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In previous work we describe a novel approach to dependent typing based on amultivalued term language. In this technical report we formalise the runtime, akind of operational semantics, for that language. We describe a fairlycomprehensive core language, and then give a small-step operational semanticsbased on an abstract machine. Errors are explicit in the semantics. We alsoprove several simple properties: that every non-terminated machine state stepsto something and that reduction is deterministic once input is fixed.

Formalisation of the lambda aleph Runtime