TO connects verbs and adjectives which take infinitival complements
to the word "to".

            +---TO--+
            |       |
        I tried     to start the car
        We intend   to be firm
    We are eager    to do it

The word "to" then makes an I link to an infinitive verb
form. "To" therefore carries "TO- & I+".  The "TO" link almost
always forms a cycle with the "IV" link, which connects
directly to the infinitive.

Verbs which take "to"+infinitive have "TO+" connectors.  Many
such verbs can also take other kinds of complements; simple
objects (O+), clauses with or without "that" (TH+/ Ce+),
indirect questions (QI+), and so on. Such connectors are
disjoined with "TO+". In some cases, the verb may take no
complement at all "We hesitated"; in others, some kind of
complement is obligatory (*"We intend"). Some verbs take a
direct object plus an infinitive ("We told him to go"); these
verbs do not use TO+, but rather TOo+. See "TOo" below.

Some adjectives also take "TO+". This is only the case for
usages where the same subject is implied before and after the
adjective: "We were ready to go", but not "It is important to
go". In the latter case, TOi is used. See "TO: Other kinds of
TO connectors".

There are other situations involving "to"+infinitive where
specially subscripted TO+ connectors are used: transitive
adjectives ("He is easy to hit"; "TOt+"), indirect
questions ("I wonder where to go"; "TOn+") and nouns that
take to+infinitive ("We made an effort to go"; "TOn+").
These connectors are explained below; see "TO: other
kinds of TO connectors".)  The word "to" (and only this word)
carries unsubscripted TO-, it is directly conjoined with
I+. The reason for the distinctions between TO, TOt, TOn TOi,
and TOo relates to post-processing.  Recall that
post-processing divides the links of a sentence into groups,
corresponding roughly to subject-verb expressions. In some
uses of infinitives - specifically, those described above
which use unsubscripted TO - the infinitive simply continues
the subject-verb expression that precedes it. Indeed, one can
use a number of infinitives, all relating to the same subject:
"I hope to be ready to consent to try to do it." In other
cases (those specially subscripted TO connectors), the
infinitive implies a different subject from what precedes ("I
told him to go", "He is easy to hit"). In these cases the link
connecting "to" with the infinitive must start a new
domain. This is particularly important in sentences like the
following, where post-processing is used to enforce the use of
certain verbs.

        There is certain to be a problem
        *There is eager to be a problem
        There might be an opportunity to refuse to do it
        *There might refuse to be an opportunity to do it

In addition, certain uses of infinitives are only permitted
with "filler-it" as the subject: "*Jane is important to
go". See "SF: Filler-it" for explanation of all this.

It is important to note that we allow any kind of
sentence to take an infinitival phrase, meaning "in order
to": "We bought some eggs to make cookies". See "MVi".
We give this connector a cost of 1. Thus many sentences
which involve incorrect uses of "filler"-only phrases
("Jane is important to do it") will receive valid linkages
using "MVi". 

TOo: Infinitival complements of transitive verbs
Some verbs can take an infinitival complement as well as a
direct object. In such cases, TOo is used.

             +---TOo--+
             +--O--+  |
             |     |  |
        I advised him to go

It will be seen that every "TOo" on verbs is conjoined with a
preceding "O+". (Usually the TOo+ is optional: "I advised
him".)  Note that in such situations, the infinitival verb
relates not to the main subject ("I" in this case), but to the
direct object of the verb ("him"). This is unlike other
infinitival complements of verbs ("I hesitated/wanted/tried to
go") where the preceding subject remains in force; for these
situations, we use "TO".

Like TO, TOo connects a verb to the word "to". The reason for
distinguishing between them relates entirely to
post-processing.  TOo begins a new domain, thus telling
post-processing that a the infinitive verb relates not to the
preceding subject but to a new subject. In addition, TOo links
start a special kind of domain, "urfl domains". Ordinary
domains contain everything that can be reached from the right
end of the domain-starting link. "Urfl domains", however, also
include anything that can be reached from the left end of the
domain-starting link as well as anything underneath that link.
(Hence the name: "urfl" stands for "under root from left".) In
the case, below, then, an ordinary domain started by the "C"
link would contain only the "D" link. An "urfl" domain started
by the C link would contain the C, the D, and the B.

            +---C---+
        +-A-+-B-+   +-D-+
        |   |   |   |   |
        bla bla bla bla bla                

This is useful in the case of verbs which take objects and
infinitives. Recall that the logic of domains is that links
relating to a single subject-verb expression should be
contained in a group. In this case, the infinitive relates to
the object of the preceding verb; thus we want the O link to
be in the same group as the infinitive. TOo starts "x"
domains, which are "urfl":

             +--TOo(x)+
        +-S--+-O(x)+  +I(x)+
        |    |     |  |    |
        I   told  him to  go

We use this to control uses of "filler-it" and "there".  "It"
and "there" have OX- connectors, which are used only in cases
like this. The use of verbs and adjectives with "filler-it"
and "there" is highly constrained; we have a complex apparatus
for enforcing these rules in post-processing (see "SF"). The
same rules apply when "it" and "there" are used with
Obj+infinitive constructions.

              +-TOo(x)-+
              +OX(x)+  +If(x)+Paf(x)+
              |     |  |     |      |
        I expected it  to   be    easy to use the program
      *I expected Jane to   be    easy to use the program

Once we have the adjective/verb connectors in the same group
as their implied subject, as in this case, we can simply apply
the same constraints to "OXt" (for "there") that we apply for
"SFst", and the same constraints to "OXi" that we apply to
"SFsi", and everything else follows naturally.

Other Kinds of TO Connectors: TOn, TOi, TOt
TOn is used with nouns that take infinitival complements: "The
EFFORT TO finish the program was successful".  (Only certain
nouns can take such complements: "*The computer to finish the
program was fast".) With such nouns, the TOn+ is conjoined with
the @M+ (used in prepositional phrases and some other kinds of
modifiers), disjoined with the "(R+ & B+)"; this is perhaps
rather arbitrary.

TOn is also used in indirect questions, to connect question
words to "to": "I wonder WHERE TO go". (In object-type
indirect questions, like "I wonder what to do next", no TOn
connection is made; see "I".) Question words such as "where"
therefore have "R- & (TOn+ or Cs+...)". Finally, TOn is used
on superlative adjectives; such adjectives can take infinitive
expressions, as in "He was the first to climb Mount Everest".

TOi is used with adjectives that take infinitival complements
but which take "filler-it" as the main subject.

               +-TOi-+
               |     |
        It is fun   to try to beat the program

In such cases, there are constraints on the verbs that may be
taken by "it" ("*It tries to be fun to beat the program"), but
not on the verbs in the infinitival phrase.  This is enforced
with post-processing; see "SF: Filler-it".

TOn and TOi both start new domains. They are therefore like
TOo, but unlike TO, which is used with adjectives and verbs
that take infinitive complements but which does not start a
new domain. The reason is that the infinitive and what follows
usually imply a new subject, rather than relating to the
subject that precedes. This is important, for uses of
"filler-it" and "there".  See "SF".

TOt is used for certain adjectives which take transitive
infinitival constructions.

                 +----B-----+
                 +-TOt-+-I--+
                 |     |    |
        John is easy   to  hit

Such adjectives take "TOt+ & B+", disjoined with their other
complement connectors (TO+, THi+, etc.). 

TOf is used to enforce the correct use of "filler-it". "TOf+"
connectors are found on adjectives which do not start new
domains, but which may also be used with "filler-it" and
"there", such as "likely" and "certain".  See "SF: Filler-it".

TOc and TOtc are used with comparatives; see "MV: Comparatives VI".