Related papers: Recursion and Sequentiality in Categories of Sheav…
The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equivalent to several well-known characterizations appearing in the…
We introduce a trace semantics for a call-by-value language with full polymorphism and higher-order references. This is an operational game semantics model based on a nominal interpretation of parametricity whereby polymorphic values are…
This paper describes an automatic termination checker for a generic first-order call-by-value language in ML style. We use the fact that value are built from variants and tuples to keep some information about how arguments of recursive call…
This article presents a pattern-based language designed to select (a set of) subterms of a given term in a concise and robust way. Building on this language, we implement a single-step rewriting tactic in the Isabelle theorem prover, which…
This paper grew out of the observation that the possibilities of proof by induction and definition by recursion are often confused. The paper reviews the distinctions. The von Neumann construction of the ordinal numbers includes a…
We propose regular expressions to abstractly model and study properties of resource-aware computations. Inspired by nominal techniques -- as those popular in process calculi -- we extend classical regular expressions with names (to model…
The category of coherent sheaves over a noetherian scheme is very important for studying the properties of a given scheme. For noetherian schemes it is a well-known fact that the topology can be fully recovered from the corresponding…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
Experience shows that the poset of levels (or dimensions) of the topos of presheaves on some elegant Reedy categories may be equipped with a monotone increasing `successor' function which, as the case of simplicial sets shows, is different…
Interventional causal models describe several joint distributions over some variables used to describe a system, one for each intervention setting. They provide a formal recipe for how to move between the different joint distributions and…
Referring expressions are natural language constructions used to identify particular objects within a scene. In this paper, we propose a unified framework for the tasks of referring expression comprehension and generation. Our model is…
Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in…
In this work, we address the problem to model all the nodes (words or phrases) in a dependency tree with the dense representations. We propose a recursive convolutional neural network (RCNN) architecture to capture syntactic and…
A new characterization of provably recursive functions of first-order arithmetic is described. Its main feature is using only terms consisting of 0, the successor S and variables in the quantifier rules, namely, universal elimination and…
One of the most basic functions of language is to refer to objects in a shared scene. Modeling reference with continuous representations is challenging because it requires individuation, i.e., tracking and distinguishing an arbitrary number…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
Shapiro's notations for natural numbers, and the associated desideratum of acceptability - the property of a notation that all recursive functions are computable in it - is well-known in philosophy of computing. Computable structure theory,…
In this paper, we present a linear and reversible programming language with inductives types and recursion. The semantics of the languages is based on pattern-matching; we show how ensuring syntactical exhaustivity and non-overlapping of…
We relate the category of sheaves on alcoves that was constructed in "Sheaves on the alcoves and modular representations I" to the representation theory of reductive algebraic groups. In particular, we show that its indecomposable…
We present a complete reasoning principle for contextual equivalence in an untyped probabilistic language. The language includes continuous (real-valued) random variables, conditionals, and scoring. It also includes recursion, since the…