Lists are common in all forms of writing. The list items can be included within the text or put on separate lines. Separate lines are used in order to draw attention to the items, to ease reading when the items are long or numerous, or to facilitate cross-reference to specific items.

The two main types of lists are enumerated lists, in which the items are numbered or labelled alphabetically, and itemized lists, in which each entry is preceded by a marker such as a bullet symbol. In these are produced by the enumerate and itemize environments, respectively. (The basic enumerate environment allows only numbers as labels, but the enumerate package extends the environment to allow letters, too.)

I have long felt unsure about how to punctuate lists, and especially the sentence that introduces the list. Advice is hard to find in books on English usage and there seems to be no agreed way to do it. Some recent reading, namely of the TUGboat article Makings Lists: A Journey Into Unknown Grammar by James. R. Hunt and the book Making a Point: The Pernickity Story of English Punctuation by David Crystal, has clarified my thinking. I will now explain how I intend to format lists in future.

My approach is based on a key principle, which stems from the fact that in English all sentences must be complete, and not mere fragments. (There is no universally agreed definition of what distinguishes a sentence from a fragment, but a sentence is usually required to contain a verb.) The principle is that

if the labels in a list are removed then what remains should make one or more complete and correctly punctuated sentences.

Here are three examples that are correctly formatted according to this principle.

Example 1. Programming languages from three decades will be compared:

• C++ (1985),
• Python (1991), and
• Julia (2012).

This type of list could readily be collapsed inline into a regular sentence: “Programming languages from three decades will be compared: C++ (1985), Python (1991), and Julia (2012).” The author must judge whether the list form, with its clearer separation of the items, is preferable. Note the “and” after the second item. This is needed, though I think many people would find the example acceptable without it.

Example 2. We used three different algorithms in the experiments. The table reports the performance of

• Algorithm 3.1 (based on a Taylor series),
• Algorithm 3.2 (with parameter ), and
• Algorithm 3.3 (with tolerance ).

The sentence that precedes the list does not end with a colon. If it did, then the principle would be violated.

Example 3. Before printing the paper carry out the following steps.

1. Run the paper through .
2. Run the paper through BibTeX.
3. Repeat steps 1 and 2 until no warnings occur about unresolved references.

In this example each list element is a complete sentence. The numbering of the elements is appropriate because they have a definite order. In some other list in which the ordering is arbitrary one might nevertheless decide to number the elements in order to be able to refer to the elements later on.

The next example does not conform to the principle.

Example 4. We will use three test matrices.

• rosser: a classic symmetric matrix with close and repeated eigenvalues,
• hilb: the Hilbert matrix, and
• pascal: a matrix with elements taken from Pascal’s triangle.

If we remove the list markers then the list items turn into a sentence fragment containing no verb. I suspect few people would object to the formatting of this example. But we can easily modify it to conform.

Example 4 (modified). We will use three test matrices:

• rosser, a classic symmetric matrix with close and repeated eigenvalues;
• hilb, the Hilbert matrix; and
• pascal, a matrix with elements taken from Pascal’s triangle.

Note the use of the semicolons to separate the items, which now contain commas. I much prefer the modified example, although in the past I might have been happy with the original.

Of course, style guidelines for individual publications may override what I have said above. However, my experience is that academic publishers tend not to change authors’ lists unless they are clearly grammatically incorrect. For example the SIAM Style Manual advises copy editors “Retain the author’s list style as long as it’s consistent”.

Finally, I note that the The Princeton Companion to Applied Mathematics follows the principle recommended here, though that is purely a coincidence. I did not think about list punctuation at all while working on the book, leaving it in the hands of copy editor Sam Clark (T&T Productions, London).