Errors and Exceptions

— Alex Reinhart and Christopher Genovese

Your code will frequently need to handle errors – either caused by a user passing the wrong input or your code hitting an exceptional case.

  • Another function passes the wrong kind of data to your function
  • Algorithm fails to converge
  • Couldn’t open the data file
  • Couldn’t connect to the SQL database
  • Network connection failed
  • …etc.

I’ve seen a lot of code like this:

def read_data_file(filename, max_rows, format_args):
  if not os.path.isfile(filename):
    return "File not found"

  f = open(filename, "r")

  # do stuff...


crowded_cows <- function(cows, K) {
    if (K > length(cows) || K < 1) {
        cat("K is out of range")

    # do stuff...

    if (there is no crowded cow) {
        cat("No crowded cows")

When you’re working interactively in the REPL, manually calling functions to do things, this isn’t a big deal. You can read the message and decide what to do.

But when you’re writing a large project with many functions, all calling each other to do some complicated analysis, you shouldn’t need to handle every error manually. Sometimes code needs to be able to detect errors and decide what to do about them. How is a function calling the above crowded_cows supposed to detect which error has occurred?

Errors are part of the logic of the program, and we should be able to write code which handles errors and does specific things to handle them.

If we simply return a special value on errors, or just print a message, it’s very easy to accidentally ignore an error or, worse, use the return value as though it were a real value. And there’s no flexibility: If sometimes you want to log a message and sometimes you want execution to stop entirely, you have to code that logic into every function.

How can we reliably indicate error conditions and write code to deal with them?

Errors versus assertions #

Earlier we discussed using assertions to make claims about facts in your code, and to program defensively. But when would I use an assertion and when would I use an error? What’s the semantic difference?

Errors are for unexpected conditions that could be handled by the calling code, which may want to perform some action to work around the error, fix it, or report it to the user.

An assertion indicates something that must be true if the program is functioning correctly. If an assertion is false, there’s nothing to handle or recover from: the code is wrong and must be fixed. Assertions are sanity checks that things are working as expected.

To give a real-life example, suppose someone gives you directions to drive to their house. (Actual directions, not just Google Maps live instructions.) An error occurs when you can’t recognize where you are and don’t know what to do next. Your mental directions-following algorithm can recover from this error: maybe go back and retrace your steps, or call your friend, or check Google Maps to see where you are. This is a recoverable error.

An assertion, which your directions-following algorithm assumes is always true, is that your vehicle is on the ground, preferably on a road. If you find yourself underwater, the assertion has failed, and you are probably not getting to your friend’s house today. You can’t simply look on Google Maps and get directions to drive out of the lake. Your “how to get to Farmer Brown’s house” instructions do not know how to deal with this case at all.

So an error is a foreseeable problem which your code can detect and potentially recover from; an assertion is something which must be true for your code to even be correct at all.

Error handling paradigms #

Exceptions #

Exceptions signal an error to be handled by code somewhere up the call stack. Exceptions have a type – there are different kinds of exceptions, and code can decide which to handle and which to pass on. You can define new kinds of exceptions for your own code.

Exceptions are available in Python, Java, C++, JavaScript, Julia, and many other languages.

Code can catch exceptions caused by functions they call, or functions called by those functions, and so on, and try to recover from the exceptions.

Consider my model-fitting function example again:

class ConvergenceError(Exception):

def fit(data, initial_guess, max_iterations=100, ...):

    current_solution = initial_guess
    current_likelihood = likelihood(data, initial_guess)

    converged = False

    for it in range(max_iterations):
        next_step = update(data, current_solution)
        new_likelihood = likelihood(data, next_step)

        assert valid(next_step), "Solution is invalid"
        assert new_likelihood >= current_likelihood, \
            "Likelihood did not decrease"

        if sufficiently_close(current_solution, next_step):
            return next_step

        current_solution = next_step
        current_likelihood = new_likelihood

    raise ConvergenceError("Failed to converge after {} iterations".format(it))

def update(data, solution):
    delta = invert_big_matrix(solution)

    # do complicated math
    # ...

    return next_step

This model-fitting involves several functions:


Suppose fit fails to converge, and raises the ConvergenceError.

A raised exception causes the function to abort, and control returns to the calling function. If the calling function (main) does not catch the exception, it also aborts. If no function catches the exception, your code crashes and an error is printed:

Traceback (most recent call last):
  File "", line 21, in <module>
  File "", line 15, in main
    fit([], 10, 30)
  File "", line 11, in fit
    raise ConvergenceError("Failed to converge after {} iterations".format(it))

To catch the exception up in main, we use a try block:

def main():
        fit(data, -4, max_iterations=10)
    except ConvergenceError as e:
        # do something clever here

Any exception inside the try block can be caught by the exception handler. Notice the exception handler specifies the kind of exceptions it handles. If your code can fail in multiple ways, you can define except clauses for each. You can also create new kinds of exceptions not built in to the language. If you don’t write a handler for a specific type of exception, that exception will abort your function and proceed upwards until something does handle it.

