Neurocognitive Linguistic Theory (NCL, Lamb 1999) stands alone as the only well-developed linguistic theory with a serious commitment to neurological plausibility. It is also set apart from much of mainstream Cognitive Science by its strictly non-symbolic approach to understanding cognition. The theory has enjoyed a long a fruitful development, but has been hampered by the difficulty of verifying complex network analyses presented entirely on paper. The need has been clear for some manner of independent testbed for the theory, and a computational context was the obvious choice. To meet this need, the PureNet modeling program has been constructed. Written in Java 1.1, the program has been designed to function in such a way as to match as closely as possible the essential elements of that which it seeks to model---the functional elements of NCL. The design and construction of the fundamental structures of the program are explicated. To demonstrate the utility of the program, three variant network analyses of portmanteau morphemes are proposed and modeled. As all three can be shown to function correctly, learnability is proposed as a discriminator. To reach the goal of a meaningful learnability test, a major learning hypotheses of NCL---the bi-directional learning hypothesis (Lamb, 1999, Ch.12)---is modeled and shown to be valid. Having demonstrated the validity of the NCL conception of bidirectional learning, a procedure for generalizing NCL networks into neutral structures for learnability tests is outlined, and then generalized network structures based upon the three portmanteau network models are constructed and run to see if they will self-organize into the target structures (the original network analyses). The methodology tentatively disfavors the lateral inhibition hypothesis for portmanteau morpheme structure as a learnable network system, and thus demonstrates the utility of PureNet as a valuable tool for future development of NCL.