always x is true.

never x is false.

conj f g lifts && over predicates f and g. It is short-circuiting: g is never called if f returns false.

Examples:

  let is_zero = Int.(conj is_non_negative is_non_positive)

  (* Short-circuiting: *)
  conj always (fun () -> failwith "oops") (); (* --> exception *)
  conj never  (fun () -> failwith "oops") (); (* --> false *)

disj f g lifts || over predicates f and g. It is short-circuiting: g is never called if f returns true.

Examples:

  let is_not_zero = Int.(disj is_negative is_positive)

  (* Short-circuiting: *)
  disj never  (fun () -> failwith "oops") (); (* --> exception *)
  disj always (fun () -> failwith "oops") (); (* --> false *)

f &&& g is conj f g.

f ||| g is disj f g.

on lift x y ~f lifts a binary function f using the lifter lift. It does the same thing as the `on` function from Haskell, but with arguments flipped to make sense without infixing.

Effectively, it's Base.Comparable.lift, but with a slightly different signature.

Example:

  let ints = on fst    ~f:Int.equal (42, "banana") (42, "apple") in
  let strs = on snd ~f:String.equal (42, "banana") (42, "apple") in
  ints, strs (* --> true, false *)