src/HOL/Tools/Quotient/quotient_def.ML

Automated lifting can be restricted to specific quotient types

(*  Title:      HOL/Tools/Quotient/quotient_def.thy
    Author:     Cezary Kaliszyk and Christian Urban

Definitions for constants on quotient types.
*)

signature QUOTIENT_DEF =
sig
  val quotient_def: (binding option * mixfix) * (Attrib.binding * (term * term)) ->
    local_theory -> (term * thm) * local_theory

  val quotdef_cmd: (binding option * mixfix) * (Attrib.binding * (string * string)) ->
    local_theory -> (term * thm) * local_theory

  val quotient_lift_const: typ list -> string * term -> local_theory ->
    (term * thm) * local_theory
end;

structure Quotient_Def: QUOTIENT_DEF =
struct

open Quotient_Info;
open Quotient_Term;

(** 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 returns the defined constant and its definition
   theorem; stores the data in the qconsts data slot.

   Restriction: At the moment the right-hand side of the
   definition must be a constant. Similarly the left-hand 
   side 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 quotient_def ((optbind, mx), (attr, (lhs, rhs))) lthy =
let
  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"
  
  fun sanity_test NONE _ = true
    | sanity_test (SOME bind) str =
        if Name.of_binding bind = str then true
        else error_msg bind str

  val _ = sanity_test optbind lhs_str

  val qconst_bname = Binding.name lhs_str
  val absrep_trm = absrep_fun AbsF lthy (fastype_of rhs, lhs_ty) $ rhs
  val prop = Logic.mk_equals (lhs, Syntax.check_term lthy absrep_trm)
  val (_, prop') = Local_Defs.cert_def lthy prop
  val (_, newrhs) = Primitive_Defs.abs_def prop'

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

  (* data storage *)
  fun qcinfo phi = transform_qconsts phi {qconst = trm, rconst = rhs, def = thm}
  fun trans_name phi = (fst o dest_Const o #qconst) (qcinfo phi)
  val lthy'' = Local_Theory.declaration true
                 (fn phi => qconsts_update_gen (trans_name phi) (qcinfo phi)) lthy'
in
  ((trm, thm), lthy'')
end

fun quotdef_cmd (decl, (attr, (lhs_str, rhs_str))) lthy =
let
  val lhs = Syntax.read_term lthy lhs_str
  val rhs = Syntax.read_term lthy rhs_str
  val lthy' = Variable.declare_term lhs lthy
  val lthy'' = Variable.declare_term rhs lthy'
in
  quotient_def (decl, (attr, (lhs, rhs))) lthy''
end

fun quotient_lift_const qtys (b, t) ctxt =
  quotient_def ((NONE, NoSyn), (Attrib.empty_binding,
    (Quotient_Term.quotient_lift_const qtys (b, t) ctxt, t))) ctxt

local
  structure P = OuterParse;
in

val quotdef_decl = (P.binding >> SOME) -- P.opt_mixfix' --| P.$$$ "where"

val quotdef_parser =
  Scan.optional quotdef_decl (NONE, NoSyn) -- 
    P.!!! (SpecParse.opt_thm_name ":" -- (P.term --| P.$$$ "is" -- P.term))
end

val _ =
  OuterSyntax.local_theory "quotient_definition"
    "definition for constants over the quotient type"
      OuterKeyword.thy_decl (quotdef_parser >> (snd oo quotdef_cmd))

end; (* structure *)