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Concourse 2

Central modal auxiliary verbs

central

There is a general and simpler guide to modality and modal auxiliary verbs which you could follow before you access this area if it is new to you (new tab if you go there).

This guide focuses only on true, central or pure modal auxiliary verbs.  All three terms are used in the literature but we are sticking with central to distinguish these verbs from those that are modal auxiliary verbs but are more peripherally so because they do not conform to the tests we shall apply.
There is another guide to semi-modal auxiliary verbs, linked in the list of related guides at the end, which covers dare, let, need and used to and marginal modal auxiliary verbs such as seem to, tend to, be about to etc.
We are also sticking with the rather clumsy expression modal auxiliary verb because it is necessary to bear in mind that there are other modal verbs which are not auxiliaries such as guess, imagine, oblige, suggest, force, intend and so on which carry modal meanings of some kind as, indeed, do a range of modal adjectives, adverbs and nouns.
Often, these verbs are simply called modals or modal verbs but that's shorthand and we'll avoid it here.
An alternative view is presented in the guide to types of modality also linked at the end.


follow

In what follows ...

What follows is a guide to the main central modal auxiliary verbs in English, taken one by one.  We will look at the possible functions of each verb and how it is used.
In the notes following each table, areas which cause specific and predictable problems for learners are often indicated.  It is these in particular that you must be able to analyse and explain in the classroom.
Tests in sections of this page only exist for the more complex verbs but there's a link to a test on all of them at the end.

The identification of central or pure modal auxiliary verbs is often limited to 10 verbs:
    can | could | may | might | must | shall | should | will | would | ought
In this analysis, however, the verb had better is included because it shares some structural characteristics with the central ten.
Elsewhere, you will find verbs included in or excluded from this list.  In particular, the verb ought is often excluded because it is usually followed by the to-infinitive.  That is not universally the case, however, and in AmE particularly uses like:
    You oughtn't come if you are tired
or
    Ought I go?
are frequent and they may be encountered in the production of BrE speakers.


tests

Ten tests for central modal auxiliary verbs

If you have followed the essential guide to this area you may recall some of the following section.  Here, we have extended it a little to include some less commonly noted characteristics of central modal auxiliary verbs.  There are 10 in all.
Traditionally, in order to be included as a pure or central modal auxiliary verb, the verb needs to conform to all these tests:

1

Central modal auxiliary verbs cannot co-occur

So, for example:
    *I must can do it
    *I will must do it

are impossible because must, will and can are pure or central modal auxiliary verbs.  However
    I may be able to do it
    I will have to see him

are possible so be able to and have to are not, by this test, central modal auxiliary verbs.  The former, in fact, is simply a modal adjective used with the copula.
Lexical or main verbs, on the other hand, can occur together and often catenate as in, e.g.:
    She wants to help to do the work
    They enjoy sitting by the fire on a winter's evening

etc.
Semi-modal auxiliary verbs may also co-occur so we may encounter, for example:
    I didn't dare let the dog go
    I used to need to get up very early

etc.

test

Central modal auxiliary verbs do not inflect for person

Central modal auxiliary verbs carry no inflexions.  So in, for example:
    She wants a cup of tea but I had one earlier
the lexical or main verb want changes to wants with an added -s to show who we are talking about.
Central modal auxiliary verbs remain unchanged for person so, for example:
    *She musts come
    *It wills rain
are disallowed.
Semi-modal auxiliary verbs do sometimes inflect so we may find:
    She needs to leave
    He dares to ask
Again, the verb used as a semi-modal auxiliary verb is exceptional because it never inflects for person.  The past-tense inflexion (d) is optional in some circumstances with that verb.

test

Central modal auxiliary verbs have abnormal time references

  1. Lexical or main verbs may or may not inflect regularly to form a past tense but the relationship to time remains clear so, for example:
        He hopes to come
        She does the work

    and
        He hoped to come
        She did the work

    are distinguished by the tense ending inflexion or by an internal change to the verb.
    (Fewer than 20 verbs in English do not inflect at all for tense but the zero inflexion in these cases is still applicable to tense so, for example:
        She quit her job
    and
        I cut my finger
    are still or may be past forms.)
    Some modal auxiliary verbs have past forms so:
        He can come
    can be expressed in the past as
        He could come
        He will do
    can be expressed in the past as
        He would do it
        I shall be there
    is sometimes expressible in the past as
        I should be there
    and
        She may go
    has a past form in
        She might go
  2. Except for the unusual verb used, semi-modal auxiliary verbs do inflect for tense and do so with the same significance as lexical or main verbs imply so we can encounter:
        She needed to get here early
        I hadn't dared to ask her

    etc.
  3. Where they exist, past forms of central modal auxiliary verbs may be used to refer to present and future time (often with a more tentative sense) so we get, e.g.:
        She could come tomorrow
        She might be angry
        I would love to come

