Related papers: Normalisation by Traversals
The connection between normalization by evaluation, logical predicates and semantic gluing constructions is a matter of folklore, worked out in varying degrees within the literature. In this note, we present an elementary version of the…
The smallest transitive relation < on well-typed normal terms such that if t is a strict subterm of u then t < u and if T is the normal form of the type of t and the term t is not a sort then T < t is well-founded in the type systems of the…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
The logical technique of focusing can be applied to the $\lambda$-calculus; in a simple type system with atomic types and negative type formers (functions, products, the unit type), its normal forms coincide with $\beta\eta$-normal forms.…
We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on…
We characterize normalization by evaluation as the composition of a self-interpreter with a self-reducer using a special representation scheme, in the sense of Mogensen (1992). We do so by deriving in a systematic way an untyped…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
We introduce a globally normalized transition-based neural network model that achieves state-of-the-art part-of-speech tagging, dependency parsing and sentence compression results. Our model is a simple feed-forward neural network that…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
In the lambda calculus a term is solvable iff it is operationally relevant. Solvable terms are a superset of the terms that convert to a final result called normal form. Unsolvable terms are operationally irrelevant and can be equated…
We consider the conversion problem for multimodal type theory (MTT) by characterizing the normal forms of the type theory and proving normalization. Normalization follows from a novel adaptation of Sterling's Synthetic Tait Computability…
We theoretically and experimentally investigate tensor-based regression and classification. Our focus is regularization with various tensor norms, including the overlapped trace norm, the latent trace norm, and the scaled latent trace norm.…
The call-by-value lambda calculus can be endowed with permutation rules, arising from linear logic proof-nets, having the advantage of unblocking some redexes that otherwise get stuck during the reduction. We show that such an extension…
The rapid expansion of English technical terminology presents a significant challenge to traditional expert-based standardization, particularly in rapidly developing areas such as artificial intelligence and quantum computing. Manual…
Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for…
We propose to achieve explainable neural machine translation (NMT) by changing the output representation to explain itself. We present a novel approach to NMT which generates the target sentence by monotonically walking through the source…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
We present a technique to study normalizing strategies when termination is asymptotic, that is, it appears as a limit, as opposite to reaching a normal form in a finite number of steps. Asymptotic termination occurs in several settings,…
This paper introduces a new machine architecture for evaluating lambda expressions using the normal-order reduction, which guarantees that every lambda expression will be evaluated if the expression has its normal form and the system has…
We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations'…