_res, lthy')
blanchet@49119
  1377
      end;
blanchet@49167
  1378
blanchet@51835
  1379
    fun wrap_types_etc (wrap_types_etcs, lthy) =
blanchet@51835
  1380
      fold_map I wrap_types_etcs lthy
blanchet@52342
  1381
      |>> apsnd split_list o apfst (apsnd split_list4 o apfst split_list4 o split_list)
blanchet@52342
  1382
        o split_list;
blanchet@49226
  1383
wenzelm@53974
  1384
    fun mk_simp_thms ({injects, distincts, case_thms, ...} : ctr_sugar) un_folds co_recs
wenzelm@53974
  1385
        mapsx rel_injects rel_distincts setss =
blanchet@53796
  1386
      injects @ distincts @ case_thms @ co_recs @ un_folds @ mapsx @ rel_injects @ rel_distincts
blanchet@53796
  1387
      @ flat setss;
blanchet@49479
  1388
blanchet@53807
  1389
    fun derive_note_induct_iters_thms_for_types
blanchet@53476
  1390
        ((((mapss, rel_injects, rel_distincts, setss), (ctrss, _, ctr_defss, ctr_sugars)),
blanchet@52342
  1391
          (iterss, iter_defss)), lthy) =
blanchet@49202
  1392
      let
blanchet@53808
  1393
        val ((induct_thms, induct_thm, induct_attrs), (fold_thmss, rec_thmss, iter_attrs)) =
traytel@53106
  1394
          derive_induct_iters_thms_for_types pre_bnfs (the iters_args_types) xtor_co_induct
traytel@55803
  1395
            xtor_co_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss abs_inverses
traytel@55803
  1396
            type_definitions abs_inverses ctrss ctr_defss iterss iter_defss lthy;
blanchet@49201
  1397
blanchet@51830
  1398
        val induct_type_attr = Attrib.internal o K o Induct.induct_type;
blanchet@51810
  1399
blanchet@51835
  1400
        val simp_thmss =
blanchet@53796
  1401
          map7 mk_simp_thms ctr_sugars fold_thmss rec_thmss mapss rel_injects rel_distincts setss;
blanchet@49438
  1402
blanchet@49337
  1403
        val common_notes =
blanchet@51808
  1404
          (if nn > 1 then [(inductN, [induct_thm], induct_attrs)] else [])
blanchet@51780
  1405
          |> massage_simple_notes fp_common_name;
blanchet@49337
  1406
blanchet@49226
  1407
        val notes =
blanchet@53808
  1408
          [(foldN, fold_thmss, K iter_attrs),
blanchet@51810
  1409
           (inductN, map single induct_thms, fn T_name => induct_attrs @ [induct_type_attr T_name]),
blanchet@53808
  1410
           (recN, rec_thmss, K iter_attrs),
blanchet@49585
  1411
           (simpsN, simp_thmss, K [])]
blanchet@51780
  1412
          |> massage_multi_notes;
blanchet@49202
  1413
      in
blanchet@51824
  1414
        lthy
blanchet@55463
  1415
        |> Spec_Rules.add Spec_Rules.Equational (map un_fold_of iterss, flat fold_thmss)
blanchet@55463
  1416
        |> Spec_Rules.add Spec_Rules.Equational (map co_rec_of iterss, flat rec_thmss)
blanchet@51824
  1417
        |> Local_Theory.notes (common_notes @ notes) |> snd
traytel@55803
  1418
        |> register_fp_sugars Xs Least_FP pre_bnfs absT_infos nested_bnfs nesting_bnfs fp_res
traytel@55803
  1419
          ctrXs_Tsss ctr_defss ctr_sugars iterss mapss [induct_thm] (map single induct_thms)
blanchet@55772
  1420
          (transpose [fold_thmss, rec_thmss]) (replicate nn []) (replicate nn [])
blanchet@49202
  1421
      end;
blanchet@49202
  1422
blanchet@53807
  1423
    fun derive_note_coinduct_coiters_thms_for_types
blanchet@53476
  1424
        ((((mapss, rel_injects, rel_distincts, setss), (_, _, ctr_defss, ctr_sugars)),
blanchet@52342
  1425
          (coiterss, coiter_defss)), lthy) =
blanchet@49212
