We introduce computational creativity theory (CCT) as an analogue in computational creativity research to computational learning theory in machine learning. In its current draft, CCT comprises the FACE descriptive model of creative acts as tuples of generative acts, and the IDEA descriptive model of the impact such creative acts may have. To introduce these, we simplify various assumptions about software development, background material given to software, how creative acts are performed by

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... ter, and how audiences consume the results. We use the two descriptive models to perform two comparisons studies, firstly for mathematical discovery software, and secondly for visual art generating programs. We conclude by discussing possible additions, improvements and refinements to CCT.