Related papers: A Deforestation of Reducts: Refocusing
We propose a generic termination proof method for rewriting under strategies, based on an explicit induction on the termination property. Rewriting trees on ground terms are modeled by proof trees, generated by alternatively applying…
We describe a formalization of higher-order rewriting theory and formally prove that an AFS is strongly normalizing if it can be interpreted in a well-founded domain. To do so, we use Coq, which is a proof assistant based on dependent type…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
Search is a key service within constraint programming systems, and it demands the restoration of previously accessed states during the exploration of a search tree. Restoration proceeds either bottom-up within the tree to roll back…
There are two well known systems formalizing total recursion beyond primitive recursion (\textbf{PR}), system \textbf{T} by G\"odel and system \textbf{F} by Girard and Reynolds. system \textbf{T} defines recursion on typed objects and can…
This notes explains how a standard algorithm that constructs the discrete Fourier transform has been formalised and proved correct in the Coq proof assistant using the SSReflect extension.
We present an unusual algorithm involving classification trees where two trees are grown in opposite directions so that they are matched at their leaves. This approach finds application in a new data mining task we formulate, called…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
A reduction of a source distribution is a collection of smaller sized distributions that are collectively equivalent to the source distribution with respect to the property of decomposability. That is, an arbitrary language is decomposable…
We consider a reinforcement learning framework where agents have to navigate from start states to goal states. We prove convergence of a cycle-detection learning algorithm on a class of tasks that we call reducible. Reducible tasks have an…
Search engines play an important role in our everyday lives by assisting us in finding the information we need. When we input a complex query, however, results are often far from satisfactory. In this work, we introduce a query…
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been…
This paper presents a gentle tutorial and a structured reformulation of Bock's 1971 Algol procedure for constructing minimum directed spanning trees. Our aim is to make the original algorithm readable and reproducible for modern readers,…
We introduce Refinement Reflection, a new framework for building SMT-based deductive verifiers. The key idea is to reflect the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses…
This paper is an expository contribution reporting on published work. It focusses on an approach followed in the rewriting community to formalize the concept of strategy. Based on rewriting concepts, several definitions of strategy are…
Factorization -- a simple form of standardization -- is concerned with reduction strategies, i.e. how a result is computed. We present a new technique for proving factorization theorems for compound rewriting systems in a modular way, which…
Refinement Reflection turns your favorite programming language into a proof assistant by reflecting the code implementing a user-defined function into the function's (output) refinement type. As a consequence, at uses of the function, the…
It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this. We…