Type inference for hierarchical multiset structures in rule-based systems

Abstract

The focus of this paper is the resource evolution in rule-based systems with some specific restrictions imposed; specifically, some resources are bounded between certain lower and upper thresholds. Such a system is proved to be correct with respect to a type system.We define types over hierarchical multiset structures, and consider well-typing with respect to a specific relation aiming to guarantee an appropriate use of resources. The dynamics of the system is given by an operational semantics; well-typedness remains invariant under the semantic transition rules. According to a typed semantics, each rule of the system can be applied only if the left-hand side of the rule is well-typed. A type inference is introduced to deduce the type of each hierarchical multiset structure. Soundness and completeness are proved for this type inference.