arXiv subjects

Ádám Kurucz

Publications and source records attributed to Ádám Kurucz.

3 recordsLinked to original sources

arXiv2026

Dependently Typed Model Composition for Matching Logic

This paper investigates model compositionâ€”often referred to as "gluing"â€”within the framework of matching logic. Specifically, we examine the systematic combination of existing signatures, variable valuations, theories, and their corresponding models. Our primary objective is to ensure that this composition preserves satisfaction proofs; that is, any theory validated by the individual constituent models is also validated by the resulting composite model. Our definitions are based on a polyadic, sorted variant of matching logic, which has also been expressed in the Rocq proof assistant. Therefore, we outline our definitions with dependent types for this work to serve as a direct blueprint for the mechanization in the short-term future.

cs.LO↗

arXiv2025

On a Dependently Typed Encoding of Matching Logic

Matching logic is a general formal framework for reasoning about a wide range of theories, with particular emphasis on programming language semantics. Notably, the intermediate language of the K semantics framework is an extension of matching $μ$-logic, a sorted, polyadic variant of the logic. Metatheoretic reasoning requires the logic to be expressed within a foundational theory; opting for a dependently typed one enables well-sortedness in the object theory to correspond directly to well-typedness in the host theory. In this paper, we present the first dependently typed definition of matching $μ$-logic, ensuring well-sortedness via sorted contexts encoded in type indices. As a result, ill-sorted syntax elements are unrepresentable, and the semantics of well-sorted elements are guaranteed to lie within the domain of their associated sort.

cs.LO↗

arXiv2024

Unification in Matching Logic -- Revisited

Matching logic is a logical framework for specifying and reasoning about programs using pattern matching semantics. A pattern is made up of a number of structural components and constraints. Structural components are syntactically matched, while constraints need to be satisfied. Having multiple structural patterns poses a practical problem as it requires multiple matching operations. This is easily remedied by unification, for which an algorithm has already been defined and proven correct in a sorted, polyadic variant of matching logic. This paper revisits the subject in the applicative variant of the language while generalising the unification problem and mechanizing a proven-sound solution in Coq.

cs.LO↗