(* Title: HOL/Library/Phantom_Type.thy
Author: Andreas Lochbihler
*)
section \<open>A generic phantom type\<close>
theory Phantom_Type
imports Main
begin
datatype ('a, 'b) phantom = phantom (of_phantom: 'b)
lemma type_definition_phantom': "type_definition of_phantom phantom UNIV"
by(unfold_locales) simp_all
lemma phantom_comp_of_phantom [simp]: "phantom \<circ> of_phantom = id"
and of_phantom_comp_phantom [simp]: "of_phantom \<circ> phantom = id"
by(simp_all add: o_def id_def)
syntax "_Phantom" :: "type \<Rightarrow> logic" ("(1Phantom/(1'(_')))")
translations
"Phantom('t)" => "CONST phantom :: _ \<Rightarrow> ('t, _) phantom"
typed_print_translation \<open>
let
fun phantom_tr' ctxt (Type (\<^type_name>\<open>fun\<close>, [_, Type (\<^type_name>\<open>phantom\<close>, [T, _])])) ts =
list_comb
(Syntax.const \<^syntax_const>\<open>_Phantom\<close> $ Syntax_Phases.term_of_typ ctxt T, ts)
| phantom_tr' _ _ _ = raise Match;
in [(\<^const_syntax>\<open>phantom\<close>, phantom_tr')] end
\<close>
lemma of_phantom_inject [simp]:
"of_phantom x = of_phantom y \<longleftrightarrow> x = y"
by(cases x y rule: phantom.exhaust[case_product phantom.exhaust]) simp
end