(*  Title:      HOL/Tools/Quotient/quotient_def.ML

     Author:     Cezary Kaliszyk and Christian Urban

 Definitions for constants on quotient types.

 *)

 signature QUOTIENT_DEF =

 sig

   val quotient_def:

     (binding * typ option * mixfix) option * (Attrib.binding * (term * term)) ->

     local_theory -> Quotient_Info.quotconsts * local_theory

   val quotient_def_cmd:

     (binding * string option * mixfix) option * (Attrib.binding * (string * string)) ->

     local_theory -> Quotient_Info.quotconsts * local_theory

   val lift_raw_const: typ list -> (string * term * mixfix) -> local_theory ->

     Quotient_Info.quotconsts * local_theory

 end;

 structure Quotient_Def: QUOTIENT_DEF =

 struct

 (** Interface and Syntax Setup **)

 (* The ML-interface for a quotient definition takes

    as argument:

     - an optional binding and mixfix annotation

     - attributes

     - the new constant as term

     - the rhs of the definition as term

    It stores the qconst_info in the quotconsts data slot.

    Restriction: At the moment the left- and right-hand

    side of the definition must be a constant.

 *)

 fun error_msg bind str =

   let

     val name = Binding.name_of bind

     val pos = Position.str_of (Binding.pos_of bind)

   in

     error ("Head of quotient_definition " ^

       quote str ^ " differs from declaration " ^ name ^ pos)

   end

 fun gen_quotient_def prep_vars prep_term (raw_var, ((name, atts), (lhs_raw, rhs_raw))) lthy =

   let

     val (vars, ctxt) = prep_vars (the_list raw_var) lthy

     val T_opt = (case vars of [(_, SOME T, _)] => SOME T | _ => NONE)

     val lhs = prep_term T_opt ctxt lhs_raw

     val rhs = prep_term NONE ctxt rhs_raw

     val (lhs_str, lhs_ty) = dest_Free lhs handle TERM _ => error "Constant already defined."

     val _ = if null (strip_abs_vars rhs) then () else error "The definiens cannot be an abstraction"

     val _ = if is_Const rhs then () else warning "The definiens is not a constant"

     val var =

       (case vars of 

         [] => (Binding.name lhs_str, NoSyn)

       | [(binding, _, mx)] =>

           if Variable.check_name binding = lhs_str then (binding, mx)

           else error_msg binding lhs_str

       | _ => raise Match)

     val absrep_trm = Quotient_Term.absrep_fun lthy Quotient_Term.AbsF (fastype_of rhs, lhs_ty) $ rhs

     val prop = Syntax.check_term lthy (Logic.mk_equals (lhs, absrep_trm))

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

     val (_, newrhs) = Local_Defs.abs_def prop'

     val ((trm, (_ , thm)), lthy') =

       Local_Theory.define (var, ((Thm.def_binding_optional (#1 var) name, atts), newrhs)) lthy

     (* data storage *)

     val qconst_data = {qconst = trm, rconst = rhs, def = thm}

     val lthy'' = lthy'

       |> Local_Theory.declaration {syntax = false, pervasive = true}

         (fn phi =>

           (case Quotient_Info.transform_quotconsts phi qconst_data of

             qcinfo as {qconst = Const (c, _), ...} =>

               Quotient_Info.update_quotconsts c qcinfo

           | _ => I));

   in

     (qconst_data, lthy'')

   end

 fun check_term' cnstr ctxt =

   Syntax.check_term ctxt o (case cnstr of SOME T => Type.constraint T | _ => I)

 fun read_term' cnstr ctxt =

   check_term' cnstr ctxt o Syntax.parse_term ctxt

 val quotient_def = gen_quotient_def Proof_Context.cert_vars check_term'

 val quotient_def_cmd = gen_quotient_def Proof_Context.read_vars read_term'

 (* a wrapper for automatically lifting a raw constant *)

 fun lift_raw_const qtys (qconst_name, rconst, mx) ctxt =

   let

     val rty = fastype_of rconst

     val qty = Quotient_Term.derive_qtyp ctxt qtys rty

     val lhs = Free (qconst_name, qty)

   in

     quotient_def (SOME (Binding.name qconst_name, NONE, mx), (Attrib.empty_binding, (lhs, rconst))) ctxt

   end

 (* parser and command *)

 val quotdef_parser =

   Scan.option Parse_Spec.constdecl --

     Parse.!!! (Parse_Spec.opt_thm_name ":" -- (Parse.term --| @{keyword "is"} -- Parse.term))

 val _ =

   Outer_Syntax.local_theory "quotient_definition"

     "definition for constants over the quotient type"

       Keyword.thy_decl (quotdef_parser >> (snd oo quotient_def_cmd))

 end; (* structure *)