Related papers: Revisiting Decidable Bounded Quantification, via D…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
Due to the undecidability of most type-related properties of System F like type inhabitation or type checking, restricted polymorphic systems have been widely investigated (the most well-known being ML-polymorphism). In this paper we…
Dependent Object Types (DOT) is a calculus with path dependent types, intersection types, and object self-references, which serves as the core calculus of Scala 3. Although the calculus has been proven sound, it remains open whether type…
We introduce constraints necessary for type checking a higher-order concurrent constraint language, and solve them with an incremental algorithm. Our constraint system extends rational unification by constraints x$\subseteq$ y saying that…
Session types are behavioural types for guaranteeing that concurrent programs are free from basic communication errors. Recent work has shown that asynchronous session subtyping is undecidable. However, since session types have become…
There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
The increasing use of deep learning across various domains highlights the importance of understanding the decision-making processes of these black-box models. Recent research focusing on the decision boundaries of deep classifiers, relies…
Type qualifiers offer a lightweight mechanism for enriching existing type systems to enforce additional, desirable, program invariants. They do so by offering a restricted but effective form of subtyping. While the theory of type qualifiers…
We introduce regular graph constraints and explore their decidability properties. The motivation for regular graph constraints is 1) type checking of changing types of objects in the presence of linked data structures, 2) shape analysis…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
Any system that models the world under finite representational capacity must compress; any compression entails a prior; and the prior is the system's bias. What has not been established is whether uncertainty participates in the dynamics…
We present $\lambda_B$, a quantum-control $\lambda$-calculus that refines previous basis-sensitive systems by allowing abstractions to be expressed with respect to arbitrary -- possibly entangled -- bases. Each abstraction and let construct…
I discuss some of the main interpretations given to explain the indeterministic nature of quantum measurements and show that all has some loopholes in one corner or another. I propose an alternative interpretation based on the notion of…
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…
In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable…
This paper defines a notion of binding trees that provide a suitable model for second-order type systems with F-bounded quantifiers and equirecursive types. It defines a notion of regular binding trees that correspond in the right way to…
We present an approach to type theory in which the typing judgments do not have explicit contexts. Instead of judgments of shape "Gamma |- A : B", our systems just have judgments of shape "A : B". A key feature is that we distinguish free…
Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its scalability (unlike Damas-Milner type inference, bidirectional typing remains decidable even for very…