Related papers: Continuation calculus
The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…
This Survey provides an overview of techniques in termination analysis for programs with numerical variables and transitions defined by linear constraints. This subarea of program analysis is challenging due to the existence of undecidable…
Driving simulators have been used in the automotive industry for many years because of their ability to perform tests in a safe, reproducible and controlled immersive virtual environment. The improved performance of the simulator and its…
We propose Kernel Predictive Control (KPC), a learning-based predictive control strategy that enjoys deterministic guarantees of safety. Noise-corrupted samples of the unknown system dynamics are used to learn several models through the…
Differential computation (DC) is a highly general incremental computation/view maintenance technique that can maintain the output of an arbitrary and possibly recursive dataflow computation upon changes to its base inputs. As such, it is a…
Associative memory has long underpinned the design of sequential models. Beyond recall, humans reason by projecting future states and selecting goal-directed actions, a capability that modern language models increasingly require but do not…
Quantum lambda calculus has been studied mainly as an idealized programming language -- the evaluation essentially corresponds to a deterministic abstract machine. Very little work has been done to develop a rewriting theory for quantum…
This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its…
The problem of determining whether or not any program terminates was shown to be undecidable by Turing, but recent advances in the area have allowed this information to be determined for a large class of programs. The classic method for…
Incremental computation has recently been studied using the concepts of change structures and derivatives of programs, where the derivative of a function allows updating the output of the function based on a change to its input. We…
Model Predictive Control (MPC) is widely used to achieve performance objectives, while enforcing operational and safety constraints. Despite its high performance, MPC often demands significant computational resources, making it challenging…
Teaching proofs is a crucial component of any undergraduate-level program that covers formal reasoning. We have developed a calculational reasoning format and refined it over several years of teaching a freshman-level course, "Logic and…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
Type and effect systems are a tool to analyse statically the behaviour of programs with effects. We present a proof based on the so called reducibility candidates that a suitable stratification of the type and effect system entails the…
The intrinsic treatment of binding in the lambda calculus makes it an ideal data structure for representing syntactic objects with binding such as formulas, proofs, types, and programs. Supporting such a data structure in an implementation…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
The calculus of constructions (CC) is a core theory for dependently typed programming and higher-order constructive logic. Originally introduced in Coquand's 1985 thesis, CC has inspired 25 years of research in programming languages and…
Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…
Prompt programming treats large language model prompts as software components with typed interfaces. Based on a literature survey of 15 recent works from 2023 to 2025, we observe a consistent trend: type systems are central to emerging…
This paper studies emulation of induction by coinduction in a call-by-name language with control operators. Since it is known that call-by-name programming languages with control operators cannot have general initial algebras, interaction…