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(* Title: HOL/Tools/BNF/bnf_fp_def_sugar.ML
Author: Jasmin Blanchette, TU Muenchen
Author: Martin Desharnais, TU Muenchen
Copyright 2012, 2013, 2014
Sugared datatype and codatatype constructions.
*)
signature BNF_FP_DEF_SUGAR =
sig
type fp_ctr_sugar =
{ctrXs_Tss: typ list list,
ctor_iff_dtor: thm,
ctr_defs: thm list,
ctr_sugar: Ctr_Sugar.ctr_sugar,
ctr_transfers: thm list,
case_transfers: thm list,
disc_transfers: thm list,
sel_transfers: thm list}
type fp_bnf_sugar =
{map_thms: thm list,
map_disc_iffs: thm list,
map_selss: thm list list,
rel_injects: thm list,
rel_distincts: thm list,
rel_sels: thm list,
rel_intros: thm list,
rel_cases: thm list,
pred_injects: thm list,
set_thms: thm list,
set_selssss: thm list list list list,
set_introssss: thm list list list list,
set_cases: thm list}
type fp_co_induct_sugar =
{co_rec: term,
common_co_inducts: thm list,
co_inducts: thm list,
co_rec_def: thm,
co_rec_thms: thm list,
co_rec_discs: thm list,
co_rec_disc_iffs: thm list,
co_rec_selss: thm list list,
co_rec_codes: thm list,
co_rec_transfers: thm list,
co_rec_o_maps: thm list,
common_rel_co_inducts: thm list,
rel_co_inducts: thm list,
common_set_inducts: thm list,
set_inducts: thm list}
type fp_sugar =
{T: typ,
BT: typ,
X: typ,
fp: BNF_Util.fp_kind,
fp_res_index: int,
fp_res: BNF_FP_Util.fp_result,
pre_bnf: BNF_Def.bnf,
fp_bnf: BNF_Def.bnf,
absT_info: BNF_Comp.absT_info,
fp_nesting_bnfs: BNF_Def.bnf list,
live_nesting_bnfs: BNF_Def.bnf list,
fp_ctr_sugar: fp_ctr_sugar,
fp_bnf_sugar: fp_bnf_sugar,
fp_co_induct_sugar: fp_co_induct_sugar option}
val co_induct_of: 'a list -> 'a
val strong_co_induct_of: 'a list -> 'a
val morph_fp_bnf_sugar: morphism -> fp_bnf_sugar -> fp_bnf_sugar
val morph_fp_co_induct_sugar: morphism -> fp_co_induct_sugar -> fp_co_induct_sugar
val morph_fp_ctr_sugar: morphism -> fp_ctr_sugar -> fp_ctr_sugar
val morph_fp_sugar: morphism -> fp_sugar -> fp_sugar
val transfer_fp_sugar: theory -> fp_sugar -> fp_sugar
val fp_sugar_of: Proof.context -> string -> fp_sugar option
val fp_sugar_of_global: theory -> string -> fp_sugar option
val fp_sugars_of: Proof.context -> fp_sugar list
val fp_sugars_of_global: theory -> fp_sugar list
val fp_sugars_interpretation: string -> (fp_sugar list -> local_theory -> local_theory) ->
theory -> theory
val interpret_fp_sugars: (string -> bool) -> fp_sugar list -> local_theory -> local_theory
val register_fp_sugars_raw: fp_sugar list -> local_theory -> local_theory
val register_fp_sugars: (string -> bool) -> fp_sugar list -> local_theory -> local_theory
val merge_type_args: BNF_Util.fp_kind -> ''a list * ''a list -> ''a list
val type_args_named_constrained_of_spec: (((('a * 'b) * 'c) * 'd) * 'e) * 'f -> 'a
val type_binding_of_spec: (((('a * 'b) * 'c) * 'd) * 'e) * 'f -> 'b
val mixfix_of_spec: ((('a * 'b) * 'c) * 'd) * 'e -> 'b
val mixfixed_ctr_specs_of_spec: (('a * 'b) * 'c) * 'd -> 'b
val map_binding_of_spec: ('a * ('b * 'c * 'd)) * 'e -> 'b
val rel_binding_of_spec: ('a * ('b * 'c * 'd)) * 'e -> 'c
val pred_binding_of_spec: ('a * ('b * 'c * 'd)) * 'e -> 'd
val sel_default_eqs_of_spec: 'a * 'b -> 'b
val mk_parametricity_goal: Proof.context -> term list -> term -> term -> term
val flat_corec_preds_predsss_gettersss: 'a list -> 'a list list list -> 'a list list list ->
'a list
val mk_ctor: typ list -> term -> term
val mk_dtor: typ list -> term -> term
val mk_bnf_sets: BNF_Def.bnf -> string * term list
val liveness_of_fp_bnf: int -> BNF_Def.bnf -> bool list
val nesting_bnfs: Proof.context -> typ list list list -> typ list -> BNF_Def.bnf list
val massage_simple_notes: string -> (bstring * 'a list * (int -> 'b)) list ->
((binding * 'c list) * ('a list * 'b) list) list
val massage_multi_notes: string list -> typ list ->
(string * 'a list list * (string -> 'b)) list ->
((binding * 'b) * ('a list * 'c list) list) list
val define_ctrs_dtrs_for_type: string -> typ -> term -> term -> thm -> thm -> int -> int list ->
term -> binding list -> mixfix list -> typ list list -> local_theory ->
(term list list * term list * thm * thm list) * local_theory
val wrap_ctrs: (string -> bool) -> BNF_Util.fp_kind -> bool -> string -> thm -> int -> int list ->
thm -> thm -> binding list -> binding list list -> term list -> term list -> thm -> thm list ->
local_theory -> Ctr_Sugar.ctr_sugar * local_theory
val derive_map_set_rel_pred_thms: (string -> bool) -> BNF_Util.fp_kind -> int -> typ list ->
typ list -> typ -> typ -> thm list -> thm list -> thm list -> thm list -> thm list ->
thm list -> thm list -> thm list -> thm list -> string -> BNF_Def.bnf -> BNF_Def.bnf list ->
typ -> term -> thm -> thm -> thm -> thm list -> thm -> thm -> thm list -> thm -> thm list ->
thm list -> thm list -> typ list list -> Ctr_Sugar.ctr_sugar -> local_theory ->
(thm list * thm list * thm list list * thm list * thm list * thm list * thm list * thm list
* thm list * thm list * thm list list list list * thm list list list list * thm list
* thm list * thm list * thm list * thm list) * local_theory
type lfp_sugar_thms = (thm list * thm * Token.src list) * (thm list list * Token.src list)
val morph_lfp_sugar_thms: morphism -> lfp_sugar_thms -> lfp_sugar_thms
val transfer_lfp_sugar_thms: theory -> lfp_sugar_thms -> lfp_sugar_thms
type gfp_sugar_thms =
((thm list * thm) list * (Token.src list * Token.src list))
* thm list list
* thm list list
* (thm list list * Token.src list)
* (thm list list list * Token.src list)
val morph_gfp_sugar_thms: morphism -> gfp_sugar_thms -> gfp_sugar_thms
val transfer_gfp_sugar_thms: theory -> gfp_sugar_thms -> gfp_sugar_thms
val mk_co_recs_prelims: Proof.context -> BNF_Util.fp_kind -> typ list list list -> typ list ->
typ list -> typ list -> typ list -> int list -> int list list -> term list ->
term list
* (typ list list * typ list list list list * term list list * term list list list list) option
* (string * term list * term list list
* (((term list list * term list list * term list list list list * term list list list list)
* term list list list) * typ list)) option
val repair_nullary_single_ctr: typ list list -> typ list list
val mk_corec_p_pred_types: typ list -> int list -> typ list list
val mk_corec_fun_arg_types: typ list list list -> typ list -> typ list -> typ list -> int list ->
int list list -> term ->
typ list list
* (typ list list list list * typ list list list * typ list list list list * typ list)
val define_co_rec_as: BNF_Util.fp_kind -> typ list -> typ -> binding -> term -> local_theory ->
(term * thm) * local_theory
val define_rec:
typ list list * typ list list list list * term list list * term list list list list ->
(string -> binding) -> typ list -> typ list -> term list -> term -> Proof.context ->
(term * thm) * Proof.context
val define_corec: 'a * term list * term list list
* (((term list list * term list list * term list list list list * term list list list list)
