src/HOL/Library/RType.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/RType.thy	Wed Feb 27 21:41:06 2008 +0100
@@ -0,0 +1,109 @@
+(*  Title:      HOL/Library/RType.thy
+    ID:         $Id$
+    Author:     Florian Haftmann, TU Muenchen
+*)
+
+header {* Reflecting Pure types into HOL *}
+
+theory RType
+imports Main Code_Message
+begin
+
+datatype "rtype" = RType message_string "rtype list"
+
+class rtype =
+  fixes rtype :: "'a\<Colon>{} itself \<Rightarrow> rtype"
+begin
+
+definition
+  rtype_of :: "'a \<Rightarrow> rtype"
+where
+  [simp]: "rtype_of x = rtype TYPE('a)"
+
+end
+
+setup {*
+let
+  fun rtype_tr (*"_RTYPE"*) [ty] =
+        Lexicon.const @{const_syntax rtype} $ (Lexicon.const "_constrain" $ Lexicon.const "TYPE" $
+          (Lexicon.const "itself" $ ty))
+    | rtype_tr (*"_RTYPE"*) ts = raise TERM ("rtype_tr", ts);
+  fun rtype_tr' show_sorts (*"rtype"*)
+          (Type ("fun", [Type ("itself", [T]), _])) (Const (@{const_syntax TYPE}, _) :: ts) =
+        Term.list_comb (Lexicon.const "_RTYPE" $ Syntax.term_of_typ show_sorts T, ts)
+    | rtype_tr' _ T ts = raise Match;
+in
+  Sign.add_syntax_i
+    [("_RTYPE", SimpleSyntax.read_typ "type => logic", Delimfix "(1RTYPE/(1'(_')))")]
+  #> Sign.add_trfuns ([], [("_RTYPE", rtype_tr)], [], [])
+  #> Sign.add_trfunsT [(@{const_syntax rtype}, rtype_tr')]
+end
+*}
+
+ML {*
+structure RType =
+struct
+
+fun mk f (Type (tyco, tys)) =
+      @{term RType} $ Message_String.mk tyco
+        $ HOLogic.mk_list @{typ rtype} (map (mk f) tys)
+  | mk f (TFree v) =
+      f v;
+
+fun rtype ty =
+  Const (@{const_name rtype}, Term.itselfT ty --> @{typ rtype})
+    $ Logic.mk_type ty;
+
+fun add_def tyco thy =
+  let
+    val sorts = replicate (Sign.arity_number thy tyco) @{sort rtype};
+    val vs = Name.names Name.context "'a" sorts;
+    val ty = Type (tyco, map TFree vs);
+    val lhs = Const (@{const_name rtype}, Term.itselfT ty --> @{typ rtype})
+      $ Free ("T", Term.itselfT ty);
+    val rhs = mk (rtype o TFree) ty;
+    val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
+  in
+    thy
+    |> TheoryTarget.instantiation ([tyco], vs, @{sort rtype})
+    |> `(fn lthy => Syntax.check_term lthy eq)
+    |-> (fn eq => Specification.definition (NONE, (("", []), eq)))
+    |> snd
+    |> Class.prove_instantiation_instance (K (Class.intro_classes_tac []))
+    |> LocalTheory.exit
+    |> ProofContext.theory_of
+  end;
+
+fun perhaps_add_def tyco thy =
+  let
+    val inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort rtype}
+  in if inst then thy else add_def tyco thy end;
+
+end;
+*}
+
+setup {*
+  RType.add_def @{type_name prop}
+  #> RType.add_def @{type_name fun}
+  #> RType.add_def @{type_name itself}
+  #> RType.add_def @{type_name bool}
+  #> RType.add_def @{type_name set}
+  #> TypedefPackage.interpretation RType.perhaps_add_def
+*}
+
+lemma [code func]:
+  "RType tyco1 tys1 = RType tyco2 tys2 \<longleftrightarrow> tyco1 = tyco2
+     \<and> list_all2 (op =) tys1 tys2"
+  by (auto simp add: list_all2_eq [symmetric])
+
+code_type rtype
+  (SML "Term.typ")
+
+code_const RType
+  (SML "Term.Type/ (_, _)")
+
+code_reserved SML Term
+
+hide (open) const rtype RType
+
+end