Related papers: Dependently Sorted Nominal Signatures
We introduce a notion of signature whose sorts form a direct category, and study computads for such signatures. Algebras for such a signature are presheaves with an interpretation of every function symbol of the signature, and we describe…
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…
This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…
We describe a realizability framework for classical first-order logic in which realizers live in (a model of) typed {\lambda}{\mu}-calculus. This allows a direct interpretation of classical proofs, avoiding the usual negative translation to…
The lambda-calculus with de Bruijn indices assembles each alpha-class of lambda-terms in a unique term, using indices instead of variable names. Intersection types provide finitary type polymorphism and can characterise normalisable…
We present a combination of raising, explicit variable dependency representation, the liberalized delta-rule, and preservation of solutions for first-order deductive theorem proving. Our main motivation is to provide the foundation for our…
The contribution of this paper is the development of the syntax and semantics of multi-sorted nominal abstract binding trees (abts), an extension of second order universal algebra to support symbol-indexed families of operators. Nominal…
In this paper we present our current development on a new formalization of nominal sets in Agda. Our first motivation in having another formalization was to understand better nominal sets and to have a playground for testing type systems…
We explore the possibility of extending Mardare et al. quantitative algebras to the structures which naturally emerge from Combinatory Logic and the lambda-calculus. First of all, we show that the framework is indeed applicable to those…
We present an approach for representing abstract argumentation frameworks based on an encoding into classical higher-order logic. This provides a uniform framework for computer-assisted assessment of abstract argumentation frameworks using…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
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.
Higher-order processes with parameterization are capable of abstraction and application (migrated from the lambda-calculus), and thus are computationally more expressive. For the minimal higher-order concurrency, it is well-known that the…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…
We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…
Many calculi exist for modelling various features of object-oriented languages. Many of them are based on $\lambda$-calculus and focus either on statically typed class-based languages or dynamic prototype-based languages. We formalize…
We characterize those intersection-type theories which yield complete intersection-type assignment systems for lambda-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics,…
Let T be Goedel's system of primitive recursive functionals of finite type in the lambda formulation. We define by constructive means using recursion on nested multisets a multivalued function I from the set of terms of T into the set of…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
Representation theorems for formal systems often take the form of an inductive translation that satisfies certain invariants, which are proved inductively. Theory morphisms and logical relations are common patterns of such inductive…