Related papers: The Different Shades of Infinite Session Types
We study the problem of parametric parallel complexity analysis of concurrent, message-passing programs. To make the analysis local and compositional, it is based on a conservative extension of binary session types, which structure the type…
Sequences diverge either because they head off to infinity or because they oscillate. Part 1 constructs a non-Archimedean framework of infinite numbers that is large enough to contain asymptotic limit points for non-oscillating sequences…
We investigate a two-parametric family of one-dimensional non-Hermitian complex potentials with parity-time ($\mathcal{PT}$) symmetry. We find that there exist two distinct types of phase transitions, from an unbroken phase (characterized…
We describe a type system for a platform called the General Intensional Programming System (GIPSY), designed to support intensional programming languages built upon intensional logic and their imperative counter-parts for the intensional…
This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…
Session types employ a linear type system that ensures that communication channels cannot be implicitly copied or discarded. As a result, many mechanizations of these systems require modeling channel contexts and carefully ensuring that…
The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
We present a formalization of session types in a multi-threaded lambda-calculus (MTLC) equipped with a linear type system, establishing for the MTLC both type preservation and global progress. The latter (global progress) implies that the…
Concurrent systems are often complex and difficult to design. Choreographic languages, such as Multiparty Session Types (MPST), allow the description of global protocols of interactions by capturing valid patterns of interactions between…
We present Most, a process language with message-observing session types. Message-observing session types extend binary session types with type-level computation to specify communication protocols that vary based on messages observed on…
We present TLLC which extends the Two-Level Linear dependent type theory (TLL) with session-based concurrency. Equipped with Martin-L\"{o}f style dependency, the session types of TLLC allow protocols to specify properties of communicated…
Infinite time Turing machines are extended in several ways to allow for iterated oracle calls. The expressive power of these machines is discussed and in some cases determined.
We present a method which allows reduction of a size of a simulated system. The method can be applied to any system where one can define a finite set of possible states of the system and an elementary process which transforms one state of…
This survey/expository article covers a variety of topics related to the "topology at infinity" of noncompact manifolds and complexes. In manifold topology and geometric group theory, the most important noncompact spaces are often…
The concept of $typed$ $topology$ is introduced. In a typed topological space, some open sets are assigned "types", and topological concepts such as closure, connectedness can be defined using types. A finite data set in $R^2$ is a…
Intersection types are an essential tool in the analysis of operational and denotational properties of lambda-terms and functional programs. Among them, non-idempotent intersection types provide precise quantitative information about the…
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
Infinite order linear recurrences are studied via kneading matrices and kneading determinants. The concepts of kneading matrix and kneading determinant of an infinite order linear recurrence, introduced in this work, are defined in a purely…
Multiparty Session Types (MPSTs) offer a structured way of specifying communication protocols and guarantee relevant communication properties, such as deadlock-freedom. In this paper, we extend a minimal MPST system with quantum data and…