strengthened tactics w.r.t. 'lets' and tuples
(* Title: HOL/BNF/Tools/bnf_gfp_rec_sugar_tactics.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2013
Tactics for corecursor sugar.
*)
signature BNF_GFP_REC_SUGAR_TACTICS =
sig
val mk_primcorec_assumption_tac: Proof.context -> thm list -> int -> tactic
val mk_primcorec_code_of_raw_code_tac: Proof.context -> thm list -> thm list -> thm -> tactic
val mk_primcorec_ctr_tac: Proof.context -> int -> thm -> thm option -> thm list -> tactic
val mk_primcorec_disc_tac: Proof.context -> thm list -> thm -> int -> int -> thm list list list ->
tactic
val mk_primcorec_disc_iff_tac: Proof.context -> string list -> thm -> thm -> thm list list ->
thm list -> tactic
val mk_primcorec_exhaust_tac: Proof.context -> string list -> int -> thm -> tactic
val mk_primcorec_nchotomy_tac: Proof.context -> thm list -> tactic
val mk_primcorec_raw_code_of_ctr_tac: Proof.context -> thm list -> thm list -> thm list ->
thm list -> int list -> thm list -> thm option -> tactic
val mk_primcorec_sel_tac: Proof.context -> thm list -> thm list -> thm list -> thm list ->
thm list -> thm list -> thm -> int -> int -> thm list list list -> tactic
end;
structure BNF_GFP_Rec_Sugar_Tactics : BNF_GFP_REC_SUGAR_TACTICS =
struct
open BNF_Util
open BNF_Tactics
open BNF_FP_Util
val atomize_conjL = @{thm atomize_conjL};
val falseEs = @{thms not_TrueE FalseE};
val neq_eq_eq_contradict = @{thm neq_eq_eq_contradict};
val split_if = @{thm split_if};
val split_if_asm = @{thm split_if_asm};
val split_connectI = @{thms allI impI conjI};
val unfold_lets = @{thms Let_def[abs_def] split_beta}
fun exhaust_inst_as_projs ctxt frees thm =
let
val num_frees = length frees;
val fs = Term.add_vars (prop_of thm) [] |> filter (can dest_funT o snd);
fun find s = find_index (curry (op =) s) frees;
fun mk_cfp (f as ((s, _), T)) =
(certify ctxt (Var f), certify ctxt (mk_proj T num_frees (find s)));
val cfps = map mk_cfp fs;
in
Drule.cterm_instantiate cfps thm
end;
val exhaust_inst_as_projs_tac = PRIMITIVE oo exhaust_inst_as_projs;
fun distinct_in_prems_tac distincts =
eresolve_tac (map (fn thm => thm RS neq_eq_eq_contradict) distincts) THEN' atac;
fun mk_primcorec_nchotomy_tac ctxt disc_exhausts =
HEADGOAL (Method.insert_tac disc_exhausts THEN' clean_blast_tac ctxt);
fun mk_primcorec_exhaust_tac ctxt frees n nchotomy =
let val ks = 1 upto n in
HEADGOAL (atac ORELSE'
cut_tac nchotomy THEN'
K (exhaust_inst_as_projs_tac ctxt frees) THEN'
EVERY' (map (fn k =>
(if k < n then etac disjE else K all_tac) THEN'
REPEAT o (dtac meta_mp THEN' atac ORELSE'
etac conjE THEN' dtac meta_mp THEN' atac ORELSE'
atac))
ks))
end;
fun mk_primcorec_assumption_tac ctxt discIs =
SELECT_GOAL (unfold_thms_tac ctxt @{thms fst_conv snd_conv not_not not_False_eq_True
not_True_eq_False de_Morgan_conj de_Morgan_disj} THEN
SOLVE (HEADGOAL (REPEAT o (rtac refl ORELSE' atac ORELSE' etac conjE ORELSE'
eresolve_tac falseEs ORELSE'
resolve_tac @{thms TrueI conjI disjI1 disjI2} ORELSE'
dresolve_tac discIs THEN' atac ORELSE'
etac notE THEN' atac ORELSE'
etac disjE))));
val ss_fst_snd_conv = simpset_of (ss_only @{thms fst_conv snd_conv} @{context});
fun case_atac ctxt = simp_tac (put_simpset ss_fst_snd_conv ctxt);
fun same_case_tac ctxt m =
HEADGOAL (if m = 0 then rtac TrueI
else REPEAT_DETERM_N (m - 1) o (rtac conjI THEN' case_atac ctxt) THEN' case_atac ctxt);
fun different_case_tac ctxt m excl =
HEADGOAL (if m = 0 then
mk_primcorec_assumption_tac ctxt []
else
dtac excl THEN' (REPEAT_DETERM_N (m - 1) o case_atac ctxt) THEN'
mk_primcorec_assumption_tac ctxt []);
fun cases_tac ctxt k m exclsss =
let val n = length exclsss in
EVERY (map (fn [] => if k = n then all_tac else same_case_tac ctxt m
| [excl] => different_case_tac ctxt m excl)
(take k (nth exclsss (k - 1))))
end;
fun prelude_tac ctxt defs thm =
unfold_thms_tac ctxt defs THEN HEADGOAL (rtac thm) THEN unfold_thms_tac ctxt unfold_lets;
fun mk_primcorec_disc_tac ctxt defs disc_corec k m exclsss =
