A wide range of evidence points toward the existence of a common algorithm underlying the processing of information throughout the cerebral cortex. Several hypothesized features of this cortical algorithm are reviewed, including sparse distributed representation, Bayesian inference, hierarchical organization composed of alternating template matching and pooling layers, temporal slowness and predictive coding. Hierarchical Temporal Memory (HTM) is a family of learning algorithms and corresponding theories of cortical function that embodies these principles. HTM has previously been applied mainly to perceptual tasks typical of posterior cortex. In order to evaluate HTM as a candidate model of cortical function, it is necessary also to investigate its compatibility with the requirements of frontal cortical function. To this end, a variety of models of frontal cortical function are reviewed and integrated, to arrive at the hypothesis that frontal functions including attention, working memory and action selection depend largely upon the same basic algorithms as do posterior functions, with the notable additions of a mechanism for the active maintenance of representations and of multiple cortico-striato-thalamo-cortical loops that allow communication between regions of frontal cortex to be gated in an adaptive manner. Computational models of this system are reviewed. Finally, there is a discussion of how HTM can contribute to the understanding of frontal cortical function, and of what the requirements of frontal cortical function mean for the future development of HTM.