Weak normalization means: there exists a reduction strategy that will lead to a normal form. People often use confluence to mean what rewriting people call "local confluence": this is the property that if a⇝b and a⇝c, then b and c can be joined -- i.e., there exists a d such that b⇝∗d and c⇝∗d.
May 11, 2015
Jun 7, 2005 · We present a general, abstract method to show confluence of weakly normalizing systems. The technique consists in constructing an ...
systems. The technique consists in constructing an interpretation of the source system into a target system which is already confluent.
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A rewriting system has the weak normalization property or is (weakly) normalizing (WN) if every object is weakly normalizing.
Note that a system can be both non-terminating and weakly normalizing at the same time. We then have some nice theorems about confluence and normalization:.
Dec 16, 2015 · We study confluence and normalization in abstract reduction systems and apply the results to combinatory logic and an abstract version of ...
On Confluence Criteria for Non-terminating Abstract Rewriting Systems ... Then. (1) (A, →) is quasi-normalizing if and only if (A, →) is (weakly) normalizing.
Dec 2, 2022 · Full βᵥ-reduction is confluent, and it is weakly but not strongly normalizing. There is an evaluation strategy that always finds a βᵥ-normal ...
In computer science and mathematics, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than one ...
Weak persistence, confluence, uniquely normalizing, etc., are defined for terms containing variables in this case. 5. Systems with confluent innermost rewriting.