adding a preliminary example to show how the quotient_definition package can be generalized
(* Title: HOL/Quotient.thy
Author: Lukas Bulwahn and Ondrey Kuncar
*)
header {* Example of lifting definitions with the quotient infrastructure *}
theory Lift_Set
imports Main
begin
typedef 'a set = "(UNIV :: ('a => bool) => bool)"
morphisms member Set by auto
text {* Here is some ML setup that should eventually be incorporated in the typedef command. *}
local_setup {* fn lthy =>
let
val quotients = {qtyp = @{typ "'a set"}, rtyp = @{typ "'a => bool"}, equiv_rel = @{term "dummy"}, equiv_thm = @{thm refl}}
val qty_full_name = @{type_name "set"}
fun qinfo phi = Quotient_Info.transform_quotients phi quotients
in lthy
|> Local_Theory.declaration {syntax = false, pervasive = true}
(fn phi => Quotient_Info.update_quotients qty_full_name (qinfo phi)
#> Quotient_Info.update_abs_rep qty_full_name (Quotient_Info.transform_abs_rep phi {abs = @{term "Set"}, rep = @{term "member"}}))
end
*}
text {* Now, we can employ quotient_definition to lift definitions. *}
quotient_definition empty where "empty :: 'a set"
is "Set.empty"
term "Lift_Set.empty"
thm Lift_Set.empty_def
quotient_definition insert where "insert :: 'a => 'a set => 'a set"
is "Set.insert"
term "Lift_Set.insert"
thm Lift_Set.insert_def
end