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(* Title: HOL/Tools/BNF/bnf_gfp_grec_sugar_tactics.ML
Author: Jasmin Blanchette, Inria, LORIA, MPII
Copyright 2016
Tactics for generalized corecursor sugar.
*)
signature BNF_GFP_GREC_SUGAR_TACTICS =
sig
val rho_transfer_simps: thm list
val mk_case_dtor_tac: Proof.context -> term -> thm -> thm -> thm list -> thm -> thm list -> tactic
val mk_cong_intro_ctr_or_friend_tac: Proof.context -> thm -> thm list -> thm -> tactic
val mk_code_tac: Proof.context -> int -> term list -> term -> term -> thm -> thm -> thm list ->
thm list -> thm list -> thm list -> thm -> thm -> thm list -> thm list -> thm -> thm list ->
thm list -> thm list -> thm list -> thm list -> thm list -> thm -> tactic
val mk_eq_algrho_tac: Proof.context -> term list -> term -> term -> term -> term -> term -> thm ->
thm -> thm list -> thm list -> thm list -> thm list -> thm -> thm -> thm -> thm list ->
thm list -> thm list -> thm -> thm list -> thm list -> thm list -> thm -> thm -> thm -> thm ->
thm list -> thm list -> thm list -> thm list -> thm list -> tactic
val mk_eq_corecUU_tac: Proof.context -> int -> term list -> term -> term -> thm -> thm ->
thm list -> thm list -> thm list -> thm list -> thm -> thm -> thm list -> thm list ->
thm list -> thm list -> thm list -> thm list -> thm list -> thm -> thm -> tactic
val mk_last_disc_tac: Proof.context -> term -> thm -> thm list -> tactic
val mk_rho_transfer_tac: Proof.context -> bool -> thm -> thm list -> tactic
val mk_unique_tac: Proof.context -> int -> term list -> term -> term -> thm -> thm -> thm list ->
thm list -> thm list -> thm list -> thm -> thm -> thm list -> thm list -> thm list ->
thm list -> thm list -> thm list -> thm list -> thm -> thm -> tactic
end;
structure BNF_GFP_Grec_Sugar_Tactics : BNF_GFP_GREC_SUGAR_TACTICS =
struct
open Ctr_Sugar
open BNF_Util
open BNF_Tactics
open BNF_FP_Def_Sugar_Tactics
open BNF_GFP_Grec_Tactics
open BNF_GFP_Grec_Sugar_Util
fun apply_func f =
let
val arg_Ts = binder_fun_types (fastype_of f);
val args = map_index (fn (j, T) => Var (("a" ^ string_of_int j, 0), T)) arg_Ts;
in
list_comb (f, args)
end;
fun instantiate_distrib thm ctxt t =
infer_instantiate' ctxt [SOME (Thm.incr_indexes_cterm 1 (Thm.cterm_of ctxt t))] thm;
val mk_if_distrib_of = instantiate_distrib @{thm if_distrib};
val mk_case_sum_distrib_of = instantiate_distrib @{thm sum.case_distrib};
fun mk_case_dtor_tac ctxt u abs_inverse dtor_ctor ctr_defs exhaust cases =
let val exhaust' = infer_instantiate' ctxt [SOME (Thm.cterm_of ctxt u)] exhaust in
HEADGOAL (rtac ctxt exhaust') THEN
REPEAT_DETERM (HEADGOAL (etac ctxt ssubst THEN'
SELECT_GOAL (unfold_thms_tac ctxt cases THEN
unfold_thms_tac ctxt (abs_inverse :: dtor_ctor :: ctr_defs @
@{thms prod.case sum.case})) THEN'
