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We present the Eager TransLucid language, an intensional programming language in which the value of a variable is a function mapping multidimensional contexts - the `possible worlds` of intensional logic - to ground values or, equivalently, that variables define multidimensional arrays of arbitrary dimensionality. The Eager TransLucid language is a natural generalisation of Wadge and Ashcroft`s Lucid dataflow language. Given a specific set of equations and a context, the operational semantics determines the value taken by a variable in that context, which may depend both on the values of dimensions within the context and the values of variables in other contexts. The contexts correspond to tags in tagged-token dataflow systems. The key contribution of the paper is to prove that it is possible to create a warehouse caching the values of already computed (identifier, context) pairs in such a way as to ensure that no reference is made to unnecessary dimensions. The method consists of storing demands for relevant dimensions in the current context as these are needed. © 2008 IEEE.