(a) The specific performance of a parol contract as to land shall be decreed if the defendant admits the contract or if the contract has been so far executed by the party seeking relief and at the instance or by the inducements of the other party that if the contract were abandoned he could not be restored to his former position.

(b) Full payment alone accepted by the vendor, or partial payment accompanied with possession, or possession alone with valuable improvements, if clearly proved in each case to have been done with reference to the parol contract, shall be sufficient part performance to justify a decree.