module FUNCTIONS (TYPES) is

function N : Nat is
   return (ord (last of Pid) + 1)
end function

function == (n: Nat, pid: Pid) : Bool is
   return (n == Nat (pid))
end function

function == (pid: Pid, n: Nat) : Bool is
   return (Nat (pid) == n)
end function

function < (n: Nat, pid: Pid) : Bool is
   return (n < Nat (pid))
end function

function < (pid: Pid, n: Nat) : Bool is
   return (Nat (pid) < n)
end function

function >= (n: Nat, pid: Pid) : Bool is
   return (n >= Nat (pid))
end function

function != (n: Nat, pid: Pid) : Bool is
   return (n != Nat (pid))
end function

function + (pid: Pid, n: Nat) : Pid is
   return ((Nat (pid) + n) of Pid)
end function

function - (n: Nat, pid: Pid) : Pid is
   return ((n - Nat (pid)) of Pid)
end function

function - (pid: Pid, n: Nat) : Pid is
   return ((Nat (pid) - n) of Pid)
end function

end module