(* Title: HOL/Tools/Ctr_Sugar/ctr_sugar_tactics.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012, 2013
Tactics for wrapping existing freely generated type's constructors.
*)
signature CTR_SUGAR_GENERAL_TACTICS =
sig
val select_prem_tac: int -> (int -> tactic) -> int -> int -> tactic
val unfold_thms_tac: Proof.context -> thm list -> tactic
end;
signature CTR_SUGAR_TACTICS =
sig
include CTR_SUGAR_GENERAL_TACTICS
val mk_alternate_disc_def_tac: Proof.context -> int -> thm -> thm -> thm -> tactic
val mk_case_tac: Proof.context -> int -> int -> thm -> thm list -> thm list list -> tactic
val mk_case_cong_tac: Proof.context -> thm -> thm list -> tactic
val mk_case_eq_if_tac: Proof.context -> int -> thm -> thm list -> thm list list ->
thm list list -> tactic
val mk_collapse_tac: Proof.context -> int -> thm -> thm list -> tactic
val mk_disc_exhaust_tac: int -> thm -> thm list -> tactic
val mk_expand_tac: Proof.context -> int -> int list -> thm -> thm -> thm list ->
thm list list list -> thm list list list -> tactic
val mk_half_disc_exclude_tac: Proof.context -> int -> thm -> thm -> tactic
val mk_nchotomy_tac: int -> thm -> tactic
val mk_other_half_disc_exclude_tac: thm -> tactic
val mk_sel_exhaust_tac: int -> thm -> thm list -> tactic
val mk_split_tac: Proof.context -> thm -> thm list -> thm list list -> thm list list ->
thm list list list -> tactic
val mk_split_asm_tac: Proof.context -> thm -> tactic
val mk_unique_disc_def_tac: int -> thm -> tactic
end;
structure Ctr_Sugar_Tactics : CTR_SUGAR_TACTICS =
struct
open Ctr_Sugar_Util
val meta_mp = @{thm meta_mp};
fun select_prem_tac n tac k = DETERM o (EVERY' [REPEAT_DETERM_N (k - 1) o etac thin_rl,
tac, REPEAT_DETERM_N (n - k) o etac thin_rl]);
fun unfold_thms_tac _ [] = all_tac
| unfold_thms_tac ctxt thms = Local_Defs.unfold_tac ctxt (distinct Thm.eq_thm_prop thms);
fun if_P_or_not_P_OF pos thm = thm RS (if pos then @{thm if_P} else @{thm if_not_P});
fun mk_nchotomy_tac n exhaust =
HEADGOAL (rtac allI THEN' rtac exhaust THEN'
EVERY' (maps (fn k => [rtac (mk_disjIN n k), REPEAT_DETERM o rtac exI, atac]) (1 upto n)));
fun mk_unique_disc_def_tac m uexhaust =
HEADGOAL (EVERY' [rtac iffI, rtac uexhaust, REPEAT_DETERM_N m o rtac exI, atac, rtac refl]);
fun mk_alternate_disc_def_tac ctxt k other_disc_def distinct uexhaust =
HEADGOAL (EVERY' ([rtac (other_disc_def RS @{thm arg_cong[of _ _ Not]} RS trans),
rtac @{thm iffI_np}, REPEAT_DETERM o etac exE,
hyp_subst_tac ctxt, SELECT_GOAL (unfold_thms_tac ctxt [not_ex]), REPEAT_DETERM o rtac allI,
rtac distinct, rtac uexhaust] @
(([etac notE, REPEAT_DETERM o rtac exI, atac], [REPEAT_DETERM o rtac exI, atac])
|> k = 1 ? swap |> op @)));
fun mk_half_disc_exclude_tac ctxt m discD disc' =
HEADGOAL (dtac discD THEN' REPEAT_DETERM_N m o etac exE THEN' hyp_subst_tac ctxt THEN'
rtac disc');
fun mk_other_half_disc_exclude_tac half = HEADGOAL (etac @{thm contrapos_pn} THEN' etac half);
fun mk_disc_or_sel_exhaust_tac n exhaust destIs =
HEADGOAL (rtac exhaust THEN'
EVERY' (map2 (fn k => fn destI => dtac destI THEN'
select_prem_tac n (etac meta_mp) k THEN' atac) (1 upto n) destIs));
val mk_disc_exhaust_tac = mk_disc_or_sel_exhaust_tac;
fun mk_sel_exhaust_tac n disc_exhaust collapses =
mk_disc_or_sel_exhaust_tac n disc_exhaust collapses ORELSE
HEADGOAL (etac meta_mp THEN' resolve_tac collapses);
fun mk_collapse_tac ctxt m discD sels =
