theory Lift_DList
imports Main
begin
subsection {* The type of distinct lists *}
typedef 'a dlist = "{xs::'a list. distinct xs}"
morphisms list_of_dlist Abs_dlist
proof
show "[] ∈ {xs. distinct xs}" by simp
qed
setup_lifting type_definition_dlist
text {* Fundamental operations: *}
lift_definition empty :: "'a dlist" is "[]"
by simp
lift_definition insert :: "'a => 'a dlist => 'a dlist" is List.insert
by simp
lift_definition remove :: "'a => 'a dlist => 'a dlist" is List.remove1
by simp
lift_definition map :: "('a => 'b) => 'a dlist => 'b dlist" is "λf. remdups o List.map f"
by simp
lift_definition filter :: "('a => bool) => 'a dlist => 'a dlist" is List.filter
by simp
text {* Derived operations: *}
lift_definition null :: "'a dlist => bool" is List.null .
lift_definition member :: "'a dlist => 'a => bool" is List.member .
lift_definition length :: "'a dlist => nat" is List.length .
lift_definition fold :: "('a => 'b => 'b) => 'a dlist => 'b => 'b" is List.fold .
lift_definition foldr :: "('a => 'b => 'b) => 'a dlist => 'b => 'b" is List.foldr .
lift_definition concat :: "'a dlist dlist => 'a dlist" is "remdups o List.concat" by auto
text {* We can export code: *}
export_code empty insert remove map filter null member length fold foldr concat in SML
end