Related papers: Abstracting Extensible Recursive Functions
The use of aggregates in recursion enables efficient and scalable support for a wide range of BigData algorithms, including those used in graph applications, KDD applications, and ML applications, which have proven difficult to be expressed…
Functionals are an important research subject in Mathematics and Computer Science as well as a challenge in Information Technologies where the current programming paradigm states that only symbolic computations are possible on higher order…
We consider two classes of computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. We argue that the task of program learning should be more tractable for these architectures…
Given a simple recursive function, we show how to extract from it a reversible and an classical iterative part. Those parts can synchronously cooperate under a Producer/Consumer pattern in order to implement the original recursive function.…
Modelling compositionality has been a longstanding area of research in the field of vector space semantics. The categorical approach to compositionality maps grammar onto vector spaces in a principled way, but comes under fire for requiring…
Recent algorithmic advances in algebraic automata theory drew attention to semigroupoids (semicategories). These are mathematical descriptions of typed computational processes, but they have not been studied systematically in the context of…
We define the concept of a logic frame, which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive…
Although RNNs have been shown to be powerful tools for processing sequential data, finding architectures or optimization strategies that allow them to model very long term dependencies is still an active area of research. In this work, we…
We present a method for synthesizing recursive functions that satisfy both a functional specification and an asymptotic resource bound. Prior methods for synthesis with a resource metric require the user to specify a concrete expression…
In this paper we demonstrate that the class of basic feasible functionals has recursion theoretic properties which naturally generalize the corresponding properties of the class of feasible functions. We also improve the Kapron - Cook…
This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational…
Extended multi-adjoint logic programming arises as an extension of multi-adjoint normal logic programming where constraints and a special type of aggregator operator have been included. The use of this general aggregator operator permits to…
This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…
Functional programming comes in two flavours: one where ``functions are first-class citizens'' (we call this applicative) and one which is based on equations (we call this declarative). In relational programming clauses play the role of…
In this work, we incorporate reversibility into structured communication-based programming, to allow parties of a session to automatically undo, in a rollback fashion, the effect of previously executed interactions. This permits taking…
We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…
Following Milner's seminal paper, the representation of functions as processes has received considerable attention. For pure $\lambda$-calculus, the process representations yield (at best) non-extensional $\lambda $-theories (i.e., $\beta$…
We introduce a neural network with a recurrent attention model over a possibly large external memory. The architecture is a form of Memory Network (Weston et al., 2015) but unlike the model in that work, it is trained end-to-end, and hence…
A circular program creates a data structure whose computation depends upon itself or refers to itself. The technique is used to implement the classic data structures circular and doubly-linked lists, threaded trees and queues, in a…
A compact set has computable type if any homeomorphic copy of the set which is semicomputable is actually computable. Miller proved that finite-dimensional spheres have computable type, Iljazovi\'c and other authors established the property…