Simply historical interest’s sake (not an implicit agreement with anything here quoted):
“Much discussion centered on the relationship between baptism and regeneration. This is a connection that conservative Protestants tend to deny or ignore, but was a commonplace in the classic Reformed period. On the one hand, Westminster did not share the Roman Catholic belief that the sacraments are efficacious ex opere operato (by the fact of being performed), but neither did they sympathize at all with the Anabaptist view that they were merely symbolic” (Robert Letham, The Westminster Assembly, p. 331).
“In the debates on the Directory for the Publick Worship of God…the Assembly considered the proposed words ‘joyne the inward baptisme with the outward baptisme.’ Except for Gataker, there was consistent agreement on the connection between baptism and regeneration. ….Later…when the chapter on baptism was being considered, the proposed clause concerning, ‘the grace of God bestowed sometime before’ was debated. Whitaker professed his inability to find how baptism conferred grace, while recognizing that ‘our divines do hold it’ and that, when opposing the papists, they say it is more than a sign and a seal. He referred to Chamier, who said the grace signified is exhibited; ‘so it is in the French Confession; it doth efficaciter donare [something like efficacious exhibiting, conveying, presenting, conferring–CD]. It does not do so ex opere operato'” (Robert Letham, The Westminster Assembly, pp. 331-332).
“Wright notes that the word ‘exhibit’ was stronger in meaning than it is in modern English, being closer to ‘convey.' In earlier debates…Dr. Smith had averred ‘that baptism saves sacramentally is noe such incongruous speech.’  Wright agrees that ‘the Westminster divines viewed baptism as the instrument and occasion of regeneration by the Spirit, of the remission of sins, of ingrafting into Christ (cf. 28.1). The Confession teaches baptismal regeneration.’  While the Catechisms speak only of baptism as a ‘sign and seal,’ the Directory’s model prayer goes much further. Wright calls this the Confession’s ‘vigorous primary affirmation.’  In it, the minister declares of the children baptized that ‘they are Christians, and federally holy before baptism, and therefore are they baptized’ 
This is accompanied by prayer that the Lord ‘would receive the infant now baptized, and solemnly entered into the household of faith, into his fatherly tuition and defence, and remember him with the favour that he sheweth to his people,’ and that he would ‘make his baptism effectual to him'” (Letham, The Westminster Assembly, pp. 332-333).
30. Wright, “Baptism at the Westminster Assembly,” 167.
31. Van Dixhoorn, 5:395.
32. Wright, “Baptism at the Westminster Assembly,” 169.
34. “The Directory for the Publick Worship of God,” in The Confession of Faith, the Larger and Shorter Catechisms with Scripture Proofs at Large Together with the Sum of Saving Knowledge (Applecross: Publications Committee of the Free Presbyterian Church of Scotland, 1970), 383.