prelude_tac ctxt defs disc_corec THEN cases_tac ctxt k m exclsss;
fun mk_primcorec_disc_iff_tac ctxt frees fun_exhaust fun_disc fun_discss disc_excludes =
HEADGOAL (rtac iffI THEN'
rtac fun_exhaust THEN'
K (exhaust_inst_as_projs_tac ctxt frees) THEN'
EVERY' (map (fn [] => etac FalseE
| [fun_disc'] =>
if Thm.eq_thm (fun_disc', fun_disc) then
REPEAT_DETERM o etac conjI THEN' (atac ORELSE' rtac TrueI)
else
rtac FalseE THEN' rotate_tac 1 THEN' dtac fun_disc' THEN' REPEAT_DETERM o atac THEN'
dresolve_tac disc_excludes THEN' etac notE THEN' atac)
fun_discss) THEN'
rtac (unfold_thms ctxt [atomize_conjL] fun_disc) THEN_MAYBE' atac);
fun mk_primcorec_sel_tac ctxt defs distincts splits split_asms map_idents map_comps fun_sel k m
exclsss =
prelude_tac ctxt defs (fun_sel RS trans) THEN
cases_tac ctxt k m exclsss THEN
HEADGOAL (REPEAT_DETERM o (rtac refl ORELSE' rtac ext ORELSE'
eresolve_tac falseEs ORELSE'
resolve_tac split_connectI ORELSE'
Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'
Splitter.split_tac (split_if :: splits) ORELSE'
eresolve_tac (map (fn thm => thm RS neq_eq_eq_contradict) distincts) THEN' atac ORELSE'
etac notE THEN' atac ORELSE'
(CHANGED o SELECT_GOAL (unfold_thms_tac ctxt
(@{thms fst_conv snd_conv id_def o_def split_def sum.cases} @ map_comps @ map_idents)))));
fun mk_primcorec_ctr_tac ctxt m collapse disc_fun_opt sel_funs =
HEADGOAL (rtac ((if null sel_funs then collapse else collapse RS sym) RS trans) THEN'
(the_default (K all_tac) (Option.map rtac disc_fun_opt)) THEN' REPEAT_DETERM_N m o atac) THEN
unfold_thms_tac ctxt (unfold_lets @ sel_funs) THEN HEADGOAL (rtac refl);
fun inst_split_eq ctxt split =
(case prop_of split of
@{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ (Var (_, Type (_, [T, _])) $ _) $ _) =>
let
val s = Name.uu;
val eq = Abs (Name.uu, T, HOLogic.mk_eq (Free (s, T), Bound 0));
val split' = Drule.instantiate' [] [SOME (certify ctxt eq)] split;
in
Thm.generalize ([], [s]) (Thm.maxidx_of split' + 1) split'
end
| _ => split);
fun raw_code_of_ctr_single_tac ctxt distincts discIs splits split_asms m fun_ctr =
let
val splits' =
map (fn th => th RS iffD2) (@{thm split_if_eq2} :: map (inst_split_eq ctxt) splits)
in
HEADGOAL (REPEAT o (resolve_tac (splits' @ split_connectI))) THEN
prelude_tac ctxt [] (fun_ctr RS trans) THEN
HEADGOAL ((REPEAT_DETERM_N m o mk_primcorec_assumption_tac ctxt discIs) THEN'
SELECT_GOAL (SOLVE (HEADGOAL (REPEAT_DETERM o
(rtac refl ORELSE' atac ORELSE'
resolve_tac (@{thm Code.abort_def} :: split_connectI) ORELSE'
Splitter.split_tac (split_if :: splits) ORELSE'
Splitter.split_asm_tac (split_if_asm :: split_asms) ORELSE'
mk_primcorec_assumption_tac ctxt discIs ORELSE'
distinct_in_prems_tac distincts ORELSE'
(TRY o dresolve_tac discIs) THEN' etac notE THEN' atac)))))
end;
fun rulify_nchotomy n = funpow (n - 1) (fn thm => thm RS @{thm Meson.make_pos_rule'});
fun mk_primcorec_raw_code_of_ctr_tac ctxt distincts discIs splits split_asms ms fun_ctrs
nchotomy_opt =
let
val n = length ms;
val (ms', fun_ctrs') =
(case nchotomy_opt of
NONE => (ms, fun_ctrs)
| SOME nchotomy =>
(ms |> split_last ||> K [n - 1] |> op @,
fun_ctrs
|> split_last
||> unfold_thms ctxt [atomize_conjL]
||> (fn thm => [rulify_nchotomy n nchotomy RS thm] handle THM _ => [thm])
|> op @));
in
EVERY (map2 (raw_code_of_ctr_single_tac ctxt distincts discIs splits split_asms)
ms' fun_ctrs') THEN
IF_UNSOLVED (unfold_thms_tac ctxt @{thms Code.abort_def} THEN
HEADGOAL (REPEAT_DETERM o resolve_tac (refl :: split_connectI)))
end;
fun mk_primcorec_code_of_raw_code_tac ctxt distincts splits raw =
HEADGOAL (rtac raw ORELSE' rtac (raw RS trans) THEN'
SELECT_GOAL (unfold_thms_tac ctxt unfold_lets) THEN' REPEAT_DETERM o
(rtac refl ORELSE' atac ORELSE'
resolve_tac split_connectI ORELSE'
Splitter.split_tac (split_if :: splits) ORELSE'
distinct_in_prems_tac distincts ORELSE'
rtac sym THEN' atac ORELSE'
etac notE THEN' atac));
end;