Andreas@48163: (*  Title:      HOL/Library/Phantom_Type.thy
Andreas@48163:     Author:     Andreas Lochbihler
Andreas@48163: *)
Andreas@48163: 
Andreas@48163: header {* A generic phantom type *}
Andreas@48163: 
wenzelm@51542: theory Phantom_Type
wenzelm@51542: imports Main
wenzelm@51542: begin
Andreas@48163: 
blanchet@58378: datatype ('a, 'b) phantom = phantom (of_phantom: 'b)
Andreas@48163: 
Andreas@48163: lemma type_definition_phantom': "type_definition of_phantom phantom UNIV"
Andreas@48163: by(unfold_locales) simp_all
Andreas@48163: 
Andreas@48163: lemma phantom_comp_of_phantom [simp]: "phantom \<circ> of_phantom = id"
Andreas@48163:   and of_phantom_comp_phantom [simp]: "of_phantom \<circ> phantom = id"
Andreas@48163: by(simp_all add: o_def id_def)
Andreas@48163: 
Andreas@48163: syntax "_Phantom" :: "type \<Rightarrow> logic" ("(1Phantom/(1'(_')))")
Andreas@48163: translations
Andreas@48163:   "Phantom('t)" => "CONST phantom :: _ \<Rightarrow> ('t, _) phantom"
Andreas@48163: 
wenzelm@52143: typed_print_translation {*
wenzelm@52143:   let
wenzelm@52147:     fun phantom_tr' ctxt (Type (@{type_name fun}, [_, Type (@{type_name phantom}, [T, _])])) ts =
wenzelm@52147:           list_comb
wenzelm@52147:             (Syntax.const @{syntax_const "_Phantom"} $ Syntax_Phases.term_of_typ ctxt T, ts)
wenzelm@52147:       | phantom_tr' _ _ _ = raise Match;
wenzelm@52143:   in [(@{const_syntax phantom}, phantom_tr')] end
Andreas@48163: *}
Andreas@48163: 
Andreas@58383: lemma of_phantom_inject [simp]:
Andreas@58383:   "of_phantom x = of_phantom y \<longleftrightarrow> x = y"
Andreas@58383: by(cases x y rule: phantom.exhaust[case_product phantom.exhaust]) simp
Andreas@58383: 
Andreas@48163: end