Related papers: A calculus for costed computations
This paper proposes first-order modal $\xi$-calculus as well as genealogical Kripke models. Inspired by modal $\mu$-calculus, first-order modal $\xi$-calculus takes a quite similar form and extends its inductive expressivity onto a…
Although randomization has long been used in distributed computing, formal methods for reasoning about probabilistic concurrent programs have lagged behind. No existing program logics can express specifications about the full distributions…
Although computational complexity is a fundamental aspect of program behavior, it is often at odds with common type theoretic principles such as function extensionality, which identifies all functions with the same $\textit{input-output}$…
This paper shows how we can make use of an asynchronous transition system, whose transitions are labelled with events and which is equipped with a notion of independence of events, to define non-interleaving semantics for the applied…
In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for…
We present $\textbf{calf}$, a $\textbf{c}$ost-$\textbf{a}$ware $\textbf{l}$ogical $\textbf{f}$ramework for studying quantitative aspects of functional programs. Taking inspiration from recent work that reconstructs traditional aspects of…
Although many investigators affirm a desire to build reasoning systems that behave consistently with the axiomatic basis defined by probability theory and utility theory, limited resources for engineering and computation can make a complete…
We present Decalf, a directed, effectful cost-aware logical framework for studying quantitative aspects of functional programs with effects. Like Calf, the language is based on an internal phase distinction between the behavior of a program…
In this paper, we establish the foundations of a novel logical framework for the {\pi}-calculus, based on the deduction-as-computation paradigm. Following the standard proof-theoretic interpretation of logic programming, we represent…
Computation is commonly defined as the execution of abstract algorithms over symbolic representations, with physical systems treated as substrates that realise predefined operations. While effective for engineered machines, this separation…
We propose an automated method for proving termination of $\pi$-calculus processes, based on a reduction to termination of sequential programs: we translate a $\pi$-calculus process to a sequential program, so that the termination of the…
The do-calculus is a well-known deductive system for deriving connections between interventional and observed distributions, and has been proven complete for a number of important identifiability problems in causal inference. Nevertheless,…
We introduce the PBS-calculus to represent and reason on quantum computations involving coherent control of quantum operations. Coherent control, and in particular indefinite causal order, is known to enable multiple computational and…
Formalising the pi-calculus is an illuminating test of the expressiveness of logical frameworks and mechanised metatheory systems, because of the presence of name binding, labelled transitions with name extrusion, bisimulation, and…
In the logic programming paradigm, it is difficult to develop an elegant solution for generating distinguishing formulae that witness the failure of open-bisimilarity between two pi-calculus processes; this was unexpected because the…
A notion of probabilistic lambda-calculus usually comes with a prescribed reduction strategy, typically call-by-name or call-by-value, as the calculus is non-confluent and these strategies yield different results. This is a break with one…
We investigate a graphical representation of session invocation interdependency in order to prove progress for the pi-calculus with sessions under the usual session typing discipline. We show that those processes whose associated dependency…
Motivated by on-chip communication, a channel model is proposed where the variance of the additive noise depends on the weighted sum of the past channel input powers. For this channel, an expression for the capacity per unit cost is…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…
Psi-calculi are a parametric framework for nominal calculi, where standard calculi are found as instances, like the pi-calculus, or the cryptographic spi-calculus and applied-pi. Psi-calculi have an interleaving operational semantics, with…