src/HOL/Library/Phantom_Type.thy
 author wenzelm Sat, 25 May 2013 17:40:44 +0200 changeset 52147 9943f8067f11 parent 52143 36ffe23b25f8 child 58249 180f1b3508ed permissions -rw-r--r--
tuned;
```
(*  Title:      HOL/Library/Phantom_Type.thy
Author:     Andreas Lochbihler
*)

header {* A generic phantom type *}

theory Phantom_Type
imports Main
begin

datatype ('a, 'b) phantom = phantom 'b

primrec of_phantom :: "('a, 'b) phantom \<Rightarrow> 'b"
where "of_phantom (phantom x) = x"

lemma of_phantom_phantom [simp]: "phantom (of_phantom x) = x"
by(cases x) simp

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 {*
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
*}

end
```