Related papers: Flattening subtyping by eta expansion

Instantiation overflow is the property of those second order types for which all instances of full comprehension can be deduced from instances of atomic comprehension. In other words, a type has instantiation overflow when one can type, by…

Model studies indicate that many climate subsystems, especially ecosystems, may be vulnerable to 'tipping': a 'catastrophic process' in which a system, driven by gradually changing external factors, abruptly transitions (or 'collapses')…

A type assignment system for lambda-calculus enjoys the principal typing property if every typable term M has a special typing, called principal, from which all typings for M can be obtained via suitable operations. The existence of…

In this essay, I present the advantages and, I dare say, the beauty of programming in a language with set-theoretic types, that is, types that include union, intersection, and negation type connectives. I show by several examples how…

Indexed Linear Logic has been introduced by Ehrhard and Bucciarelli, it can be seen as a logical presentation of non-idempotent intersection types extended through the relational semantics to the full linear logic. We introduce an…

While most deep learning architectures are built on convolution, alternative foundations like morphology are being explored for purposes like interpretability and its connection to the analysis and processing of geometric structures. The…

Deep inference is a proof theoretic methodology that generalizes the standard notion of inference of the sequent calculus, whereby inference rules become applicable at any depth inside logical expressions. Deep inference provides more…

In this paper we define several notions of term expansion, used to define terms with less sharing, but with the same computational properties of terms typable in an intersection type system. Expansion relates terms typed by associative,…

Existing subset selection methods for efficient learning predominantly employ discrete combinatorial and model-specific approaches which lack generalizability. For an unseen architecture, one cannot use the subset chosen for a different…

Bidirectional typing combines two modes of typing: type checking, which checks that a program satisfies a known type, and type synthesis, which determines a type from the program. Using checking enables bidirectional typing to support…

Intersection and union types denote conjunctions and disjunctions of properties. Using bidirectional typechecking, intersection types are relatively straightforward, but union types present challenges. For union types, we can case-analyze a…

Ultra-fine entity typing (UFET) is the task of inferring the semantic types, from a large set of fine-grained candidates, that apply to a given entity mention. This task is especially challenging because we only have a small number of…

The Dependent Object Types (DOT) calculus formalizes key features of Scala. The D$_{<: }$ calculus is the core of DOT. To date, presentations of D$_{<: }$ have used declarative typing and subtyping rules, as opposed to algorithmic.…

Test time adaptation (TTA) equips deep learning models to handle unseen test data that deviates from the training distribution, even when source data is inaccessible. While traditional TTA methods often rely on entropy as a confidence…

Deep neural networks do not discriminate between spurious and causal patterns, and will only learn the most predictive ones while ignoring the others. This shortcut learning behaviour is detrimental to a network's ability to generalize to…

We propose to use orthologic as the basis for designing type systems supporting intersection, union, and negation types in the presence of subtyping assumptions. We show how to extend orthologic to support monotonic and antimonotonic…

We present the system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…

We introduce a new two-sided type system for verifying the correctness and incorrectness of functional programs with atoms and pattern matching. A key idea in the work is that types should range over sets of normal forms, rather than sets…

Many programming languages in the OO tradition now support pattern matching in some form. Historical examples include Scala and Ceylon, with the more recent additions of Java, Kotlin, TypeScript, and Flow. But pattern matching on generic…

Recent research has shown great progress on fine-grained entity typing. Most existing methods require pre-defining a set of types and training a multi-class classifier from a large labeled data set based on multi-level linguistic features.…