(*  Title:      HOL/Codatatype/Tools/bnf_fp_sugar.ML

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2012

Sugar for constructing LFPs and GFPs.

*)

signature BNF_FP_SUGAR =

sig

end;

structure BNF_FP_Sugar : BNF_FP_SUGAR =

struct

open BNF_Util

open BNF_Wrap

open BNF_FP_Util

open BNF_LFP

open BNF_GFP

open BNF_FP_Sugar_Tactics

fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";

fun merge_type_arg_constrained ctxt (T, c) (T', c') =

  if T = T' then

    (case (c, c') of

      (_, NONE) => (T, c)

    | (NONE, _) => (T, c')

    | _ =>

      if c = c' then

        (T, c)

      else

        error ("Inconsistent sort constraints for type variable " ^

          quote (Syntax.string_of_typ ctxt T)))

  else

    cannot_merge_types ();

fun merge_type_args_constrained ctxt (cAs, cAs') =

  if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs'

  else cannot_merge_types ();

fun type_args_constrained_of (((cAs, _), _), _) = cAs;

val type_args_of = map fst o type_args_constrained_of;

fun type_name_of (((_, b), _), _) = b;

fun mixfix_of_typ ((_, mx), _) = mx;

fun ctr_specs_of (_, ctr_specs) = ctr_specs;

fun disc_of (((disc, _), _), _) = disc;

fun ctr_of (((_, ctr), _), _) = ctr;

fun args_of ((_, args), _) = args;

fun mixfix_of_ctr (_, mx) = mx;

val lfp_info = bnf_lfp;

val gfp_info = bnf_gfp;

fun prepare_data prepare_typ construct specs fake_lthy lthy =

  let

    val constrained_As =

      map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs

      |> Library.foldr1 (merge_type_args_constrained lthy);

    val As = map fst constrained_As;

    val _ = (case duplicates (op =) As of [] => ()

      | T :: _ => error ("Duplicate type parameter " ^ quote (Syntax.string_of_typ lthy T)));

    (* TODO: check that no type variables occur in the rhss that's not in the lhss *)

    (* TODO: use sort constraints on type args *)

    val N = length specs;

    fun mk_T b =

      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),

        As);

    val bs = map type_name_of specs;

    val Ts = map mk_T bs;

    val mixfixes = map mixfix_of_typ specs;

    val _ = (case duplicates Binding.eq_name bs of [] => ()

      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));

    val ctr_specss = map ctr_specs_of specs;

    val disc_namess = map (map disc_of) ctr_specss;

    val ctr_namess = map (map ctr_of) ctr_specss;

    val ctr_argsss = map (map args_of) ctr_specss;

    val ctr_mixfixess = map (map mixfix_of_ctr) ctr_specss;

    val sel_namesss = map (map (map fst)) ctr_argsss;

    val ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;

    val (Bs, C) =

      lthy

      |> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs

      |> mk_TFrees N

      ||> the_single o fst o mk_TFrees 1;

    fun freeze_rec (T as Type (s, Ts')) =

        (case find_index (curry (op =) T) Ts of

          ~1 => Type (s, map freeze_rec Ts')

        | i => nth Bs i)

      | freeze_rec T = T;

    val ctr_TsssBs = map (map (map freeze_rec)) ctr_Tsss;

    val sum_prod_TsBs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssBs;

    val eqs = map dest_TFree Bs ~~ sum_prod_TsBs;

    val ((raw_unfs, raw_flds, unf_flds, fld_unfs, fld_injects), lthy') =

      fp_bnf construct bs eqs lthy;

    fun mk_unf_or_fld get_foldedT Ts t =

      let val Type (_, Ts0) = get_foldedT (fastype_of t) in

        Term.subst_atomic_types (Ts0 ~~ Ts) t

      end;

    val mk_unf = mk_unf_or_fld domain_type;

    val mk_fld = mk_unf_or_fld range_type;

    val unfs = map (mk_unf As) raw_unfs;

    val flds = map (mk_fld As) raw_flds;

