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(* 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: Proof.context -> 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_distrib_tac: Proof.context -> cterm -> 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_eq_case_tac: Proof.context -> cterm -> thm -> thm list -> thm list -> thm list ->
tactic
val mk_exhaust_disc_tac: Proof.context -> int -> thm -> thm list -> tactic
val mk_exhaust_sel_tac: Proof.context -> 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_distinct_disc_tac: Proof.context -> int -> thm -> thm -> tactic
val mk_nchotomy_tac: Proof.context -> int -> thm -> tactic
val mk_other_half_distinct_disc_tac: Proof.context -> thm -> 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: Proof.context -> 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 ctxt n tac k = DETERM o (EVERY' [REPEAT_DETERM_N (k - 1) o etac ctxt thin_rl,
tac, REPEAT_DETERM_N (n - k) o etac ctxt thin_rl]);
val unfold_thms_tac = Local_Defs.unfold0_tac;
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 ctxt n exhaust =
HEADGOAL (rtac ctxt allI THEN' rtac ctxt exhaust THEN'
EVERY' (maps (fn k =>
[rtac ctxt (mk_disjIN n k), REPEAT_DETERM o rtac ctxt exI, assume_tac ctxt])
(1 upto n)));
fun mk_unique_disc_def_tac ctxt m uexhaust =
HEADGOAL (EVERY'
[rtac ctxt iffI, rtac ctxt uexhaust, REPEAT_DETERM_N m o rtac ctxt exI,
assume_tac ctxt, rtac ctxt refl]);
fun mk_alternate_disc_def_tac ctxt k other_disc_def distinct uexhaust =
HEADGOAL (EVERY' ([rtac ctxt (other_disc_def RS @{thm arg_cong[of _ _ Not]} RS trans),
rtac ctxt @{thm iffI_np}, REPEAT_DETERM o etac ctxt exE,
hyp_subst_tac ctxt, SELECT_GOAL (unfold_thms_tac ctxt [not_ex]), REPEAT_DETERM o rtac ctxt allI,
rtac ctxt distinct, rtac ctxt uexhaust] @
(([etac ctxt notE, REPEAT_DETERM o rtac ctxt exI, assume_tac ctxt],
[REPEAT_DETERM o rtac ctxt exI, assume_tac ctxt])
|> k = 1 ? swap |> op @)));
fun mk_half_distinct_disc_tac ctxt m discD disc' =
HEADGOAL (dtac ctxt discD THEN' REPEAT_DETERM_N m o etac ctxt exE THEN' hyp_subst_tac ctxt THEN'
rtac ctxt disc');
fun mk_other_half_distinct_disc_tac ctxt half =
HEADGOAL (etac ctxt @{thm contrapos_pn} THEN' etac ctxt half);
fun mk_exhaust_disc_or_sel_tac ctxt n exhaust destIs =
HEADGOAL (rtac ctxt exhaust THEN'
EVERY' (map2 (fn k => fn destI => dtac ctxt destI THEN'
select_prem_tac ctxt n (etac ctxt meta_mp) k THEN' assume_tac ctxt) (1 upto n) destIs));
val mk_exhaust_disc_tac = mk_exhaust_disc_or_sel_tac;
fun mk_exhaust_sel_tac ctxt n exhaust_disc collapses =
mk_exhaust_disc_or_sel_tac ctxt n exhaust_disc collapses ORELSE
HEADGOAL (etac ctxt meta_mp THEN' resolve_tac ctxt collapses);
fun mk_collapse_tac ctxt m discD sels =
HEADGOAL (dtac ctxt discD THEN'
(if m = 0 then
assume_tac ctxt
else
REPEAT_DETERM_N m o etac ctxt exE THEN' hyp_subst_tac ctxt THEN'
SELECT_GOAL (unfold_thms_tac ctxt sels) THEN' rtac ctxt refl));
fun mk_disc_eq_case_tac ctxt ct exhaust discs distincts cases =
HEADGOAL Goal.conjunction_tac THEN
ALLGOALS (rtac ctxt (infer_instantiate' ctxt [SOME ct] exhaust) THEN_ALL_NEW
(hyp_subst_tac ctxt THEN'
SELECT_GOAL (unfold_thms_tac ctxt (@{thms not_True_eq_False not_False_eq_True} @ cases @
((refl :: discs @ distincts) RL [eqTrueI, eqFalseI]))) THEN'
resolve_tac ctxt @{thms TrueI True_not_False False_not_True}));
fun mk_expand_tac ctxt n ms uexhaust_disc vexhaust_disc uncollapses distinct_discsss
