Related papers: Representing Nonterminating Rewriting with $\mathb…
We study a type checking algorithm that is able to type check a nontrivial subclass of functional programs that use features such as higher-rank, impredicative and second-order types. The only place the algorithm requires type annotation is…
Productivity is the property that finite prefixes of an infinite constructor term can be computed using a given term rewrite system. Hitherto, productivity has only been considered for orthogonal systems, where non-determinism is not…
In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and…
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…
Proving program termination is typically done by finding a well-founded ranking function for the program states. Existing termination provers typically find ranking functions using either linear algebra or templates. As such they are often…
The class of type-two basic feasible functionals ($\mathtt{BFF}_2$) is the analogue of $\mathtt{FP}$ (polynomial time functions) for type-2 functionals, that is, functionals that can take (first-order) functions as arguments.…
Dedukti is a type-checker for the $\lambda$$\Pi$-calculus modulo rewriting, an extension of Edinburgh's logicalframework LF where functions and type symbols can be defined by rewrite rules. It thereforecontains an engine for rewriting LF…
There are two possible computational interpretations of second-order arithmetic: Girard's system F or Spector's bar recursion and its variants. While the logic is the same, the programs obtained from these two interpretations have a…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a…
Many automatic theorem-provers rely on rewriting. Using theorems as rewrite rules helps to simplify the subgoals that arise during a proof. LCF is an interactive theorem-prover intended for reasoning about computation. Its implementation of…
In this contribution we revisit regular model checking, a powerful framework that has been successfully applied for the verification of infinite-state systems, especially parameterized systems (concurrent systems with an arbitrary number of…
We present a logically principled foundation for systematizing, in a way that works with any computational effect and evaluation order, SMT constraint generation seen in refinement type systems for functional programming languages. By…
There are two well known systems formalizing total recursion beyond primitive recursion (\textbf{PR}), system \textbf{T} by G\"odel and system \textbf{F} by Girard and Reynolds. system \textbf{T} defines recursion on typed objects and can…
We study increasingly expressive type systems, from $F^\mu$ -- an extension of the polymorphic lambda calculus with equirecursive types -- to $F^{\mu;}_\omega$ -- the higher-order polymorphic lambda calculus with equirecursive types and…
Rewriting techniques based on reduction orderings generate "just enough" consequences to retain first-order completeness. This is ideal for superposition-based first-order theorem proving, but for at least one approach to inductive…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
A new technique is presented to prove non-termination of term rewriting. The basic idea is to find a non-empty regular language of terms that is closed under rewriting and does not contain normal forms. It is automated by representing the…
In this paper we deal with verification of safety properties of term-rewriting systems. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which further resolved by…
Rewriting logic and its implementation Maude are an expressive framework for the formal specification and verification of software and other kinds of systems. Concurrency is naturally represented by nondeterministic local transformations…