* term list list list) * typ list) -> (string -> binding) -> 'b list -> typ list ->
term list -> term -> local_theory -> (term * thm) * local_theory
val mk_induct_raw_prem: (term -> term) -> Proof.context -> typ list list ->
(string * term list) list -> term -> term -> typ list -> typ list ->
term list * ((term * (term * term)) list * (int * term)) list * term
val finish_induct_prem: Proof.context -> int -> term list ->
term list * ((term * (term * term)) list * (int * term)) list * term -> term
val mk_coinduct_prem: Proof.context -> typ list list -> typ list list -> term list -> term ->
term -> term -> int -> term list -> term list list -> term list -> term list list ->
typ list list -> term
val mk_induct_attrs: term list list -> Token.src list
val mk_coinduct_attrs: typ list -> term list list -> term list list -> int list list ->
Token.src list * Token.src list
val derive_induct_recs_thms_for_types: (string -> bool) -> BNF_Def.bnf list ->
('a * typ list list list list * term list list * 'b) option -> thm -> thm list ->
BNF_Def.bnf list -> BNF_Def.bnf list -> typ list -> typ list -> typ list ->
typ list list list -> thm list -> thm list -> thm list -> term list list -> thm list list ->
term list -> thm list -> Proof.context -> lfp_sugar_thms
val derive_coinduct_thms_for_types: Proof.context -> bool -> (term -> term) -> BNF_Def.bnf list ->
thm -> thm list -> BNF_Def.bnf list -> typ list -> typ list -> typ list list list -> int list ->
thm list -> thm list -> (thm -> thm) -> thm list list -> Ctr_Sugar.ctr_sugar list ->
(thm list * thm) list
val derive_coinduct_corecs_thms_for_types: Proof.context -> BNF_Def.bnf list ->
string * term list * term list list
* (((term list list * term list list * term list list list list * term list list list list)
* term list list list) * typ list) ->
thm -> thm list -> thm list -> thm list -> BNF_Def.bnf list -> typ list -> typ list ->
typ list -> typ list list list -> int list list -> int list list -> int list -> thm list ->
thm list -> (thm -> thm) -> thm list list -> Ctr_Sugar.ctr_sugar list -> term list ->
thm list -> gfp_sugar_thms
val co_datatypes: BNF_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
binding list -> binding list list -> binding list -> (string * sort) list ->
typ list * typ list list -> BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory ->
BNF_FP_Util.fp_result * local_theory) ->
Ctr_Sugar.ctr_options
* ((((((binding option * (typ * sort)) list * binding) * mixfix)
* ((binding, binding * typ) Ctr_Sugar.ctr_spec * mixfix) list) *
(binding * binding * binding))
* term list) list ->
local_theory -> local_theory
val co_datatype_cmd: BNF_Util.fp_kind ->
(mixfix list -> binding list -> binding list -> binding list -> binding list list ->
binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list ->
BNF_Comp.absT_info list -> local_theory -> BNF_FP_Util.fp_result * Proof.context) ->
((Proof.context -> Plugin_Name.filter) * bool)
* ((((((binding option * (string * string option)) list * binding) * mixfix)
* ((binding, binding * string) Ctr_Sugar.ctr_spec * mixfix) list)
* (binding * binding * binding)) * string list) list ->
Proof.context -> local_theory
val parse_ctr_arg: (binding * string) parser
val parse_ctr_specs: ((binding, binding * string) Ctr_Sugar.ctr_spec * mixfix) list parser
val parse_spec: ((((((binding option * (string * string option)) list * binding) * mixfix)
* ((binding, binding * string) Ctr_Sugar.ctr_spec * mixfix) list)
* (binding * binding * binding)) * string list) parser
val parse_co_datatype: (Ctr_Sugar.ctr_options_cmd
* ((((((binding option * (string * string option)) list * binding) * mixfix)
* ((binding, binding * string) Ctr_Sugar.ctr_spec * mixfix) list)
* (binding * binding * binding)) * string list) list) parser
val parse_co_datatype_cmd: BNF_Util.fp_kind -> (mixfix list -> binding list -> binding list ->
binding list -> binding list list -> binding list -> (string * sort) list ->
typ list * typ list list -> BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory ->
BNF_FP_Util.fp_result * local_theory) ->
(local_theory -> local_theory) parser
end;
structure BNF_FP_Def_Sugar : BNF_FP_DEF_SUGAR =
struct
open Ctr_Sugar
open BNF_FP_Rec_Sugar_Util
open BNF_Util
open BNF_Comp
open BNF_Def
open BNF_FP_Util
open BNF_FP_Def_Sugar_Tactics
val Eq_prefix = "Eq_";
val case_transferN = "case_transfer";
val ctor_iff_dtorN = "ctor_iff_dtor";
val ctr_transferN = "ctr_transfer";
val disc_transferN = "disc_transfer";
val sel_transferN = "sel_transfer";
val corec_codeN = "corec_code";
val corec_transferN = "corec_transfer";
val map_disc_iffN = "map_disc_iff";
val map_o_corecN = "map_o_corec";
val map_selN = "map_sel";
val pred_injectN = "pred_inject";
val rec_o_mapN = "rec_o_map";
val rec_transferN = "rec_transfer";
val set0N = "set0";
val set_casesN = "set_cases";
val set_introsN = "set_intros";
val set_inductN = "set_induct";
val set_selN = "set_sel";
type fp_ctr_sugar =
{ctrXs_Tss: typ list list,
ctor_iff_dtor: thm,
ctr_defs: thm list,
ctr_sugar: Ctr_Sugar.ctr_sugar,
ctr_transfers: thm list,
case_transfers: thm list,
disc_transfers: thm list,
sel_transfers: thm list};
type fp_bnf_sugar =
{map_thms: thm list,
map_disc_iffs: thm list,
map_selss: thm list list,
rel_injects: thm list,
rel_distincts: thm list,
rel_sels: thm list,
rel_intros: thm list,
rel_cases: thm list,
pred_injects: thm list,
set_thms: thm list,
set_selssss: thm list list list list,
set_introssss: thm list list list list,
set_cases: thm list};
type fp_co_induct_sugar =
{co_rec: term,
common_co_inducts: thm list,
co_inducts: thm list,
co_rec_def: thm,
co_rec_thms: thm list,
co_rec_discs: thm list,
co_rec_disc_iffs: thm list,
co_rec_selss: thm list list,
co_rec_codes: thm list,
co_rec_transfers: thm list,
co_rec_o_maps: thm list,
common_rel_co_inducts: thm list,
rel_co_inducts: thm list,
common_set_inducts: thm list,
set_inducts: thm list};
type fp_sugar =
{T: typ,
BT: typ,
X: typ,
fp: fp_kind,
fp_res_index: int,
fp_res: fp_result,
pre_bnf: bnf,
fp_bnf: bnf,
absT_info: absT_info,
fp_nesting_bnfs: bnf list,
live_nesting_bnfs: bnf list,
fp_ctr_sugar: fp_ctr_sugar,
fp_bnf_sugar: fp_bnf_sugar,
fp_co_induct_sugar: fp_co_induct_sugar option};
fun co_induct_of (i :: _) = i;
fun strong_co_induct_of [_, s] = s;
fun morph_fp_bnf_sugar phi ({map_thms, map_disc_iffs, map_selss, rel_injects, rel_distincts,
rel_sels, rel_intros, rel_cases, pred_injects, set_thms, set_selssss, set_introssss,
set_cases} : fp_bnf_sugar) =
{map_thms = map (Morphism.thm phi) map_thms,
map_disc_iffs = map (Morphism.thm phi) map_disc_iffs,
map_selss = map (map (Morphism.thm phi)) map_selss,
rel_injects = map (Morphism.thm phi) rel_injects,
rel_distincts = map (Morphism.thm phi) rel_distincts,
rel_sels = map (Morphism.thm phi) rel_sels,
rel_intros = map (Morphism.thm phi) rel_intros,