rtac ctxt refl))
end;
fun mk_cong_intro_ctr_or_friend_tac ctxt ctr_or_friend_def extra_simps cong_alg_intro =
HEADGOAL (REPEAT_DETERM_N 2 o subst_tac ctxt NONE [ctr_or_friend_def] THEN'
rtac ctxt cong_alg_intro) THEN
unfold_thms_tac ctxt (extra_simps @ sumprod_thms_rel @
@{thms vimage2p_def prod.rel_eq sum.rel_eq}) THEN
REPEAT_DETERM (HEADGOAL (rtac ctxt conjI ORELSE' assume_tac ctxt ORELSE' rtac ctxt refl ORELSE'
etac ctxt subst));
val shared_simps =
@{thms map_prod_simp map_sum.simps sum.case prod.case_eq_if split_beta' prod.sel
sum.disc(1)[THEN eq_True[THEN iffD2]] sum.disc(2)[THEN eq_False[THEN iffD2]] sum.sel
isl_map_sum map_sum_sel if_True if_False if_True_False Let_def[abs_def] o_def[abs_def] id_def
BNF_Composition.id_bnf_def};
fun mk_code_tac ctxt num_args fpsig_nesting_maps ssig_map eval pre_map_def abs_inverse
fpsig_nesting_map_ident0s fpsig_nesting_map_comps fpsig_nesting_map_thms
live_nesting_map_ident0s fp_map_ident case_trivial ctr_defs case_eq_ifs corecUU all_sig_maps
ssig_map_thms all_algLam_alg_pointfuls all_algrho_eqs eval_simps inner_fp_simps fun_def =
let
val fun_def' =
if null inner_fp_simps andalso num_args > 0 then
HOLogic.mk_obj_eq fun_def RS (mk_curry_uncurryN_balanced ctxt num_args RS iffD2) RS sym
else
fun_def;
val case_trivial' = unfold_thms ctxt (case_eq_ifs @ ctr_defs @ shared_simps) case_trivial;
val case_eq_ifs' = map (Drule.abs_def o (fn thm => thm RS eq_reflection)) case_eq_ifs;
val if_distribs = @{thm if_distrib_fun} :: map (mk_if_distrib_of ctxt)
(eval :: map apply_func (ssig_map :: fpsig_nesting_maps));
val unfold_tac = unfold_thms_tac ctxt (case_trivial' :: pre_map_def :: abs_inverse ::
fp_map_ident :: (if null inner_fp_simps then [] else [corecUU]) @ fpsig_nesting_map_ident0s @
fpsig_nesting_map_comps @ fpsig_nesting_map_thms @ live_nesting_map_ident0s @ ctr_defs @
case_eq_ifs' @ all_sig_maps @ ssig_map_thms @ all_algLam_alg_pointfuls @ all_algrho_eqs @
eval_simps @ if_distribs @ shared_simps);
in
HEADGOAL (subst_tac ctxt NONE [fun_def] THEN' subst_tac ctxt NONE [corecUU] THEN'
(if null inner_fp_simps then K all_tac else subst_tac ctxt NONE inner_fp_simps)) THEN
unfold_thms_tac ctxt [fun_def'] THEN
unfold_tac THEN HEADGOAL (CONVERSION Thm.eta_long_conversion) THEN unfold_tac THEN
HEADGOAL (rtac ctxt refl)
end;
fun mk_eq_algrho_tac ctxt fpsig_nesting_maps abs rep ctor ssig_map eval pre_map_def abs_inverse
fpsig_nesting_map_ident0s fpsig_nesting_map_comps fpsig_nesting_map_thms
live_nesting_map_ident0s fp_map_ident dtor_ctor ctor_iff_dtor ctr_defs nullary_disc_defs
disc_sel_eq_cases case_dtor case_eq_ifs const_pointful_naturals fp_nesting_k_map_disc_sels'
rho_def dtor_algrho corecUU_unique eq_corecUU all_sig_maps ssig_map_thms
all_algLam_alg_pointfuls all_algrho_eqs eval_simps =
let
