(* Title: HOL/Codatatype/Tools/bnf_fp_sugar_tactics.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012
Tactics for datatype and codatatype sugar.
*)
signature BNF_FP_SUGAR_TACTICS =
sig
val mk_case_tac: Proof.context -> int -> int -> int -> thm -> thm -> thm -> tactic
val mk_coiter_like_tac: thm list -> thm list -> thm -> thm -> thm -> Proof.context -> tactic
val mk_ctor_iff_dtor_tac: Proof.context -> ctyp option list -> cterm -> cterm -> thm -> thm ->
tactic
val mk_disc_coiter_like_iff_tac: thm list -> thm list -> thm list -> Proof.context -> tactic
val mk_exhaust_tac: Proof.context -> int -> thm list -> thm -> thm -> tactic
val mk_half_distinct_tac: Proof.context -> thm -> thm list -> tactic
val mk_induct_tac: Proof.context -> int list -> int list list -> int list list list -> thm list ->
thm -> thm list -> thm list list -> tactic
val mk_inject_tac: Proof.context -> thm -> thm -> tactic
val mk_iter_like_tac: thm list -> thm list -> thm list -> thm -> thm -> Proof.context -> tactic
end;
structure BNF_FP_Sugar_Tactics : BNF_FP_SUGAR_TACTICS =
struct
open BNF_Tactics
open BNF_Util
open BNF_FP
val meta_mp = @{thm meta_mp};
val meta_spec = @{thm meta_spec};
fun inst_spurious_fs lthy thm =
let
val fs =
Term.add_vars (prop_of thm) []
|> filter (fn (_, Type (@{type_name fun}, [_, T'])) => T' <> HOLogic.boolT | _ => false);
val cfs =
map (fn f as (_, T) => (certify lthy (Var f), certify lthy (id_abs (domain_type T)))) fs;
in
Drule.cterm_instantiate cfs thm
end;
val inst_spurious_fs_tac = PRIMITIVE o inst_spurious_fs;
fun mk_case_tac ctxt n k m case_def ctr_def dtor_ctor =
unfold_defs_tac ctxt [case_def, ctr_def, dtor_ctor] THEN
(rtac (mk_sum_casesN_balanced n k RS ssubst) THEN'
REPEAT_DETERM_N (Int.max (0, m - 1)) o rtac (@{thm split} RS ssubst) THEN'
rtac refl) 1;
fun mk_exhaust_tac ctxt n ctr_defs ctor_iff_dtor sumEN' =
unfold_defs_tac ctxt (ctor_iff_dtor :: ctr_defs) THEN rtac sumEN' 1 THEN
unfold_defs_tac ctxt @{thms all_prod_eq} THEN
EVERY' (maps (fn k => [select_prem_tac n (rotate_tac 1) k, REPEAT_DETERM o dtac meta_spec,
etac meta_mp, atac]) (1 upto n)) 1;
fun mk_ctor_iff_dtor_tac ctxt cTs cctor cdtor ctor_dtor dtor_ctor =
(rtac iffI THEN'
EVERY' (map3 (fn cTs => fn cx => fn th =>
dtac (Drule.instantiate' cTs [NONE, NONE, SOME cx] arg_cong) THEN'
SELECT_GOAL (unfold_defs_tac ctxt [th]) THEN'
atac) [rev cTs, cTs] [cdtor, cctor] [dtor_ctor, ctor_dtor])) 1;
fun mk_half_distinct_tac ctxt ctor_inject ctr_defs =
unfold_defs_tac ctxt (ctor_inject :: @{thms sum.inject} @ ctr_defs) THEN
rtac @{thm sum.distinct(1)} 1;
fun mk_inject_tac ctxt ctr_def ctor_inject =
unfold_defs_tac ctxt [ctr_def] THEN rtac (ctor_inject RS ssubst) 1 THEN
unfold_defs_tac ctxt @{thms sum.inject Pair_eq conj_assoc} THEN rtac refl 1;
val iter_like_unfold_thms =
@{thms case_unit comp_def convol_def id_apply map_pair_def sum.simps(5,6) sum_map.simps
