A direct proof of the confluence of combinatory strong reduction
نویسنده
چکیده
I give a proof of the confluence of combinatory strong reduction that does not use the one of λ-calculus. I also give simple and direct proofs of a standardization theorem for this reduction and the strong normalization of simply typed terms.
منابع مشابه
A solution to Curry and Hindley's problem on combinatory strong reduction
It has often been remarked that the metatheory of strong reduction , the combinatory analogue of βη-reduction βη in λ -calculus, is rather complicated. In particular, although the confluence of is an easy consequence of βη 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 , one which mak...
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Klop, J.W., V. van Oostrom and F. van Raamsdonk, Combinatory reduction systems: introduction and survey, Theoretical Computer Science 121 (1993) 279-308. Combinatory reduction systems, or CRSs for short, were designed to combine the usual first-order format of term rewriting with the presence of bound variables as in pure I-calculus and various typed I-calculi. Bound variables are also present ...
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عنوان ژورنال:
- Theor. Comput. Sci.
دوره 410 شماره
صفحات -
تاریخ انتشار 2009