Linguists regard will as a present tense, so it's correct to me. Learners and language coursebooks often talk about it as a future tense, but linguists tend not to agree. They say it's a modal- will in the present tense and would in the past. Time and tense in English are not synonymous in linguistics.
Correct, Tdol. The problem is the confusion between grammatical form and usage (its actual meaning). Some old-fashioned type of English grammar book will tell you that " I am leaving now" is present progressive tense but that the intended meaning is future tense. If a grammar book fails to mention and/or teach it, it should not be used by students. I studied English at school some 45 years ago at a time when my native country (Estonia) still formed part of the former Soviet Union and when we were given these terrible English textbooks with focus on grammar form and disregarding grammatical function completely.
I have a text called "Friendly English Grammar" by Robert de Beaugrande, an American linguist (died in 2008). Robert was an outstanding linguist and held positions as a univeristy professor at unis worldwide with quite a long list of publications to his credit. He was able to give lectures and seminars in 7 different languages, and one of his advanced degrees includes a Master degree in German Language and Literaturer from Berlin Free Univeristy, one of the best universites in Germany. His grammar is based on text-linguistic research as to what form is used when in what piece of text (literary genre).
The book is out of copyright and I am thinking about editing it a bit and re-publishing it. It's also somewhat entertaining because of all the jokes and funny pictures in it...LOL
Not quite. In my opinion, it should be as follows:
[S ((Pronoun) +VP (modal verb + V)))]
When generating a syntactic tree, you would have to add "He" below the Pronoun string, "would" below the modal verb and "play" below the V string, the latter two of which belong to the VP.