A constructive proof contains computable evidence, e.g. a circuit, of the truth of the proposition it proves. Robert L Constable and Douglas J Howe. Nuprl as a general logic . Academic Press, 1990. This feature was used to relate the switch level and threshold models of hardware formally, i.e. as a theorem in hol.
Proof checkers are proof assistants which have to be supplied with all details of a proof.
Their function is to validate proofs. Robert L Constable and Douglas J Howe. Nuprl as a general logic . Academic Press, 1990. R. L. Constable and D. J. Howe.