(*  Title:      HOL/BNF/Tools/bnf_fp_rec_sugar_util.ML

    Author:     Lorenz Panny, TU Muenchen

    Author:     Jasmin Blanchette, TU Muenchen

    Copyright   2013

Library for recursor and corecursor sugar.

*)

signature BNF_FP_REC_SUGAR_UTIL =

sig

  val indexed: 'a list -> int -> int list * int

  val indexedd: 'a list list -> int -> int list list * int

  val indexeddd: ''a list list list -> int -> int list list list * int

  val indexedddd: 'a list list list list -> int -> int list list list list * int

  val find_index_eq: ''a list -> ''a -> int

  val finds: ('a * 'b -> bool) -> 'a list -> 'b list -> ('a * 'b list) list * 'b list

  val drop_All: term -> term

  val mk_partial_compN: int -> typ -> term -> term

  val mk_partial_comp: typ -> typ -> term -> term

  val mk_compN: int -> typ list -> term * term -> term

  val mk_comp: typ list -> term * term -> term

  val get_indices: ((binding * typ) * 'a) list -> term -> int list

end;

structure BNF_FP_Rec_Sugar_Util : BNF_FP_REC_SUGAR_UTIL =

struct

fun indexed xs h = let val h' = h + length xs in (h upto h' - 1, h') end;

fun indexedd xss = fold_map indexed xss;

fun indexeddd xsss = fold_map indexedd xsss;

fun indexedddd xssss = fold_map indexeddd xssss;

fun find_index_eq hs h = find_index (curry (op =) h) hs;

fun finds eq = fold_map (fn x => List.partition (curry eq x) #>> pair x);

fun drop_All t =

  subst_bounds (strip_qnt_vars @{const_name all} t |> map Free |> rev,

    strip_qnt_body @{const_name all} t);

fun mk_partial_comp gT fT g =

  let val T = domain_type fT --> range_type gT in

    Const (@{const_name Fun.comp}, gT --> fT --> T) $ g

  end;

fun mk_partial_compN 0 _ g = g

  | mk_partial_compN n fT g =

    let val g' = mk_partial_compN (n - 1) (range_type fT) g in

      mk_partial_comp (fastype_of g') fT g'

    end;

fun mk_compN n bound_Ts (g, f) =

  let val typof = curry fastype_of1 bound_Ts in

    mk_partial_compN n (typof f) g $ f

  end;

val mk_comp = mk_compN 1;

fun get_indices fixes t = map (fst #>> Binding.name_of #> Free) fixes

  |> map_index (fn (i, v) => if exists_subterm (equal v) t then SOME i else NONE)

  |> map_filter I;

end;