Theory Datatype

(*  Title:      ZF/Datatype.thy
    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
    Copyright   1997  University of Cambridge
*)

section‹Datatype and CoDatatype Definitions›

theory Datatype
imports Inductive Univ QUniv
keywords "datatype" "codatatype" :: thy_decl
begin

ML_file ‹Tools/datatype_package.ML›

ML ‹
(*Typechecking rules for most datatypes involving univ*)
structure Data_Arg =
  struct
  val intrs =
      [@{thm SigmaI}, @{thm InlI}, @{thm InrI},
       @{thm Pair_in_univ}, @{thm Inl_in_univ}, @{thm Inr_in_univ},
       @{thm zero_in_univ}, @{thm A_into_univ}, @{thm nat_into_univ}, @{thm UnCI}];


  val elims = [make_elim @{thm InlD}, make_elim @{thm InrD},   (*for mutual recursion*)
               @{thm SigmaE}, @{thm sumE}];                    (*allows * and + in spec*)
  end;


structure Data_Package =
  Add_datatype_def_Fun
   (structure Fp=Lfp and Pr=Standard_Prod and CP=Standard_CP
    and Su=Standard_Sum
    and Ind_Package = Ind_Package
    and Datatype_Arg = Data_Arg
    val coind = false);


(*Typechecking rules for most codatatypes involving quniv*)
structure CoData_Arg =
  struct
  val intrs =
      [@{thm QSigmaI}, @{thm QInlI}, @{thm QInrI},
       @{thm QPair_in_quniv}, @{thm QInl_in_quniv}, @{thm QInr_in_quniv},
       @{thm zero_in_quniv}, @{thm A_into_quniv}, @{thm nat_into_quniv}, @{thm UnCI}];

  val elims = [make_elim @{thm QInlD}, make_elim @{thm QInrD},   (*for mutual recursion*)
               @{thm QSigmaE}, @{thm qsumE}];                    (*allows * and + in spec*)
  end;

structure CoData_Package =
  Add_datatype_def_Fun
   (structure Fp=Gfp and Pr=Quine_Prod and CP=Quine_CP
    and Su=Quine_Sum
    and Ind_Package = CoInd_Package
    and Datatype_Arg = CoData_Arg
    val coind = true);



(*Simproc for freeness reasoning: compare datatype constructors for equality*)
structure DataFree =
struct
  val trace = Unsynchronized.ref false;

  fun mk_new ([],[]) = Const(\<^const_name>‹True›,FOLogic.oT)
    | mk_new (largs,rargs) =
        Balanced_Tree.make FOLogic.mk_conj
                 (map FOLogic.mk_eq (ListPair.zip (largs,rargs)));

 val datatype_ss = simpset_of \<^context>;

 fun proc ctxt ct =
   let val old = Thm.term_of ct
       val thy = Proof_Context.theory_of ctxt
       val _ =
         if !trace then writeln ("data_free: OLD = " ^ Syntax.string_of_term ctxt old)
         else ()
       val (lhs,rhs) = FOLogic.dest_eq old
       val (lhead, largs) = strip_comb lhs
       and (rhead, rargs) = strip_comb rhs
       val lname = #1 (dest_Const lhead) handle TERM _ => raise Match;
       val rname = #1 (dest_Const rhead) handle TERM _ => raise Match;
       val lcon_info = the (Symtab.lookup (ConstructorsData.get thy) lname)
         handle Option.Option => raise Match;
       val rcon_info = the (Symtab.lookup (ConstructorsData.get thy) rname)
         handle Option.Option => raise Match;
       val new =
           if #big_rec_name lcon_info = #big_rec_name rcon_info
               andalso not (null (#free_iffs lcon_info)) then
               if lname = rname then mk_new (largs, rargs)
               else Const(\<^const_name>‹False›,FOLogic.oT)
           else raise Match
       val _ =
         if !trace then writeln ("NEW = " ^ Syntax.string_of_term ctxt new)
         else ();
       val goal = Logic.mk_equals (old, new)
       val thm = Goal.prove ctxt [] [] goal
         (fn _ => resolve_tac ctxt @{thms iff_reflection} 1 THEN
           simp_tac (put_simpset datatype_ss ctxt addsimps #free_iffs lcon_info) 1)
         handle ERROR msg =>
         (warning (msg ^ "\ndata_free simproc:\nfailed to prove " ^ Syntax.string_of_term ctxt goal);
          raise Match)
   in SOME thm end
   handle Match => NONE;


  val conv =
    Simplifier.make_simproc \<^context> "data_free"
     {lhss = [\<^term>‹(x::i) = y›], proc = K proc};

end;
›

setup ‹
  Simplifier.map_theory_simpset (fn ctxt => ctxt addsimprocs [DataFree.conv])
›

end