Computational learning of natural language is often attempted without using the knowledge available from other research areas such as psychology and linguistics. This can lead to systems that solve problems that are neither theoretically or practically useful. In this paper we present a system CLL which aims to learn natural language syntax in a way that is both computationally effective and psychologically plausible. This theoretically plausible system can also perform the practically useful task of unsupervised learning of syntax. CLL has then been applied to a corpus of declarative sentences from the Penn Treebank (Marcus et al., 1993; Marcus et al., 1994) on which it has been shown to perform comparatively well with respect to much less psychologically plausible systems, which are significantly more supervised and are applied to somewhat simpler problems.