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(* Title: HOL/Tools/BNF/bnf_lfp_basic_sugar.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2014
Registration of basic types as BNF least fixpoints (datatypes).
*)
structure BNF_LFP_Basic_Sugar : sig end =
struct
open Ctr_Sugar
open BNF_Util
open BNF_Def
open BNF_Comp
open BNF_FP_Rec_Sugar_Util
open BNF_FP_Util
open BNF_FP_Def_Sugar
fun trivial_absT_info_of fpT =
{absT = fpT, repT = fpT, abs = Const (\<^const_name>\<open>id_bnf\<close>, fpT --> fpT),
rep = Const (\<^const_name>\<open>id_bnf\<close>, fpT --> fpT),
abs_inject = @{thm type_definition.Abs_inject[OF type_definition_id_bnf_UNIV UNIV_I UNIV_I]},
abs_inverse = @{thm type_definition.Abs_inverse[OF type_definition_id_bnf_UNIV UNIV_I]},
type_definition = @{thm type_definition_id_bnf_UNIV}};
fun the_frozen_ctr_sugar_of ctxt fpT_name =
the (ctr_sugar_of ctxt fpT_name)
|> morph_ctr_sugar (Morphism.typ_morphism "BNF" Logic.unvarifyT_global
$> Morphism.term_morphism "BNF" (Term.map_types Logic.unvarifyT_global));
fun trivial_fp_result_of fp_bnf fpT C xtor_map xtor_sets xtor_rel ctor_rec_o_map
xtor_rel_induct ctor_rec_transfer =
let
val xtors = [Const (\<^const_name>\<open>xtor\<close>, fpT --> fpT)];
val co_recs = [Const (\<^const_name>\<open>ctor_rec\<close>, (fpT --> C) --> (fpT --> C))];
val co_rec_thms = [map_id0_of_bnf fp_bnf RS @{thm ctor_rec}];
val co_rec_unique_thm = map_id0_of_bnf fp_bnf RS @{thm ctor_rec_unique};
in
{Ts = [fpT], bnfs = [fp_bnf], pre_bnfs = [ID_bnf], absT_infos = [trivial_absT_info_of fpT],
ctors = xtors, dtors = xtors, xtor_un_folds = co_recs,
xtor_co_recs = co_recs, xtor_co_induct = @{thm xtor_induct}, dtor_ctors = @{thms xtor_xtor},
ctor_dtors = @{thms xtor_xtor}, ctor_injects = @{thms xtor_inject},
dtor_injects = @{thms xtor_inject}, xtor_maps = [xtor_map],
xtor_map_unique = @{thm xtor_map_unique}, xtor_setss = [xtor_sets], xtor_rels = [xtor_rel],
xtor_un_fold_thms = co_rec_thms, xtor_co_rec_thms = co_rec_thms,
xtor_un_fold_unique = co_rec_unique_thm, xtor_co_rec_unique = co_rec_unique_thm,
xtor_un_fold_o_maps = [ctor_rec_o_map], xtor_co_rec_o_maps = [ctor_rec_o_map],
xtor_un_fold_transfers = [ctor_rec_transfer],
xtor_co_rec_transfers = [ctor_rec_transfer],
xtor_rel_co_induct = xtor_rel_induct, dtor_set_inducts = []}
end;
fun fp_sugar_of_sum ctxt =
let
val fpT as Type (fpT_name, As) = \<^typ>\<open>'a + 'b\<close>;
val fpBT = \<^typ>\<open>'c + 'd\<close>;
val C = \<^typ>\<open>'e\;
val X = \<^typ>\<open>'sum\;
val ctr_Tss = map single As;
val fp_bnf = the (bnf_of ctxt fpT_name);
val xtor_map = @{thm xtor_map[of "map_sum f1 f2" for f1 f2]};
val xtor_sets = @{thms xtor_set[of setl] xtor_set[of setr]};
val xtor_rel = @{thm xtor_rel[of "rel_sum R1 R2" for R1 R2]};
val ctor_rec_o_map = @{thm ctor_rec_o_map[of _ "map_sum g1 g2" for g1 g2]};
val xtor_rel_induct = @{thm xtor_rel_induct[of "rel_sum R1 R2" for R1 R2]};
val ctor_rec_transfer = @{thm ctor_rec_transfer[of "rel_sum R1 R2" for R1 R2]};
in
{T = fpT,
BT = fpBT,
X = X,
fp = Least_FP,
fp_res_index = 0,
fp_res =
trivial_fp_result_of fp_bnf fpT C xtor_map xtor_sets xtor_rel ctor_rec_o_map xtor_rel_induct
ctor_rec_transfer,
pre_bnf = ID_bnf (*wrong*),
fp_bnf = fp_bnf,
absT_info = trivial_absT_info_of fpT,
fp_nesting_bnfs = [],
live_nesting_bnfs = [],
fp_ctr_sugar =
{ctrXs_Tss = ctr_Tss,
ctor_iff_dtor = @{thm xtor_iff_xtor},
ctr_defs = @{thms Inl_def_alt Inr_def_alt},
ctr_sugar = the_frozen_ctr_sugar_of ctxt fpT_name,
ctr_transfers = @{thms Inl_transfer Inr_transfer},
case_transfers = @{thms case_sum_transfer},
disc_transfers = @{thms isl_transfer},
sel_transfers = []},
fp_bnf_sugar =
{map_thms = @{thms map_sum.simps},
map_disc_iffs = @{thms isl_map_sum},
map_selss = map single @{thms map_sum_sel},
rel_injects = @{thms rel_sum_simps(1,4)},
rel_distincts = @{thms rel_sum_simps(2,3)[THEN eq_False[THEN iffD1]]},
rel_sels = @{thms rel_sum_sel},
rel_intros = @{thms rel_sum.intros},
rel_cases = @{thms rel_sum.cases},
pred_injects = @{thms pred_sum_inject},
set_thms = @{thms sum_set_simps},
set_selssss = [[[@{thms set_sum_sel(1)}], [[]]], [[[]], [@{thms set_sum_sel(2)}]]],
set_introssss = [[[@{thms setl.intros[OF refl]}], [[]]],
[[[]], [@{thms setr.intros[OF refl]}]]],
set_cases = @{thms setl.cases[simplified hypsubst_in_prems]
setr.cases[simplified hypsubst_in_prems]}},
fp_co_induct_sugar = SOME
{co_rec = Const (\<^const_name>\<open>case_sum\<close>, map (fn Ts => (Ts ---> C)) ctr_Tss ---> fpT --> C),
common_co_inducts = @{thms sum.induct},
co_inducts = @{thms sum.induct},
co_rec_def = @{thm ctor_rec_def_alt[of "case_sum f1 f2" for f1 f2]},
co_rec_thms = @{thms sum.case},
co_rec_discs = [],
co_rec_disc_iffs = [],
co_rec_selss = [],
co_rec_codes = [],
co_rec_transfers = @{thms case_sum_transfer},
co_rec_o_maps = @{thms case_sum_o_map_sum},
common_rel_co_inducts = @{thms rel_sum.inducts},
rel_co_inducts = @{thms rel_sum.induct},
common_set_inducts = [],
set_inducts = []}}
end;
fun fp_sugar_of_prod ctxt =
let
val fpT as Type (fpT_name, As) = \<^typ>\<open>'a * 'b\<close>;
val fpBT = \<^typ>\<open>'c * 'd\<close>;
val C = \<^typ>\<open>'e\;
val X = \<^typ>\<open>'prod\;
val ctr_Ts = As;
val fp_bnf = the (bnf_of ctxt fpT_name);
val xtor_map = @{thm xtor_map[of "map_prod f1 f2" for f1 f2]};
val xtor_sets = @{thms xtor_set[of fsts] xtor_set[of snds]};
val xtor_rel = @{thm xtor_rel[of "rel_prod R1 R2" for R1 R2]};
val ctor_rec_o_map = @{thm ctor_rec_o_map[of _ "map_prod g1 g2" for g1 g2]};
val xtor_rel_induct = @{thm xtor_rel_induct[of "rel_prod R1 R2" for R1 R2]};
val ctor_rec_transfer = @{thm ctor_rec_transfer[of "rel_prod R1 R2" for R1 R2]};
in
{T = fpT,
BT = fpBT,
X = X,
fp = Least_FP,
fp_res_index = 0,
fp_res =
trivial_fp_result_of fp_bnf fpT C xtor_map xtor_sets xtor_rel ctor_rec_o_map xtor_rel_induct
ctor_rec_transfer,
pre_bnf = ID_bnf (*wrong*),
fp_bnf = fp_bnf,
absT_info = trivial_absT_info_of fpT,
fp_nesting_bnfs = [],
live_nesting_bnfs = [],
fp_ctr_sugar =
{ctrXs_Tss = [ctr_Ts],
ctor_iff_dtor = @{thm xtor_iff_xtor},
ctr_defs = @{thms Pair_def_alt},
ctr_sugar = the_frozen_ctr_sugar_of ctxt fpT_name,
ctr_transfers = @{thms Pair_transfer},
case_transfers = @{thms case_prod_transfer},
disc_transfers = [],
sel_transfers = @{thms fst_transfer snd_transfer}},
fp_bnf_sugar =
{map_thms = @{thms map_prod_simp},
map_disc_iffs = [],
map_selss = [@{thms fst_map_prod snd_map_prod}],
rel_injects = @{thms rel_prod_inject},
rel_distincts = [],
rel_sels = @{thms rel_prod_sel},
rel_intros = @{thms rel_prod.intros},
rel_cases = @{thms rel_prod.cases},
pred_injects = @{thms pred_prod_inject},
set_thms = @{thms prod_set_simps},
set_selssss = [[[@{thms fsts.intros}, []]], [[[], @{thms snds.intros}]]],
set_introssss = [[[@{thms fsts.intros[of "(a, b)" for a b, simplified fst_conv]}, []]],
[[[], @{thms snds.intros[of "(a, b)" for a b, simplified snd_conv]}]]],
set_cases = @{thms fsts.cases[simplified eq_fst_iff ex_neg_all_pos]
snds.cases[simplified eq_snd_iff ex_neg_all_pos]}},
fp_co_induct_sugar = SOME
{co_rec = Const (\<^const_name>\<open>case_prod\<close>, (ctr_Ts ---> C) --> fpT --> C),
common_co_inducts = @{thms prod.induct},
co_inducts = @{thms prod.induct},
co_rec_def = @{thm ctor_rec_def_alt[of "case_prod f" for f]},
co_rec_thms = @{thms prod.case},
co_rec_discs = [],
co_rec_disc_iffs = [],
co_rec_selss = [],
co_rec_codes = [],
co_rec_transfers = @{thms case_prod_transfer},
co_rec_o_maps = @{thms case_prod_o_map_prod},
common_rel_co_inducts = @{thms rel_prod.inducts},
rel_co_inducts = @{thms rel_prod.induct},
common_set_inducts = [],
set_inducts = []}}
end;
val _ = Theory.setup (Named_Target.theory_map (fn lthy =>
fold (BNF_FP_Def_Sugar.register_fp_sugars (K true) o single o (fn f => f lthy))
[fp_sugar_of_sum, fp_sugar_of_prod] lthy));
end;
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