What we call a dictionary that link positional synonymous words? Is there one already?

I found a dictionary that list words with the same root meaning but different in position, either as subject or object or even predicate, useful.

As an example, when we look for the word "eat", it will provide what synonymous words as subject ("eater"), as adjective ("eatable"), as object ("eatable" too?), as adverb of place ("eatery"), as adverb of time (not exist), and as verb itself ("eat" / "eat" / "eaten").

Does this kind of dictionary exists? What people call this kind of dictionary?

My copy of Chambers Dictionary (revised 13th edition) includes, under the headword eat, more or less information on the words: eating, ate, eatable, eatage, eater, eatery, eaterie, eating and then a slew of expressions such as eating apple, eat into, eat one's words.

I just call it a dictionary. I expect to find similar coverage in other good dictionaries.