(* Title: HOL/BNF/Tools/bnf_ctr_sugar_tactics.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2012
Tactics for wrapping existing freely generated type's constructors.
*)
signature BNF_CTR_SUGAR_TACTICS =
sig
val mk_alternate_disc_def_tac: Proof.context -> int -> thm -> thm -> thm -> tactic
val mk_case_cong_tac: Proof.context -> thm -> thm list -> tactic
val mk_case_conv_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_split_tac: Proof.context ->
thm -> thm 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 BNF_Ctr_Sugar_Tactics : BNF_CTR_SUGAR_TACTICS =
struct
open BNF_Util
open BNF_Tactics
val meta_mp = @{thm meta_mp};
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 =
(rtac allI THEN' rtac exhaust THEN'
EVERY' (maps (fn k => [rtac (mk_disjIN n k), REPEAT_DETERM o rtac exI, atac]) (1 upto n))) 1;
fun mk_unique_disc_def_tac m uexhaust =
EVERY' [rtac iffI, rtac uexhaust, REPEAT_DETERM_N m o rtac exI, atac, rtac refl] 1;
fun mk_alternate_disc_def_tac ctxt k other_disc_def distinct uexhaust =
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 @)) 1;
fun mk_half_disc_exclude_tac ctxt m discD disc' =
(dtac discD THEN' REPEAT_DETERM_N m o etac exE THEN' hyp_subst_tac ctxt THEN' rtac disc') 1;
fun mk_other_half_disc_exclude_tac half = (etac @{thm contrapos_pn} THEN' etac half) 1;
fun mk_disc_exhaust_tac n exhaust discIs =
(rtac exhaust THEN'
EVERY' (map2 (fn k => fn discI =>
dtac discI THEN' select_prem_tac n (etac meta_mp) k THEN' atac) (1 upto n) discIs)) 1;
fun mk_collapse_tac ctxt m discD sels =
(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)) 1;
fun mk_expand_tac ctxt n ms udisc_exhaust vdisc_exhaust uncollapses disc_excludesss
disc_excludesss' =
if ms = [0] then
(rtac (@{thm trans_sym} OF (replicate 2 (the_single uncollapses))) THEN'
TRY o EVERY' [rtac udisc_exhaust, atac, rtac vdisc_exhaust, atac]) 1
else
let val ks = 1 upto n in
(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)) 1
end;
fun mk_case_conv_tac ctxt n uexhaust cases discss' selss =
(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)) 1;
fun mk_case_cong_tac ctxt uexhaust cases =
(rtac uexhaust THEN'
EVERY' (maps (fn casex => [dtac sym, asm_simp_tac (ss_only [casex] ctxt)]) cases)) 1;
val naked_ctxt = @{theory_context HOL};
(* TODO: More precise "simp_thms"; get rid of "blast_tac" *)
fun mk_split_tac ctxt uexhaust cases injectss distinctsss =
rtac uexhaust 1 THEN
ALLGOALS (fn k => (hyp_subst_tac ctxt THEN'
simp_tac (ss_only (@{thms simp_thms} @ cases @ nth injectss (k - 1) @
flat (nth distinctsss (k - 1))) ctxt)) k) THEN
ALLGOALS (blast_tac naked_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 =
rtac (split RS trans) 1 THEN unfold_thms_tac ctxt split_asm_thms THEN rtac refl 1;
end;