I think it would be useful to compile a running list of quotes from reformed people on the definition of faith and/or saving faith.
By faith we understand the habit or principle which God the Holy Spirit pours into the hearts of the elect together with a new nature as its first and most important element by which believers obtain out of Christ and passing into them from Christ the ability to receive all the impressions which the divine Word makes upon this faculty and accordingly to be itself, active.
Alexander Comrie, (from a sermon entitiled Does Assurance Belong to the Essence of Faith? by Joel Beeke. The following note appears after this quote: "Personal translation from Kersten, Reformed Dogmatics 2:404; taken from HC 428- 29."
Now we shall possess a right definition of faith if we call it a firm and certain knowledge of God's benevolence toward us, founded upon the truth of the freely given promise in Christ, both revealed to our minds and sealed upon our hearts through the Holy Spirit.
John Calvin, Institutes, Book 3, Chapter 2, Section VII