rel_cases = map (Morphism.thm phi) rel_cases,
pred_injects = map (Morphism.thm phi) pred_injects,
set_thms = map (Morphism.thm phi) set_thms,
set_selssss = map (map (map (map (Morphism.thm phi)))) set_selssss,
set_introssss = map (map (map (map (Morphism.thm phi)))) set_introssss,
set_cases = map (Morphism.thm phi) set_cases};
fun morph_fp_co_induct_sugar phi ({co_rec, common_co_inducts, co_inducts, co_rec_def, co_rec_thms,
co_rec_discs, co_rec_disc_iffs, co_rec_selss, co_rec_codes, co_rec_transfers, co_rec_o_maps,
common_rel_co_inducts, rel_co_inducts, common_set_inducts, set_inducts} : fp_co_induct_sugar) =
{co_rec = Morphism.term phi co_rec,
common_co_inducts = map (Morphism.thm phi) common_co_inducts,
co_inducts = map (Morphism.thm phi) co_inducts,
co_rec_def = Morphism.thm phi co_rec_def,
co_rec_thms = map (Morphism.thm phi) co_rec_thms,
co_rec_discs = map (Morphism.thm phi) co_rec_discs,
co_rec_disc_iffs = map (Morphism.thm phi) co_rec_disc_iffs,
co_rec_selss = map (map (Morphism.thm phi)) co_rec_selss,
co_rec_codes = map (Morphism.thm phi) co_rec_codes,
co_rec_transfers = map (Morphism.thm phi) co_rec_transfers,
co_rec_o_maps = map (Morphism.thm phi) co_rec_o_maps,
common_rel_co_inducts = map (Morphism.thm phi) common_rel_co_inducts,
rel_co_inducts = map (Morphism.thm phi) rel_co_inducts,
common_set_inducts = map (Morphism.thm phi) common_set_inducts,
set_inducts = map (Morphism.thm phi) set_inducts};
fun morph_fp_ctr_sugar phi ({ctrXs_Tss, ctor_iff_dtor, ctr_defs, ctr_sugar, ctr_transfers,
case_transfers, disc_transfers, sel_transfers} : fp_ctr_sugar) =
{ctrXs_Tss = map (map (Morphism.typ phi)) ctrXs_Tss,
ctor_iff_dtor = Morphism.thm phi ctor_iff_dtor,
ctr_defs = map (Morphism.thm phi) ctr_defs,
ctr_sugar = morph_ctr_sugar phi ctr_sugar,
ctr_transfers = map (Morphism.thm phi) ctr_transfers,
case_transfers = map (Morphism.thm phi) case_transfers,
disc_transfers = map (Morphism.thm phi) disc_transfers,
sel_transfers = map (Morphism.thm phi) sel_transfers};
fun morph_fp_sugar phi ({T, BT, X, fp, fp_res, fp_res_index, pre_bnf, fp_bnf, absT_info,
fp_nesting_bnfs, live_nesting_bnfs, fp_ctr_sugar, fp_bnf_sugar,
fp_co_induct_sugar} : fp_sugar) =
{T = Morphism.typ phi T,
BT = Morphism.typ phi BT,
X = Morphism.typ phi X,
fp = fp,
fp_res = morph_fp_result phi fp_res,
fp_res_index = fp_res_index,
pre_bnf = morph_bnf phi pre_bnf,
fp_bnf = morph_bnf phi fp_bnf,
absT_info = morph_absT_info phi absT_info,
fp_nesting_bnfs = map (morph_bnf phi) fp_nesting_bnfs,
live_nesting_bnfs = map (morph_bnf phi) live_nesting_bnfs,
fp_ctr_sugar = morph_fp_ctr_sugar phi fp_ctr_sugar,
fp_bnf_sugar = morph_fp_bnf_sugar phi fp_bnf_sugar,
fp_co_induct_sugar = Option.map (morph_fp_co_induct_sugar phi) fp_co_induct_sugar};
val transfer_fp_sugar = morph_fp_sugar o Morphism.transfer_morphism;
structure Data = Generic_Data
(
type T = fp_sugar Symtab.table;
val empty = Symtab.empty;
val extend = I;
fun merge data : T = Symtab.merge (K true) data;
);
fun fp_sugar_of_generic context =
Option.map (transfer_fp_sugar (Context.theory_of context)) o Symtab.lookup (Data.get context);
fun fp_sugars_of_generic context =
Symtab.fold (cons o transfer_fp_sugar (Context.theory_of context) o snd) (Data.get context) [];
val fp_sugar_of = fp_sugar_of_generic o Context.Proof;
val fp_sugar_of_global = fp_sugar_of_generic o Context.Theory;
val fp_sugars_of = fp_sugars_of_generic o Context.Proof;
val fp_sugars_of_global = fp_sugars_of_generic o Context.Theory;
structure FP_Sugar_Plugin = Plugin(type T = fp_sugar list);
fun fp_sugars_interpretation name f =
FP_Sugar_Plugin.interpretation name (fn fp_sugars => fn lthy =>
f (map (transfer_fp_sugar (Proof_Context.theory_of lthy)) fp_sugars) lthy);
val interpret_fp_sugars = FP_Sugar_Plugin.data;
val register_fp_sugars_raw =
fold (fn fp_sugar as {T = Type (s, _), ...} =>
Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Data.map (Symtab.update (s, morph_fp_sugar phi fp_sugar))));
fun register_fp_sugars plugins fp_sugars =
register_fp_sugars_raw fp_sugars #> interpret_fp_sugars plugins fp_sugars;
fun interpret_bnfs_register_fp_sugars plugins Ts BTs Xs fp pre_bnfs absT_infos fp_nesting_bnfs
live_nesting_bnfs fp_res ctrXs_Tsss ctor_iff_dtors ctr_defss ctr_sugars co_recs co_rec_defs
map_thmss common_co_inducts co_inductss co_rec_thmss co_rec_discss co_rec_selsss rel_injectss
rel_distinctss map_disc_iffss map_selsss rel_selss rel_intross rel_casess pred_injectss
set_thmss set_selsssss set_introsssss set_casess ctr_transferss case_transferss disc_transferss
sel_transferss co_rec_disc_iffss co_rec_codess co_rec_transferss common_rel_co_inducts
rel_co_inductss common_set_inducts set_inductss co_rec_o_mapss noted =
let
val fp_sugars =
map_index (fn (kk, T) =>
{T = T, BT = nth BTs kk, X = nth Xs kk, fp = fp, fp_res = fp_res, fp_res_index = kk,
pre_bnf = nth pre_bnfs kk, absT_info = nth absT_infos kk,
fp_bnf = nth (#bnfs fp_res) kk,
fp_nesting_bnfs = fp_nesting_bnfs, live_nesting_bnfs = live_nesting_bnfs,
fp_ctr_sugar =
{ctrXs_Tss = nth ctrXs_Tsss kk,
ctor_iff_dtor = nth ctor_iff_dtors kk,
ctr_defs = nth ctr_defss kk,
ctr_sugar = nth ctr_sugars kk,
ctr_transfers = nth ctr_transferss kk,
case_transfers = nth case_transferss kk,
disc_transfers = nth disc_transferss kk,
sel_transfers = nth sel_transferss kk},
fp_bnf_sugar =
{map_thms = nth map_thmss kk,
map_disc_iffs = nth map_disc_iffss kk,
map_selss = nth map_selsss kk,
rel_injects = nth rel_injectss kk,
rel_distincts = nth rel_distinctss kk,
rel_sels = nth rel_selss kk,
rel_intros = nth rel_intross kk,
rel_cases = nth rel_casess kk,
pred_injects = nth pred_injectss kk,
set_thms = nth set_thmss kk,
set_selssss = nth set_selsssss kk,
set_introssss = nth set_introsssss kk,
set_cases = nth set_casess kk},
fp_co_induct_sugar = SOME
{co_rec = nth co_recs kk,
common_co_inducts = common_co_inducts,
co_inducts = nth co_inductss kk,
co_rec_def = nth co_rec_defs kk,
co_rec_thms = nth co_rec_thmss kk,
co_rec_discs = nth co_rec_discss kk,
co_rec_disc_iffs = nth co_rec_disc_iffss kk,
co_rec_selss = nth co_rec_selsss kk,
co_rec_codes = nth co_rec_codess kk,
co_rec_transfers = nth co_rec_transferss kk,
co_rec_o_maps = nth co_rec_o_mapss kk,
common_rel_co_inducts = common_rel_co_inducts,
rel_co_inducts = nth rel_co_inductss kk,
common_set_inducts = common_set_inducts,
set_inducts = nth set_inductss kk}}
|> morph_fp_sugar (substitute_noted_thm noted)) Ts;
in
register_fp_sugars_raw fp_sugars
#> fold (interpret_bnf plugins) (#bnfs fp_res)
#> interpret_fp_sugars plugins fp_sugars
end;
fun quasi_unambiguous_case_names names =
let
val ps = map (`Long_Name.base_name) names;
val dups = Library.duplicates (op =) (map fst ps);
fun underscore s =
let val ss = Long_Name.explode s
in space_implode "_" (drop (length ss - 2) ss) end;
in
map (fn (base, full) => if member (op =) dups base then underscore full else base) ps
