Related papers: Strong Nominal Semantics for Fixed-Point Constrain…
We investigate final coalgebras in nominal sets. This allows us to define types of infinite data with binding for which all constructions automatically respect alpha equivalence. We give applications to the infinitary lambda calculus.
This paper contributes to the Alpay Algebra by demonstrating that the stable outcome of a self referential process, obtained by iterating a transformation through all ordinal stages, is identical to the unique equilibrium of an unbounded…
This paper provides a model theoretic semantics to feature terms augmented with set descriptions. We provide constraints to specify HPSG style set descriptions, fixed cardinality set descriptions, set-membership constraints, restricted…
Term algebras are important objects in computer science and are correspondingly well-studied. A natural generalization is to quotient these algebras by finitely many ground term equations, obtaining what we call almost free algebras. One of…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
We show that three fixed point structures equipped with (sequential) composition, a sum operation, and a fixed point operation share the same valid equations. These are the theories of (context-free) languages, (regular) tree languages, and…
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a minimal term-generated model for the…
The elementary affine lambda-calculus was introduced as a polyvalent setting for implicit computational complexity, allowing for characterizations of polynomial time and hyperexponential time predicates. But these results rely on type…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…
We develop a fixed-point extension of quantitative equational logic and give semantics in one-bounded complete quantitative algebras. Unlike previous related work about fixed-points in metric spaces, we are working with the notion of…
We show how to compute efficiently with nominal sets over the total order symmetry, by developing a direct representation of such nominal sets and basic constructions thereon. In contrast to previous approaches, we work directly at the…
Permissive-Nominal Logic (PNL) is an extension of first-order predicate logic in which term-formers can bind names in their arguments. This allows for direct axiomatisations with binders, such as of the lambda-binder of the lambda-calculus…
Logically constrained term rewriting is a relatively new formalism where rules are equipped with constraints over some arbitrary theory. Although there are many recent advances with respect to rewriting induction, completion, complexity…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
Coalgebras provide a uniform framework to study dynamical systems, including several types of automata. In this paper, we make use of the coalgebraic view on systems to investigate, in a uniform way, under which conditions calculi that are…
Automata models for data languages (i.e. languages over infinite alphabets) often feature either global or local freshness operators. We show that Bollig et al.'s session automata, which focus on global freshness, are equivalent to regular…
Alternating parity automata (APAs) provide a robust formalism for modelling infinite behaviours and play a central role in formal verification. Despite their widespread use, the algebraic theory underlying APAs has remained largely…
Our goal is to define an algebraic language for reasoning about non-deterministic computations. Towards this goal, we introduce an algebra of string-to-string transductions. Specifically, it is an algebra of partial functions on words over…
Data words with binders formalize concurrently allocated memory. Most name-binding mechanisms in formal languages, such as the $\lambda$-calculus, adhere to properly nested scoping. In contrast, stateful programming languages with explicit…
A modal logic is \emph{non-iterative} if it can be defined by axioms that do not nest modal operators, and \emph{rank-1} if additionally all propositional variables in axioms are in scope of a modal operator. It is known that every…