Abstract. The technique of reflection is a way to automate proof construction in type theoretical proof assistants. Reflection is based on the definition of a type of syntactic expressions that gets interpreted in the domain of discourse. By allowing the interpretation function to be partial or even a relation one gets a more general method known as ``partial reflection''. In this paper we show how one can take advantage of the partiality of the interpretation to uniformly define a family of tactics for equational reasoning that will work in different algebraic structures. The tactics then follow the hierarchy of those algebraic structures in a natural way.

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TPHOLs conference covers all aspects of theorem proving in higher order logics as well as related topics in theorem proving and verification. There were 42 papers submitted to TPHOLs 2004 in the full research category, each of which was refereed by at least 3 reviewers selected by the program committee. Of these submissions, 21 were accepted for presentation at the conference and publication in volume 3223 of Springer’s Lecture Notes in Computer Science series. In keeping with longstanding tradition, TPHOLs 2004 also offered a venue for the presentation of work in progress, where researchers invite discussion by means of a brief introductory talk and then discuss their work at a poster