Related papers: Nominal Unification Revisited
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as of the lambda-binder of the lambda-calculus…
Ten years ago, it was shown that nominal techniques can be used to design coalgebraic data types with variable binding, so that alpha-equivalence classes of infinitary terms are directly endowed with a corecursion principle. We introduce…
Nominal techniques provide a mathematically principled approach to dealing with names and variable binding in programming languages. This paper explores an attempt to make nominal techniques accessible as an Agda library. We aim for a…
Nominal abstract syntax is a popular first-order technique for encoding, and reasoning about, abstract syntax involving binders. Many of its applications involve constraint solving. The most commonly used constraint solving algorithm over…
Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement…
We investigate a learning algorithm in the context of nominal automata, an extension of classical automata to alphabets featuring names. This class of automata captures nominal regular languages; analogously to the classical language…
We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the $\mathbb{K}$ framework, used to specify programming…
There are many ways to represent the syntax of a language with binders. In particular, nominal frameworks are metalanguages that feature (among others) name abstraction types, which can be used to specify the type of binders. The resulting…
A new hierarchy of "exact" unification types is introduced, motivated by the study of admissible rules for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
Classically, in saturation-based proof systems, unification has been considered atomic. However, it is also possible to move unification to the calculus level, turning the steps of the unification algorithm into inferences. For calculi that…
We define the pattern fragment for higher-order unification problems in linear and affine type theory and give a deterministic unification algorithm that computes most general unifiers.
A new hierarchy of "exact" unification types is introduced, motivated by the study of admissibility for equational classes and non-classical logics. In this setting, unifiers of identities in an equational class are preordered, not by…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
It has been hypothesized that some form of "modular" structure in artificial neural networks should be useful for learning, compositionality, and generalization. However, defining and quantifying modularity remains an open problem. We cast…
We present a sound and complete unification procedure for deterministic higher-order patterns, a class of simply-typed lambda terms introduced by Yokoyama et al. which comes with a deterministic matching problem. Our unification procedure…
We investigate an extension of nominal many-sorted signatures in which abstraction has a form of instantiation, called generalised concretion, as elimination operator (similarly to lambda-calculi). Expressions are then classified using a…
In this paper, a novel approach for coding nominal data is proposed. For the given nominal data, a rank in a form of complex number is assigned. The proposed method does not lose any information about the attribute and brings other…