This section of Lane/Calvin's Institutes (3.3 - 3.5) is all about the gritty details of repentance. Lane puts forth the question "What is repentance?" This question could be answered in many ways. We might say that it is feeling sorry for our sins. But this would not be strictly be true. We might feel sorry about a particular sin because the sin might have bad worldly consequences for us. We might also conjecture that asking forgiveness for our sins is repentance. But, of course, we can all see the problem here. The request may just be a hollow mouthing of words to avoid the consequences of a sinful act. The seeds of the answer to this question actually lie in Lane's second question.
So, just how is repentance equivalent to the newness of life? Well, we cannot be truly repentant unless we first have faith. In fact, it is our faith that prompts us repent in the first place. Now we know that it is sin that has put us out of a right relationship with God. It is to God we must be justified, and as Luther and Calvin and Paul, for that matter, have told us, we can only be justified by faith alone. Thus, it is only through faith, with the mediation of Jesus that we are forgiven. As Calvin points out, repentance and forgiveness, though two separate acts occur simultaneously. This is because a person who is truly repentant must already know that she/he "belongs to God" (3.3.2).
Wait, we are not to "newness of life" just yet. We still have to go through the process of mortification and vivification. Mortification occurs when the sinner comes to "truly hate and abhor sin". (3.3.3) In other words, the sinner dies to sin. Vivification occurs when the sinner "takes heart...recovers courage, and as it were, returns from death to life." Now we see how repentance = new life.
But there is more: repentance = sanctification. Since we die to sin, we become better people, "sanctified". But unfortunately, like our infinite approach to zero in the equation above, we never reach total sanctification. We may approach it, but we never get there.
Is this still relevant today? Undoubtedly, there is plenty of sin for which to seek repentance. Luckily, there is even more mercy and grace available from God. We just need a little faith.
There is a bit to more to Calvin's thoughts on repentance. There is a very interesting notion about what it has to do with the "image of God" and how we are made. My question is, do you see a connection there? What is it?