Joel Beeke & Brian Najapfour in Taking Hold of God: Reformed & Puritan Perspectives on Prayer list what John Calvin (Institutes: book 3, chapter 20) sees as the six (at least) purposes of prayer.
- To fly to God with every need and gain from Him what is lacking in ourselves to live the Christian life
- To learn to desire wholeheartedly only what is right as we place all our petitions before God
- To prepare us to receive God's benefits and responses to to our petitions with humble gratitude
- To meditate on God's kindness to us as we receive what we have asked for
- To instill the proper spirit of delight for God's answers in prayer
- To confirm God's faithful providence so that we may glorify Him and trust in His present help more readily as we witness His regularly answering our prayers
"All of these purposes are designed to foster communion with God so that 'the promises of God should have their way with us.'" (quoting Niesel, Theology of Calvin, 157)
From Taking Hold of God, pg 31-32.