    Past forms of lexical or main verbs cannot perform this present-time function.
  4. The central modal auxiliary verbs must and ought (to) have no tense forms at all and could as the past of can or might as the past of may are restricted to certain meanings (see below).
  5. Some central modal auxiliary verbs have alternative verb forms to express other tenses which are in themselves not central so have to is often used to form the past and future of must and be able to has the same function for can and could.  Some of these alternatives are discussed in this guide.
  6. When a central modal auxiliary verb is used in a past form such as in:
        She should have come
        They ought to have been there
        It must have snowed last night

    etc.
    the sense of the present perfect which would be implied with a lexical or main verb of embedding a past in the present is not apparent.  So, for example:
        I have finished
    refers to the present state with the past embedded within it (it's a present perfect form) but
        I should have been kinder
    does not necessarily carry the sense of present relevance and may just be reference to a finished event which has no present relevance.  However, because modal auxiliary verbs express the speaker / writer's current view of an event or state, some sense of present relevance is often maintained.
4

Negatives of central modal auxiliary verbs are formed by the inclusion of the negator not after them

Most of these verbs allow the negator to be contracted to n't which is added to the verb so, for example:
    I will not do it
    Mustn't she come?
    I can't go

    You shouldn't really
are all possible, but
    *I didn't the work
    *I talked not to John

    *They don't should be here
    *I don't must come
etc. are not possible because lexical or main verbs are negated with the do operator in the simple present and past tenses and must and should are central modal auxiliary verbs.
The verb will whether it is functioning as a central modal auxiliary verb or as a primary auxiliary verb referring to the future is unusual in that the vowel mutates from 'i' to 'o' and loses the ending when the negator is appended.  Thus we have won't not *willn't.
The verbs may and shall are infrequently negated with a contracted form of not so:
    She mayn't be there
    I shan't arrive late

are quite rare even in BrE and almost impossible in other varieties.
Semi-modal auxiliary verbs sometimes form their negatives with the simple addition of n't / not but are also able to form the negatives with the do / does / did operator as in:
    He usedn't to be so grumpy
    He didn't use(d) to be so grumpy
    She daren't go
    She doesn't dare go

etc.

5

Interrogatives are formed by simple inversion of the verb and its subject

As in:
    They must do it → Must they do it?
    He can see it → Can he see it?
    She will be early → Will she be early?

and negative questions are formed in the same way:
    Mustn't we do it?
    Won't we be late?
    Can't we go now?

etc.
Lexical or main verb questions cannot be formed this way because they require the do operator so:
    Did you the work?
    Talked not you to John?

are not encountered in Modern English.
Semi-modal auxiliary verbs can also form questions by simple inversion (although this is becoming rare) or by using the forms of lexical or main verbs so we get, e.g.:
    Did he use(d) to work here?
    Used she to be a teacher?
    Did she need to pay?
    Need she have asked?
    Did she need to ask?

    Dared she complain?
    Did she dare complain?

etc.

6

Central modal auxiliary verbs cannot be non-finite

So while, for example:
    Opening the parcel, he was delighted to find the new lens
    She wants to go home

are possible non-finite forms of lexical or main verbs, but no such form exists for central modal auxiliary verbs and:
    *Musting go early, he ran off
    *To can do it is a useful skill

are not permitted.
Semi-modal auxiliary verbs are also possible in non-finite forms so we see:
    Daring his displeasure, she put up her hand
    Needing to leave urgently, they called a cab

etc.
The semi-auxiliary verb used is an exception and is not seen in the non-finite form so there are no forms *to used or *useding.

7

Quantifiers which modify the subject of the clause may occur after a central modal auxiliary verbs

So we allow, for example:
    They can all be here
    The sisters must both pay for a ticket

etc.
This cannot occur with lexical or main verbs so:
    *They hope all to come
    *They do both the work

are disallowed because the determiner must precede a lexical verb as in:
    They all hope to come
    They both do the work.

Semi-modal auxiliary verbs occupy an uneasy middle ground.  We may encounter:
    They all dared to swim
but not
    *They dared all to swim
and
    They used all to work well together
as well as
    They all used to work well together.