    fun wrap_type (((((((((T, fld), unf), fld_unf), unf_fld), fld_inject), ctr_names), ctr_Tss),

        disc_names), sel_namess) no_defs_lthy =

      let

        val n = length ctr_names;

        val ks = 1 upto n;

        val ms = map length ctr_Tss;

        val unf_T = domain_type (fastype_of fld);

        val prod_Ts = map HOLogic.mk_tupleT ctr_Tss;

        val (((u, v), xss), _) =

          lthy

          |> yield_singleton (mk_Frees "u") unf_T

          ||>> yield_singleton (mk_Frees "v") T

          ||>> mk_Freess "x" ctr_Tss;

        val rhss =

          map2 (fn k => fn xs =>

            fold_rev Term.lambda xs (fld $ mk_InN prod_Ts (HOLogic.mk_tuple xs) k)) ks xss;

        val ((raw_ctrs, raw_ctr_defs), (lthy', lthy)) = no_defs_lthy

          |> apfst split_list o fold_map2 (fn b => fn rhs =>

               Local_Theory.define ((b, NoSyn), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)

             ctr_names rhss

          ||> `Local_Theory.restore;

        val raw_caseof =

          Const (@{const_name undefined}, map (fn Ts => Ts ---> C) ctr_Tss ---> T --> C);

        (*transforms defined frees into consts (and more)*)

        val phi = Proof_Context.export_morphism lthy lthy';

        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;

        val ctrs = map (Morphism.term phi) raw_ctrs;

        val caseof = Morphism.term phi raw_caseof;

        val fld_iff_unf_thm =

          let

            val goal =

              fold_rev Logic.all [u, v]

                (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));

          in

            Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>

              mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unf_T, T]) (certify lthy fld)

                (certify lthy unf) fld_unf unf_fld)

            |> Thm.close_derivation

          end;

        val sumEN_thm = mk_sumEN n;

        val sumEN_thm' =

          let val cTs = map (SOME o certifyT lthy) prod_Ts in

            Local_Defs.unfold lthy @{thms all_unit_eq} (Drule.instantiate' cTs [] sumEN_thm)

          end;

        fun exhaust_tac {context = ctxt, ...} =

          mk_exhaust_tac ctxt n ms ctr_defs fld_iff_unf_thm sumEN_thm';

        val inject_tacss =

          map2 (fn 0 => K []

                 | _ => fn ctr_def => [fn {context = ctxt, ...} =>

                     mk_inject_tac ctxt ctr_def fld_inject])

            ms ctr_defs;

        (*###*)

        fun cheat_tac {context = ctxt, ...} = Skip_Proof.cheat_tac (Proof_Context.theory_of ctxt);

        val half_distinct_tacss = map (map (K cheat_tac)) (mk_half_pairss ks);

        val case_tacs = map (K cheat_tac) ks;

        val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];

      in

        wrap_data tacss ((ctrs, caseof), (disc_names, sel_namess)) lthy'

      end;

  in

    lthy'

    |> fold wrap_type (Ts ~~ flds ~~ unfs ~~ fld_unfs ~~ unf_flds ~~ fld_injects ~~ ctr_namess ~~

      ctr_Tsss ~~ disc_namess ~~ sel_namesss)

  end;

fun data_cmd info specs lthy =

  let

    val fake_lthy =

      Proof_Context.theory_of lthy

      |> Theory.copy

      |> Sign.add_types_global (map (fn spec =>

        (type_name_of spec, length (type_args_constrained_of spec), mixfix_of_typ spec)) specs)

      |> Proof_Context.init_global

  in

    prepare_data Syntax.read_typ info specs fake_lthy lthy

  end;

val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_name

val parse_ctr_arg =

  Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" ||

  (Parse.typ >> pair no_name);

val parse_single_spec =

  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --

  (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --

    Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));

val _ =

  Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"

    (Parse.and_list1 parse_single_spec >> data_cmd lfp_info);

val _ =

  Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"

    (Parse.and_list1 parse_single_spec >> data_cmd gfp_info);

end;