(* 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 -> 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 nesting_rel_eqs0
nesting_rel_monos0 {context = ctxt, prems = raw_C_IHs} =
let
val nesting_rel_eqs = @{thms prod.rel_eq sum.rel_eq} @ nesting_rel_eqs0;
val nesting_rel_monos = map (fn thm => rotate_prems ~1 (thm RS @{thm predicate2D}))
(@{thms prod.rel_mono sum.rel_mono} @ nesting_rel_monos0);
val co_inducts = map (unfold_thms ctxt (vimage2p_unfolds @ nesting_rel_eqs)) 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 =
@{map 3} (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 ctxt @{thm context_conjI})
(fn thm => rtac ctxt thm THEN_ALL_NEW (rotate_tac ~1 THEN'
REPEAT_ALL_NEW (FIRST' [eresolve_tac ctxt C_IHs, eresolve_tac ctxt C_IH_monos,
SELECT_GOAL (unfold_thms_tac ctxt nesting_rel_eqs) THEN' rtac ctxt @{thm order_refl},
assume_tac ctxt, resolve_tac ctxt co_inducts,
resolve_tac ctxt C_IH_monos THEN' REPEAT_ALL_NEW (eresolve_tac ctxt nesting_rel_monos)])))
co_inducts)
end;
end;