val nullary_disc_defs' = nullary_disc_defs
|> map (fn thm => thm RS sym)
|> maps (fn thm => [thm, thm RS @{thm subst[OF eq_commute, of "%e. e = z" for z]}]);
val case_dtor' = unfold_thms ctxt shared_simps case_dtor;
val disc_sel_eq_cases' = map (mk_abs_def
o unfold_thms ctxt (case_dtor' :: ctr_defs @ shared_simps)) disc_sel_eq_cases;
val extra_naturals = Facts.retrieve (Context.Proof ctxt) (Proof_Context.facts_of ctxt)
("friend_of_corec_simps", Position.none) |> #thms;
val const_pointful_naturals' = map (unfold_thms ctxt shared_simps)
(extra_naturals @ const_pointful_naturals);
val const_pointful_naturals_sym' = map (fn thm => thm RS sym) const_pointful_naturals';
val case_eq_ifs' = map mk_abs_def (@{thm sum.case_eq_if} :: case_eq_ifs);
val distrib_consts =
abs :: rep :: ctor :: eval :: map apply_func (ssig_map :: fpsig_nesting_maps);
val if_distribs = @{thm if_distrib_fun} :: map (mk_if_distrib_of ctxt) distrib_consts;
val case_sum_distribs = map (mk_case_sum_distrib_of ctxt) distrib_consts;
val simp_ctxt = (ctxt
|> Context_Position.set_visible false
|> put_simpset (simpset_of (Proof_Context.init_global \<^theory>\<open>Main\<close>))
|> Raw_Simplifier.add_cong @{thm if_cong})
addsimps pre_map_def :: abs_inverse :: fp_map_ident :: dtor_ctor :: rho_def ::
@{thm convol_def} :: fpsig_nesting_map_ident0s @ fpsig_nesting_map_comps @
fpsig_nesting_map_thms @ live_nesting_map_ident0s @ ctr_defs @ disc_sel_eq_cases' @
fp_nesting_k_map_disc_sels' @ case_eq_ifs' @ all_sig_maps @ ssig_map_thms @
all_algLam_alg_pointfuls @ all_algrho_eqs @ eval_simps @ if_distribs @ case_sum_distribs @
shared_simps;
fun mk_main_simp const_pointful_naturals_maybe_sym' =
simp_tac (simp_ctxt addsimps const_pointful_naturals_maybe_sym');
in
unfold_thms_tac ctxt [eq_corecUU] THEN
HEADGOAL (REPEAT_DETERM o rtac ctxt ext THEN'
rtac ctxt (corecUU_unique RS sym RS fun_cong) THEN'
subst_tac ctxt NONE [dtor_algrho RS (ctor_iff_dtor RS iffD2)] THEN' rtac ctxt ext) THEN
unfold_thms_tac ctxt (nullary_disc_defs' @ shared_simps) THEN
HEADGOAL (rtac ctxt meta_eq_to_obj_eq) THEN
REPEAT_DETERM_N (length const_pointful_naturals' + 1)
(ALLGOALS (mk_main_simp const_pointful_naturals_sym') THEN
ALLGOALS (mk_main_simp const_pointful_naturals'))
end;
fun mk_eq_corecUU_tac ctxt num_args fpsig_nesting_maps ssig_map eval pre_map_def abs_inverse
fpsig_nesting_map_ident0s fpsig_nesting_map_comps fpsig_nesting_map_thms
live_nesting_map_ident0s fp_map_ident case_trivial ctr_defs case_eq_ifs all_sig_maps
ssig_map_thms all_algLam_alg_pointfuls all_algrho_eqs eval_simps corecUU_unique fun_code =
let
val case_trivial' = unfold_thms ctxt (case_eq_ifs @ ctr_defs @ shared_simps) case_trivial;
val case_eq_ifs' = map (Drule.abs_def o (fn thm => thm RS eq_reflection)) case_eq_ifs;
val if_distribs = @{thm if_distrib_fun} :: map (mk_if_distrib_of ctxt)
