(* 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_of_dtr_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_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
val falseEs = @{thms not_TrueE FalseE};
val Let_def = @{thm Let_def};
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};
fun mk_primcorec_assumption_tac ctxt discIs =
SELECT_GOAL (unfold_thms_tac ctxt
@{thms 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))));
fun mk_primcorec_same_case_tac m =
HEADGOAL (if m = 0 then rtac TrueI
else REPEAT_DETERM_N (m - 1) o (rtac conjI THEN' atac) THEN' atac);
fun mk_primcorec_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 atac) THEN' mk_primcorec_assumption_tac ctxt []);
fun mk_primcorec_cases_tac ctxt k m exclsss =
let val n = length exclsss in
EVERY (map (fn [] => if k = n then all_tac else mk_primcorec_same_case_tac m
| [excl] => mk_primcorec_different_case_tac ctxt m excl)
(take k (nth exclsss (k - 1))))
end;
fun mk_primcorec_prelude ctxt defs thm =
unfold_thms_tac ctxt defs THEN HEADGOAL (rtac thm) THEN
unfold_thms_tac ctxt @{thms Let_def split};
fun mk_primcorec_disc_tac ctxt defs disc_corec k m exclsss =
mk_primcorec_prelude ctxt defs disc_corec THEN mk_primcorec_cases_tac ctxt k m exclsss;
fun mk_primcorec_sel_tac ctxt defs distincts splits split_asms map_idents map_comps f_sel k m
exclsss =
mk_primcorec_prelude ctxt defs (f_sel RS trans) THEN
mk_primcorec_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 id_def o_def split_def sum.cases} @ map_comps @ map_idents)))));
fun mk_primcorec_ctr_of_dtr_tac ctxt m collapse maybe_disc_f sel_fs =
HEADGOAL (rtac ((if null sel_fs then collapse else collapse RS sym) RS trans) THEN'
(the_default (K all_tac) (Option.map rtac maybe_disc_f)) THEN' REPEAT_DETERM_N m o atac) THEN
unfold_thms_tac ctxt (Let_def :: sel_fs) 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 distinct_in_prems_tac distincts =
eresolve_tac (map (fn thm => thm RS neq_eq_eq_contradict) distincts) THEN' atac;
fun mk_primcorec_raw_code_of_ctr_single_tac ctxt distincts discIs splits split_asms m f_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
mk_primcorec_prelude ctxt [] (f_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_exhaust 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 f_ctrs
maybe_exhaust =
let
val n = length ms;
val (ms', f_ctrs') =
(case maybe_exhaust of
NONE => (ms, f_ctrs)
| SOME exhaust =>
(ms |> split_last ||> K [n - 1] |> op @,
f_ctrs |> split_last ||> (fn thm => [rulify_exhaust n exhaust RS thm]) |> op @));
in
EVERY (map2 (mk_primcorec_raw_code_of_ctr_single_tac ctxt distincts discIs splits split_asms)
ms' f_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 [Let_def]) 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;