Related papers: Upward confluence in the interaction calculus
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…
The stack calculus is a functional language in which is in a Curry-Howard correspondence with classical logic. It enjoys confluence but, as well as Parigot's lambda-mu, does not admit the Bohm Theorem, typical of the lambda-calculus. We…
The confluence of untyped lambda-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of lambda-calculus with conditional rewriting and provide general results in…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
We show that the physical requirement of flux conservation can substitute for the usual matching conditions in point interactions. The study covers an arbitrary superposition of $\delta$ and $\delta'$ potentials on the real line and can be…
Concurrent pattern calculus (CPC) drives interaction between processes by comparing data structures, just as sequential pattern calculus drives computation. By generalising from pattern matching to pattern unification, interaction becomes…
Living organisms, ecosystems, and social systems are examples of complex systems in which robustness against inclusion of new elements is an essential feature. A recently proposed simple model has revealed a general mechanism by which such…
We prove that a first-order cooperative system of interacting agents converges to consensus if the so-called Persistence Excitation condition holds. This condition requires that the interaction function between any pair of agents satisfies…
We prove that there are continuum-many axiomatic extensions of the full Lambek calculus with exchange that have the deductive interpolation property. Further, we extend this result to both classical and intuitionistic linear logic as well…
Interacting quantum systems evolving from an uncorrelated composite initial state generically develop quantum correlations -- entanglement. As a consequence, a local description of interacting quantum system is impossible as a rule. A…
In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called "Lambek's restriction," that is, the antecedent of any provable…
The confluence of untyped \lambda-calculus with unconditional rewriting is now well un- derstood. In this paper, we investigate the confluence of \lambda-calculus with conditional rewriting and provide general results in two directions.…
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
The intrinsic treatment of binding in the lambda calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs, types, and programs. Supporting such a data structure in an implementation…
Recent works have derived non-asymptotic upper bounds for convergence of underdamped Langevin MCMC. We revisit these bound and consider introducing scaling terms in the underlying underdamped Langevin equation. In particular, we provide…
We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by…
The $\lambda$-superposition calculus is a successful approach to proving higher-order formulas. However, some parts of the calculus are extremely explosive, notably due to the higher-order unifier enumeration and the functional…