This paper introduces a semi-supervised contrastive learning framework and its application to text-independent speaker verification. The proposed framework employs generalized contrastive loss (GCL). GCL unifies losses from two different learning frameworks, supervised metric learning and unsupervised contrastive learning, and thus it naturally determines the loss for semi-supervised learning. In experiments, we applied the proposed framework to text-independent speaker verification on the VoxCeleb dataset. We demonstrate that GCL enables the learning of speaker embeddings in three manners, supervised learning, semi-supervised learning, and unsupervised learning, without any changes in the definition of the loss function.