|> Name.variant_list []
end;
fun zipper_map f =
let
fun zed _ [] = []
| zed xs (y :: ys) = f (xs, y, ys) :: zed (xs @ [y]) ys;
in zed [] end;
fun cannot_merge_types fp =
error ("Mutually " ^ co_prefix fp ^ "recursive types must have the same type parameters");
fun merge_type_arg fp T T' = if T = T' then T else cannot_merge_types fp;
fun merge_type_args fp (As, As') =
if length As = length As' then map2 (merge_type_arg fp) As As' else cannot_merge_types fp;
fun type_args_named_constrained_of_spec (((((ncAs, _), _), _), _), _) = ncAs;
fun type_binding_of_spec (((((_, b), _), _), _), _) = b;
fun mixfix_of_spec ((((_, mx), _), _), _) = mx;
fun mixfixed_ctr_specs_of_spec (((_, mx_ctr_specs), _), _) = mx_ctr_specs;
fun map_binding_of_spec ((_, (b, _, _)), _) = b;
fun rel_binding_of_spec ((_, (_, b, _)), _) = b;
fun pred_binding_of_spec ((_, (_, _, b)), _) = b;
fun sel_default_eqs_of_spec (_, ts) = ts;
fun ctr_sugar_kind_of_fp_kind Least_FP = Datatype
| ctr_sugar_kind_of_fp_kind Greatest_FP = Codatatype;
fun uncurry_thm 0 thm = thm
| uncurry_thm 1 thm = thm
| uncurry_thm n thm = rotate_prems ~1 (uncurry_thm (n - 1) (rotate_prems 1 (conjI RS thm)));
fun choose_binary_fun fs AB =
find_first (fastype_of #> binder_types #> (fn [A, B] => AB = (A, B))) fs;
fun build_binary_fun_app fs t u =
Option.map (rapp u o rapp t) (choose_binary_fun fs (fastype_of t, fastype_of u));
fun build_the_rel ctxt Rs Ts A B =
build_rel [] ctxt Ts [] (the o choose_binary_fun Rs) (A, B);
fun build_rel_app ctxt Rs Ts t u =
build_the_rel ctxt Rs Ts (fastype_of t) (fastype_of u) $ t $ u;
fun build_set_app ctxt A t = Term.betapply (build_set ctxt A (fastype_of t), t);
fun mk_parametricity_goal ctxt Rs t u =
let val prem = build_the_rel ctxt Rs [] (fastype_of t) (fastype_of u) in
HOLogic.mk_Trueprop (prem $ t $ u)
end;
val name_of_set = name_of_const "set function" domain_type;
val fundefcong_attrs = @{attributes [fundef_cong]};
val nitpicksimp_attrs = @{attributes [nitpick_simp]};
val simp_attrs = @{attributes [simp]};
val lists_bmoc = fold (fn xs => fn t => Term.list_comb (t, xs));
fun flat_corec_predss_getterss qss gss = maps (op @) (qss ~~ gss);
fun flat_corec_preds_predsss_gettersss [] [qss] [gss] = flat_corec_predss_getterss qss gss
| flat_corec_preds_predsss_gettersss (p :: ps) (qss :: qsss) (gss :: gsss) =
p :: flat_corec_predss_getterss qss gss @ flat_corec_preds_predsss_gettersss ps qsss gsss;
fun mk_flip (x, Type (_, [T1, Type (_, [T2, T3])])) =
Abs ("x", T1, Abs ("y", T2, Var (x, T2 --> T1 --> T3) $ Bound 0 $ Bound 1));
fun flip_rels ctxt n thm =
let
val Rs = Term.add_vars (Thm.prop_of thm) [];
val Rs' = rev (drop (length Rs - n) Rs);
in
infer_instantiate ctxt (map (fn f => (fst f, Thm.cterm_of ctxt (mk_flip f))) Rs') thm
end;
fun mk_ctor_or_dtor get_T Ts t =
let val Type (_, Ts0) = get_T (fastype_of t) in
Term.subst_atomic_types (Ts0 ~~ Ts) t
end;
val mk_ctor = mk_ctor_or_dtor range_type;
val mk_dtor = mk_ctor_or_dtor domain_type;
fun mk_bnf_sets bnf =
let
val Type (T_name, Us) = T_of_bnf bnf;
val lives = lives_of_bnf bnf;
val sets = sets_of_bnf bnf;
fun mk_set U =
(case find_index (curry (op =) U) lives of
~1 => Term.dummy
| i => nth sets i);
in
(T_name, map mk_set Us)
end;
fun mk_xtor_co_recs thy fp fpTs Cs ts0 =
let
val nn = length fpTs;
val (fpTs0, Cs0) =
map ((fp = Greatest_FP ? swap) o dest_funT o snd o strip_typeN nn o fastype_of) ts0
|> split_list;
val rho = tvar_subst thy (fpTs0 @ Cs0) (fpTs @ Cs);
in
map (Term.subst_TVars rho) ts0
end;
fun liveness_of_fp_bnf n bnf =
(case T_of_bnf bnf of
Type (_, Ts) => map (not o member (op =) (deads_of_bnf bnf)) Ts
| _ => replicate n false);
fun add_nesting_bnf_names Us =
let
fun add (Type (s, Ts)) ss =
let val (needs, ss') = fold_map add Ts ss in
if exists I needs then (true, insert (op =) s ss') else (false, ss')
end
| add T ss = (member (op =) Us T, ss);
in snd oo add end;
fun nesting_bnfs ctxt ctr_Tsss Us =
map_filter (bnf_of ctxt) (fold (fold (fold (add_nesting_bnf_names Us))) ctr_Tsss []);
fun indexify proj xs f p = f (find_index (curry (op =) (proj p)) xs) p;
fun massage_simple_notes base =
filter_out (null o #2)
#> map (fn (thmN, thms, f_attrs) =>
((Binding.qualify true base (Binding.name thmN), []),
map_index (fn (i, thm) => ([thm], f_attrs i)) thms));
fun massage_multi_notes b_names Ts =
maps (fn (thmN, thmss, attrs) =>
@{map 3} (fn b_name => fn Type (T_name, _) => fn thms =>
((Binding.qualify true b_name (Binding.name thmN), attrs T_name), [(thms, [])]))
b_names Ts thmss)
#> filter_out (null o fst o hd o snd);
fun define_ctrs_dtrs_for_type fp_b_name fpT ctor dtor ctor_dtor dtor_ctor n ks abs ctr_bindings
ctr_mixfixes ctr_Tss lthy =
let
val ctor_absT = domain_type (fastype_of ctor);
val (((w, xss), u'), _) = lthy
|> yield_singleton (mk_Frees "w") ctor_absT
||>> mk_Freess "x" ctr_Tss
||>> yield_singleton Variable.variant_fixes fp_b_name;
val u = Free (u', fpT);
val ctor_iff_dtor_thm =
let
val goal =
fold_rev Logic.all [w, u]
(mk_Trueprop_eq (HOLogic.mk_eq (u, ctor $ w), HOLogic.mk_eq (dtor $ u, w)));
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, ...} =>
mk_ctor_iff_dtor_tac ctxt (map (SOME o Thm.ctyp_of lthy) [ctor_absT, fpT])
(Thm.cterm_of lthy ctor) (Thm.cterm_of lthy dtor) ctor_dtor dtor_ctor)
|> Thm.close_derivation \<^here>
end;
val ctr_rhss =
map2 (fn k => fn xs => fold_rev Term.lambda xs (ctor $ mk_absumprod ctor_absT abs n k xs))
ks xss;
val ((raw_ctrs, raw_ctr_defs), (lthy, lthy_old)) = lthy
|> (snd o Local_Theory.begin_nested)
|> apfst split_list o @{fold_map 3} (fn b => fn mx => fn rhs =>
Local_Theory.define ((b, mx),
((Thm.make_def_binding (Config.get lthy bnf_internals) b, []), rhs))
#>> apsnd snd) ctr_bindings ctr_mixfixes ctr_rhss
||> `Local_Theory.end_nested;
val phi = Proof_Context.export_morphism lthy_old lthy;
val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
val ctrs0 = map (Morphism.term phi) raw_ctrs;
in
((xss, ctrs0, ctor_iff_dtor_thm, ctr_defs), lthy)
end;
fun wrap_ctrs plugins fp discs_sels fp_b_name ctor_inject n ms abs_inject type_definition
disc_bindings sel_bindingss sel_default_eqs ctrs0 ctor_iff_dtor_thm ctr_defs lthy =
let
val sumEN_thm' = unfold_thms lthy @{thms unit_all_eq1} (mk_absumprodE type_definition ms);
fun exhaust_tac {context = ctxt, prems = _} =
mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor_thm sumEN_thm';
val inject_tacss =
map2 (fn ctr_def => fn 0 => [] | _ => [fn {context = ctxt, ...} =>
mk_inject_tac ctxt ctr_def ctor_inject abs_inject]) ctr_defs ms;
val half_distinct_tacss =
map (map (fn (def, def') => fn {context = ctxt, ...} =>
mk_half_distinct_tac ctxt ctor_inject abs_inject [def, def']))
(mk_half_pairss (`I ctr_defs));
val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss;
fun ctr_spec_of disc_b ctr0 sel_bs = ((disc_b, ctr0), sel_bs);
val ctr_specs = @{map 3} ctr_spec_of disc_bindings ctrs0 sel_bindingss;