  1426
      let
blanchet@52345
  1427
        val (([(coinduct_thms, coinduct_thm), (strong_coinduct_thms, strong_coinduct_thm)],
blanchet@51810
  1428
              coinduct_attrs),
blanchet@51843
  1429
             (unfold_thmss, corec_thmss, coiter_attrs),
blanchet@51843
  1430
             (disc_unfold_thmss, disc_corec_thmss, disc_coiter_attrs),
blanchet@51843
  1431
             (disc_unfold_iff_thmss, disc_corec_iff_thmss, disc_coiter_iff_attrs),
blanchet@53475
  1432
             (sel_unfold_thmsss, sel_corec_thmsss, sel_coiter_attrs)) =
traytel@53106
  1433
          derive_coinduct_coiters_thms_for_types pre_bnfs (the coiters_args_types) xtor_co_induct
blanchet@54235
  1434
            dtor_injects dtor_ctors xtor_co_iter_thmss nesting_bnfs fpTs Cs Xs ctrXs_Tsss kss mss ns
traytel@55803
  1435
            abs_inverses abs_inverses I ctr_defss ctr_sugars coiterss coiter_defss
traytel@55803
  1436
            (Proof_Context.export lthy' no_defs_lthy) lthy;
blanchet@49212
  1437
blanchet@53475
  1438
        val sel_unfold_thmss = map flat sel_unfold_thmsss;
blanchet@53475
  1439
        val sel_corec_thmss = map flat sel_corec_thmsss;
blanchet@53475
  1440
blanchet@51830
  1441
        val coinduct_type_attr = Attrib.internal o K o Induct.coinduct_type;
blanchet@49479
  1442
blanchet@54030
  1443
        val flat_coiter_thms = append oo append;
blanchet@49479
  1444
blanchet@49479
  1445
        val simp_thmss =
blanchet@53796
  1446
          map7 mk_simp_thms ctr_sugars
blanchet@54030
  1447
            (map3 flat_coiter_thms disc_unfold_thmss disc_unfold_iff_thmss sel_unfold_thmss)
blanchet@54030
  1448
            (map3 flat_coiter_thms disc_corec_thmss disc_corec_iff_thmss sel_corec_thmss)
blanchet@53476
  1449
            mapss rel_injects rel_distincts setss;
blanchet@49479
  1450
blanchet@49342
  1451
        val common_notes =
blanchet@49591
  1452
          (if nn > 1 then
blanchet@51810
  1453
             [(coinductN, [coinduct_thm], coinduct_attrs),
blanchet@51810
  1454
              (strong_coinductN, [strong_coinduct_thm], coinduct_attrs)]
blanchet@49591
  1455
           else
blanchet@49591
  1456
             [])
blanchet@51780
  1457
          |> massage_simple_notes fp_common_name;
blanchet@49342
  1458
blanchet@49212
  1459
        val notes =
blanchet@51780
  1460
          [(coinductN, map single coinduct_thms,
blanchet@51810
  1461
            fn T_name => coinduct_attrs @ [coinduct_type_attr T_name]),
blanchet@51843
  1462
           (corecN, corec_thmss, K coiter_attrs),
blanchet@51843
  1463
           (disc_corecN, disc_corec_thmss, K disc_coiter_attrs),
blanchet@51843
  1464
           (disc_corec_iffN, disc_corec_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1465
           (disc_unfoldN, disc_unfold_thmss, K disc_coiter_attrs),
blanchet@51843
  1466
           (disc_unfold_iffN, disc_unfold_iff_thmss, K disc_coiter_iff_attrs),
blanchet@51843
  1467
           (sel_corecN, sel_corec_thmss, K sel_coiter_attrs),
blanchet@51843
  1468
           (sel_unfoldN, sel_unfold_thmss, K sel_coiter_attrs),
blanchet@51780
  1469
           (simpsN, simp_thmss, K []),
blanchet@51810
  1470
           (strong_coinductN, map single strong_coinduct_thms, K coinduct_attrs),
blanchet@51843
  1471
           (unfoldN, unfold_thmss, K coiter_attrs)]
blanchet@51780
  1472
          |> massage_multi_notes;
blanchet@55463
  1473
blanchet@55463
  1474
        (* TODO: code theorems *)
