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Must the evaluation strategy for a language be specified in order to apply the Church-Rosser Theorem?

The Church-Rosser theorem gives you the following guarantees: A term has at most one normal form. That is, there aren't different normal forms depending on your choice of evaluation strategy. If a ...
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Is there a hierarchy of computational expressivity that is sensitive to evaluation strategies?

Most (or all) reasonable programming are Turing-complete, and thus can be used to compute exactly the computable functions, i.e., to decide the decidable languages, nothing more and nothing less. So ...
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