Related papers: Guarded Computational Type Theory
In the shared variable model of concurrency, guarded atomic actions restrict the possible interference between processes by regions of atomic execution. The guard specifies the condition for entering an atomic region. That is a convenient…
Temporal logics stands for a widely adopted family of formalisms for the verification of computational devices, enriching propositional logics by operators predicating on the step-wise behaviour of a system. Its quantified extensions allow…
We present the topos S of trees as a model of guarded recursion. We study the internal dependently-typed higher-order logic of S and show that S models two modal operators, on predicates and types, which serve as guards in recursive…
Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…
Causal discovery from observational data is a challenging task that can only be solved up to a set of equivalent solutions, called an equivalence class. Such classes, which are often large in size, encode uncertainties about the orientation…
Precise and autonomous clocks are of fundamental interest and central importance to both foundational studies and practical applications. Here, we construct a blueprint for a quantum clock governed by time-independent interactions. By…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
Computing expected predictions of discriminative models is a fundamental task in machine learning that appears in many interesting applications such as fairness, handling missing values, and data analysis. Unfortunately, computing…
We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph rewriting. By examples, we show how this paradigm of software development makes it…
We argue that (1) our perception of time through change and (2) the gap between reality and our observation of it are at the heart of both quantum mechanics and the dynamical mechanism of physical systems. We suggest that the origin of…
We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…
Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…
An oblivious computation is one that is free of direct and indirect information leaks, e.g., due to observable differences in timing and memory access patterns. This paper presents Lambda Obliv, a core language whose type system enforces…
Structured stochastic processes evolving in continuous time present a widely adopted framework to model phenomena occurring in nature and engineering. However, such models are often chosen to satisfy the Markov property to maintain…
We give an account of the basic combinatorial structure underlying the notion of type dependency. We do so by considering the category of all dependent sequent calculi, and exhibiting it as the category of algebras for a monad on a presheaf…
A fundamental description of time can be consistent not only with the usual monotonic behavior but also with a periodic physical clock variable, coupled to the degrees of freedom of a system evolving in time. Generically, one would in fact…
Generative models for source code are an interesting structured prediction problem, requiring to reason about both hard syntactic and semantic constraints as well as about natural, likely programs. We present a novel model for this problem…
We formulate an attention mechanism for continuous and ordered sequences that explicitly functions as an alignment model, which serves as the core of many sequence-to-sequence tasks. Standard scaled dot-product attention relies on…