Related papers: A dependent nominal type theory
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…
We study languages over infinite alphabets equipped with some structure that can be tested by recognizing automata. We develop a framework for studying such alphabets and the ensuing automata theory, where the key role is played by an…
The contribution of this paper is the development of the syntax and semantics of multi-sorted nominal abstract binding trees (abts), an extension of second order universal algebra to support symbol-indexed families of operators. Nominal…
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…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…
Nominalistic Logic (NL) is a new presentation of Paul Gilmore's Intensional Type Theory (ITT) as a sequent calculus together with a succinct nominalization axiom (N) that permits names of predicates as individuals in certain cases. The…
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…
We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to…
Nominal abstract syntax and higher-order abstract syntax provide a means for describing binding structure which is higher-level than traditional techniques. These approaches have spawned two different communities which have developed along…
We develop formal theories of conversion for Church-style lambda-terms with Pi-types in first-order syntax using one-sorted variables names and Stoughton's multiple substitutions. We then formalize the Pure Type Systems along some…
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…
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…
Recursive relational specifications are commonly used to describe the computational structure of formal systems. Recent research in proof theory has identified two features that facilitate direct, logic-based reasoning about such…
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…
Nominal logic is a variant of first-order logic that provides support for reasoning about bound names in abstract syntax. A key feature of nominal logic is the new-quantifier, which quantifies over fresh names (names not appearing in any…
We investigate a class of nominal algebraic Henkin-style models for the simply typed lambda-calculus in which variables map to names in the denotation and lambda-abstraction maps to a (non-functional) name-abstraction operation. The…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
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…
When using interactive theorem provers based on dependent type theory to define and reason about languages involving binding constructs, we advocate the use of a well-scoped version of the locally nameless method of representing syntax.…
Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates…