(* 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 id_bnf}, fpT --> fpT),
rep = Const (@{const_name id_bnf}, 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 =
{Ts = [fpT],
bnfs = [fp_bnf],
ctors = [Const (@{const_name xtor}, fpT --> fpT)],
dtors = [Const (@{const_name xtor}, fpT --> fpT)],
xtor_co_recs = [Const (@{const_name ctor_rec}, (fpT --> C) --> (fpT --> C))],
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_map_thms = [xtor_map],
xtor_set_thmss = [xtor_sets],
xtor_rel_thms = [xtor_rel],
xtor_co_rec_thms = [map_id0_of_bnf fp_bnf RS @{thm ctor_rec}],
xtor_co_rec_o_map_thms = [ctor_rec_o_map],
rel_xtor_co_induct_thm = xtor_rel_induct,
dtor_set_induct_thms = [],
xtor_co_rec_transfer_thms = []};
fun fp_sugar_of_sum ctxt =
let
val fpT as Type (fpT_name, As) = @{typ "'a + 'b"};
val fpBT = @{typ "'c + 'd"};
val C = @{typ 'e};
val X = @{typ '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]};
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,
pre_bnf = ID_bnf (*wrong*),
absT_info = trivial_absT_info_of fpT,
fp_nesting_bnfs = [],
live_nesting_bnfs = [],
ctrXs_Tss = ctr_Tss,
ctr_defs = @{thms Inl_def_alt Inr_def_alt},
ctr_sugar = the_frozen_ctr_sugar_of ctxt fpT_name,
co_rec = Const (@{const_name case_sum}, map (fn Ts => (Ts ---> C)) ctr_Tss ---> fpT --> C),
co_rec_def = @{thm ctor_rec_def_alt[of "case_sum f1 f2" for f1 f2]},
maps = @{thms map_sum.simps},
common_co_inducts = @{thms sum.induct},
co_inducts = @{thms sum.induct},
co_rec_thms = @{thms sum.case},
co_rec_discs = [],
co_rec_selss = [],
fp_ctr_sugar = {},
fp_bnf_sugar = {
rel_injects = @{thms rel_sum_simps(1,4)},
rel_distincts = @{thms rel_sum_simps(2,3)[THEN eq_False[THEN iffD1]]}},
fp_co_induct_sugar = {}}
end;
fun fp_sugar_of_prod ctxt =
let
val fpT as Type (fpT_name, As) = @{typ "'a * 'b"};
val fpBT = @{typ "'c * 'd"};
val C = @{typ 'e};
val X = @{typ '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]};
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,
pre_bnf = ID_bnf (*wrong*),
absT_info = trivial_absT_info_of fpT,
fp_nesting_bnfs = [],
live_nesting_bnfs = [],
ctrXs_Tss = [ctr_Ts],
ctr_defs = @{thms Pair_def_alt},
ctr_sugar = the_frozen_ctr_sugar_of ctxt fpT_name,
co_rec = Const (@{const_name case_prod}, (ctr_Ts ---> C) --> fpT --> C),
co_rec_def = @{thm ctor_rec_def_alt[of "case_prod f" for f]},
maps = @{thms map_prod_simp},
common_co_inducts = @{thms prod.induct},
co_inducts = @{thms prod.induct},
co_rec_thms = @{thms prod.case},
co_rec_discs = [],
co_rec_selss = [],
fp_ctr_sugar = {},
fp_bnf_sugar = {
rel_injects = @{thms rel_prod_apply},
rel_distincts = []},
fp_co_induct_sugar = {}}
end;
val _ = Theory.setup (map_local_theory (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;