We present a programme of research for pluralist formalisations, that is, formalisations that involve proving results in more than one foundation. A foundation consists of two parts: a logical part, which provides a notion of inference, and a non-logical part, which provides the entities to be reasoned about. An LTT is a formal system composed of two such separate parts. We show how LTTs may be used as the basis for a pluralist formalisation. We show how different foundations may be formalised

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... s LTTs, and also describe a new method for proof reuse. If we know that a translation Φ exists between two logic-enriched type theories (LTTs) S and T , and we have formalised a proof of a theorem α in S , we may wish to make use of the fact that Φ(α) is a theorem of T . We show how this is sometimes possible by writing a proof script M Φ . For any proof script M α that proves a theorem α in S , if we change M α so it first imports M Φ , the resulting proof script will still parse, and will be a proof of Φ(α) in T . In this paper, we focus on the logical part of an LTT-framework and show how the above method of proof reuse is done for four cases of Φ: inclusion, the double negation translation, the A-translation and the Russell-Prawitz modality. This work has been carried out using the proof assistant Plastic. † The framework LF should not be confused with the Edinburgh Logical Framework (Harper et al. 1987; Harper et al. 1993) , which, unfortunately, is also called LF. One of the main differences between LF and the Edinburgh LF is that the former system is intended to be used to specify type theories, and hence allows computation rules to be declared. ‡ LF has a variant called PAL + (Luo 2003) , where applications are fully applied or saturated. Luo (2006) adopted the notations of PAL + , but this is not essential, and we shall use LF and the associated notations in this paper.