distinct_discsss' =
if ms = [0] then
HEADGOAL (rtac ctxt (@{thm trans_sym} OF (replicate 2 (the_single uncollapses))) THEN'
TRY o
EVERY' [rtac ctxt uexhaust_disc, assume_tac ctxt, rtac ctxt vexhaust_disc, assume_tac ctxt])
else
let val ks = 1 upto n in
HEADGOAL (rtac ctxt uexhaust_disc THEN'
EVERY' (@{map 5} (fn k => fn m => fn distinct_discss => fn distinct_discss' =>
fn uuncollapse =>
EVERY' [rtac ctxt (uuncollapse RS trans) THEN'
TRY o assume_tac ctxt, rtac ctxt sym, rtac ctxt vexhaust_disc,
EVERY' (@{map 4} (fn k' => fn distinct_discs => fn distinct_discs' => fn vuncollapse =>
EVERY'
(if k' = k then
[rtac ctxt (vuncollapse RS trans), TRY o assume_tac ctxt] @
(if m = 0 then
[rtac ctxt refl]
else
[if n = 1 then
K all_tac
else
EVERY' [dtac ctxt meta_mp, assume_tac ctxt, dtac ctxt meta_mp,
assume_tac ctxt],
REPEAT_DETERM_N (Int.max (0, m - 1)) o etac ctxt conjE,
asm_simp_tac (ss_only [] ctxt)])
else
[dtac ctxt (the_single (if k = n then distinct_discs else distinct_discs')),
etac ctxt (if k = n then @{thm iff_contradict(1)}
else @{thm iff_contradict(2)}),
assume_tac ctxt, assume_tac ctxt]))
ks distinct_discss distinct_discss' uncollapses)])
ks ms distinct_discsss distinct_discsss' uncollapses))
end;
fun mk_case_same_ctr_tac ctxt injects =
REPEAT_DETERM o etac ctxt exE THEN' etac ctxt conjE THEN'
(case injects of
[] => assume_tac ctxt
| [inject] => dtac ctxt (inject RS iffD1) THEN' REPEAT_DETERM o etac ctxt conjE THEN'
hyp_subst_tac ctxt THEN' rtac ctxt refl);
fun mk_case_distinct_ctrs_tac ctxt distincts =
REPEAT_DETERM o etac ctxt exE THEN' etac ctxt 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) (HOLogic.mk_obj_eq case_def);
val ks = 1 upto n;
in
HEADGOAL (rtac ctxt (case_def' RS trans) THEN' rtac ctxt @{thm the_equality} THEN'
rtac ctxt (mk_disjIN n k) THEN' REPEAT_DETERM o rtac ctxt exI THEN' rtac ctxt conjI THEN'
rtac ctxt refl THEN' rtac ctxt refl THEN'
EVERY' (map2 (fn k' => fn distincts =>
(if k' < n then etac ctxt 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_distrib_tac ctxt ct exhaust cases =
HEADGOAL (rtac ctxt (infer_instantiate' ctxt [SOME ct] exhaust)) THEN
ALLGOALS (hyp_subst_tac ctxt THEN' SELECT_GOAL (unfold_thms_tac ctxt cases) THEN' rtac ctxt refl);
fun mk_case_cong_tac ctxt uexhaust cases =
HEADGOAL (rtac ctxt uexhaust THEN'
EVERY' (maps (fn casex => [dtac ctxt sym, asm_simp_tac (ss_only [casex] ctxt)]) cases));
fun mk_case_eq_if_tac ctxt n uexhaust cases discss' selss =
HEADGOAL (rtac ctxt uexhaust THEN'
EVERY' (@{map 3} (fn casex => fn if_discs => fn sels =>
EVERY' [hyp_subst_tac ctxt, SELECT_GOAL (unfold_thms_tac ctxt (if_discs @ sels)),
rtac ctxt 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 ctxt 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 (etac ctxt thin_rl THEN' rtac ctxt iffI THEN'
REPEAT_DETERM o rtac ctxt allI THEN' rtac ctxt impI THEN'
REPEAT_DETERM o etac ctxt conjE THEN'
hyp_subst_tac ctxt THEN' assume_tac ctxt THEN'
REPEAT_DETERM o etac ctxt allE THEN' etac ctxt impE THEN'
REPEAT_DETERM o (rtac ctxt conjI THEN' rtac ctxt refl) THEN'
rtac ctxt refl THEN' assume_tac 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 ctxt (split RS trans)) THEN unfold_thms_tac ctxt split_asm_thms THEN
HEADGOAL (rtac ctxt refl);
end;
structure Ctr_Sugar_General_Tactics : CTR_SUGAR_GENERAL_TACTICS = Ctr_Sugar_Tactics;
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