Related papers: Initial Algebra Semantics for Cyclic Sharing Tree …

Graphs are a generalized concept that encompasses more complex data structures than trees, such as difference lists, doubly-linked lists, skip lists, and leaf-linked trees. Normally, these structures are handled with destructive assignments…

In this paper we provide a semantic and syntactic analysis of parametrised natural numbers object in coherent categories, or pr-coherent categories. Semantically, we show the definable functions in the initial pr-coherent category are…

Circuit representations are becoming the lingua franca to express and reason about tractable generative and discriminative models. In this paper, we show how complex inference scenarios for these models that commonly arise in machine…

We give a formal treatment of simple type theories, such as the simply-typed $\lambda$-calculus, using the framework of abstract clones. Abstract clones traditionally describe first-order structures, but by equipping them with additional…

We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…

We present a new model of computation, described in terms of monoidal categories. It conforms the Church-Turing Thesis, and captures the same computable functions as the standard models. It provides a succinct categorical interface to most…

We present AlgCo (Algebraic Coinductives), a practical framework for inductive reasoning over commonly used coinductive types such as conats, streams, and infinitary trees with finite branching factor. The key idea is to exploit the notion…

We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up…

Implicative algebras have been recently introduced by Miquel in order to provide a unifying notion of model, encompassing the most relevant and used ones, such as realizability (both classical and intuitionistic), and forcing. In this work,…

We propose a modal logic tailored to describe graph transformations and discuss some of its properties. We focus on a particular class of graphs called termgraphs. They are first-order terms augmented with sharing and cycles. Termgraphs…

Separation Logic (SL) with inductive definitions is a natural formalism for specifying complex recursive data structures, used in compositional verification of programs manipulating such structures. The key ingredient of any automated…

This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…

We introduce the Rebound library that supports well-scoped term representations in Haskell and automates the definition of substitution, alpha-equivalence, and other operations that work with binding structures. The key idea of our design…

Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…

We suggest a compositional vector representation of parse trees that relies on a recursive combination of recurrent-neural network encoders. To demonstrate its effectiveness, we use the representation as the backbone of a greedy, bottom-up…

We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…

Succinct data structures give space-efficient representations of large amounts of data without sacrificing performance. They rely one cleverly designed data representations and algorithms. We present here the formalization in Coq/SSReflect…

We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by…

Techniques in which words are represented as vectors have proved useful in many applications in computational linguistics, however there is currently no general semantic formalism for representing meaning in terms of vectors. We present a…

Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…