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A materialised faceted taxonomy is an information source where the objects of interest are indexed according to a faceted taxonomy. This paper shows how from a materialised faceted taxonomy, we can mine an expression of the Compound Term Composition Algebra that specifies exactly those compound terms (conjunctions of terms) that have non-empty interpretation. The mined expressions can be used for encoding in a very compact form (and subsequently reusing), the domain knowledge that is stored in existing materialised faceted taxonomies. A distinctive characteristic of this mining task is that the focus is given on minimising the storage space requirements of the mined set of compound terms. This paper formulates the problem of expression mining, gives several algorithms for expression mining, analyses their computational complexity, provides techniques for optimisation, and discusses several novel applications that now become possible.