adding some basic handling that unfolds a conjecture in a locale before testing it with quickcheck
(* Title: HOL/Quotient_Examples/Lift_Set.thy
Author: Lukas Bulwahn and Ondrej Kuncar
*)
header {* Example of lifting definitions with the quotient infrastructure *}
theory Lift_Set
imports Main
begin
definition set where "set = (UNIV :: ('a \<Rightarrow> bool) set)"
typedef (open) 'a set = "set :: ('a \<Rightarrow> bool) set"
morphisms member Set
unfolding set_def 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 "bot :: 'a \<Rightarrow> bool"
term "Lift_Set.empty"
thm Lift_Set.empty_def
definition insertp :: "'a \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> 'a \<Rightarrow> bool" where
"insertp x P y \<longleftrightarrow> y = x \<or> P y"
quotient_definition insert where "insert :: 'a => 'a set => 'a set"
is insertp
term "Lift_Set.insert"
thm Lift_Set.insert_def
end