8

Reduced clauses with ellipted complements can be used with central modal auxiliary verbs

So we allow, for example, we see:
    She can be there if you can
    They said they could come to the party but couldn't in the end

where the main verbs, respectively be and come, are ellipted.
Lexical or main verbs are not used in this way so:
    *I hope to be there if you hope
    *She spoke about the problems as you spoke

are not permitted because, again, the do operator it required as a substitute for the verb.
Semi-modal auxiliary verbs share this characteristic to some extent but can also occur with the do pro-form so we see:
    She used to be as happy as he did
    They dared ask one question but didn't dare two

9

Central modal auxiliary verbs cannot be emphasised with the do operator

Emphasis in denying a negative assumption or placing stress on the verb is achieved with lexical or main verbs by the use of the do operator as in:
    We do hope to be there
    No, you're right, I do smoke too much
    I did like the music

but this cannot be achieved with central modal auxiliary verbs so:
    *I do can be there
    *She does must have more time
    *I do should go now

are not allowed and adverbials such as definitely, in fact and really are used instead.
Semi-modal auxiliary verbs may be emphasised with the do operator as in:
    They did dare to swim
    She does need to go
    He did used to drive too quickly

10

Time adverbs of indefinite frequency may (not must) follow central modal auxiliary verbs

So we allow, e.g.:
    I should usually be there
    I can often meet him

but
    *I smoke often too much
    ?*She arrived frequently late

are rarer when they are allowed at all.
Semi-modal auxiliary verbs can operate in both ways so we allow:
    She used frequently to start early
    She dared often to stay out late
    She needed occasionally to ask for help

and
    She frequently used to start early
    She often dared to stay out late
    She occasionally needed to ask for help


penguins

One by one

You can use this menu to go to the verb which interests you or work through the page, taking the tests as you go along.
The comments here cover the main uses of each verb and are not entirely exhaustive.

could might should would must can may will shall ought to had better

Clicking on -index- at any time will return you to this menu.

postman

could / was able to

That could be the postman  

Essentially, could performs the following functions in English but the expression was able to is more restricted because it usually only refers to a specific instance of an ability and is always a past time marker.  The word able in this setting is purely adjectival.

Function Example Restrictions with was able to
present possibility That could be the postman now. was able to is not possible:
*That was able to be the postman
future possibility It could rain tomorrow. was able to is not possible
past possibility He could have seen her.  I'm not sure. was able to is not possible
present ability I could do that. It is possible to replace this with the present tense but not with the past form in this meaning:
I am able to do that
present offer I could help with that, if you like. It is possible to replace this with the present tense:
I am able to help with that
but this refers to ability not to an offer.  (See under can below.)
future ability I could finish in an hour if I get some peace. was able to is not possible
past ability When I was only two, I could swim pretty well. was able to is possible:
I was able to swim pretty well
permission Could I ask you a question? was able to is not possible
complaint You could have warned me! was able to is not possible

Notes:

  1. Present possibility and future possibility are not always easy to distinguish.  For teaching purposes, it's rarely important to do so because the forms and functions are the same.  For example:
        A: Are you coming to the meeting?
        B: I could do.

    is an exchange which can apply to right now or the future because we do not know when the meeting will be.
  2. Most uses of could refer to possibility or ability.
        She could have left her keys with John
    can refer to both possibility and ability.  It means either:
        John offered to look after the keys so she was able to leave them with him
    or
        It is possible that she left her keys with John (and that's why she can't find them now)
    Only
    the second use of could can be replaced with might (see below).
  3. be able to is only an alternative if the sense expresses ability.  General ability in the past can be expressed either with could or was able to:
        I could speak French = I was able to speak French
    .
    However, if we refer to a specific instance of success, only was able to is possible:
        I was able to remember the word in French
    not
        *I could remember the word in French.
    This restriction does not apply to negative or interrogative clauses so:
        I wasn't able to remember the word in French
        I couldn't remember the word in French
        Were you able to remember the word in French?
        Could you remember the word in French?
        I wasn't able to swim when I was a child
        I couldn't swim when I was a child
        Were you able to swim as a child?
        Could you swim as a child?

    are all allowed.
  4. When used for permission, could is generally confined to tentative, polite questions.
  5. For the negative deduction uses of could/couldn't have, see under must below.
  6. When used for complaints, the verb is usually interchangeable with might and always in the past form.  So:
        You might have told me = You could have told me
    with very little, if any, difference in meaning.
  7. When used for future ability or possibility, the question forms often imply a request rather than an enquiry about ability or possibility.  For example:
        Could you open the door?
    is not about enquiring about future ability.  It is usually a request.
    However, it could be enquiring about past ability and mean:
        Were you able to open the door?
    or it is a request for some help and means:
        Please open the door.

Try the test.

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snake

might

There might be a snake in the hall  

Essentially, might performs the following functions in English:

Function Example
present possibility Careful.  There might be a snake in the hall.
future possibility It might rain tomorrow.
past possibility He might have telephoned while I was out.
suggestion You might try taking an aspirin.
permission Might I talk to you?
complaint You might have warned me!

