(* Title: HOL/BNF/Tools/bnf_fp_rec_sugar_tactics.ML
Author: Jasmin Blanchette, TU Muenchen
Copyright 2013
Tactics for recursor and corecursor sugar.
*)
signature BNF_FP_REC_SUGAR_TACTICS =
sig
val mk_primcorec_assumption_tac: Proof.context -> thm list -> tactic
val mk_primcorec_code_of_ctr_tac: Proof.context -> thm list -> thm list -> thm list -> thm list ->
int list -> thm list -> tactic
val mk_primcorec_code_of_raw_tac: 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_sel_tac: Proof.context -> thm list -> thm list -> thm list -> thm list ->
thm list -> thm list -> thm list -> thm -> int -> int -> thm list list list -> tactic
val mk_primrec_tac: Proof.context -> int -> thm list -> thm list -> thm list -> thm -> tactic
end;
structure BNF_FP_Rec_Sugar_Tactics : BNF_FP_REC_SUGAR_TACTICS =
struct
open BNF_Util
open BNF_Tactics
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};
fun mk_primrec_tac ctxt num_extra_args map_idents map_comps fun_defs recx =
unfold_thms_tac ctxt fun_defs THEN
HEADGOAL (rtac (funpow num_extra_args (fn thm => thm RS fun_cong) recx RS trans)) THEN
unfold_thms_tac ctxt (@{thms id_def split o_def fst_conv snd_conv} @ map_comps @ map_idents) THEN
HEADGOAL (rtac refl);
fun mk_primcorec_assumption_tac ctxt discIs =
HEADGOAL (SELECT_GOAL (unfold_thms_tac ctxt
@{thms not_not not_False_eq_True de_Morgan_conj de_Morgan_disj} THEN
SOLVE (HEADGOAL (REPEAT o (rtac refl ORELSE' atac ORELSE' etac conjE ORELSE'
resolve_tac @{thms TrueI conjI disjI1 disjI2} ORELSE'
dresolve_tac discIs THEN' atac)))));
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 excl =
unfold_thms_tac ctxt @{thms not_not not_False_eq_True not_True_eq_False} THEN
HEADGOAL (rtac excl THEN_ALL_NEW SELECT_GOAL (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 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 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 maps 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
unfold_thms_tac ctxt (@{thms o_def split_def sum.cases} @ maps @ map_comps @ map_idents) THEN
HEADGOAL (REPEAT_DETERM o (rtac refl 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));
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 sel_fs THEN HEADGOAL (rtac refl);
(* TODO: reduce code duplication with selector tactic above *)
fun mk_primcorec_code_of_ctr_single_tac ctxt distincts discIs splits split_asms m f_ctr =
HEADGOAL (REPEAT o (resolve_tac split_connectI ORELSE' split_tac (split_if :: splits))) THEN
mk_primcorec_prelude ctxt [] (f_ctr RS trans) THEN
REPEAT_DETERM_N m (mk_primcorec_assumption_tac ctxt discIs) THEN
HEADGOAL (SELECT_GOAL (HEADGOAL (REPEAT_DETERM o
(rtac refl ORELSE' atac 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'
(TRY o dresolve_tac discIs) THEN' etac notE THEN' atac))));
fun mk_primcorec_code_of_ctr_tac ctxt distincts discIs splits split_asms ms ctr_thms =
EVERY (map2 (mk_primcorec_code_of_ctr_single_tac ctxt distincts discIs splits split_asms)
ms ctr_thms);
fun mk_primcorec_code_of_raw_tac splits disc_excludes raw =
HEADGOAL (rtac raw ORELSE' rtac (raw RS trans) THEN' REPEAT_DETERM o
(rtac refl ORELSE'
(TRY o rtac sym) THEN' atac ORELSE'
resolve_tac split_connectI ORELSE'
Splitter.split_tac (split_if :: splits) ORELSE'
etac notE THEN' atac ORELSE'
(TRY o dresolve_tac disc_excludes) THEN' etac notE THEN' atac));
end;