An agreement between two parties, pledging faithfulness, entered into for the purpose of drawing closer together in mutual love. Like marriage. It must be added that usually, and by usually I mean almost always, the two parties are estranged or hostile and need a mediator.
Given this broad definition of a covenant and the iron clad evidence from Hosea it's not inconceivable that Adam had a covenant with God. We read:
Genesis 1:28-29, 2:6 "Then God blessed them, and God said to them, "Be fruitful and multiply; fill the earth and subdue it; have dominion over the fish of the sea, over the birds of the air, and over every living thing that moves on the earth."And God said, "See, I have given you every herb [that] yields seed which [is] on the face of all the earth, and every tree whose fruit yields seed; to you it shall be for food... Of every tree of the garden you may freely eat; but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die."
But upon careful examination this notion of covenant doesn't hold up as a good explanation for this text. It feels stretched, imported, out of place.
It seems more sensible just to say God created Adam as a son, in His own image, and told him the creation was his to rule and manage, then instructs him not to eat the forbidden fruit lest he die. But that's not a covenant. Adam didn't pledge anything, there was no other party, there was no agreement, no Biblical language indicating they cut any kind of agreement. They were already a family, in harmony, in a relationship, walking and talking together about how things were. The theologians will offer the rejoinder: that's why it's a unilateral covenant, a Suzerain-Vassal style covenant. There are not two parties because it's not that kind of covenant.
However, that reduces Adam to a kind of slave, to someone who is not already the expression of God's goodness. It doesn't fit at all. The more simple and straightforward answer is that God gave His son Adam the rules as boundary markers on their relationship -
But if there is no covenant with Adam then what to do about Hosea? Could the covenant in mind there be the protoevangel? No because how would Adam have disobeyed that? It's either Genesis 1:28 or bust.
But if it's bust then how do we manage that passage? I think the KJV has the right answer. "But like men they transgressed the covenant; There they dealt treacherously with Me."
The simpler explanation is that men are by their nature faithless, treacherous, covenant breakers. Abraham didn't listen to God. Jacob told God "If you bless me then." Moses did not honor God as holy and could not enter the promised land. David committed adultery. Solomon took wives and turned his back on God.
There was and is not a man that didn't disobey, that didn't transgress. That does what is right, what is Good. There are none. The people in Hosea's day did not obey because that's what men are. That's why it took God coming down in the flesh, in humanity, because men are faithless even to their own fathers who love them deeply and desire the best for them, and it takes a supernatural act to put the machinery right.
The main things are the plain things, and the plain things are the main things. The Genesis narrative is really not complete enough to give me a firm basis for seeing Adam as a covenant breaker because I'm not seeing him as in a covenant sense. That may indeed constrain all covenants in the Bible to being redemptive covenants, and it may also mean that the argument of God upholding a covenant with Moses that He made with Adam still needs to be dealt with. It may also mean that I'm wrong about this, and the text of Genesis will bear up under the weight of the term 'covenant.'
I'll have to think it over still. But it seems more likely at this point that the theologians impulse to mash all the stories into the idea of 'covenant' comes from the necessity of the Covenant of Works, and once that is let go as obsolete, the notion of 'covenant with Adam' starts to wither.