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The virtues of eta-expansion. (English) Zbl 0833.68072

Summary: Interpreting \(\eta\)-conversion as an expansion rule in the simply-typed \(\lambda\)-calculus maintains the confluence of reduction in a richer type structure. This use of expansions is supported by categorical models of reduction, where \(\beta\)-contraction, as the local counit, and \(\eta\)- expansion, as the local unit, are linked by local triangle laws. The latter from reduction loops, but strong normalization (to the long \(\beta\eta\)-normal forms) can be recovered by ‘cutting’ the loops.

MSC:

68Q42 Grammars and rewriting systems
68W30 Symbolic computation and algebraic computation
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