On composable properties of term rewriting systems

Abstract

A property of term rewriting system (TRS, for short) is said to be composable if it is preserved under unions. We present composable properties of TRSs on the base of modularity results for direct sums of TRSs. We propose a decomposition by a naive sort attachment, and show that modular properties for direct sums of TRSs are τ-composable for a naive sort attachment τ. Here, a decomposition of a TRS R is a pair (R ₁,R ₂) of (not necessary disjoint) subsets of R such that R = R ₁ U R ₂; and for a naive sort attachment T a property ø of TRSs is said to be τ-composable if for any TRS R such that τ is consistent with R, ø(R₁) Λ φ(R₂) implies φ(R) where (R ₁, R ₂) is the decomposition of R by τ.