When verb strings have just a single word, we call these verb forms the simple present and the simple past. But the verbs we use in our everyday speech and writing are often expanded forms that include auxiliaries, sometimes called helping verbs. In the sentence examples below, the auxiliary is shown in red; the main verb, in blue.
The following six auxiliary + main verb combinations represent only a small sample of the possibilities for expanding verb strings. With little or no effort our linguistic computer can come up with many other two-word variations--and with three- and four-word strings as well:
To emphasize form rather than meaning, we will rename the five verb
A comparison of eat, which is an irregular verb, with the regular verb walk will provide the rationale for the labels -ed and -en.
In the language of traditional grammar, a verb is regular when both its simple past tense and its past participle forms (forms 3 and 5) are formed by adding the inflectional ending -ed (or in some cases -d or -t); this means that the past tense and the past participle of regular verbs are always identical in form. This description applies to most verbs. Only a small number, one hundred or so, are irregular, although, like eat, they are among the verbs we use most frequently. The regular past tense inflection (-ed) provides the label for the past tense; the -en form of irregular verbs such as eat (and drive, give, break, speak, choose, etc.) provides the past participle label.
The subtle differences in verb meanings we are able to express result
not from variations in the verb itself, with its limit of five forms, but
rather from the auxiliaries we add. Here again are the versions of eat
that we used in the sentences above:
To discover the system underlying these verb strings, we will make some observations about these twelve variations of eat, observations that apply to all verbs in English, both regular and irregular.
1. The base form is used alone in  and with should  and
Observations  and  can be stated as a formula: (have + -en) + (be + -ing)
This formula means that we can use have as an auxiliary, but when we do, we follow it with the -en form of the verb. It also states that we can use the -ing form of the verb, but when we do, we precede it with a form of be. The parentheses mean that have + -en and be + -ing are optional auxiliaries; that is, a well-formed verb string does not require either or both of them.
Based on the twelve variations of eat, we can make some more
5. If you choose both have and be  as auxiliaries,
they appear in that order, first have and then be.
Now we can add another element to the formula: (M) + (have + -en) + (be + -ing)
Once again, the parentheses mean "optional." That is, if we choose a modal auxiliary, it comes first; if we choose have as an auxiliary, it is followed by an -en form of the verb; if we choose be as an auxiliary it is followed by the -ing form of the verb. But we do not have to choose any of these elements to produce a grammatical verb string.
One last observation:
8. A form of eat, the main verb, represented in the formula by MV, is the last word in the verb string.
And we can add another element to the verb expansion formula: (M) + (have + -en) + (be + -ing) + MV
Because it is not optional, MV is not in parentheses; all verb strings have a main verb.
Interpret the formula in this way: In generating a verb string, we can use a modal auxiliary if we choose; when we do, it comes first. We can also choose have; when we do, the -en form follows it. We can also choose be; when we do, the -ing form follows. When we use more than one auxiliary, they appear in the order give: modal, have, be. Notice too that the -en and the -ing get attached to whatever follows, for example have + -en + be + -ing + go produces have been going.
But something is still missing from our formula. How can the formula generate had eaten and was eaten? Had and was are past tense (-ed) forms of have and be. So we have to add one more component to the formula: tense, which refers to time. Among the five forms of the verb, you will recall, the present and the past forms are the only tenses, so T will represent either present or past tense. Here, then, is the complete formula for the verb expansion rule:
T + (M) + (have + -en) + (be + -ing) + MV
T is the tense marker that attaches itself to whatever follows it--that is, to the first word in the string, either M, have, be, or MV. Notice as well that T is not in parentheses; like a main verb, tense is not an option in a grammatical verb string. So to generate had eaten, and was eating, we choose past as the tense marker:
past + have + -en + eat = had eaten
When there is no auxiliary word intervening, the tense gets attached to the main verb, thus producing either the simple past tense or the simple present.
past + eat = ate
The modal auxiliaries differ from the auxiliaries have and be,
both of which can fill the role of the main verb in addition to their auxiliary
role. The modals never fill the main verb slot, nor do they have all five
forms that verbs have. They have a maximum of two forms, the base, which
is also the present tense, and the -ed. To formulate the tense of
a modal, we will pair them, assigning the base form and present tense to
one, and the -ed (or past tense) to the other:
According to our formula, T (M) + (have + -en) + (be + -ing) + MV, if we choose M, the modal auxiliary will carry the tense marker:
pres + shall + eat = shall eat
past + can + have + -en + eat = could have eaten
past + can + have + -en + be + -ing + eat = could have been eating
pres + will + be + -ing + eat = will be eating
T (M) + (have + -en) + (be + -ing)
In generating a verb string, there are only two requirements--tense (either present or past) and the main verb; the other components are optional. The tense marker will apply to the first word in the string. We have the option of using three different kinds of auxiliaries: modal, have, and be. When we use more than one, we use them in that order. The formula also specifies that with have we use the -en form of the following auxiliary or verb; with be, the -ing form of the following verb. The last word in the string is the main verb.