Notes:

  1. Some of these are quite unusual and wouldn't be taught at lower levels.  E.g., might for permission and suggestions.
  2. might never refers to ability so:
        She might have left her keys with John
    can only refer to possibility.  it means:
        It is possible that she left her keys with John (and that's why she can't find them now)
    This use of might can also be replaced with could (see above).
  3. The negative of the use for permission is usually expressed with mustn't or can't:
        We mustn't/can't go
    not
        We mightn't go
    because that implies an unlikelihood.
  4. The negative of the use for past possibility:
    when the speaker is quite sure of something this is usually expressed using couldn't have / can't have:
        He couldn't / can't have got out
    when the speaker is unsure we use might:
        He might not have tried to telephone me
  5. might is often seen as adding 'distance' – making possibilities less likely and requests or suggestions more polite.  Compare
        It could rain
        It might rain
        Could I go now?
        Might I go now?

Try the test.

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headache

should

You should take an aspirin  

Essentially, should performs the following functions in English:

Function Example
advice You should see a doctor.
You should have called me.
obligation
present, past and future
You should not talk that way!
You shouldn't have said that.
conditional uses We should love to come (if we are invited).
(See note 2)
Should you need any help, just ask.
logical deduction Mary should be home soon.
They should have arrived by now.

Notes:

  1. The distinction between strong advice and obligation is often blurred – the roles of the speakers usually give the game away.  If someone in authority such as a teacher or manager uses should it usually expresses obligation.
  2. The conditional use of should for 1st person forms instead of would is often seen as formal and pretty much confined to British English.  This is also called the contingent use.
    In the past we prefer:
        We would have loved to come but were away at the time
    to
        We should have loved to come but were away at the time
    although both are possible.
  3. should is occasionally used in rather odd, formal expressions such as:
        I regret that it should have happened.
    This is the putative use of the verb.

Arguably, the contingent use of this verb is a tense form and, therefore the verb is acting as a primary auxiliary verb.

Try the test.

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bench

would

He would often take his dog  

Essentially, would performs the following functions in English:

Function Example
request/volition Would you leave me alone, please?
conditional uses You would be in danger if you tried it without training.
habit We would always have tea at 5.
characteristic That's just the sort of thing he would say.

Notes:

  1. Would is one of the most common words in English, ranking approximately in 60th place.
  2. The conditional uses are extremely common.  This is also called the contingent use.
  3. When used to describe past habit, it frequently follows an initial use of used to and often expresses nostalgia.  As in, e.g.:
        We used to take our holidays in France where we would stay in a small guest house and would eat good, local food every evening.
  4. When followed by rather, with or without ... than ..., the verb indicates preference:
         I'd rather stay in and watch television (than ...).
  5. There is a slightly unusual use of would to express an uncertain deduction about a past event (see under will below).  Compare, e.g.,
        That'll be Mr Brown you saw in the classroom
    which implies the speaker is more confident than:
        That would be Mr Brown you saw in the classroom.

Arguably, would also functions as a tense-forming primary auxiliary verbs to which there is a guide linked below.

Try the test.

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sisters

must / have to / needn't

That must be her sister  

Essentially, must performs the following functions in English:

Function Example Restrictions with have to and needn't
obligation Must I take the test? None.
Do I have to take the test?
No, you needn't take the test
No, you don't have to take the test
logical deduction That must be his brother.  Aren't they alike? needn't is not possible in this meaning
advice You really mustn't make such a fuss. Neither needn't nor have to can be used in this sense because they imply a greater sense of negative obligation.

Notes:

