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