Related papers: Datatype defining rewrite systems for naturals and…
Basically information means selection within a domain (value or definition set) of possibilities. For objectifiable, comparable and precise information the domain should be the same for all. Therefore the global (online) definition of the…
Considering patterns as sets of their instances, a difference operator over patterns computes a finite set of two given patterns, which represents the difference between the dividend pattern and the divisor pattern. A complement of a…
DATR is a declarative representation language for lexical information and as such, in principle, neutral with respect to particular processing strategies. Previous DATR compiler/interpreter systems support only one access strategy that…
Streams are infinite sequences over a given data type. A stream specification is a set of equations intended to define a stream. We propose a transformation from such a stream specification to a term rewriting system (TRS) in such a way…
This paper presents differential-algebraic refinement logic (dARL) with which one can deductively verify both properties and relations of differential-algebraic programs (DAPs) that extend hybrid dynamical systems with…
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
Date and Darwen have proposed a theory of types, the latter forms the basis of a detailed presentation of a panoply of simple and complex types. However, this proposal has not been structured in a formal system. Specifically, Date and…
Refinement types turn typechecking into lightweight verification. The classic form of refinement type is the datasort refinement, in which datasorts identify subclasses of inductive datatypes. Existing type systems for datasort refinements…
Rewriting systems are often defined as binary relations over a given set of objects. This simple definition is used to describe various properties of rewriting such as termination, confluence, normal forms etc. In this paper, we introduce a…
The treatment of equality as a type in type theory gives rise to an interesting type-theoretic structure known as `identity type'. The idea is that, given terms $a,b$ of a type $A$, one may form the type $Id_{A}(a,b)$, whose elements are…
Streaming Data String Transducers (SDSTs) were introduced to model a class of imperative and a class of functional programs, manipulating lists of data items. These can be used to write commonly used routines such as insert, delete and…
We use a labelled deduction system based on the concept of computational paths (sequences of rewrites) as equalities between two terms of the same type. We also define a term rewriting system that is used to make computations between these…
We tackle the problem of data-structure rewriting including pointer redirections. We propose two basic rewrite steps: (i) Local Redirection and Replacement steps the aim of which is redirecting specific pointers determined by means of a…
String diagrams are a powerful tool for reasoning about physical processes, logic circuits, tensor networks, and many other compositional structures. Dixon, Duncan and Kissinger introduced string graphs, which are a combinatoric…
Any file is fundamentally a binary data stream. A practical solution was achieved to interpret binary data stream. A new scripting language named Data Format Scripting Language (DFSL) was developed to describe the physical layout of the…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…
Statement autoformalization acts as a critical bridge between human mathematics and formal mathematics by translating natural language problems into formal language. While prior works have focused on data synthesis and diverse training…
We introduce a term algebra as a new formal specification language for the coordinating architectures of distributed systems consisting of a finite yet unbounded number of components. The language allows to describe infinite sets of systems…
The Normalization transformation plays a key role in the compilation of Diderot programs. The transformations are complicated and it would be easy for a bug to go undetected. To increase our confidence in normalization part of the compiler…
Resolution refinements called w-resolution trees with lemmas (WRTL) and with input lemmas (WRTI) are introduced. Dag-like resolution is equivalent to both WRTL and WRTI when there is no regularity condition. For regular proofs, an…