val (ctr_sugar as {case_cong, ...}, lthy) =
free_constructors (ctr_sugar_kind_of_fp_kind fp) tacss
((((plugins, discs_sels), standard_binding), ctr_specs), sel_default_eqs) lthy;
val anonymous_notes =
[([case_cong], fundefcong_attrs)]
|> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
val notes =
if Config.get lthy bnf_internals then
[(ctor_iff_dtorN, [ctor_iff_dtor_thm], K [])]
|> massage_simple_notes fp_b_name
else
[];
in
(ctr_sugar, lthy |> Local_Theory.notes (anonymous_notes @ notes) |> snd)
end;
fun derive_map_set_rel_pred_thms plugins fp live As Bs C E abs_inverses ctr_defs fp_nesting_set_maps
fp_nesting_rel_eq_onps live_nesting_map_id0s live_nesting_set_maps live_nesting_rel_eqs
live_nesting_rel_eq_onps fp_nested_rel_eq_onps fp_b_name fp_bnf fp_bnfs fpT ctor ctor_dtor
dtor_ctor pre_map_def pre_set_defs pre_rel_def fp_map_thm fp_set_thms fp_rel_thm
extra_unfolds_map extra_unfolds_set extra_unfolds_rel ctr_Tss
({casex, case_thms, discs, selss, sel_defs, ctrs, exhaust, exhaust_discs, disc_thmss, sel_thmss,
injects, distincts, distinct_discsss, ...} : ctr_sugar)
lthy =
let
val n = length ctr_Tss;
val ms = map length ctr_Tss;
val B_ify_T = Term.typ_subst_atomic (As ~~ Bs);
val fpBT = B_ify_T fpT;
val live_AsBs = filter (op <>) (As ~~ Bs);
val live_As = map fst live_AsBs;
val fTs = map (op -->) live_AsBs;
val ((((((((xss, yss), fs), Ps), Rs), ta), tb), thesis), names_lthy) = lthy
|> fold (fold Variable.declare_typ) [As, Bs]
|> mk_Freess "x" ctr_Tss
||>> mk_Freess "y" (map (map B_ify_T) ctr_Tss)
||>> mk_Frees "f" fTs
||>> mk_Frees "P" (map mk_pred1T live_As)
||>> mk_Frees "R" (map (uncurry mk_pred2T) live_AsBs)
||>> yield_singleton (mk_Frees "a") fpT
||>> yield_singleton (mk_Frees "b") fpBT
||>> apfst HOLogic.mk_Trueprop o yield_singleton (mk_Frees "thesis") HOLogic.boolT;
val ctrAs = map (mk_ctr As) ctrs;
val ctrBs = map (mk_ctr Bs) ctrs;
val ctr_defs' =
map2 (fn m => fn def => mk_unabs_def m (HOLogic.mk_obj_eq def)) ms ctr_defs;
val ABfs = live_AsBs ~~ fs;
fun derive_rel_case relAsBs rel_inject_thms rel_distinct_thms =
let
val rel_Rs_a_b = list_comb (relAsBs, Rs) $ ta $ tb;
fun mk_assms ctrA ctrB ctxt =
let
val argA_Ts = binder_types (fastype_of ctrA);
val argB_Ts = binder_types (fastype_of ctrB);
val ((argAs, argBs), names_ctxt) = ctxt
|> mk_Frees "x" argA_Ts
||>> mk_Frees "y" argB_Ts;
val ctrA_args = list_comb (ctrA, argAs);
val ctrB_args = list_comb (ctrB, argBs);
in
(fold_rev Logic.all (argAs @ argBs) (Logic.list_implies
(mk_Trueprop_eq (ta, ctrA_args) :: mk_Trueprop_eq (tb, ctrB_args) ::
map2 (HOLogic.mk_Trueprop oo build_rel_app lthy Rs []) argAs argBs,
thesis)),
names_ctxt)
end;
val (assms, names_lthy) = @{fold_map 2} mk_assms ctrAs ctrBs names_lthy;
val goal = Logic.list_implies (HOLogic.mk_Trueprop rel_Rs_a_b :: assms, thesis);
in
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} =>
mk_rel_case_tac ctxt (Thm.cterm_of ctxt ta) (Thm.cterm_of ctxt tb) exhaust injects
rel_inject_thms distincts rel_distinct_thms live_nesting_rel_eqs)
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation \<^here>
end;
fun derive_case_transfer rel_case_thm =
let
val (S, names_lthy) = yield_singleton (mk_Frees "S") (mk_pred2T C E) names_lthy;
val caseA = mk_case As C casex;
val caseB = mk_case Bs E casex;
val goal = mk_parametricity_goal names_lthy (S :: Rs) caseA caseB;
in
Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, prems = _} =>
mk_case_transfer_tac ctxt rel_case_thm case_thms)
|> singleton (Proof_Context.export names_lthy lthy)
|> Thm.close_derivation \<^here>
end;
in
if live = 0 then
if plugins transfer_plugin then
let
val relAsBs = HOLogic.eq_const fpT;
val rel_case_thm = derive_rel_case relAsBs [] [];
val case_transfer_thm = derive_case_transfer rel_case_thm;
val notes =
[(case_transferN, [case_transfer_thm], K [])]
|> massage_simple_notes fp_b_name;
val (noted, lthy') = lthy
|> Local_Theory.notes notes;
val subst = Morphism.thm (substitute_noted_thm noted);
in
(([], [], [], [], [], [], [], [], [], [], [], [], [], [], [subst case_transfer_thm], [],
[]), lthy')
end
else
(([], [], [], [], [], [], [], [], [], [], [], [], [], [], [], [], []), lthy)
else
let
val mapx = mk_map live As Bs (map_of_bnf fp_bnf);
val relAsBs = mk_rel live As Bs (rel_of_bnf fp_bnf);
val setAs = map (mk_set As) (sets_of_bnf fp_bnf);
val discAs = map (mk_disc_or_sel As) discs;
val discBs = map (mk_disc_or_sel Bs) discs;
val selAss = map (map (mk_disc_or_sel As)) selss;
val selBss = map (map (mk_disc_or_sel Bs)) selss;
val map_ctor_thm =
if fp = Least_FP then
fp_map_thm
else
let
val ctorA = mk_ctor As ctor;
val ctorB = mk_ctor Bs ctor;
val y_T = domain_type (fastype_of ctorA);
val (y as Free (y_s, _), _) = lthy
|> yield_singleton (mk_Frees "y") y_T;
val ctor_cong =
infer_instantiate' lthy [NONE, NONE, SOME (Thm.cterm_of lthy ctorB)] arg_cong;
val fp_map_thm' = fp_map_thm
|> infer_instantiate' lthy (replicate live NONE @
[SOME (Thm.cterm_of lthy (ctorA $ y))])
|> unfold_thms lthy [dtor_ctor];
in
(fp_map_thm' RS ctor_cong RS (ctor_dtor RS sym RS trans))
|> Drule.generalize ([], [y_s])
end;
val map_thms =
let
fun mk_goal ctrA ctrB xs ys =
let
val fmap = list_comb (mapx, fs);
fun mk_arg (x as Free (_, T)) (Free (_, U)) =
if T = U then x
else build_map lthy [] [] (the o AList.lookup (op =) ABfs) (T, U) $ x;
val xs' = map2 mk_arg xs ys;
in
mk_Trueprop_eq (fmap $ list_comb (ctrA, xs), list_comb (ctrB, xs'))
end;
val goals = @{map 4} mk_goal ctrAs ctrBs xss yss;
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} =>
mk_map_tac ctxt abs_inverses pre_map_def map_ctor_thm live_nesting_map_id0s ctr_defs'
extra_unfolds_map)
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end;
val set0_thms =
let
fun mk_goal A setA ctrA xs =
let
val sets = map (build_set_app lthy A)
(filter (exists_subtype_in [A] o fastype_of) xs);
in
mk_Trueprop_eq (setA $ list_comb (ctrA, xs),
(if null sets then HOLogic.mk_set A [] else Library.foldl1 mk_union sets))
end;
val goals =
@{map 2} (fn live_A => fn setA => map2 (mk_goal live_A setA) ctrAs xss) live_As setAs
|> flat;
in
if null goals then
[]
else
let
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} =>
mk_set0_tac ctxt abs_inverses pre_set_defs dtor_ctor fp_set_thms
fp_nesting_set_maps live_nesting_set_maps ctr_defs' extra_unfolds_set)
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end
end;
val set_thms = set0_thms
|> map (unfold_thms lthy @{thms insert_is_Un[THEN sym] Un_empty_left Un_insert_left});
val rel_ctor_thm =
if fp = Least_FP then
fp_rel_thm
else
let
val ctorA = mk_ctor As ctor;
val ctorB = mk_ctor Bs ctor;
val y_T = domain_type (fastype_of ctorA);
val z_T = domain_type (fastype_of ctorB);
val ((y as Free (y_s, _), z as Free (z_s, _)), _) = lthy
|> yield_singleton (mk_Frees "y") y_T
||>> yield_singleton (mk_Frees "z") z_T;
in
fp_rel_thm
|> infer_instantiate' lthy (replicate live NONE @
