signature QUOTIENT_DEF =
sig
  datatype flag = absF | repF
  val get_fun: flag -> Proof.context -> typ * typ -> term
  val quotient_def: mixfix -> Attrib.binding -> term -> term ->
    Proof.context -> (term * thm) * local_theory
  val quotdef_cmd: (Attrib.binding * string) * (mixfix * string) ->
    local_theory -> local_theory
end;

structure Quotient_Def: QUOTIENT_DEF =
struct

(* wrapper for define *)
fun define name mx attr rhs lthy =
let
  val ((rhs, (_ , thm)), lthy') =
     Local_Theory.define ((name, mx), (attr, rhs)) lthy
in
  ((rhs, thm), lthy')
end

datatype flag = absF | repF

fun negF absF = repF
  | negF repF = absF

fun mk_identity ty = Const (@{const_name "id"}, ty --> ty)

fun get_fun_aux lthy s fs =
  case (maps_lookup (ProofContext.theory_of lthy) s) of
    SOME info => list_comb (Const (#mapfun info, dummyT), fs)
  | NONE      => raise 
        (LIFT_MATCH (space_implode " " ["get_fun_aux: no map for type", quote s, "."]))

fun get_const flag lthy _ qty =
(* FIXME: check here that _ and qty are related *)
let 
  val thy = ProofContext.theory_of lthy
  val qty_name = Long_Name.base_name (fst (dest_Type qty))
in
  case flag of
    absF => Const (Sign.full_bname thy ("ABS_" ^ qty_name), dummyT)
  | repF => Const (Sign.full_bname thy ("REP_" ^ qty_name), dummyT)
end


(* calculates the aggregate abs and rep functions for a given type; 
   repF is for constants' arguments; absF is for constants;
   function types need to be treated specially, since repF and absF
   change *)

fun get_fun flag lthy (rty, qty) =
  if rty = qty then mk_identity qty else
  case (rty, qty) of 
    (Type ("fun", [ty1, ty2]), Type ("fun", [ty1', ty2'])) =>
     let
       val fs_ty1 = get_fun (negF flag) lthy (ty1, ty1')
       val fs_ty2 = get_fun flag lthy (ty2, ty2')
     in  
       get_fun_aux lthy "fun" [fs_ty1, fs_ty2]
     end 
  | (Type (s, []), Type (s', [])) =>
     if s = s'
     then mk_identity qty 
     else get_const flag lthy rty qty
  | (Type (s, tys), Type (s', tys')) =>
     if s = s'
     then get_fun_aux lthy s' (map (get_fun flag lthy) (tys ~~ tys'))
     else get_const flag lthy rty qty
  | (TFree x, TFree x') =>
     if x = x'
     then mk_identity qty 
     else raise (LIFT_MATCH "get_fun")
  | (TVar _, TVar _) => raise (LIFT_MATCH "get_fun")
  | _ => raise (LIFT_MATCH "get_fun")

(* interface and syntax setup *)

(* the ML-interface takes a 4-tuple consisting of *)
(*                                                *)
(* - the mixfix annotation                        *)
(* - name and attributes of the meta eq           *)
(* - the new constant including its type          *)
(* - the rhs of the definition                    *)
fun quotient_def mx attr lhs rhs lthy =
let
  val Free (lhs_str, lhs_ty) = lhs;
  val qconst_bname = Binding.name lhs_str;
  val absrep_trm = get_fun absF lthy (fastype_of rhs, lhs_ty) $ rhs
                   |> Syntax.check_term lthy
  val prop = Logic.mk_equals (lhs, absrep_trm)
  val (_, prop') = LocalDefs.cert_def lthy prop
  val (_, newrhs) = Primitive_Defs.abs_def prop'

  val ((trm, thm), lthy') = define qconst_bname mx attr newrhs lthy

  fun qcinfo phi = qconsts_transfer phi {qconst = trm, rconst = rhs, def = thm}
  val lthy'' = Local_Theory.declaration true
                 (fn phi => qconsts_update_gen lhs_str (qcinfo phi)) lthy'
in
  ((trm, thm), lthy'')
end

fun quotdef_cmd ((attr, lhsstr), (mx, rhsstr)) lthy =
let
  val lhs = Syntax.read_term lthy lhsstr
  val rhs = Syntax.read_term lthy rhsstr
in
  quotient_def mx attr lhs rhs lthy |> snd
end

val _ = OuterKeyword.keyword "as";

val quotdef_parser =
  (SpecParse.opt_thm_name ":" --
  OuterParse.term) --
  (OuterParse.opt_mixfix' --| OuterParse.$$$ "as" --
  OuterParse.term)

val _ = OuterSyntax.local_theory "quotient_def" "lifted definition of constants"
  OuterKeyword.thy_decl (quotdef_parser >> quotdef_cmd)

end; (* structure *)

open Quotient_Def;