(* Author: Florian Haftmann, TU Muenchen *)

 header {* Reflecting Pure types into HOL *}

 theory Typerep

 imports String

 begin

 datatype typerep = Typerep String.literal "typerep list"

 class typerep =

   fixes typerep :: "'a itself \<Rightarrow> typerep"

 begin

 definition typerep_of :: "'a \<Rightarrow> typerep" where

   [simp]: "typerep_of x = typerep TYPE('a)"

 end

 syntax

   "_TYPEREP" :: "type => logic"  ("(1TYPEREP/(1'(_')))")

 parse_translation {*

   let

     fun typerep_tr (*"_TYPEREP"*) [ty] =

           Syntax.const @{const_syntax typerep} $

             (Syntax.const @{syntax_const "_constrain"} $ Syntax.const @{const_syntax "TYPE"} $

               (Syntax.const @{type_syntax itself} $ ty))

       | typerep_tr (*"_TYPEREP"*) ts = raise TERM ("typerep_tr", ts);

   in [(@{syntax_const "_TYPEREP"}, K typerep_tr)] end

 *}

 typed_print_translation {*

   let

     fun typerep_tr' ctxt (*"typerep"*)

             (Type (@{type_name fun}, [Type (@{type_name itself}, [T]), _]))

             (Const (@{const_syntax TYPE}, _) :: ts) =

           Term.list_comb

             (Syntax.const @{syntax_const "_TYPEREP"} $ Syntax_Phases.term_of_typ ctxt T, ts)

       | typerep_tr' _ T ts = raise Match;

   in [(@{const_syntax typerep}, typerep_tr')] end

 *}

 setup {*

 let

 fun add_typerep tyco thy =

   let

     val sorts = replicate (Sign.arity_number thy tyco) @{sort typerep};

     val vs = Name.invent_names Name.context "'a" sorts;

     val ty = Type (tyco, map TFree vs);

     val lhs = Const (@{const_name typerep}, Term.itselfT ty --> @{typ typerep})

       $ Free ("T", Term.itselfT ty);

     val rhs = @{term Typerep} $ HOLogic.mk_literal tyco

       $ HOLogic.mk_list @{typ typerep} (map (HOLogic.mk_typerep o TFree) vs);

     val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));

   in

     thy

     |> Class.instantiation ([tyco], vs, @{sort typerep})

     |> `(fn lthy => Syntax.check_term lthy eq)

     |-> (fn eq => Specification.definition (NONE, (Attrib.empty_binding, eq)))

     |> snd

     |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))

   end;

 fun ensure_typerep tyco thy =

   if not (Sorts.has_instance (Sign.classes_of thy) tyco @{sort typerep})

     andalso Sorts.has_instance (Sign.classes_of thy) tyco @{sort type}

   then add_typerep tyco thy else thy;

 in

 add_typerep @{type_name fun}

 #> Typedef.interpretation ensure_typerep

 #> Code.datatype_interpretation (ensure_typerep o fst)

 #> Code.abstype_interpretation (ensure_typerep o fst)

 end

 *}

 lemma [code]:

   "HOL.equal (Typerep tyco1 tys1) (Typerep tyco2 tys2) \<longleftrightarrow> HOL.equal tyco1 tyco2

      \<and> list_all2 HOL.equal tys1 tys2"

   by (auto simp add: eq_equal [symmetric] list_all2_eq [symmetric])

 lemma [code nbe]:

   "HOL.equal (x :: typerep) x \<longleftrightarrow> True"

   by (fact equal_refl)

 code_type typerep

   (Eval "Term.typ")

 code_const Typerep

   (Eval "Term.Type/ (_, _)")

 code_reserved Eval Term

 hide_const (open) typerep Typerep

 end