(*  Title:      nominal_library.ML
    Author:     Christian Urban

  Basic functions for nominal.
*)

signature NOMINAL_LIBRARY =
sig
  val dest_listT: typ -> typ

  val mk_minus: term -> term
  val mk_plus: term -> term -> term

  val perm_ty: typ -> typ 
  val mk_perm_ty: typ -> term -> term -> term
  val mk_perm: term -> term -> term
  val dest_perm: term -> term * term

  val mk_sort_of: term -> term
  val atom_ty: typ -> typ
  val mk_atom_ty: typ -> term -> term
  val mk_atom: term -> term

  val supp_ty: typ -> typ
  val supp_const: typ -> term
  val mk_supp_ty: typ -> term -> term
  val mk_supp: term -> term

  val mk_equiv: thm -> thm
  val safe_mk_equiv: thm -> thm

  val mk_diff: term * term -> term
  val mk_append: term * term -> term
  val mk_union: term * term -> term
  val fold_union: term list -> term

  (* datatype operations *)
  val all_dtyps: Datatype_Aux.descr -> (string * sort) list -> typ list
  val nth_dtyp: Datatype_Aux.descr -> (string * sort) list -> int -> typ
  val all_dtyp_constrs_types: Datatype_Aux.descr -> (string * sort) list -> 
    (term * typ * typ list * bool list) list list
  val nth_dtyp_constrs_types: Datatype_Aux.descr -> (string * sort) list -> int -> 
    (term * typ * typ list * bool list) list
  val prefix_dt_names: Datatype_Aux.descr -> (string * sort) list -> string -> string list

end


structure Nominal_Library: NOMINAL_LIBRARY =
struct

(* this function should be in hologic.ML *)
fun dest_listT (Type (@{type_name list}, [T])) = T
  | dest_listT T = raise TYPE ("dest_listT: list type expected", [T], [])

fun mk_minus p = @{term "uminus::perm => perm"} $ p;

fun mk_plus p q = @{term "plus::perm => perm => perm"} $ p $ q;

fun perm_ty ty = @{typ "perm"} --> ty --> ty; 
fun mk_perm_ty ty p trm = Const (@{const_name "permute"}, perm_ty ty) $ p $ trm;
fun mk_perm p trm = mk_perm_ty (fastype_of trm) p trm;

fun dest_perm (Const (@{const_name "permute"}, _) $ p $ t) = (p, t)
  | dest_perm t = raise TERM ("dest_perm", [t]);

fun mk_sort_of t = @{term "sort_of"} $ t;

fun atom_ty ty = ty --> @{typ "atom"};
fun mk_atom_ty ty t = Const (@{const_name "atom"}, atom_ty ty) $ t;
fun mk_atom t = mk_atom_ty (fastype_of t) t;


fun supp_ty ty = ty --> @{typ "atom set"};
fun supp_const ty = Const (@{const_name "supp"}, supp_ty ty)
fun mk_supp_ty ty t = supp_const ty $ t;
fun mk_supp t = mk_supp_ty (fastype_of t) t;


fun mk_equiv r = r RS @{thm eq_reflection};
fun safe_mk_equiv r = mk_equiv r handle Thm.THM _ => r;


(* functions that construct differences, appends and unions
   but avoid producing empty atom sets or empty atom lists *)

fun mk_diff (@{term "{}::atom set"}, _) = @{term "{}::atom set"}
  | mk_diff (t1, @{term "{}::atom set"}) = t1
  | mk_diff (t1, t2) = HOLogic.mk_binop @{const_name minus} (t1, t2)

fun mk_append (@{term "[]::atom list"}, @{term "[]::atom list"}) = @{term "[]::atom list"}
  | mk_append (t1, @{term "[]::atom list"}) = t1
  | mk_append (@{term "[]::atom list"}, t2) = t2
  | mk_append (t1, t2) = HOLogic.mk_binop @{const_name "append"} (t1, t2) 

fun mk_union (@{term "{}::atom set"}, @{term "{}::atom set"}) = @{term "{}::atom set"}
  | mk_union (t1 , @{term "{}::atom set"}) = t1
  | mk_union (@{term "{}::atom set"}, t2) = t2
  | mk_union (t1, t2) = HOLogic.mk_binop @{const_name "sup"} (t1, t2)  
 
fun fold_union trms = fold (curry mk_union) trms @{term "{}::atom set"}




(** datatypes **)


(* returns the type of the nth datatype *)
fun all_dtyps descr sorts = 
  map (fn n => Datatype_Aux.typ_of_dtyp descr sorts (Datatype_Aux.DtRec n)) (0 upto (length descr - 1))

fun nth_dtyp descr sorts n = 
  Datatype_Aux.typ_of_dtyp descr sorts (Datatype_Aux.DtRec n);

(* returns info about constructors in a datatype *)
fun all_dtyp_constrs_info descr = 
  map (fn (_, (ty, vs, constrs)) => map (pair (ty, vs)) constrs) descr

(* returns the constants of the constructors plus the 
   corresponding type and types of arguments *)
fun all_dtyp_constrs_types descr sorts = 
let
  fun aux ((ty_name, vs), (cname, args)) =
  let
    val vs_tys = map (Datatype_Aux.typ_of_dtyp descr sorts) vs
    val ty = Type (ty_name, vs_tys)
    val arg_tys = map (Datatype_Aux.typ_of_dtyp descr sorts) args
    val is_rec = map Datatype_Aux.is_rec_type args
  in
    (Const (cname, arg_tys ---> ty), ty, arg_tys, is_rec)
  end
in
  map (map aux) (all_dtyp_constrs_info descr)
end

fun nth_dtyp_constrs_types descr sorts n =
  nth (all_dtyp_constrs_types descr sorts) n


(* generates for every datatype a name str ^ dt_name 
   plus and index for multiple occurences of a string *)
fun prefix_dt_names descr sorts str = 
let
  fun get_nth_name (i, _) = 
    Datatype_Aux.name_of_typ (nth_dtyp descr sorts i) 
in
  Datatype_Prop.indexify_names 
    (map (prefix str o get_nth_name) descr)
end


end (* structure *)

open Nominal_Library;