  1. The difference between strong advice and obligation is often very blurred (if it exists at all).  Much depends on the authority with which the speaker is endowed.
  2. must can be replaced by have to in certain circumstances only.
    1. External vs. internal obligation: it is often asserted that have to implies an external obligation but must refers to an internal one.  Compare
          I must get this done
      which can mean that this is a self-imposed obligation, with
          I have to get this done
      which can imply an external obligation.
      Too much can be made of this dubious distinction and it's probably not worth teaching it because native speakers use the verbs in free variation in most cases.
      It is also difficult at times to state categorically whether an obligation is internal or external especially if there is little context.
    2. Tenses: must used for obligation has no future or past forms (but it does in the sense of deduction, see note 4.) so the use of have to is obligatory in, e.g.:
          I had to do it yesterday
          We'll have to wait and see
      etc. and:
          *I must do it yesterday
      is not allowed, although
          We must wait and see
      expresses current obligation with a prospective aspect.
  3. The negative of must for obligation has two forms:
    1. No obligation: needn't / don't have to
          You needn't / don't have to go
      )
      Only didn't have to / didn't need to express a lack of obligation in the past.  The expression needn't have suggests something was unnecessarily done.  Compare:
          He didn't need to do it (so didn't)
      with
          He needn't have done it (but did).
    2. Negative obligation is expressed with must not
          You mustn't go
  4. The negative of the use for deduction in standard British English is formed with could not or cannot:
        He can't have done it by himself
        It couldn't have been the same man
    However, in some varieties must not is used for a negative logical deduction.
  5. Interrogative clauses asking for speculation or deduction are also formed with can and could as in, e.g:
        Can it have been forgotten?
    or
        Could that be her mother?
    so:
        Must it have been forgotten?
    refers rather oddly to obligation and
        *Must that be her mother?
    is disallowed.
  6. The deductive sense of the verb does have a past form:
        He must have escaped
    etc.
type

The types of obligation signified by have to

A certain mythology has grown up around the use of must vs. have to to express obligation which it may be as well not to allow to propagate too widely.  In particular:

  1. We noted above (2a) that it is sometimes averred that have to applies to external obligation placed on a person and must is used for internal senses of obligation and duty.  It follows that:
        I have to write to my mother
    is an obligation placed on me by another and
        I must write to my mother
    is a sense of duty I am imposing on myself to commit to an action.
    This is a very doubtful assertion and the forms in the present tense are used in free variation by many speakers with those from the USA, in particular, often preferring have to to must in all senses.
    Furthermore, it is not always clear whether an obligation is internal or external so, for example:
        This tooth is getting worse and I must get to a dentist
    is as likely as:
        This tooth is getting worse and I have to get to a dentist
    There are other problems with this assertion:
    1. It cannot apply to past and future forms because must is structurally unable to occur so:
          I had to write to my mother
      or
          I will have to write to my mother
      cannot be compared to some kind of internal obligation using must because no form with that verb is available.
    2. have to (like must) can signify other forms of modality so, for example:
          He must be the bride's father
      cannot be contrasted with
          He has to be the bride's father
      because neither sentence denotes any kind of obligation, internal or otherwise.  The sense concerns the likelihood of a proposition being true and that is epistemic modality.
      By the same token:
          The answer must be between 0 and 1
      cannot be contrasted with
          The answer has to be between 0 and 1
      because, again, neither sentence refers to obligation at all but to a necessary truth.
  2. It is also suggested that must refers to a specific obligation and have to refers to more general obligations so, it is averred:
        I must tell her the truth
    is correct and so is:
        We have to tell the truth at all times
    but the alternative formulations:
        I have to tell her the truth
    and
        We must tell the truth at all times
    are somehow wrong.
    That is nonsense, of course, and the same issues with other tenses intervene to show that.  The only way to express the past or future obligation is:
        I had to tell her the truth
        I will have to tell her the truth
    and
        We had to tell the truth at all times
        We will have to tell the truth at all times
    so, whether the obligation is general or specific cannot be a consideration.  The same applies to the insertion of progressive or perfect aspects.
  3. Finally, it is also often suggested that we use must to refer to duties we impose on others and we reserve have to to imply that the obligation comes from elsewhere (a similar but slightly subtler idea than the external-internal distinction).  So, it would follow that we should prefer:
        You must be careful (because I require it)
    to
        You have to be careful (because other authorities require it).
    There is slightly more substantiation for this distinction and little doubt that some English speakers will prefer have to to signify a rule and must to signify a personal admonition so making a difference between:
        Must I wear a uniform?
    to mean:
        Do you insist that I wear a uniform
    and
        Do I have to wear a uniform
    to mean
        Is there a rule about uniform wearing?
    However, whether this distinction exists is slightly doubtful and whether it is worth troubling most learners with it is even more doubtful.  It is unlikely that most native speakers would wince if the modal auxiliary verbs were used in reverse.

- index -

jail

can / be able to

She can't get out  

Essentially, can performs the following functions in English but be able to is more restricted in use because it only refers to ability.  It is, in fact simply a dynamic modal adjective phrase.