split_conv};
fun mk_iter_like_tac pre_map_defs map_ids iter_like_defs ctor_iter_like ctr_def ctxt =
unfold_defs_tac ctxt (ctr_def :: ctor_iter_like :: iter_like_defs @ pre_map_defs @ map_ids @
iter_like_unfold_thms) THEN unfold_defs_tac ctxt @{thms id_def} THEN rtac refl 1;
val coiter_like_ss = ss_only @{thms if_True if_False};
val coiter_like_unfold_thms = @{thms id_apply map_pair_def sum_map.simps prod.cases};
fun mk_coiter_like_tac coiter_like_defs map_ids ctor_dtor_coiter_like pre_map_def ctr_def ctxt =
unfold_defs_tac ctxt (ctr_def :: coiter_like_defs) THEN
subst_tac ctxt [ctor_dtor_coiter_like] 1 THEN asm_simp_tac coiter_like_ss 1 THEN
unfold_defs_tac ctxt (pre_map_def :: coiter_like_unfold_thms @ map_ids) THEN
unfold_defs_tac ctxt @{thms id_def} THEN
TRY ((rtac refl ORELSE' subst_tac ctxt @{thms unit_eq} THEN' rtac refl) 1);
fun mk_disc_coiter_like_iff_tac case_splits' coiter_likes discs ctxt =
EVERY (map3 (fn case_split_tac => fn coiter_like_thm => fn disc =>
case_split_tac 1 THEN unfold_defs_tac ctxt [coiter_like_thm] THEN
asm_simp_tac (ss_only @{thms simp_thms(7,8,12,14,22,24)}) 1 THEN
(if is_refl disc then all_tac else rtac disc 1))
(map rtac case_splits' @ [K all_tac]) coiter_likes discs);
val solve_prem_prem_tac =
REPEAT o (eresolve_tac @{thms bexE rev_bexI} ORELSE' rtac @{thm rev_bexI[OF UNIV_I]} ORELSE'
hyp_subst_tac ORELSE' resolve_tac @{thms disjI1 disjI2}) THEN'
(rtac refl ORELSE' atac ORELSE' rtac @{thm singletonI});
val induct_prem_prem_thms =
@{thms SUP_empty Sup_empty Sup_insert UN_insert Un_empty_left Un_empty_right Un_iff
Union_Un_distrib collect_def[abs_def] image_def o_apply map_pair_simp
mem_Collect_eq mem_UN_compreh_eq prod_set_simps sum_map.simps sum_set_simps};
fun mk_induct_leverage_prem_prems_tac ctxt nn kks set_natural's pre_set_defs =
EVERY' (maps (fn kk => [select_prem_tac nn (dtac meta_spec) kk, etac meta_mp,
SELECT_GOAL (unfold_defs_tac ctxt (pre_set_defs @ set_natural's @ induct_prem_prem_thms)),
solve_prem_prem_tac]) (rev kks)) 1;
fun mk_induct_discharge_prem_tac ctxt nn n set_natural's pre_set_defs m k kks =
let val r = length kks in
EVERY' [select_prem_tac n (rotate_tac 1) k, rotate_tac ~1, hyp_subst_tac,
REPEAT_DETERM_N m o (dtac meta_spec THEN' rotate_tac ~1)] 1 THEN
EVERY [REPEAT_DETERM_N r
(rotate_tac ~1 1 THEN dtac meta_mp 1 THEN rotate_tac 1 1 THEN prefer_tac 2),
if r > 0 then PRIMITIVE Raw_Simplifier.norm_hhf else all_tac, atac 1,
mk_induct_leverage_prem_prems_tac ctxt nn kks set_natural's pre_set_defs]
end;
fun mk_induct_tac ctxt ns mss kkss ctr_defs ctor_induct' set_natural's pre_set_defss =
let
val nn = length ns;
val n = Integer.sum ns;
in
unfold_defs_tac ctxt ctr_defs THEN rtac ctor_induct' 1 THEN inst_spurious_fs_tac ctxt THEN
EVERY (map4 (EVERY oooo map3 o mk_induct_discharge_prem_tac ctxt nn n set_natural's)
pre_set_defss mss (unflat mss (1 upto n)) kkss)
end;
end;