(* 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