haftmann@31048: (* Author: Florian Haftmann, TU Muenchen *)
haftmann@26168: 
haftmann@26168: header {* Reflecting Pure types into HOL *}
haftmann@26168: 
haftmann@28952: theory Typerep
haftmann@31048: imports Plain String
haftmann@26168: begin
haftmann@26168: 
haftmann@31205: datatype typerep = Typerep String.literal "typerep list"
haftmann@26168: 
haftmann@28335: class typerep =
haftmann@31031:   fixes typerep :: "'a itself \<Rightarrow> typerep"
haftmann@26168: begin
haftmann@26168: 
haftmann@29574: definition typerep_of :: "'a \<Rightarrow> typerep" where
haftmann@28335:   [simp]: "typerep_of x = typerep TYPE('a)"
haftmann@26168: 
haftmann@26168: end
haftmann@26168: 
wenzelm@35115: syntax
wenzelm@35115:   "_TYPEREP" :: "type => logic"  ("(1TYPEREP/(1'(_')))")
wenzelm@35115: 
wenzelm@35115: parse_translation {*
haftmann@26168: let
haftmann@28335:   fun typerep_tr (*"_TYPEREP"*) [ty] =
wenzelm@35115:         Syntax.const @{const_syntax typerep} $
wenzelm@35115:           (Syntax.const @{syntax_const "_constrain"} $ Syntax.const @{const_syntax "TYPE"} $
wenzelm@35363:             (Syntax.const @{type_syntax itself} $ ty))
haftmann@28335:     | typerep_tr (*"_TYPEREP"*) ts = raise TERM ("typerep_tr", ts);
wenzelm@35115: in [(@{syntax_const "_TYPEREP"}, typerep_tr)] end
wenzelm@35115: *}
wenzelm@35115: 
wenzelm@35115: typed_print_translation {*
wenzelm@35115: let
wenzelm@35363:   fun typerep_tr' show_sorts (*"typerep"*)
wenzelm@35430:           (Type (@{type_name fun}, [Type (@{type_name itself}, [T]), _]))
wenzelm@35363:           (Const (@{const_syntax TYPE}, _) :: ts) =
wenzelm@35115:         Term.list_comb
wenzelm@35115:           (Syntax.const @{syntax_const "_TYPEREP"} $ Syntax.term_of_typ show_sorts T, ts)
haftmann@28335:     | typerep_tr' _ T ts = raise Match;
wenzelm@35115: in [(@{const_syntax typerep}, typerep_tr')] end
haftmann@26168: *}
haftmann@26168: 
haftmann@31137: setup {*
haftmann@31137: let
haftmann@26168: 
haftmann@31137: fun add_typerep tyco thy =
haftmann@26168:   let
haftmann@28335:     val sorts = replicate (Sign.arity_number thy tyco) @{sort typerep};
haftmann@26168:     val vs = Name.names Name.context "'a" sorts;
haftmann@26168:     val ty = Type (tyco, map TFree vs);
haftmann@28335:     val lhs = Const (@{const_name typerep}, Term.itselfT ty --> @{typ typerep})
haftmann@26168:       $ Free ("T", Term.itselfT ty);
haftmann@31205:     val rhs = @{term Typerep} $ HOLogic.mk_literal tyco
haftmann@31137:       $ HOLogic.mk_list @{typ typerep} (map (HOLogic.mk_typerep o TFree) vs);
haftmann@26168:     val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
haftmann@26168:   in
haftmann@26168:     thy
wenzelm@33553:     |> Theory_Target.instantiation ([tyco], vs, @{sort typerep})
haftmann@26168:     |> `(fn lthy => Syntax.check_term lthy eq)
haftmann@28965:     |-> (fn eq => Specification.definition (NONE, (Attrib.empty_binding, eq)))
haftmann@26168:     |> snd
haftmann@31137:     |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
haftmann@26168:   end;
haftmann@26168: 
haftmann@31137: fun ensure_typerep tyco thy = if not (can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort typerep})
haftmann@31137:   andalso can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort type}
haftmann@31137:   then add_typerep tyco thy else thy;
haftmann@31137: 
haftmann@31137: in
haftmann@26168: 
haftmann@31137: add_typerep @{type_name fun}
haftmann@31723: #> Typedef.interpretation ensure_typerep
haftmann@35299: #> Code.datatype_interpretation (ensure_typerep o fst)
haftmann@35299: #> Code.abstype_interpretation (ensure_typerep o fst)
haftmann@26168: 
haftmann@31137: end
haftmann@26168: *}
haftmann@26168: 
haftmann@28562: lemma [code]:
haftmann@28346:   "eq_class.eq (Typerep tyco1 tys1) (Typerep tyco2 tys2) \<longleftrightarrow> eq_class.eq tyco1 tyco2
haftmann@28346:      \<and> list_all2 eq_class.eq tys1 tys2"
haftmann@28346:   by (auto simp add: equals_eq [symmetric] list_all2_eq [symmetric])
haftmann@26168: 
haftmann@28335: code_type typerep
haftmann@31031:   (Eval "Term.typ")
haftmann@26168: 
haftmann@28335: code_const Typerep
haftmann@31031:   (Eval "Term.Type/ (_, _)")
haftmann@26168: 
haftmann@31031: code_reserved Eval Term
haftmann@26168: 
wenzelm@36176: hide_const (open) typerep Typerep
haftmann@26168: 
haftmann@26168: end