src/HOL/Tools/BNF/bnf_fp_n2m_tactics.ML

tuned signature;

(*  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 @{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,
           SELECT_GOAL (unfold_thms_tac ctxt nesting_rel_eqs) THEN' rtac @{thm order_refl},
           assume_tac ctxt, resolve_tac co_inducts,
           resolve_tac C_IH_monos THEN' REPEAT_ALL_NEW (eresolve_tac nesting_rel_monos)])))
    co_inducts)
  end;

end;