Nominal sets provide a promising new mathematical analysis of names in formal languages
based upon symmetry, with many applications to the syntax and semantics of programming …

Formal systems that describe computations over syntactic structures occur frequently in
computer science. Logic programming provides a natural framework for encoding and …

This paper describes a formalisation of the lambda-calculus in a HOL-based theorem prover
using nominal techniques. Central to the formalisation is an inductive set that is bijective with …

In this paper we define an inductive set that is bijective with the α-equated lambda-terms.
Unlike de-Bruijn indices, however, our inductive definition includes names and reasoning …

This paper is a contribution to the meta-theory of systems featuring syntax with bindings,
such as 𝜆-calculi and logics. It provides a general criterion that targets inductively defined …

Combining higher-order abstract syntax and (co)-induction in a logical framework is well
known to be problematic. We describe the theory and the practice of a tool called Hybrid …

The paper develops a mathematical theory in the spirit of categorical algebra that provides a
model theory for second-order and dependently-sorted syntax. The theory embodies notions …

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 …

This paper provides a new mathematical foundation for the locally nameless representation
of syntax with binders, one informed by nominal techniques. It gives an equational …

Recursive relational specifications are commonly used to describe the computational
structure of formal systems. Recent research in proof theory has identified two features that …