Related papers: E-unification for Second-Order Abstract Syntax
Cooperation among constraint solvers is difficult because different solving paradigms have different theoretical foundations. Recent works have shown that abstract interpretation can provide a unifying theory for various constraint solvers.…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
Uniform one-dimensional fragment UF1^= is a formalism obtained from first-order logic by limiting quantification to applications of blocks of existential (universal) quantifiers such that at most one variable remains free in the quantified…
We prove a general congruence result for bisimilarity in higher-order languages, which generalises previous work to languages specified by a labelled transition system in which programs may occur as labels, and which may rely on operations…
Analysis of (partial) groundness is an important application of abstract interpretation. There are several proposals for improving the precision of such an analysis by exploiting type information, icluding our own work with Hill and King,…
We developed a procedure to enumerate complete sets of higher-order unifiers based on work by Jensen and Pietrzykowski. Our procedure removes many redundant unifiers by carefully restricting the search space and tightly integrating decision…
So-called combined approaches answer a conjunctive query over a description logic ontology in three steps: first, they materialise certain consequences of the ontology and the data; second, they evaluate the query over the data; and third,…
Equational Unification is a critical problem in many areas such as automated theorem proving and security protocol analysis. In this paper, we focus on XOR-Unification, that is, unification modulo the theory of exclusive-or. This theory…
We sketch a tentative proof of P-completeness for the $\beta$-convertibility problem on untyped planar (a.k.a. ordered or non-commutative) $\lambda$-terms.
E-generalization computes common generalizations of given ground terms w.r.t. a given equational background theory E. In 2005 [arXiv:1403.8118], we had presented a computation approach based on standard regular tree grammar algorithms, and…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
Higher-order constrained Horn clauses (HoCHC) are a semantically-invariant system of higher-order logic modulo theories. With semi-decidable unsolvability over a semi-decidable background theory, HoCHC is suitable for safety verification.…
An aggregative composition is a binary operation obeying the principle that the whole is determined by the sum of its parts. The development of graph algebras, on which the theory of formal graph languages is built, relies on aggregative…
The characterization of second-order type isomorphisms is a purely syntactical problem that we propose to study under the enlightenment of game semantics. We study this question in the case of second-order λ$\mu$-calculus, which can be…
Even though many machine algorithms have been proposed for entity resolution, it remains very challenging to find a solution with quality guarantees. In this paper, we propose a novel HUman and Machine cOoperation (HUMO) framework for…
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…
Equational unification of two terms consists of finding a substitution that, when applied to both terms, makes them equal modulo some equational properties. A narrowing-based equational unification algorithm relying on the concept of the…
Higher order cohomology of arithmetic groups is expressed in terms of (g,K)-cohomology. Generalizing results of Borel, it is shown that the latter can be computed using functions of (uniform) moderate growth. A higher order versions of…
Word embedding, a high-dimensional (HD) numerical representation of words generated by machine learning models, has been used for different natural language processing tasks, e.g., translation between two languages. Recently, there has been…