Talk:Church–Rosser theorem

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Distinct vs possibly empty sequence of reductions[edit]

We say, "The Church–Rosser theorem states that if there are two distinct reductions starting from the same lambda calculus term, then there exists a term that is reachable via a (possibly empty) sequence of reductions from both reducts."

If the reducts are distinct, how can there exist a term that is reachable by an empty sequence of reductions? — Matt Crypto 09:20, 26 September 2009 (UTC)[reply]

What's the problem? Two distinct reductions could end at the same term. Or two reductions could end at terms a and b where b can be reduced to a by further reductions; then the common reachable term is a, and the reduction sequence from a is empty.

The only misstatement I see is grammatical; it should say "from each reduct". —Dominus (talk) 00:59, 28 September 2009 (UTC)[reply]