Related papers: Initial Algebra Semantics for Cyclic Sharing Tree …

The notion of term graph encodes a refinement of inductively generated syntax in which regard is paid to the the sharing and discard of subterms. Inductively generated syntax has an abstract expression in terms of initial algebras for…

String diagrams are a graphical language used to represent processes that can be composed sequentially or in parallel, which correspond graphically to horizontal or vertical juxtaposition. In this paper we demonstrate how to compute the…

In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…

We study the notion of extensibility in functional data types, as a new approach to the problem of decorating abstract syntax trees with additional sets of information. We observed the need for such extensibility while redesigning the data…

This study presents a systematic approach to specifying data objects with the help of initial algebras. The primary aim is to describe the set-up to be found in modern functional programming languages such as Haskell and ML, although it can…

We report on work in progress on 'nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent…

User defined recursive types are a fundamental feature of modern functional programming languages like Haskell, Clean, and the ML family of languages. Properties of programs defined by recursion on the structure of recursive types are…

We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…

Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…

Manifestly and logically displaying the line of reasoning from evidence to answer is significant to explainable question answering (QA). The entailment tree exhibits the lines structurally, which is different from the self-explanation…

In this thesis we give an algebraic characterization of the syntax and semantics of simply-typed languages. More precisely, we characterize simply-typed binding syntax equipped with reduction rules via a universal property, namely as the…

Representing a proof tree by a combinator term that reduces to the tree lets subtle forms of duplication within the tree materialize as duplicated subterms of the combinator term. In a DAG representation of the combinator term these…

In heap-based languages, knowing that a variable x points to an acyclic data structure is useful for analyzing termination: this information guarantees that the depth of the data structure to which x points is greater than the depth of the…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

In this document, we propose a description, via a Haskell implementation, of a generalization of the notion of regular expression allowing us to group the definitions and the methods of (tree or word) automata constructions over one generic…

The primary goal of this paper is to present a unified way to transform the syntax of a logic system into certain initial algebraic structure so that it can be studied algebraically. The algebraic structures which one may choose for this…

We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized by iterated block products of…

A Concept Tree is a structure for storing knowledge where the trees are stored in a database called a Concept Base. It sits between the highly distributed neural architectures and the distributed information systems, with the intention of…

We design the Arboretum$.$hs package for symbolic computations with algebras of trees and more general graphs in Haskell. Thanks to the declarative nature of functional programming, the package's implementation closely follows mathematical…

In recent years, algebraic topology and its modern development, the theory of persistent homology, has shown great potential in graph representation learning. In this paper, based on the mathematics of algebraic topology, we propose a novel…