src/HOL/Library/Phantom_Type.thy
 author wenzelm Wed, 08 Mar 2017 10:50:59 +0100 changeset 65151 a7394aa4d21c parent 60500 903bb1495239 child 69593 3dda49e08b9d permissions -rw-r--r--
tuned proofs;
```
(*  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"

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 fun}, [_, Type (@{type_name phantom}, [T, _])])) ts =
list_comb
(Syntax.const @{syntax_const "_Phantom"} \$ Syntax_Phases.term_of_typ ctxt T, ts)
| phantom_tr' _ _ _ = raise Match;
in [(@{const_syntax phantom}, 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
```