Function Example Restrictions with be able to
ability Can you do it before tomorrow? Are you able to do it?
permission You can go now. be able to is not possible in this sense
possibility The weather can be dreadful in March. be able to is not possible in this sense
request / offer Can you help me?
Can I help?
Are you able to help me?
Am I able to help?
are both possible but do not carry the sense of a request as they refer to ability only

Notes:

  1. When the request form uses the 1st person, it functions as an offer:
        Can I help?
  2. The negative of the permission function can be expressed using can or must:
        You can't leave yet
        You mustn't leave yet
  3. cannot have / can't have only occurs as negative past deduction (see under must).  It is not used for permission or ability in the past.
  4. be able to is only an alternative if the sense expresses ability:
        I can speak French = I am able to speak French
    However, able to is not possible in other senses: you can't give permission by saying:
        *You are able to ask questions at the end
    and there is a functional difference between:
        Are you able to help me?
    and
        Can you help me?
    The first enquires about ability and the second about willingness so it's a request.
    Like must, can has no future form (although it does have a past in some senses of ability only, see under could, above).  For this reason, future senses are expressed as follows:
    1. Future ability:
          She will be able to help tomorrow
          She can help tomorrow

      In the second of these examples, there is a possible ambiguity because it also has the meaning of
          I will allow her to help tomorrow
    2. Future permission:
          They will be allowed to go later
          They can go later
    3. Future possibility:
          The weather might be dreadful next March
      but
          *The weather can be dreadful next March
      is not possible).

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question

may

May I ask a question?  

Essentially, may performs the following functions in English:

Function Example
permission May I sit here?
possibility/doubt That may be his brother.

Notes:

  1. The permission use is often seen as a more formal version of can.  Compare might.
  2. The possibility use often implies less likelihood than could.  Compare
        I can be cold in April
    with
        It may be cold in April
    The former also implies in general whereas the latter often refers to a particular future.
  3. The negative is slightly peculiar:
    may not cannot express impossibility because there remains some doubt in the speaker's mind.  We use can't/couldn't for that function:
        That may not be his brother
    (but it may be)
        That can't/couldn't be his brother
    (and I'm sure it isn't)
    It does, however, express doubt in, e.g.:
        That may not be what you need
  4. may not for prohibition (i.e., negative permission) is used but is very rarely contracted to mayn't.  For example:
        You may not leave until the examination time is up

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letter

will

I will write when I can  

Essentially, will performs the following functions in English (see also the section on tenses, linked below, for the use of will to talk about the future):

Function Example
requests Will you walk this way?
logical deduction That will be the postman.
promise I'll write when I can.
willingness / volition Will you marry me?
insistence He will keep complaining.
ability The restaurant will seat 50 people
futurity I will be 28 tomorrow

Notes:

  1. The insistence use never contracts will to 'll. So,
        He'll keep complaining
    is a prediction about the future but
        He will keep complaining
    is a comment on his insistence.
  2. The promissory use is almost always only first person unless we are reporting what someone else intended to do:
        I'll come early to help
        He said he'll write when he can
        You said you'll do it
    etc.
  3. The negative of the use for deduction is often formed with cannot:
        That can't be the postman
    but if the speaker is more certain or is basing the statement on evidence or experience then won't can be used:
        That won't be the postman; it's too early.
  4. The use for ability is somewhat formal and may be replaced by the present simple tense.  For example:
        The bottle will hold 3 litres = The bottle holds three litres
  5. There is often a confusion between volition and futurity which is unhelpful for learners.  For example:
        Will you marry me?
    refers to the hearer's present willingness or volition but
        Will she marry him
    asks for the hearer's speculation about the future.
    See the guides to tense and aspect for more on this common confusion.

Arguably, will also functions as a tense-forming primary auxiliary verbs to which there is a guide linked below.

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dance

shall

Shall we dance?  

Essentially, shall performs limited modal functions in English (see also the guide to tenses, linked below for the use of shall to talk about the future):

Function Example
suggestion/offer Shall we go?
Shall I help?
obligation That shall not happen.
futurity We shall be in France tomorrow

Notes:

  1. The suggestion/offer use only occurs as an interrogative.  This use is confined to the first person, singular or plural.
  2. The obligation function expresses great determination and is generally perceived as formal.
  3. In neither of the first two functions can the verb be contracted to 'll but it can, and usually is, contracted when it refers to futurity.
  4. The use of the verb to signal futurity is, in fact, a function of a primary auxiliary verb and that is how it is considered in the guide to them linked below.

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train

ought to

She ought to be on the train  

Essentially, ought to performs the following functions in English:

Function Example
obligation You ought to go now.
logical deduction She ought to be here around 6.
(This could also imply obligation.)
advice You ought to take him to the vet.

