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This paper presents the ongoing project Computational Models of First Language Acquisition, together with its current product, the learning algorithm GraSp. GraSp is designed specifically for inducing grammars from large, unlabelled corpora of spontaneous (i.e. unscripted) speech. The learning algorithm does not assume a predefined grammatical taxonomy; rather the determination of categories and their relations is considered as part of the learning task. While GraSp learning can be used for a range of practical tasks, the long-term goal of the project is to contribute to the debate of innate linguistic knowledge -- under the hypothesis that there is no such.