package preface

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Source file join_semilattice.ml

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module type LAWS = sig
  type t

  val join_semilattice_1 : unit -> (t, t -> t -> t) Law.t
  val join_semilattice_2 : unit -> (t, t -> t) Law.t
  val join_semilattice_3 : unit -> (t, t) Law.t
end

module For (L : Preface_specs.JOIN_SEMILATTICE) : LAWS with type t := L.t =
struct
  open Law

  let join_semilattice_1 () =
    let lhs x y z = L.join x (L.join y z)
    and rhs x y z = L.join (L.join x y) z in
    law ("join x (join y z)" =~ lhs) ("join (join x y) z" =~ rhs)
  ;;

  let join_semilattice_2 () =
    let lhs x y = L.join x y
    and rhs x y = L.join y x in
    law ("join x y" =~ lhs) ("join y x" =~ rhs)
  ;;

  let join_semilattice_3 () =
    let lhs x = L.join x x
    and rhs x = x in
    law ("join x x" =~ lhs) ("x" =~ rhs)
  ;;
end