Related papers: Reconciling positional and nominal binding
Logics and automata models for languages over infinite alphabets, such as Freeze LTL and register automata, serve the verification of processes or documents with data. They relate tightly to formalisms over nominal sets, such as…
This paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations and…
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…
We present some lambda calculus with explicit substitutions and named variables. The characteristic feature of this calculus is as follows: renaming of bound variables when performing substitutions is done using special reductions and may…
We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…
Nominal sets provide a framework to study key notions of syntax and semantics such as fresh names, variable binding and $\alpha$-equivalence on a conveniently abstract categorical level. Coalgebras for endofunctors on nominal sets model,…
The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the…
We propose Equivariant ZFA with Choice as a foundation for nominal techniques that is stronger than ZFC and weaker than FM, and why this may be particularly helpful in the context of automated reasoning.
In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple,…
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…
Software security can be ensured by specifying and verifying security properties of software using formal methods with strong theoretical bases. In particular, programs can be modeled in the framework of lambda-calculi, and interesting…
Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with…
We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…
We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying…
In each variant of the lambda-calculus, factorization and normalization are two key-properties that show how results are computed. Instead of proving factorization/normalization for the call-by-name (CbN) and call-by-value (CbV) variants…
It is well known that the action functional can be used to define classical, quantum, closed, and open dynamics in a generalization of the variational principle and in the path integral formalism in classical and quantum dynamics,…
Reconfiguration paths express sequences of successive reconfiguration operations within a component-based approach allowing dynamic reconfigurations. We use constructs from regular expressions-pin particular, alternatives-to introduce…
Nominal automata models serve as a formalism for data languages, and in fact often relate closely to classical register models. The paradigm of name allocation in nominal automata helps alleviate the pervasive computational hardness of…