Notes:

  1. The difference between strong advice and obligation is often very blurred (if it exists at all).
  2. It is often asserted that ought to implies a sense of duty rather than pure obligation or advice.  Compare:
        You should write to him
    with
        You ought to write to him
    For most learners of English, this is irrelevant.
    (This distinction may stem from the fact that ought is an old past participle form of the verb owe and we owe a duty.)
  3. The negative of ought to for obligation has two forms:
    1. No obligation: needn't / don't have to:
          You needn't / don't have to go
    2. Negative obligation: ought not:
          You oughtn't (to) go.
      Omitting the 'to' is rare and formal.
  4. The negative of the use for deduction is formed with cannot:
        She can't have left already
  5. There is some evidence of the existence of ought as a non-modal auxiliary verb with forms such as:
        You didn't ought to do that
        Did he ought to ask permission?
    etc.
    Such forms are at best non-standard; many would consider them illiterate.
  6. In American English in particular (but increasingly evident in other standards) the bare infinitive is quite common in the negative:
        You oughtn't do that

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had better

had better

You had better not!  

This structure is not considered a central modal in all analyses but it is included here because it acts like a central modal auxiliary verb in many ways.
Essentially, had better performs the following functions in English:

Function Example
advice You had better wear something warm on the boat trip.
warning / threat You had better not do that again or there'll be trouble.
future (desperate) wishes It had better rain soon or the garden will die.
suggestions Hadn't we better ask for permission?

Notes:
  1. The word had is frequently contracted to 'd, causing some to confuse it with would.  E.g.:
        I'd better go = had better
        I'd rather go = would rather
  2. The form is only used for present or future events.  There is no past form and in reported speech the verb is often replaced, so
        You had better not do it
    is reported as:
        He said we shouldn't do it
    or remains unchanged
        She told us we had better not be late
  3. The negative form for advice is formed as had better not.  For example
        We had better not be late
  4. There is a common negative question form for tentative suggestions:
        Hadn't you better get some sleep?
  5. The advice function only refers to specific situations or actions.  Compare:
        You had better not listen to him
    with
        *You had better not listen to bad advice
    For general situations or actions rather than specific ones, the preferred verb is should:
        You should not listen to bad advice.
  6. The warning / threat function is often implicit in the verb:
        You had better not be late
    may be responded to with
        Or else?
    The verb should does not routinely imply this.
  7. The functions of hopes and warnings usually refer to a near future.  Hence the form is often accompanied by time adverbials such as soon:
        You had better finish that soon
        He had better arrive in the next day or so or he'll be too late
  8. The form is often used as an ersatz conditional:
        You had better do that carefully or you'll get paint on the floor
    equals
        If you don't do that carefully, you'll get paint on the floor
  9. Informally, better may be replaced with best:
        You'd best tell the truth
    Some consider this colloquial or even illiterate.
  10. Question forms are as for other modal auxiliary verbs but are quite formal and rarer:
        Had I better talk to him?
    In fact, the negative question form is a lot more common:
        Hadn't I better talk to him?
  11. The form is not used to talk about preferences (that's the function of would rather, see above under would).
  12. The form cannot be used for obligation although its use by someone in authority often implies obligation rather than advice..
  13. In rapid speech the 'd is often not audible and the form sounds like, e.g., you better, leading some to leave the word out deliberately in speech and in writing.

- index -

Summary

Here's a summary diagram of much (not all) of this.  In particular, restrictions are not included here.
The use of some verbs to signal futurity is distinguished here in purple boxes because that function is that of a primary not modal auxiliary verb.

summary


languages

Other languages

The concept of modality is common to all languages.  We all have a need to express things like willingness, probability, likelihood, obligation, requirement and so on.  Modality may not only be achieved by the use of modal auxiliary verbs, of course.  Saying something like:
    I'm almost certain he'll be late
instead of
    He'll be late
is still using modality in language.
Modal auxiliary verbs are, however, very variable across languages.  Here's a brief run-down by major language groupings explaining a little of how it all works.  There won't be enough detail here for your particular students and your setting but it is somewhere to start.  You can get more on line but beware the unreliability of many sites.
Swan and Smith, 2001, is a usually reliable source albeit frustratingly inconsistent in covering modality.

Languages What they do
Arabic
Standard Arabic does not have modal auxiliary verbs which correspond exactly to English modal auxiliaries.
However, it does have many precise and detailed ways to express modal concepts.  For example
must, have to, should, might, may, it is possible to, it is impossible to, it is expected that, it is easy to, it is hard to, it's worth mentioning that, it's well-established that, it's most likely that, it's forbidden to, it's permitted to, it's more proper to
and a range of other concepts are all expressed through a form of modal construction.
The problem, of course, is that these categories do not mirror the modal categories of English so expect a good deal of confusion, especially with modal auxiliary verbs like may and could which have a range of functions.
The concept of having a large range of modality in the language will not be mysterious to learners from an Arabic-speaking background.
(Source: Arabic learning resources at http://arabic.desert-sky.net/g_modals.html)
Chinese languages Modern Standard Chinese, too, has a range of modal auxiliary verbs, as one would expect of an isolating language.  They are, however, not at all parallel to those in English.  There are, for example, three modal auxiliary verbs which perform the functions associated with can (ability, permission, possibility) in English.  The most commonly used modal auxiliaries in Chinese languages express
want; ask for; wish; desire
want to; would like to; feel like (something)
should; ought to; must
can; be able to; be capable of
like; love; prefer; enjoy; be fond of
can; may
be good at; be skilful in
be willing to