[SOME (Thm.cterm_of lthy (ctorA $ y)), SOME (Thm.cterm_of lthy (ctorB $ z))])
|> unfold_thms lthy [dtor_ctor]
|> Drule.generalize ([], [y_s, z_s])
end;
val rel_inject_thms =
let
fun mk_goal ctrA ctrB xs ys =
let
val lhs = list_comb (relAsBs, Rs) $ list_comb (ctrA, xs) $ list_comb (ctrB, ys);
val conjuncts = map2 (build_rel_app lthy Rs []) xs ys;
in
HOLogic.mk_Trueprop
(if null conjuncts then lhs
else HOLogic.mk_eq (lhs, Library.foldr1 HOLogic.mk_conj conjuncts))
end;
val goals = @{map 4} mk_goal ctrAs ctrBs xss yss;
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} =>
mk_rel_tac ctxt abs_inverses pre_rel_def rel_ctor_thm live_nesting_rel_eqs ctr_defs'
extra_unfolds_rel)
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end;
val half_rel_distinct_thmss =
let
fun mk_goal ((ctrA, xs), (ctrB, ys)) =
HOLogic.mk_Trueprop (HOLogic.mk_not
(list_comb (relAsBs, Rs) $ list_comb (ctrA, xs) $ list_comb (ctrB, ys)));
val rel_infos = (ctrAs ~~ xss, ctrBs ~~ yss);
val goalss = map (map mk_goal) (mk_half_pairss rel_infos);
val goals = flat goalss;
in
unflat goalss
(if null goals then
[]
else
let
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} =>
mk_rel_tac ctxt abs_inverses pre_rel_def rel_ctor_thm live_nesting_rel_eqs
ctr_defs' extra_unfolds_rel)
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end)
end;
val rel_flip = rel_flip_of_bnf fp_bnf;
fun mk_other_half_rel_distinct_thm thm =
flip_rels lthy live thm RS (rel_flip RS sym RS @{thm arg_cong[of _ _ Not]} RS iffD2);
val other_half_rel_distinct_thmss =
map (map mk_other_half_rel_distinct_thm) half_rel_distinct_thmss;
val (rel_distinct_thms, _) =
join_halves n half_rel_distinct_thmss other_half_rel_distinct_thmss;
fun mk_rel_intro_thm m thm =
uncurry_thm m (thm RS iffD2) handle THM _ => thm;
val rel_intro_thms = map2 mk_rel_intro_thm ms rel_inject_thms;
val rel_code_thms =
map (fn thm => thm RS @{thm eq_False[THEN iffD2]}) rel_distinct_thms @
map2 (fn thm => fn 0 => thm RS @{thm eq_True[THEN iffD2]} | _ => thm) rel_inject_thms ms;
val ctr_transfer_thms =
let
val goals = map2 (mk_parametricity_goal names_lthy Rs) ctrAs ctrBs;
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal
(fn {context = ctxt, prems = _} =>
mk_ctr_transfer_tac ctxt rel_intro_thms live_nesting_rel_eqs)
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end;
val (set_cases_thms, set_cases_attrss) =
let
fun mk_prems assms elem t ctxt =
(case fastype_of t of
Type (type_name, xs) =>
(case bnf_of ctxt type_name of
NONE => ([], ctxt)
| SOME bnf =>
apfst flat (fold_map (fn set => fn ctxt =>
let
val T = HOLogic.dest_setT (range_type (fastype_of set));
val new_var = not (T = fastype_of elem);
val (x, ctxt') =
if new_var then yield_singleton (mk_Frees "x") T ctxt else (elem, ctxt);
in
mk_prems (mk_Trueprop_mem (x, set $ t) :: assms) elem x ctxt'
|>> map (new_var ? Logic.all x)
end) (map (mk_set xs) (sets_of_bnf bnf)) ctxt))
| T => rpair ctxt
(if T = fastype_of elem then [fold (curry Logic.mk_implies) assms thesis] else []));
in
split_list (map (fn set =>
let
val A = HOLogic.dest_setT (range_type (fastype_of set));
val (elem, names_lthy) = yield_singleton (mk_Frees "e") A names_lthy;
val premss =
map (fn ctr =>
let
val (args, names_lthy) =
mk_Frees "z" (binder_types (fastype_of ctr)) names_lthy;
in
flat (zipper_map (fn (prev_args, arg, next_args) =>
let
val (args_with_elem, args_without_elem) =
if fastype_of arg = A then
(prev_args @ [elem] @ next_args, prev_args @ next_args)
else
`I (prev_args @ [arg] @ next_args);
in
mk_prems [mk_Trueprop_eq (ta, Term.list_comb (ctr, args_with_elem))]
elem arg names_lthy
|> fst
|> map (fold_rev Logic.all args_without_elem)
end) args)
end) ctrAs;
val goal = Logic.mk_implies (mk_Trueprop_mem (elem, set $ ta), thesis);
val vars = Variable.add_free_names lthy goal [];
val thm =
Goal.prove_sorry lthy vars (flat premss) goal (fn {context = ctxt, prems} =>
mk_set_cases_tac ctxt (Thm.cterm_of ctxt ta) prems exhaust set_thms)
|> Thm.close_derivation \<^here>
|> rotate_prems ~1;
val cases_set_attr =
Attrib.internal (K (Induct.cases_pred (name_of_set set)));
val ctr_names = quasi_unambiguous_case_names (flat
(map (uncurry mk_names o map_prod length name_of_ctr) (premss ~~ ctrAs)));
in
(* TODO: @{attributes [elim?]} *)
(thm, [Attrib.consumes 1, cases_set_attr, Attrib.case_names ctr_names])
end) setAs)
end;
val (set_intros_thmssss, set_intros_thms) =
let
fun mk_goals A setA ctr_args t ctxt =
(case fastype_of t of
Type (type_name, innerTs) =>
(case bnf_of ctxt type_name of
NONE => ([], ctxt)
| SOME bnf =>
apfst flat (fold_map (fn set => fn ctxt =>
let
val T = HOLogic.dest_setT (range_type (fastype_of set));
val (y, ctxt') = yield_singleton (mk_Frees "y") T ctxt;
val assm = mk_Trueprop_mem (y, set $ t);
in
apfst (map (Logic.mk_implies o pair assm)) (mk_goals A setA ctr_args y ctxt')
end) (map (mk_set innerTs) (sets_of_bnf bnf)) ctxt))
| T => (if T = A then [mk_Trueprop_mem (t, setA $ ctr_args)] else [], ctxt));
val (goalssss, _) =
fold_map (fn set =>
let val A = HOLogic.dest_setT (range_type (fastype_of set)) in
@{fold_map 2} (fn ctr => fn xs =>
fold_map (mk_goals A set (Term.list_comb (ctr, xs))) xs)
ctrAs xss
end) setAs lthy;
val goals = flat (flat (flat goalssss));
in
`(unflattt goalssss)
(if null goals then
[]
else
let
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal
(fn {context = ctxt, prems = _} => mk_set_intros_tac ctxt set0_thms)
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end)
end;
val rel_sel_thms =
let
val n = length discAs;
fun mk_conjunct n k discA selAs discB selBs =
(if k = n then [] else [HOLogic.mk_eq (discA $ ta, discB $ tb)]) @
(if null selAs then
[]
else
[Library.foldr HOLogic.mk_imp
(if n = 1 then [] else [discA $ ta, discB $ tb],
Library.foldr1 HOLogic.mk_conj (map2 (build_rel_app names_lthy Rs [])
(map (rapp ta) selAs) (map (rapp tb) selBs)))]);
val goals =
if n = 0 then
[]
else
[mk_Trueprop_eq (build_rel_app names_lthy Rs [] ta tb,
(case flat (@{map 5} (mk_conjunct n) (1 upto n) discAs selAss discBs selBss) of
[] => \<^term>\<open>True\<close>
| conjuncts => Library.foldr1 HOLogic.mk_conj conjuncts))];
fun prove goal =
Variable.add_free_names lthy goal []
|> (fn vars => Goal.prove_sorry lthy vars [] goal (fn {context = ctxt, prems = _} =>
mk_rel_sel_tac ctxt (Thm.cterm_of ctxt ta) (Thm.cterm_of ctxt tb) exhaust
(flat disc_thmss) (flat sel_thmss) rel_inject_thms distincts rel_distinct_thms
live_nesting_rel_eqs))
|> Thm.close_derivation \<^here>;
in
map prove goals
end;
val (rel_case_thm, rel_case_attrs) =
let
val thm = derive_rel_case relAsBs rel_inject_thms rel_distinct_thms;
val ctr_names = quasi_unambiguous_case_names (map name_of_ctr ctrAs);
in
(thm, [Attrib.case_names ctr_names, Attrib.consumes 1] @ @{attributes [cases pred]})
end;
val case_transfer_thm = derive_case_transfer rel_case_thm;
val sel_transfer_thms =
