Forgive and Forget?

I've been contemplating forgiveness and what it looks like in the Christian life, what it looks like in action.
I asked myself, "Is it possible to 'forgive and forget'? Is that what God does with our sin? What is a biblical view of repentance?"
I found this great article in the archives of Credenda Agenda that addressed these very questions, asking:
How many of these cultural errors (like 'forgive and forget') have crept into the working theology of the church?

Here's an excerpt from the article:

When you forgive, are you obligated to forget the sin? This is a misconception about Scripture. We see this by understanding, again, God's forgiveness toward us. At this point, some may object, using verses like Jeremiah 31:34 "...saith the LORD: for I will forgive their iniquity, and I will remember their sin no more." Did God forget their sin? No. That's not what it said.

God does not somehow develop a case of cosmic Alzheimer's in His otherwise omniscient mind. He does not somehow voluntarily limit His divine attributes. We need only look at other passages to see this. 1 Corinthians 6 spoke to sanctified, justified saints (i.e., forgiven sinners). The Holy Spirit reminded them that the unrighteous shall not inherit God's kingdom. He enumerates fornicators, adulterers, thieves, drunkards, and sodomites, to name a few and then says "and such were some of you" (v.11). If God forgot their sin, how did He instruct them by reminding them of specific sinful acts? Is He reneging on Jer. 31:34? Obviously, God cannot lie any more than He can forget. What then?

In these contexts, "remember" is not about cognition. It is about action with a purpose: to recount their guilt in order to punish and visit judgment for sin. Again Jeremiah instructs: "The LORD doth not accept them: He will now remember their iniquity, and visit their sins" (14:10). The passage then details God's severe chastisement for their sins. When God forgives, He does not erase some cosmic computer memory. Rather He covenants to never recount our sin in order to visit punishment on us. Christ bore that punishment once and for all on our behalf on the cross.

When someone repents and confesses to us, he covenants not to commit this sin against us again. Where possible, restitution is also required. When we forgive, we in turn covenant not to malevolently recount (or remember) these sins again. Forgiveness is not some feel-good therapy. It is restoration or renewal of a covenant that was broken. Fellowship was severed over sin. Biblical forgiveness re-establishes that intimate fellowship. Hollow apologies know nothing of covenant.