Conceptually, modality poses no problems but overlapping meanings will make life difficult.
Slavonic languages including Russian, Polish, Ukrainian, Czech, Slovak etc. Slavonic languages also have modal auxiliary verbs but, as usual, the categories don't exactly match (although they are closer than many languages).  A single verb form (roughly translatable as must) serves in Polish for the English verbs must, need to and ought to, for example.
In Czech, there is a clear distinction between externally and internally imposed obligations, often rendered in English by must vs. have to, should or ought to.
Russian has a simpler modal system than English so you may encounter, e.g., He must not used to mean He needn't / doesn't have to.
Germanic languages These languages use modality is ways quite similar to English which makes life easier for learners from these language backgrounds.  The most important exceptions often concern the negative uses.  For example, in German the translation of needn't / don't have to, expressing the lack of obligation either way, would be must not [muss nicht] and that causes confusion.  To translate the English sense of must not meaning prohibition, German uses a different modal auxiliary verb [darf nicht], roughly translatable as may not.
In Swedish, the verb used for the sense of needn't is cognate with the English expression behove.
In these languages, too, there are usually more tense forms available so an equivalent of had to may be rendered as *musted.  Learners may be confused by a logically constructed tense form in their first language, the past or future of must, for example, not existing in English.
The overlap in meanings between cognate modal auxiliary verbs is not precise so expect errors such as It can be used to mean It might be.
There are few serious conceptual difficulties otherwise.
Romance languages including French, Spanish, Italian, Portuguese, Romanian etc. These languages do not have a separate grammatical category for modal auxiliary verbs and usually render the concepts as a verb followed by an infinitive form, e.g., in French Je peux aller (I can go) or in Spanish Puedo ir.  Expect, therefore, errors such as
    *I can to eat
    *You must to enter
etc. because many learners perceive the to-form as the infinitive in English.
Some modal concepts, e.g., for obligation, are expressed in the passive (It is necessary that ...).
There is, in these languages, no equivalent to the use of be to express obligation as in, e.g.:
    You are to be here at 6
and a modal auxiliary verb (often an impersonal one) will be used instead.
Swedish, Danish and Norwegian Scandinavian languages have a separate class of modal auxiliary verbs although use is an issue.  The verb kan, for example, is used to talk about the possible future where English would use may or might.  Expect, therefore,
    *It can rain tomorrow.
Other uses of modal auxiliaries are close parallels with English.
Japanese Japanese has two classes of modal auxiliary verbs: those which are attached to stems and cannot function independently and those which are ordinary verbs which lose their meanings when acting as auxiliaries.  We have, therefore, structures such as miru (to see) leading to mirareru (to be able to see).
The concept of modality will not be strange but the forms will cause problems in English.
Greek, Turkish and other languages Some languages have a very reduced set of modal auxiliary verbs to call on.  Greek, e.g., really has only two (must and can), one of which only exists in the It is necessary / necessarily true that sense in the third person.  Added to these problems is the tendency to make past modal auxiliary verbs in completely different ways (often rendering the modal auxiliary in the present with the main verb in the past) so mistakes such as
    *I can saw it (for I was able to see it)
are possible.
Turkish speakers will have few problems with the modal system of English as such because the language has many parallel structures if not always parallel senses.


Try a test on all these modal auxiliary verbs.



Related guides
essential guide to modality for a simpler guide in the initial training section
semi-modal auxiliary verbs in guide which also considers marginal modal auxiliary verbs such as seem, tend, be about to etc.
types of modality for a more technical (some say more useful) guide to types of modality such as epistemic and deontic modality
modal auxiliary verbs: tense and aspect a guide which considers the modal auxiliary verbs in relation to perfect and progressive forms
primary auxiliary verbs for the guide to how verbs function to form tenses and other aspects of the verb including passive clauses
complex tenses a guide which considers complex tenses in relation to modality (I shouldn't have done it etc.)
multiple modalities this guide considers how, despite the prohibition on co-occurrence, English manages to signal multiple modality
teaching modality for some ideas on how to use this analysis which includes the consideration of other languages set out here
the modality index for links to a range of related guides