Here is John Gill on Exodus 4:21 (“…but I will harden his heart, that he shall not let the people go.”):
“that is, not directly, not for some time, not until all the wonders are wrought, and plagues inflicted to bring him to it: he first hardening his own heart against God, and all remonstrances made unto him, it was but a righteous thing in God to give him up to the hardness of his heart, to deny him his grace, which only could soften it, and to leave him to the corruptions of his nature, and the temptations of Satan; and by leaving him to strong delusions, to believe the lying miracles of his magicians: this the Lord thought fit to acquaint Moses with, lest he should be discouraged by his refusal to dismiss Israel”(John Gill).
Note that Gill says that God did not harden Pharaoh’s heart until Pharaoh FIRST hardened his own heart. And by hardening, Gill does not mean Biblical direct and active hardening, but indirect and passive hardening. Gill agrees with men such as Dabney, Shedd, the Hodges, Turretin, Owen, etc., on this particular view of partially sovereign permission.