HEADGOAL (dtac discD THEN'
(if m = 0 then
atac
else
REPEAT_DETERM_N m o etac exE THEN' hyp_subst_tac ctxt THEN'
SELECT_GOAL (unfold_thms_tac ctxt sels) THEN' rtac refl));
fun mk_expand_tac ctxt n ms udisc_exhaust vdisc_exhaust uncollapses disc_excludesss
disc_excludesss' =
if ms = [0] then
HEADGOAL (rtac (@{thm trans_sym} OF (replicate 2 (the_single uncollapses))) THEN'
TRY o EVERY' [rtac udisc_exhaust, atac, rtac vdisc_exhaust, atac])
else
let val ks = 1 upto n in
HEADGOAL (rtac udisc_exhaust THEN'
EVERY' (map5 (fn k => fn m => fn disc_excludess => fn disc_excludess' => fn uuncollapse =>
EVERY' [rtac (uuncollapse RS trans) THEN' TRY o atac, rtac sym, rtac vdisc_exhaust,
EVERY' (map4 (fn k' => fn disc_excludes => fn disc_excludes' => fn vuncollapse =>
EVERY'
(if k' = k then
[rtac (vuncollapse RS trans), TRY o atac] @
(if m = 0 then
[rtac refl]
else
[if n = 1 then K all_tac else EVERY' [dtac meta_mp, atac, dtac meta_mp, atac],
REPEAT_DETERM_N (Int.max (0, m - 1)) o etac conjE,
asm_simp_tac (ss_only [] ctxt)])
else
[dtac (the_single (if k = n then disc_excludes else disc_excludes')),
etac (if k = n then @{thm iff_contradict(1)} else @{thm iff_contradict(2)}),
atac, atac]))
ks disc_excludess disc_excludess' uncollapses)])
ks ms disc_excludesss disc_excludesss' uncollapses))
end;
fun mk_case_same_ctr_tac ctxt injects =
REPEAT_DETERM o etac exE THEN' etac conjE THEN'
(case injects of
[] => atac
| [inject] => dtac (inject RS iffD1) THEN' REPEAT_DETERM o etac conjE THEN'
hyp_subst_tac ctxt THEN' rtac refl);
fun mk_case_distinct_ctrs_tac ctxt distincts =
REPEAT_DETERM o etac exE THEN' etac conjE THEN' full_simp_tac (ss_only distincts ctxt);
fun mk_case_tac ctxt n k case_def injects distinctss =
let
val case_def' = mk_unabs_def (n + 1) (case_def RS meta_eq_to_obj_eq);
val ks = 1 upto n;
in
HEADGOAL (rtac (case_def' RS trans) THEN' rtac @{thm the_equality} THEN'
rtac (mk_disjIN n k) THEN' REPEAT_DETERM o rtac exI THEN' rtac conjI THEN' rtac refl THEN'
rtac refl THEN'
EVERY' (map2 (fn k' => fn distincts =>
(if k' < n then etac disjE else K all_tac) THEN'
(if k' = k then mk_case_same_ctr_tac ctxt injects
else mk_case_distinct_ctrs_tac ctxt distincts)) ks distinctss))
end;
fun mk_case_cong_tac ctxt uexhaust cases =
HEADGOAL (rtac uexhaust THEN'
EVERY' (maps (fn casex => [dtac sym, asm_simp_tac (ss_only [casex] ctxt)]) cases));
fun mk_case_eq_if_tac ctxt n uexhaust cases discss' selss =
HEADGOAL (rtac uexhaust THEN'
EVERY' (map3 (fn casex => fn if_discs => fn sels =>
EVERY' [hyp_subst_tac ctxt, SELECT_GOAL (unfold_thms_tac ctxt (if_discs @ sels)),
rtac casex])
cases (map2 (seq_conds if_P_or_not_P_OF n) (1 upto n) discss') selss));
fun mk_split_tac ctxt uexhaust cases selss injectss distinctsss =
HEADGOAL (rtac uexhaust) THEN
ALLGOALS (fn k => (hyp_subst_tac ctxt THEN'
simp_tac (ss_only (@{thms simp_thms} @ cases @ nth selss (k - 1) @ nth injectss (k - 1) @
flat (nth distinctsss (k - 1))) ctxt)) k) THEN
ALLGOALS (blast_tac (put_claset (claset_of @{theory_context HOL}) ctxt));
val split_asm_thms = @{thms imp_conv_disj de_Morgan_conj de_Morgan_disj not_not not_ex};
fun mk_split_asm_tac ctxt split =
HEADGOAL (rtac (split RS trans)) THEN unfold_thms_tac ctxt split_asm_thms THEN
HEADGOAL (rtac refl);
end;
structure Ctr_Sugar_General_Tactics : CTR_SUGAR_GENERAL_TACTICS = Ctr_Sugar_Tactics;