What could we do here? We could imagine that, if we catch a ConvergenceError, main may want to retry the model fit with different parameters or maybe a different type of fitting algorithm. It could do this entirely automatically, without our intervention. Or it could do nothing, not catching the exception, in which case the program will crash and the user will have to do something.

Exceptions allow some clever error handling. For example, the tenacity package wraps functions to automatically catch certain kinds of errors and retry:

from tenacity import retry

@retry(wait=wait_exponential(min=1, max=10), stop=stop_after_attempt(5),
def geocode(addr, cur, tract=None, max_rating=5):
    """Geocode an address following a tiered strategy.

    coordinates = geopy.geocode(addr) # might fail


The geocoder has to call an external service (Google Maps), and if the network connection fails or Google’s API goes down for a moment, we can catch the error and retry.

Exceptions in R #

R doesn’t actually use exceptions. It has a system of conditions, which are more powerful and flexible than exceptions, except that I’ve never seen them used in R code. Conditions were pioneered in Common Lisp and its predecessors, which used them extensively for error handling.

The condition system can act like an exception system. To raise a condition (like throwing an exception), call stop. It can take an error message (or multiple things it will paste() together to make an error message) as an argument:

foo <- function(x) {
    if (x < 0) {
        stop(x, " is not positive")

    ## would be easier with
    ## assert_that(x >= 0)
    ## but that's beside the point

There are other types of conditions that can be raised; for example, warning prints a warning message but does not abort the function, and message prints a message. You might use warning messages for things like “Model fit didn’t converge to full precision” or some other case where the code can proceed anyway.

(Why use warning or message instead of just printing a message? A user can use a condition handler, like suppressMessages, to hide messages if they want.)

The tryCatch function runs a block of code, and if a condition is raised, runs the appropriate handler based on what you’ve provided.

    data <- read_big_file(file)
    fit_model(data) },

    error=function(e) { (handle error) },
    file_not_found_error=function(e) { (do something) },
    convergence_error=function(e) { (do something else) }

(To learn how to define new kinds of errors in R, look at Advanced R’s conditions chapter.)

Conditions #

Exceptions have a weakness: the code recovering from the error (the except or catch block) is completely separate from the code that was running when the error occurred.

If function main calls fit which calls update, which calls invert_big_matrix, which throws a SingularMatrixError, how can main handle the error and recover appropriately without knowing the details about how fit and update work?

R has a sophisticated condition handling system, stolen from Common Lisp, for handling these kinds of problems. You probably haven’t seen it before – R is usually used interactively, so you are the condition handler. But for robust, reliable programs, you need automation.

But we can imagine there are many possible ways to handle this SingularMatrixError. We could

  • Rescale the data to avoid numerical issues
  • Remove variables from the data which are nearly colinear and might be causing this problem
  • Calculate an approximate inverse
  • Fall back to an alternative way of calculating the update step

A condition handler is a bit like an exception handler, except it allows the function which raised the condition to continue running – the handler decides what the function should do to recover.

invert_big_matrix <- function(mat) {
    if (invertible(mat)) {
        ## calculate big inverse with fancy algorithm


        rescale_matrix=function() { invert_big_matrix(rescaled(mat)) },
        approximate_inverse=function() { approx_inverse(mat) },
        replace_with=function(replacement) { invert_big_matrix(replacement) },

If we encounter an error inverting the matrix, we raise a singular_matrix_error condition. (Conditions use R’s object-oriented programming system; see the resources below to see how to define a new one.) We provide several restarts: possible ways of handling and recovering from the error.

The function calling invert_big_matrix chooses which restart should run:

update <- function(data, solution) {
        delta <- invert_big_matrix(solution)
    singular_matrix_error=function(mat) {

When invert_big_matrix raises the singular_matrix_error, notice it returns the value returned by the chosen restart, so rescale_matrix can return an inverse from a rescaled version.

R has default condition handlers for certain conditions. For example, stop normally aborts like an exception would. message writes its output to the console:

fit_model <- function(data, max_iters=100) {
    for it in 1:max_iters {
        message("Iteration ", it, " of ", max_iters)

        ## calculate stuff

fit_model() # noisy
suppressMessages(fit_model()) # quiet

There is also warning for non-fatal errors, like convergence problems, and a similar suppressWarnings function to set a restart that doesn’t display them.

(Famously, some Lisp Machines had a default condition handler that displayed the error to the user, and let you edit the code and resume where it stopped. You could fix a bug while the program was running!)

Resources #