if null selAss then
[]
else
let
val shared_sels = foldl1 (uncurry (inter (op =))) (map (op ~~) (selAss ~~ selBss));
val goals = map (uncurry (mk_parametricity_goal names_lthy Rs)) shared_sels;
in
if null goals then
[]
else
let
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal
(fn {context = ctxt, prems = _} =>
mk_sel_transfer_tac ctxt n sel_defs case_transfer_thm)
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end
end;
val disc_transfer_thms =
let val goals = map2 (mk_parametricity_goal names_lthy Rs) discAs discBs in
if null goals then
[]
else
let
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal
(fn {context = ctxt, prems = _} => mk_disc_transfer_tac ctxt
(the_single rel_sel_thms) (the_single exhaust_discs)
(flat (flat distinct_discsss)))
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end
end;
val map_disc_iff_thms =
let
val discsB = map (mk_disc_or_sel Bs) discs;
val discsA_t = map (fn disc1 => Term.betapply (disc1, ta)) discAs;
fun mk_goal (discA_t, discB) =
if head_of discA_t aconv HOLogic.Not orelse is_refl_bool discA_t then
NONE
else
SOME (mk_Trueprop_eq (betapply (discB, (Term.list_comb (mapx, fs) $ ta)), discA_t));
val goals = map_filter mk_goal (discsA_t ~~ discsB);
in
if null goals then
[]
else
let
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal
(fn {context = ctxt, prems = _} =>
mk_map_disc_iff_tac ctxt (Thm.cterm_of ctxt ta) exhaust (flat disc_thmss)
map_thms)
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end
end;
val (map_sel_thmss, map_sel_thms) =
let
fun mk_goal discA selA selB =
let
val prem = Term.betapply (discA, ta);
val lhs = selB $ (Term.list_comb (mapx, fs) $ ta);
val lhsT = fastype_of lhs;
val map_rhsT =
map_atyps (perhaps (AList.lookup (op =) (map swap live_AsBs))) lhsT;
val map_rhs = build_map lthy [] []
(the o (AList.lookup (op =) (live_AsBs ~~ fs))) (map_rhsT, lhsT);
val rhs = (case map_rhs of
Const (\<^const_name>\<open>id\<close>, _) => selA $ ta
| _ => map_rhs $ (selA $ ta));
val concl = mk_Trueprop_eq (lhs, rhs);
in
if is_refl_bool prem then concl
else Logic.mk_implies (HOLogic.mk_Trueprop prem, concl)
end;
val goalss = @{map 3} (map2 o mk_goal) discAs selAss selBss;
val goals = flat goalss;
in
`(unflat goalss)
(if null goals then
[]
else
let
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal
(fn {context = ctxt, prems = _} =>
mk_map_sel_tac ctxt (Thm.cterm_of ctxt ta) exhaust (flat disc_thmss)
map_thms (flat sel_thmss) live_nesting_map_id0s)
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end)
end;
val (set_sel_thmssss, set_sel_thms) =
let
fun mk_goal setA discA selA ctxt =
let
val prem = Term.betapply (discA, ta);
val sel_rangeT = range_type (fastype_of selA);
val A = HOLogic.dest_setT (range_type (fastype_of setA));
fun travese_nested_types t ctxt =
(case fastype_of t of
Type (type_name, innerTs) =>
(case bnf_of ctxt type_name of
NONE => ([], ctxt)
| SOME bnf =>
let
fun seq_assm a set ctxt =
let
val T = HOLogic.dest_setT (range_type (fastype_of set));
val (x, ctxt') = yield_singleton (mk_Frees "x") T ctxt;
val assm = mk_Trueprop_mem (x, set $ a);
in
travese_nested_types x ctxt'
|>> map (Logic.mk_implies o pair assm)
end;
in
fold_map (seq_assm t o mk_set innerTs) (sets_of_bnf bnf) ctxt
|>> flat
end)
| T =>
if T = A then ([mk_Trueprop_mem (t, setA $ ta)], ctxt) else ([], ctxt));
val (concls, ctxt') =
if sel_rangeT = A then ([mk_Trueprop_mem (selA $ ta, setA $ ta)], ctxt)
else travese_nested_types (selA $ ta) ctxt;
in
if exists_subtype_in [A] sel_rangeT then
if is_refl_bool prem then (concls, ctxt')
else (map (Logic.mk_implies o pair (HOLogic.mk_Trueprop prem)) concls, ctxt')
else
([], ctxt)
end;
val (goalssss, _) =
fold_map (fn set => @{fold_map 2} (fold_map o mk_goal set) discAs selAss)
setAs names_lthy;
val goals = flat (flat (flat goalssss));
in
`(unflattt goalssss)
(if null goals then
[]
else
let
val goal = Logic.mk_conjunction_balanced goals;
val vars = Variable.add_free_names lthy goal [];
in
Goal.prove_sorry lthy vars [] goal
(fn {context = ctxt, prems = _} =>
mk_set_sel_tac ctxt (Thm.cterm_of ctxt ta) exhaust (flat disc_thmss)
(flat sel_thmss) set0_thms)
|> Thm.close_derivation \<^here>
|> Conjunction.elim_balanced (length goals)
end)
end;
val pred_injects =
let
fun top_sweep_rewr_conv rewrs =
Conv.top_sweep_conv (K (Conv.rewrs_conv rewrs)) \<^context>;
val rel_eq_onp_with_tops_of = Conv.fconv_rule (HOLogic.Trueprop_conv (Conv.arg1_conv
(top_sweep_rewr_conv @{thms eq_onp_top_eq_eq[symmetric, THEN eq_reflection]})));
val eq_onps = map rel_eq_onp_with_tops_of
(map rel_eq_onp_of_bnf fp_bnfs @ fp_nesting_rel_eq_onps @ live_nesting_rel_eq_onps @
fp_nested_rel_eq_onps);
val cTs = map (SOME o Thm.ctyp_of lthy) (maps (replicate 2) live_As);
val cts = map (SOME o Thm.cterm_of lthy) (map mk_eq_onp Ps);
val get_rhs = Thm.concl_of #> HOLogic.dest_Trueprop #> HOLogic.dest_eq #> snd;
val pred_eq_onp_conj =
List.foldr (fn (_, thm) => thm RS @{thm eq_onp_live_step}) @{thm refl[of True]};
fun predify_rel_inject rel_inject =
let
val conjuncts = try (get_rhs #> HOLogic.dest_conj) rel_inject |> the_default [];
fun postproc thm =
if null conjuncts then
thm RS (@{thm eq_onp_same_args} RS iffD1)
else
@{thm box_equals} OF [thm, @{thm eq_onp_same_args},
pred_eq_onp_conj conjuncts |> unfold_thms lthy @{thms simp_thms(21)}];
in
rel_inject
|> Thm.instantiate' cTs cts
|> Conv.fconv_rule (HOLogic.Trueprop_conv (Conv.arg_conv
(Raw_Simplifier.rewrite lthy false
@{thms eq_onp_top_eq_eq[symmetric, THEN eq_reflection]})))
|> unfold_thms lthy eq_onps
|> postproc
|> unfold_thms lthy @{thms top_conj}
end;
in
rel_inject_thms
|> map (unfold_thms lthy [@{thm conj_assoc}])
|> map predify_rel_inject
|> Proof_Context.export names_lthy lthy
end;
val anonymous_notes =
[(rel_code_thms, nitpicksimp_attrs)]
|> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
val notes =
(if Config.get lthy bnf_internals then
[(set0N, set0_thms, K [])]
else
[]) @
[(case_transferN, [case_transfer_thm], K []),
(ctr_transferN, ctr_transfer_thms, K []),
(disc_transferN, disc_transfer_thms, K []),
(sel_transferN, sel_transfer_thms, K []),
(mapN, map_thms, K (nitpicksimp_attrs @ simp_attrs)),
(map_disc_iffN, map_disc_iff_thms, K simp_attrs),
(map_selN, map_sel_thms, K []),
(pred_injectN, pred_injects, K simp_attrs),
(rel_casesN, [rel_case_thm], K rel_case_attrs),
(rel_distinctN, rel_distinct_thms, K simp_attrs),
(rel_injectN, rel_inject_thms, K simp_attrs),
(rel_introsN, rel_intro_thms, K []),
(rel_selN, rel_sel_thms, K []),
(setN, set_thms, K (case_fp fp nitpicksimp_attrs [] @ simp_attrs)),
(set_casesN, set_cases_thms, nth set_cases_attrss),
(set_introsN, set_intros_thms, K []),
(set_selN, set_sel_thms, K [])]
|> massage_simple_notes fp_b_name;
val (noted, lthy') = lthy
|> uncurry (Spec_Rules.add Binding.empty Spec_Rules.equational)
(`(single o lhs_head_of o hd) map_thms)
|> fp = Least_FP ?
