Formalisation of the lambda aleph Runtime

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