Related papers: Tracing sharing in an imperative pure calculus (Ex…
We investigate, in the context of functional prototype-based lan- guages, a calculus of objects which might extend themselves upon receiving a message, a capability referred to by Cardelli as a self-inflicted operation. We present a sound…
Exchangeable arrays are natural tools to model common forms of dependence between units of a sample. Jointly exchangeable arrays are well suited to dyadic data, where observed random variables are indexed by two units from the same…
Effectus theory is a new branch of categorical logic that aims to capture the essentials of quantum logic, with probabilistic and Boolean logic as special cases. Predicates in effectus theory are not subobjects having a Heyting algebra…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…
E prover is a state-of-the-art theorem prover for first-order logic with equality. E prover is built around a saturation loop, where new clauses are derived by inference rules from previously derived clauses. Selection of clauses for the…
In this article, we discuss a flow--sensitive analysis of equality relationships for imperative programs. We describe its semantic domains, general purpose operations over abstract computational states (term evaluation and identification,…
We define a proof system for exceptions which is close to the syntax for exceptions, in the sense that the exceptions do not appear explicitly in the type of any expression. This proof system is sound with respect to the intended…
Implicit models, an emerging model class, compute outputs by iterating a single parameter block to a fixed point. This architecture realizes an infinite-depth, weight-tied network that trains with constant memory, significantly reducing…
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…
In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs…
Reversible computation is key in developing new, energy-efficient paradigms, but also in providing forward-only concepts with broader definitions and finer frames of study.Among other fields, the algebraic specification and representation…
Recently, Miller and Wu introduced the positive $\lambda$-calculus, a call-by-value $\lambda$-calculus with sharing obtained by assigning proof terms to the positively polarized focused proofs for minimal intuitionistic logic. The positive…
For data-centric systems, provenance tracking is particularly important when the system is open and decentralised, such as the Web of Linked Data. In this paper, a concise but expressive calculus which models data updates is presented. The…
For models of concurrent and distributed systems, it is important and also challenging to establish correctness in terms of safety and/or liveness properties. Theories of distributed systems consider equivalences fundamental, since they (1)…
We introduce a conceptually simple and effective method to quantify the similarity between relations in knowledge bases. Specifically, our approach is based on the divergence between the conditional probability distributions over entity…
We propose a type-based resource usage analysis for the π-calculus extended with resource creation/access primitives. The goal of the resource usage analysis is to statically check that a program accesses resources such as files and…
We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…
The aim of this paper is to offer the first systematic exploration and definition of equivalent causal models in the context where both models are not made up of the same variables. The idea is that two models are equivalent when they agree…
We extend two kinds of causal models, structural equation models and simulation models, to infinite variable spaces. This enables a semantics for conditionals founded on a calculus of intervention, and axiomatization of causal reasoning for…