Confluence in Probabilistic Rewriting

Confluence in Probabilistic Rewriting

Driven by the interest of reasoning about probabilistic programming languages, we set out to study a notion of unicity of normal forms for them. To provide a tractable proof method for it, we define a property of distribution confluence which is shown to imply the desired unicity (even for infinite sequences of reduction) and further properties. We then carry over several criteria from the clas...

Confluence Problems for Trace Rewriting

Polymorphic Rewriting Conserves Algebraic Confluence

We study combinations of many-sorted algebraic term rewriting systems and polymorphic lambda term rewriting. Algebraic and lambda terms are mixed by adding the symbols of the algebraic signature to the polymorphic lambda calculus, as higher-order constants. We show that if a many-sorted algebraic rewrite system R has the Church-Rosser property (is confluent), then R + β + type-β + type-η rewrit...

Termination and Confluence in Infinitary Term Rewriting

The basic notions of the theory of term rewriting are defined for terms that may involve function letters of infinite arity. A sufficient condition for completeness is derived, and its use demonstrated by the example of abstract clones over infinitary signatures. Introduction In general, to see that two terms of some equational theory A are not equivalent requires a model of A in which their in...

Confluence of Graph Rewriting with Interfaces

For terminating double-pushout (DPO) graph rewriting systems confluence is, in general, undecidable. We show that confluence is decidable for an extension of DPO rewriting to graphs with interfaces. This variant is important due to it being closely related to rewriting of string diagrams. We show that our result extends, under mild conditions, to decidability of confluence for terminating rewri...