The traditional reformed covenant of works treats the two trees in the midst of the garden as sacraments but unequally. Broadly speaking, Calvinist sacramental theology is applied to the prohibited tree but a Zwinglian understanding of sacraments is applied to the tree of life.
Calvin’s definition of a sacrament integrates a word of promise with a sacrament so that one never has
a sacrament without an antecedent promise, the sacrament being added as a kind of appendix, with the view of confirming and sealing the promise, and giving a better attestation, or rather, in a manner, confirming it [Institutes Book 4 Ch14].
It is in this way that God faithfully and immediately sealed his promise signified by the tree of the knowledge of good and evil the first time Adam and Eve ate the fruit of that tree, their eyes were opened (Gen 3:7). The covenant of works holds that Adam and Eve freely and frequently ate from the tree of life but that God did not seal on them the promise of eternal life as they ate. Rather, the covenant of works is Zwinglian with respect to the promise made by God by the tree of life. Adam is simply reminded each time he eats freely from that tree of what he must hope for, which is eternal life. His eating binds him in oath to God’s covenant of works.
The reformers had to discriminate against the tree of life in this way because of a Platonic or Aristotlean presupposition that that Adam and Evil were created with immortality, at least with an immortal soul.
Calvin writes in his commentary on Genesis
Three gradations, indeed, are to be noted in the creation of man; that his dead body was formed out of the dust of the earth; that it was endued with a soul, whence it should receive vital motion; and that on this soul God engraved his own image, to which immortality is annexed.
This presupposition renders the Calvin’s sacramental theology redundant with respect to the tree of life. Why would God promise, by means of a sacrament, to give Adam and Eve what they already possessed?
Had the reformers applied Calvin’s sacramental theology to both trees equally, they would have been required to reject a Platonic or Aristotlean understanding of the immortality of the soul and conclude instead that Adam and Eve did not possess immortality because God had not yet promised it to them.
Does the bible state that the human soul is immortal? I can’t think of any supporting references. We are told that God alone is immortal (1 Tim 6:16) and that the soul can be destroyed (Ps 109:31, Isa 10:18, Matt 10:28) . Unless explicitly stated in scripture we cannot simply assume that immortality is a communicable attribute.