(* Title: HOL/Tools/BNF/bnf_fp_n2m_tactics.ML
Author: Dmitriy Traytel, TU Muenchen
Copyright 2013
Tactics for mutualization of nested (co)datatypes.
*)
signature BNF_FP_N2M_TACTICS =
sig
val mk_rel_xtor_co_induct_tactic: BNF_Util.fp_kind -> thm list -> thm list -> thm list ->
thm list -> {prems: thm list, context: Proof.context} -> tactic
end;
structure BNF_FP_N2M_Tactics : BNF_FP_N2M_TACTICS =
struct
open BNF_Util
open BNF_Tactics
open BNF_FP_Util
val vimage2p_unfolds = o_apply :: @{thms vimage2p_def};
fun mk_rel_xtor_co_induct_tactic fp abs_inverses co_inducts0 rel_defs rel_monos
{context = ctxt, prems = raw_C_IHs} =
let
val co_inducts = map (unfold_thms ctxt vimage2p_unfolds) co_inducts0;
val unfolds = map (fn def =>
unfold_thms ctxt (id_apply :: vimage2p_unfolds @ abs_inverses @ no_reflexive [def])) rel_defs;
val folded_C_IHs = map (fn thm => thm RS @{thm spec2} RS mp) raw_C_IHs;
val C_IHs = map2 (curry op |>) folded_C_IHs unfolds;
val C_IH_monos =
map3 (fn C_IH => fn mono => fn unfold =>
(mono RSN (2, @{thm vimage2p_mono}), C_IH)
|> fp = Greatest_FP ? swap
|> op RS
|> unfold)
folded_C_IHs rel_monos unfolds;
in
unfold_thms_tac ctxt vimage2p_unfolds THEN
HEADGOAL (CONJ_WRAP_GEN' (rtac @{thm context_conjI})
(fn thm => rtac thm THEN_ALL_NEW (rotate_tac ~1 THEN'
REPEAT_ALL_NEW (FIRST' [eresolve_tac C_IHs, eresolve_tac C_IH_monos,
rtac @{thm order_refl}, atac, resolve_tac co_inducts])))
co_inducts)
end;
end;