uncurry (Spec_Rules.add Binding.empty Spec_Rules.equational)
(`(single o lhs_head_of o hd) rel_code_thms)
|> uncurry (Spec_Rules.add Binding.empty Spec_Rules.equational)
(`(single o lhs_head_of o hd) set0_thms)
|> plugins code_plugin ? Code.declare_default_eqns (map (rpair true) (rel_code_thms @ map_thms @ set_thms))
|> Local_Theory.notes (anonymous_notes @ notes);
val subst = Morphism.thm (substitute_noted_thm noted);
in
((map subst map_thms,
map subst map_disc_iff_thms,
map (map subst) map_sel_thmss,
map subst rel_inject_thms,
map subst rel_distinct_thms,
map subst rel_sel_thms,
map subst rel_intro_thms,
[subst rel_case_thm],
map subst pred_injects,
map subst set_thms,
map (map (map (map subst))) set_sel_thmssss,
map (map (map (map subst))) set_intros_thmssss,
map subst set_cases_thms,
map subst ctr_transfer_thms,
[subst case_transfer_thm],
map subst disc_transfer_thms,
map subst sel_transfer_thms), lthy')
end
end;
type lfp_sugar_thms = (thm list * thm * Token.src list) * (thm list list * Token.src list);
fun morph_lfp_sugar_thms phi ((inducts, induct, induct_attrs), (recss, rec_attrs)) =
((map (Morphism.thm phi) inducts, Morphism.thm phi induct, induct_attrs),
(map (map (Morphism.thm phi)) recss, rec_attrs)) : lfp_sugar_thms;
val transfer_lfp_sugar_thms = morph_lfp_sugar_thms o Morphism.transfer_morphism;
type gfp_sugar_thms =
((thm list * thm) list * (Token.src list * Token.src list))
* thm list list
* thm list list
* (thm list list * Token.src list)
* (thm list list list * Token.src list);
fun morph_gfp_sugar_thms phi ((coinducts_pairs, coinduct_attrs_pair),
corecss, corec_discss, (corec_disc_iffss, corec_disc_iff_attrs),
(corec_selsss, corec_sel_attrs)) =
((map (apfst (map (Morphism.thm phi)) o apsnd (Morphism.thm phi)) coinducts_pairs,
coinduct_attrs_pair),
map (map (Morphism.thm phi)) corecss,
map (map (Morphism.thm phi)) corec_discss,
(map (map (Morphism.thm phi)) corec_disc_iffss, corec_disc_iff_attrs),
(map (map (map (Morphism.thm phi))) corec_selsss, corec_sel_attrs)) : gfp_sugar_thms;
val transfer_gfp_sugar_thms = morph_gfp_sugar_thms o Morphism.transfer_morphism;
fun unzip_recT (Type (\<^type_name>\<open>prod\<close>, [_, TFree x]))
(T as Type (\<^type_name>\<open>prod\<close>, Ts as [_, TFree y])) =
if x = y then [T] else Ts
| unzip_recT _ (Type (\<^type_name>\<open>prod\<close>, Ts as [_, TFree _])) = Ts
| unzip_recT _ T = [T];
fun mk_recs_args_types ctxt ctr_Tsss Cs absTs repTs ns mss ctor_rec_fun_Ts =
let
val Css = map2 replicate ns Cs;
val x_Tssss =
@{map 6} (fn absT => fn repT => fn n => fn ms => fn ctr_Tss => fn ctor_rec_fun_T =>
map2 (map2 unzip_recT)
ctr_Tss (dest_absumprodT absT repT n ms (domain_type ctor_rec_fun_T)))
absTs repTs ns mss ctr_Tsss ctor_rec_fun_Ts;
val x_Tsss' = map (map flat_rec_arg_args) x_Tssss;
val f_Tss = map2 (map2 (curry (op --->))) x_Tsss' Css;
val ((fss, xssss), _) = ctxt
|> mk_Freess "f" f_Tss
||>> mk_Freessss "x" x_Tssss;
in
(f_Tss, x_Tssss, fss, xssss)
end;
fun unzip_corecT (Type (\<^type_name>\<open>sum\<close>, _)) T = [T]
| unzip_corecT _ (Type (\<^type_name>\<open>sum\<close>, Ts)) = Ts
| unzip_corecT _ T = [T];
(*avoid "'a itself" arguments in corecursors*)
fun repair_nullary_single_ctr [[]] = [[HOLogic.unitT]]
| repair_nullary_single_ctr Tss = Tss;
fun mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss fun_Ts =
let
val ctr_Tsss' = map repair_nullary_single_ctr ctr_Tsss;
val g_absTs = map range_type fun_Ts;
val g_Tsss =
map repair_nullary_single_ctr (@{map 5} dest_absumprodT absTs repTs ns mss g_absTs);
val g_Tssss = @{map 3} (fn C => map2 (map2 (map (curry (op -->) C) oo unzip_corecT)))
Cs ctr_Tsss' g_Tsss;
val q_Tssss = map (map (map (fn [_] => [] | [_, T] => [mk_pred1T (domain_type T)]))) g_Tssss;
in
(q_Tssss, g_Tsss, g_Tssss, g_absTs)
end;
fun mk_corec_p_pred_types Cs ns = map2 (fn n => replicate (Int.max (0, n - 1)) o mk_pred1T) ns Cs;
fun mk_corec_fun_arg_types ctr_Tsss Cs absTs repTs ns mss dtor_corec =
(mk_corec_p_pred_types Cs ns,
mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss
(binder_fun_types (fastype_of dtor_corec)));
fun mk_corecs_args_types ctxt ctr_Tsss Cs absTs repTs ns mss dtor_corec_fun_Ts =
let
val p_Tss = mk_corec_p_pred_types Cs ns;
val (q_Tssss, g_Tsss, g_Tssss, corec_types) =
mk_corec_fun_arg_types0 ctr_Tsss Cs absTs repTs ns mss dtor_corec_fun_Ts;
val (((((Free (x, _), cs), pss), qssss), gssss), _) = ctxt
|> yield_singleton (mk_Frees "x") dummyT
||>> mk_Frees "a" Cs
||>> mk_Freess "p" p_Tss
||>> mk_Freessss "q" q_Tssss
--> --------------------
--> maximum size reached
--> --------------------
¤ Dauer der Verarbeitung: 0.89 Sekunden
(vorverarbeitet)
¤
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