How can I reference an Idris interface method from within the same interface declaration? - idris

Question

I built a little TotalOrder class that has stronger proof properties than the regular Ord class. The problem is that these properties need to refer to each other in ways I'm not sure how to do, syntactically.
I need to reference my lessThan type in the other methods in the interface, but it seems to be getting treated as a regular (implicitly forall'd) variable.
module Order
%default total
public export
data Ordering : (t -> t -> Type) -> t -> t -> Type where
LessThan : f x y -> Ordering f x y
Equal : x = y -> Ordering f x y
GreaterThan : f y x -> Ordering f x y
public export
interface TotalOrder a where
lessThan : a -> a -> Type
compare : (x, y : a) -> Ordering lessThan x y
ltNeq : lessThan x y -> x = y -> Void
ltNgt : lessThan x y -> lessThan y x -> Void
-- Implementation for Nats
compareNat : (x, y : Nat) -> Ordering LT x y
compareNat x y = ...
ltNeqNat : LT x y -> x = y -> Void
ltNeqNat lt eq = ...
ltNgtNat : LT x y -> LT y x -> Void
ltNgtNat lt gt = ...
implementation TotalOrder Nat where
lessThan = LT
compare = compareNat -- THIS LINE REFUSES TO COMPILE
ltNeq = ltNeqNat
ltNgt = ltNgtNat
As best I can determine, the typechecker automatically assumes that the lessThans in function position in ltNeq and ltNgt are the same as the lessThan declared in the interface, but the lessThan in argument position in compare is treated as a regular argument to compare, meaning that the type for the Nat implementation is
compare : {lessThan : Nat -> Nat -> Type} -> (x, y : Nat) -> Ordering lessThan x y
rather than
compare : (x, y : Nat) -> Ordering LT x y
and compare = compareNat no longer typechecks. When I run into this problem in top-level functions, fully-qualifying the name works, but I'm not sure what the fully-qualified name here would be, and the obvious ideas (Order.lessThan, TotalOrder.lessThan, Order.TotalOrder.lessThan) all get "no such variable"d.