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

Question

I'm a well-educated, native English speaker in the United States. I have (what I would consider) advanced English grammatical understanding from my deep study of Spanish and French. I understand and can recognize various verbal forms, like the nominal gerund form: "I like walking", the present progressive/present participle: "I am walking", the infinitive with "to": "I like to walk", the past participle: "I have walked", the simple past: "I walked", the present subjunctive: "Let them walk", the past subjunctive ("were") followed by a gerund in present participle form ("walking"): "I wish I were walking", etc. But, I need help to better understand this form: "What I have done is walk."

However, I need confirmation what I am seeing below is correct.

1. Is my original sentence below correct?
2. Is my verbal usage of the two words in bold a form of the infinitive without the word "to"? Or, is it the imperative (I don't think it's this, but it has the same conjugation), or is it something else? What grammatical concept am I using? If the infinitive without "to", then when should one omit "to" in the infinitive?

On the Ask Ubuntu Stack exchange, I have this answer here.

My original wording was this. It sounds natural, native, and correct to me. Is it? The two verbs in question (I think they are infinitive without the word "to") are in bold:

What I have done to fix this problem (on my Pi3) is modify /etc/rc.local to sleep 20 seconds (by calling sleep 20) and then call mount -a.

Someone from Greece just changed the wording to this, catching only the first verb and changing it to a gerund:

What I have done to fix this problem (on my Pi3) is modifying /etc/rc.local to sleep 20 seconds (by calling sleep 20) and then call mount -a.

I think my original form is correct, and the correction sounds to me not only grammatically incorrect, but non-native.

Reading I've done:

1. Grammar Monster: Non-finite Verbs. One particularly interesting part (but they seem ignorant of the English subjunctive entirely, since it's a bit archaic, not well-understood by most, and generally not formally-taught):

   Not all infinitives are preceded by "to." Infinitives also feature in verb chains after verbs like "could," "may," "should," and "would" (i.e., auxiliary verbs) and verbs like "to make" and "to let."

   • If the highest aim of a captain were to preserve his ship, he would keep it in port forever. (Saint Thomas Aquinas)
   • Let them eat cake. (Queen of France Marie Antoinette)

Related:

1. What is the correct way to use infinitive after the verb "help": with or without "to"?
2. Wikipedia: "bare infinitive" - https://en.wikipedia.org/wiki/Uses_of_English_verb_forms#Bare_infinitive

Answer 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.

Answer 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

Answer 3

In my non-native ears (but English speaker since the 1970s), I want to fill in the "to". Without, it sounds really strange to me.

What I have done (...) is to modify /etc/rc.local to sleep 20 seconds.

regardless of the many other "to" in the sentence