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Call-by-name extensionality and confluence. (English) Zbl 1418.68033
Summary: Designing rewriting systems that respect functional extensionality for call-by-name languages with effects turns out to be surprisingly challenging. Simply interpreting extensional laws like $$\eta$$ as reduction rules easily breaks confluence. We explore these issues in the setting of a sequent calculus. Building on an insight that appears in different aspects of the theory of call-by-name functional languages – confluent rewriting for two independent control calculi and sound continuation-passing style transformations – we give a confluent reduction system for lazy extensional functions. Finally, we consider limitations to this approach when used for strict evaluation and types beyond functions.
MSC:
 68N18 Functional programming and lambda calculus 68Q42 Grammars and rewriting systems
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