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  1. A solution to Curry and Hindley’s problem on combinatory strong reduction.Pierluigi Minari - 2009 - Archive for Mathematical Logic 48 (2):159-184.
    It has often been remarked that the metatheory of strong reduction $\succ$ , the combinatory analogue of βη-reduction ${\twoheadrightarrow_{\beta\eta}}$ in λ-calculus, is rather complicated. In particular, although the confluence of $\succ$ is an easy consequence of ${\twoheadrightarrow_{\beta\eta}}$ being confluent, no direct proof of this fact is known. Curry and Hindley’s problem, dating back to 1958, asks for a self-contained proof of the confluence of $\succ$ , one which makes no detour through λ-calculus. We answer positively to this question, by extending (...)
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