theory Tacs

imports Main

begin

(* General not-nominal/quotient functionality useful for proving *)

(* A version of case_rule_tac that takes more exhaust rules *)

ML {*

fun case_rules_tac ctxt0 s rules i st =

let

  val (_, ctxt) = Variable.focus_subgoal i st ctxt0;

  val ty = fastype_of (ProofContext.read_term_schematic ctxt s)

  fun exhaust_ty thm = fastype_of (hd (Induct.vars_of (Thm.term_of (Thm.cprem_of thm 1))));

  val ty_rules = filter (fn x => exhaust_ty x = ty) rules;

in

  InductTacs.case_rule_tac ctxt0 s (hd ty_rules) i st

end

*}

ML {*

fun mk_conjl props =

  fold (fn a => fn b =>

    if a = @{term True} then b else

    if b = @{term True} then a else

    HOLogic.mk_conj (a, b)) (rev props) @{term True};

*}

ML {*

val split_conj_tac = REPEAT o etac conjE THEN' TRY o REPEAT_ALL_NEW (CHANGED o rtac conjI)

*}

ML {*

fun prove_by_rel_induct alphas build_goal ind utac inputs ctxt =

let

  val tys = map (domain_type o fastype_of) alphas;

  val names = Datatype_Prop.make_tnames tys;

  val (namesl, ctxt') = Variable.variant_fixes names ctxt;

  val (namesr, ctxt'') = Variable.variant_fixes names ctxt';

  val freesl = map Free (namesl ~~ tys);

  val freesr = map Free (namesr ~~ tys);

  val (gls_lists, ctxt'') = fold_map (build_goal (tys ~~ (freesl ~~ freesr))) inputs ctxt'';

  val gls = flat gls_lists;

  fun trm_gls_map t = filter (exists_subterm (fn s => s = t)) gls;

  val trm_gl_lists = map trm_gls_map freesl;

  val trm_gls = map mk_conjl trm_gl_lists;

  val pgls = map

    (fn ((alpha, gl), (l, r)) => HOLogic.mk_imp (alpha $ l $ r, gl)) 

    ((alphas ~~ trm_gls) ~~ (freesl ~~ freesr))

  val gl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj pgls);

  fun tac {context,...} = (rtac ind THEN_ALL_NEW split_conj_tac THEN_ALL_NEW

    TRY o rtac @{thm TrueI} THEN_ALL_NEW utac context) 1

  val th_loc = Goal.prove ctxt'' [] [] gl tac

  val ths_loc = HOLogic.conj_elims th_loc

  val ths = Variable.export ctxt'' ctxt ths_loc

in

  filter (fn x => not (prop_of x = prop_of @{thm TrueI})) ths

end

*}

ML {*

fun repeat_mp thm = repeat_mp (mp OF [thm]) handle THM _ => thm

*}

(* Introduces an implication and immediately eliminates it by cases *)

ML {*

fun imp_elim_tac case_rules =

  Subgoal.FOCUS (fn {concl, context, ...} =>

    case term_of concl of

      _ $ (_ $ asm $ _) =>

        let

          fun filter_fn case_rule = (

            case Logic.strip_assums_hyp (prop_of case_rule) of

              ((_ $ asmc) :: _) =>

                let

                  val thy = ProofContext.theory_of context

                in

                  Pattern.matches thy (asmc, asm)

                end

            | _ => false)

          val matching_rules = filter filter_fn case_rules

        in

         (rtac impI THEN' rotate_tac (~1) THEN' eresolve_tac matching_rules) 1

        end

    | _ => no_tac)

*}

ML {*

fun is_ex (Const ("Ex", _) $ Abs _) = true

  | is_ex _ = false;

*}

ML {*

fun dtyp_no_of_typ _ (TFree (_, _)) = error "dtyp_no_of_typ: Illegal free"

  | dtyp_no_of_typ _ (TVar _) = error "dtyp_no_of_typ: Illegal schematic"

  | dtyp_no_of_typ dts (Type (tname, _)) =

      case try (find_index (curry op = tname o fst)) dts of

        NONE => error "dtyp_no_of_typ: Illegal recursion"

      | SOME i => i

*}

end