Jonah 3.10 When God saw what they did, how they turned from their evil ways, God changed his mind about the calamity that he had said he would bring upon them; and he did not do it.
The Hebrew term "nhΩm" is translated in the NRSV as "God changed his mind." The term as defined in Brown-Driver-Briggs indicates something more along the lines semantically of "relent," "rue," "be sorry" or "repent." I believe you can make a rather cogent argument that God responds to repentance with repentance, not unlike God's responding to human sin by becoming human.
Although how we express this matters quite a bit, a base line for me is that we really can't make sense of what prayer is and what it signifies unless we are free to talk about God "changing," and specifically God being a God of mercy who relents and repents.