Derek Walcott's poem "Adam's Song" is, in a sense, a retelling of the story of Adam and Eve. The poem focuses on the loss of innocence symbolized by that story, and the anguish consequent of that lost innocence.
In the opening stanza, the speaker uses metaphors when he says that an adulteress is "killed . . . by whispers," and that her "flesh" is "film(ed) . . . with slime." These metaphors imply that attitudes towards adulteresses are too judgmental, and too cruel. These cruel judgements create a metaphorical "slime" that covers the woman's body, making her repellent to society.
In the third stanza, the speaker says that men "still sing the song . . . against the world of vipers." This is an example of symbolism, and the vipers here are symbolic of treachery and evil. Vipers are venomous, and snakes more generally are often used as symbols of evil. This is because the snake in the story of the Garden of Evil is an incarnation of the devil.
In the final stanza the speaker uses personification when he writes that his heart "weep(s)" within him. The speaker also uses a simile, and another example of personification, when he compares the weeping of his heart to the weeping of the rain. He says that his heart weeps "as the rain weeps." The first example of personification here implies that there is a sadness within the speaker (in his heart) originating from the expulsion of Adam and Eve from the Garden of Eden. The second example of personification suggests that the world around the speaker also feels this same sadness. The simile comparing the sadness within the speaker to that outside of the speaker suggests that this sadness is constant, and ubiquitous.