This article is an exposition of composition theory, the cognitive theory of processes of music composition. The text is in three parts. In the first part, a compositional task environment typical for the mid-1980s is discussed, to demonstrate the heterogeneity of tools a composer needs when creating a musical work. The second part presents a written lecture-demonstration of a compositional process for producing a score for saxophone solo. In the third part, an abstract model of compositional problem-solving is proposed using the blackboard paradigm from artificial intelligence research. The point of the article is to show that, far from inhibiting compositional intuition, the computer program has become an indispensable alter ego for composers who care to work systematically. The article proposes a framework for studies in composition theory as a discipline based on artificial intelligence.