blanchet@55463
  1475
        fun add_spec_rules coiter_of sel_thmss ctr_thmss =
blanchet@55463
  1476
          fold (curry (Spec_Rules.add Spec_Rules.Equational) (map coiter_of coiterss))
blanchet@55463
  1477
            [flat sel_thmss, flat ctr_thmss]
blanchet@49212
  1478
      in
blanchet@51824
  1479
        lthy
blanchet@55463
  1480
        |> add_spec_rules un_fold_of sel_unfold_thmss unfold_thmss
blanchet@55463
  1481
        |> add_spec_rules co_rec_of sel_corec_thmss corec_thmss
blanchet@54030
  1482
        |> Local_Theory.notes (common_notes @ notes) |> snd
traytel@55803
  1483
        |> register_fp_sugars Xs Greatest_FP pre_bnfs absT_infos nested_bnfs nesting_bnfs fp_res
traytel@55803
  1484
          ctrXs_Tsss ctr_defss ctr_sugars coiterss mapss [coinduct_thm, strong_coinduct_thm]
blanchet@55409
  1485
          (transpose [coinduct_thms, strong_coinduct_thms])
blanchet@53475
  1486
          (transpose [unfold_thmss, corec_thmss]) (transpose [disc_unfold_thmss, disc_corec_thmss])
blanchet@53475
  1487
          (transpose [sel_unfold_thmsss, sel_corec_thmsss])
blanchet@49212
  1488
      end;
blanchet@49212
  1489
blanchet@52367
  1490
    val lthy'' = lthy'
blanchet@52968
  1491
      |> fold_map define_ctrs_dtrs_for_type (fp_bnfs ~~ fp_bs ~~ fpTs ~~ ctors ~~ dtors ~~
blanchet@52330
  1492
        xtor_co_iterss ~~ ctor_dtors ~~ dtor_ctors ~~ ctor_injects ~~ pre_map_defs ~~
blanchet@52314
  1493
        pre_set_defss ~~ pre_rel_defs ~~ xtor_map_thms ~~ xtor_set_thmss ~~ xtor_rel_thms ~~ ns ~~
traytel@55803
  1494
        kss ~~ mss ~~ abss ~~ abs_injects ~~ abs_inverses ~~ type_definitions ~~
traytel@55803
  1495
        ctr_bindingss ~~ ctr_mixfixess ~~ ctr_Tsss ~~ disc_bindingss ~~ sel_bindingsss ~~
traytel@55803
  1496
        raw_sel_defaultsss)
blanchet@51835
  1497
      |> wrap_types_etc
blanchet@53807
  1498
      |> fp_case fp derive_note_induct_iters_thms_for_types
blanchet@53807
  1499
           derive_note_coinduct_coiters_thms_for_types;
blanchet@49167
  1500
blanchet@49167
  1501
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@52899
  1502
      co_prefix fp ^ "datatype"));
blanchet@49112
  1503
  in
blanchet@52367
  1504
    timer; lthy''
blanchet@49112
  1505
  end;
blanchet@49112
  1506
wenzelm@53974
  1507
fun co_datatypes x = define_co_datatypes (K I) (K I) (K I) x;
blanchet@49297
  1508
wenzelm@53974
  1509
fun co_datatype_cmd x =
wenzelm@53974
  1510
  define_co_datatypes Typedecl.read_constraint Syntax.parse_typ Syntax.parse_term x;
blanchet@49119
  1511
blanchet@55469
  1512
val parse_ctr_arg =
blanchet@55469
  1513
  @{keyword "("} |-- parse_binding_colon -- Parse.typ --| @{keyword ")"} ||
blanchet@55469
  1514
  (Parse.typ >> pair Binding.empty);
blanchet@55469
  1515
blanchet@55469
  1516
val parse_ctr_specs =
blanchet@55469
  1517
  Parse.enum1 "|" (parse_ctr_spec parse_binding parse_ctr_arg -- Parse.opt_mixfix);
blanchet@51767
  1518
blanchet@51767
  1519
val parse_spec =
blanchet@51790
  1520
  parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
blanchet@55469
  1521
  Parse.opt_mixfix -- (@{keyword "="} |-- parse_ctr_specs);
blanchet@51767
  1522
blanchet@55469
  1523
val parse_co_datatype = parse_ctr_options -- Parse.and_list1 parse_spec;
blanchet@49278
  1524
blanchet@52207
  1525
fun parse_co_datatype_cmd fp construct_fp = parse_co_datatype >> co_datatype_cmd fp construct_fp;
blanchet@49112
  1526
blanchet@49112
  1527
end;