We prove modularity of constructive confluence for term rewriting systems using a novel decomposition of terms into tall aliens and bases. The proof is modular itself in that it factors through the decreasing diagrams theorem for abstract rewriting systems.

Toyama's Theorem states that connuence is a modular property of disjoint term rewriting systems. This theorem does not generalize to combined systems with shared constructors. Thus the question arises naturally whether there are suucient conditions which ensure the modu-larity of connuence in the presence of shared constructors. In particular, Kurihara and Krishna Rao posed the problem whether ...

The coinductive λ-calculus Λ arises by a coinductive interpretation of the grammar of the standard λ-calculus Λ and contains non-wellfounded λ-terms. An appropriate notion of reduction is analyzed and proven to be confluent by means of a detailed analysis of the usual Tait/MartinLöf style development argument. This yields bounds for the lengths of those joining reduction sequences that are guar...

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The light-gated ion-channel protein is expected to be able to improve the performance of ionchannel devices for the multi-point screening and neural network devices based on the planar patch clamp. However, no studies with light-gated ion channels on a planar patch clamp have been reported. We constructed an incubation type of planar patch clamp biosensor using silicon-on-insulator substrates w...

PURPOSE To evaluate fibroblast proliferation activity of the Tenon capsule from primary and recurrent pterygia. METHODS A randomized prospective study was performed with 43 surgical samples from 30 primary and 13 recurrent pterygia, and samples of normal Tenon capsule from the same pterygium patients. Proliferation, migration, and confluence rate, and patient age, lesion location and type (fl...

We prove that fully-extended, orthogonal infinitary combinatory reduction systems with finite right-hand sides are confluent modulo identification of hypercollapsing subterms. This provides the first general confluence result for infinitary higher-order rewriting.

Using graph transformation as a formalism to specify model transformation, termination and confluence of the graph transformation system are required properties. Only under these two conditions, existence and uniqueness of the outcoming model is ensured. Verifying confluence of a graph transformation system is equivalent to checking both local confluence and termination. A graph transformation ...