signature QUOTIENT_DEF =

sig

  datatype flag = absF | repF

  val get_fun: flag -> Proof.context -> typ * typ -> term

  val make_def: binding -> typ -> mixfix -> Attrib.binding -> term ->

    Proof.context -> (term * thm) * local_theory

  val quotdef: (binding * typ * mixfix) * (Attrib.binding * term) ->

    local_theory -> (term * thm) * local_theory

  val quotdef_cmd: (binding * string * mixfix) * (Attrib.binding * 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 ty_strs lthy (ty1, ty2) = 

  (quote (Syntax.string_of_typ lthy ty1),

   quote (Syntax.string_of_typ lthy ty2))

fun ty_lift_error1 lthy rty qty =

let

  val (rty_str, qty_str) = ty_strs lthy (rty, qty) 

  val msg = ["quotient type", qty_str, "and lifted type", rty_str, "do not match."]

in

  raise LIFT_MATCH (space_implode " " msg)

end

fun ty_lift_error2 lthy rty qty =

let

  val (rty_str, qty_str) = ty_strs lthy (rty, qty)   

  val msg = ["No type variables allowed in", qty_str, "and", rty_str, "."]

in

  raise LIFT_MATCH (space_implode " " msg)

end

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 " " ["No map function 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

fun get_fun flag lthy (rty, qty) =

  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 ty_lift_error1 lthy rty qty

  | (TVar _, TVar _) => ty_lift_error2 lthy rty qty

  | _ => ty_lift_error1 lthy rty qty

let

  val rty = fastype_of rhs

  val (arg_rtys, res_rty) = strip_type rty

  val (arg_qtys, res_qty) = strip_type qty

  val rep_fns = map (get_fun repF lthy) (arg_rtys ~~ arg_qtys)

  val abs_fn  = get_fun absF lthy (res_rty, res_qty)

  fun mk_fun_map t s =  

        Const (@{const_name "fun_map"}, dummyT) $ t $ s

  val absrep_trm = (fold_rev mk_fun_map rep_fns abs_fn $ rhs)

                   |> Syntax.check_term lthy 

  fun qcinfo phi = qconsts_transfer phi {qconst = trm, rconst = rhs}

  val lthy'' = Local_Theory.declaration true

in

  ((trm, thm), lthy'')

end

(* interface and syntax setup *)

(* the ML-interface takes a 5-tuple consisting of  *)

(*                                                 *)

(* - the name of the constant to be lifted         *)

(* - its type                                      *)

(* - its mixfix annotation                         *)

(* - a meta-equation defining the constant,        *)

(*   and the attributes of for this meta-equality  *)

fun quotdef ((bind, qty, mx), (attr, prop)) lthy =

let   

  val (_, prop') = LocalDefs.cert_def lthy prop

  val (_, rhs) = Primitive_Defs.abs_def prop'

in

  make_def bind qty mx attr rhs lthy 

end

fun quotdef_cmd ((bind, qtystr, mx), (attr, propstr)) lthy = 

let

  val qty  = Syntax.read_typ lthy qtystr

  val prop = Syntax.read_prop lthy propstr

in

  quotdef ((bind, qty, mx), (attr, prop)) lthy |> snd

end

val quotdef_parser =

  (OuterParse.binding --

    (OuterParse.$$$ "::" |-- OuterParse.!!! (OuterParse.typ -- 

      OuterParse.opt_mixfix' --| OuterParse.where_)) >> OuterParse.triple2) -- 

       (SpecParse.opt_thm_name ":" -- OuterParse.prop)

val _ = OuterSyntax.local_theory "quotient_def" "lifted definition of constants"

  OuterKeyword.thy_decl (quotdef_parser >> quotdef_cmd)

end; (* structure *)

open Quotient_Def;