(eval :: map apply_func (ssig_map :: fpsig_nesting_maps));
val unfold_tac = unfold_thms_tac ctxt (case_trivial' :: pre_map_def :: abs_inverse ::
fp_map_ident :: fpsig_nesting_map_ident0s @ fpsig_nesting_map_comps @ fpsig_nesting_map_thms @
live_nesting_map_ident0s @ ctr_defs @ case_eq_ifs' @ all_sig_maps @ ssig_map_thms @
all_algLam_alg_pointfuls @ all_algrho_eqs @ eval_simps @ if_distribs @ shared_simps);
in
HEADGOAL (rtac ctxt (mk_curry_uncurryN_balanced ctxt num_args RS iffD1) THEN'
rtac ctxt corecUU_unique THEN' rtac ctxt ext) THEN
unfold_thms_tac ctxt @{thms prod.case_eq_if} THEN
HEADGOAL (rtac ctxt (fun_code RS trans)) THEN
unfold_tac THEN HEADGOAL (CONVERSION Thm.eta_long_conversion) THEN unfold_tac THEN
HEADGOAL (rtac ctxt refl)
end;
fun mk_last_disc_tac ctxt u exhaust discs' =
let val exhaust' = infer_instantiate' ctxt [SOME (Thm.cterm_of ctxt u)] exhaust in
HEADGOAL (rtac ctxt exhaust') THEN
REPEAT_DETERM (HEADGOAL (etac ctxt ssubst THEN'
simp_tac (ss_only (distinct Thm.eq_thm discs' @ @{thms simp_thms}) ctxt)))
end;
val rho_transfer_simps = @{thms BNF_Def.vimage2p_def[abs_def] BNF_Composition.id_bnf_def};
fun mk_rho_transfer_tac ctxt unfold rel_def const_transfers =
(if unfold then unfold_thms_tac ctxt (rel_def :: rho_transfer_simps) else all_tac) THEN
HEADGOAL (transfer_prover_add_tac ctxt [] const_transfers);
fun mk_unique_tac ctxt num_args fpsig_nesting_maps ssig_map eval pre_map_def abs_inverse
fpsig_nesting_map_ident0s fpsig_nesting_map_comps fpsig_nesting_map_thms
live_nesting_map_ident0s fp_map_ident case_trivial ctr_defs case_eq_ifs all_sig_maps
ssig_map_thms all_algLam_alg_pointfuls all_algrho_eqs eval_simps corecUU_unique eq_corecUU =
let
val case_trivial' = unfold_thms ctxt (case_eq_ifs @ ctr_defs @ shared_simps) case_trivial;
val case_eq_ifs' = map (Drule.abs_def o (fn thm => thm RS eq_reflection)) case_eq_ifs;
val if_distribs = @{thm if_distrib_fun} :: map (mk_if_distrib_of ctxt)
(eval :: map apply_func (ssig_map :: fpsig_nesting_maps));
val unfold_tac = unfold_thms_tac ctxt (case_trivial' :: pre_map_def :: abs_inverse ::
fp_map_ident :: fpsig_nesting_map_ident0s @ fpsig_nesting_map_comps @ fpsig_nesting_map_thms @
live_nesting_map_ident0s @ ctr_defs @ case_eq_ifs' @ all_sig_maps @ ssig_map_thms @
all_algLam_alg_pointfuls @ all_algrho_eqs @ eval_simps @ if_distribs @ shared_simps);
in
HEADGOAL (subst_tac ctxt NONE [eq_corecUU] THEN'
rtac ctxt (mk_curry_uncurryN_balanced ctxt num_args RS iffD1) THEN'
rtac ctxt corecUU_unique THEN' rtac ctxt ext THEN'
etac ctxt @{thm ssubst[of _ _ "\x. f x = u" for f u]}) THEN
unfold_tac THEN HEADGOAL (CONVERSION Thm.eta_long_conversion) THEN unfold_tac THEN
HEADGOAL (rtac ctxt refl)
end;
end;
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