HarmTrace (Harmony Analysis and Retrieval of Music with Type-level Representations of Abstract Chords Entities) is a system for automatic harmony analysis of music. It takes a sequence of chords as input and produces a harmony analysis, which can be visualised as a tree. Music theory has been essential in composing and performing music for centuries. Within Western tonal music, from the early Baroque on to modern-day jazz and pop music, the function of chords within a chord sequence can be explained by harmony theory. Although Western tonal harmony theory is a thoroughly studied area, formalising this theory is a hard problem. With HarmTrace we have developed a formalisation of the rules of tonal harmony as a Haskell (generalized) algebraic datatype. Given a sequence of chord labels, the harmonic function of a chord in its tonal context is automatically derived. For this, we use several advanced functional programming techniques, such as type-level computations, datatype-generic programming, and error-correcting parsers. Our functional model of harmony offers various benefits: it can be used to define harmonic similarity measures and facilitate music retrieval, or it can help musicologists in batch-analysing large corpora of digitised scores, for instance. More information about HarmTrace, including how to use and example output, is available on its webpage: http://www.cs.uu.nl/wiki/GenericProgramming/HarmTrace