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