Need help identifying if this is 1) grammatically correct, and 2) an infinitive verb without the word "to" (when to use infinitive without "to"?)

Solution 1:

A somewhat simplified version, presplit for parsing, is

• What I have done to fix this problem is
  • modify local to sleep 20 seconds (by calling sleep)
    • and then
  • call mount.

This is a Wh-cleft sentence, related to (or derived from, depending on your religion) the basic sentence

• To fix this problem I have modified local to sleep 20 seconds
  (by calling sleep) and then called mount.

Both the modify clause and the call clause here are perfect participles, deriving from the have in the first clause, but they're infinitives in the original Wh-cleft sentence. Why?

The reason is the insertion of Action do (in this case, done, a perfect participle) by the cleft transformation as the past participle completing the perfect in the first cleft, thus requiring the verbs in the second cleft to be infinitives, because Action do takes infinitive complements in clefts, and the to complementizer is optional:

• What he did/has done was/is (to) find the phone.

So, yes, infinitive complements are grammatical, with or without to, in this kind of Wh-cleft. As in some other kinds of constructions. But not all. The individual verb or construction (or a combination, as here) governs everything.

Solution 2:

You could have written the sentence more simply e.g.

I have fixed this problem by modifying /etc/rc.local to sleep 20 seconds and then calling mount -a.

However, you made a valid choice to focus emphasis on the actions that you took, by creating a 'pseudo-cleft' (or Wh-cleft) sentence of the form 'What I did [to be verb] something [and something else]'. Thus the emphasis falls on the part of the sentence after the what-clause + be. If the verb in the first part is 'do' then we use an infinitive verb (with or without 'to') in the second part, e.g. What I have done is (to) write a letter to the editor.

Pseudo-cleft sentences