Related papers: Formalizing Box Inference for Capture Calculus
Solving a system of nonlinear inequalities is an important problem for which conventional numerical analysis has no satisfactory method. With a box-consistency algorithm one can compute a cover for the solution set to arbitrarily close…
The Functional Machine Calculus (Heijltjes 2022) is a new approach to unifying the imperative and functional programming paradigms. It extends the lambda-calculus, preserving the key features of confluent reduction and typed termination, to…
Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the…
The continuous functional calculus is perhaps the most fundamental construction in the theory of operator algebras, especially $C^{*}$-algebras. Here we document our formalization of the continuous functional calculus in Lean, which…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
Session types have emerged as a typing discipline for communication protocols. Existing calculi with session types come equipped with many different primitives that combine communication with the introduction or elimination of the…
Region-based type systems are a powerful tool for various kinds of program analysis. We introduce a new inference algorithm for region types based on an abstract notion of environment transformation. It analyzes the code of a method only…
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
We introduce two-sided type systems, which are sequent calculi for typing formulas. Two-sided type systems allow for hypothetical reasoning over the typing of compound program expressions, and the refutation of typing formulas. By…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
Algebraic effects & handlers have become a standard approach for side-effects in functional programming. Their modular composition with other effects and clean separation of syntax and semantics make them attractive to a wide audience.…
With the wide range of quantum programming languages on offer now, efficient program verification and type checking for these languages presents a challenge -- especially when classical debugging techniques may affect the states in a…
Box folding represents a crucial challenge for automated packaging systems. This work bridges the gap between existing methods for folding sequence extraction and approaches focused on the adaptability of automated systems to specific box…
Sets have been used for modeling various types of objects (e.g., a document as the set of keywords in it and a customer as the set of the items that she has purchased). Measuring similarity (e.g., Jaccard Index) between sets has been a key…
Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved. One approach is to model the unknown quantity of interest as a random variable, and to constrain this…
This article presents a bidirectional type system for the Calculus of Inductive Constructions (CIC). It introduces a new judgement intermediate between the usual inference and checking, dubbed constrained inference, to handle the presence…
We present a type system and inference algorithm for a rich subset of JavaScript equipped with objects, structural subtyping, prototype inheritance, and first-class methods. The type system supports abstract and recursive objects, and is…
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
Reinforcement learning with evaluation metrics as rewards is widely used to enhance specific capabilities of language models. However, for tasks such as factually consistent summarisation, existing metrics remain underdeveloped, limiting…
Algorithms like those for differentiating functional expressions manipulate the syntactic structure of mathematical expressions in a mathematically meaningful way. A formalization of such an algorithm should include a specification of its…