Which of these sentences is more appropriate?
The reasons for these decisions are as following:
The reasons for these decisions are as follows:
This operator is defined as following:
This operator is defined as follows:
In case anyone like myself a few minutes ago wonders why we use "as follows" and not "as follow", here is an interesting explanation:
The construction is always singular: “My position is as follows” … “The three points are as follows” … “Her favorite books were as follows,” and so on.
The Oxford English Dictionary describes the phrase “as follows” as “a prefatory formula used to introduce a statement, enumeration, or the like.”
In this formula, the OED says, the verb is impersonal and should always be used in the singular—“follows.” Use of the plural verb “follow,” Oxford adds, is “incorrect.”
Merriam-Webster’s Dictionary of English Usage concurs, saying “All experts agree” that “as follows regularly has the singular form of the verb—follows—even if preceded by a plural.”
The OED’s earliest examples of the phrase in writing are in the singular: “als her fast folowys” (as here directly follows), from 1426, and “He openly sayde as foloweth” (He openly said as follows), from 1548.
A more telling example, from George Campbell’s The Philosophy of Rhetoric (1776), discusses the correct use of the phrase:
“Analogy as well as usage favour this mode of expression. ‘The conditions of the agreement were as follows’; and not as follow. A few late writers have inconsiderately adopted this last form through a mistake of the construction.”
An inquiring mind might well ask why this is true. Here’s an answer from Fowler’s Modern English Usage (rev. 3rd ed.), edited by R. W. Burchfield:
“The phrase as follows is naturally always used cataphorically, i.e. with forward reference, and is not replaced by as follow even when the subject of the sentence is plural: His preferences are as follows … ; his view is as follows.”
“The reason for its fixed form,” the usage guide adds, “is that it was originally an impersonal construction = ‘as it follows.’ ”
In case you’re still not convinced, Garner’s Modern American Usage (3rd ed.) has this to say:
“As follows is always the correct form, even for an enumeration of many things. The expression is elliptical for as it follows—not as they follow.”
Also, the Columbia Guide to Standard American English says:
Whether the preceding matter is plural or not, as follows is always singular: The reasons for these decisions are as follows. To use as follow instead is sufficiently precious sounding to make your reader break stride: don’t do it. You can use the following instead (e.g. "You must do the following: blah blah blah"), but you needn’t. Less stiff would be The reasons for these decisions are these, or Here are my reasons, or My reasons are, first,…, and the like.