相关论文: Strict Ideal Completions of the Lambda Calculus

We study the semantics of a resource-sensitive extension of the lambda calculus in a canonical reflexive object of a category of sets and relations, a relational version of Scott's original model of the pure lambda calculus. This calculus…

We study the complexity of deciding the equality of infinite objects specified by systems of equations, and of infinite objects specified by lambda-terms. For equational specifications there are several natural notions of equality: equality…

We consider a certain class of infinitary rules of inference, called here restriction rules, using of which allows us to deduce complete theories of given models. The first instance of such rules was the $\omega$-rule introduced by Hilbert,…

We present a new and formal coinductive proof of confluence and normalisation of B\"ohm reduction in infinitary lambda calculus. The proof is simpler than previous proofs of this result. The technique of the proof is new, i.e., it is not…

We address a problem connected to the unfolding semantics of functional programming languages: give a useful characterization of those infinite lambda-terms that are lambda_{letrec}-expressible in the sense that they arise as infinite…

We introduce infinitary action logic with exponentiation -- that is, the multiplicative-additive Lambek calculus extended with Kleene star and with a family of subexponential modalities, which allows some of the structural rules…

We study propositional and first-order G\"odel logics over infinitary languages which are motivated semantically by corresponding interpretations into the unit interval [0,1]. We provide infinitary Hilbert-style calculi for the particular…

We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…

This paper aims to apply the tool of generalized existential completions of conjunctive doctrines, concerning a class $\Lambda$ of morphisms of their base category, to deepen the study of regular and exact completions of existential…

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.

Model checking properties are often described by means of finite automata. Any particular such automaton divides the set of infinite trees into finitely many classes, according to which state has an infinite run. Building the full type…

We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a…

In this paper we introduce several quantitative methods for the lambda-calculus based on partial metrics, a well-studied variant of standard metric spaces that have been used to metrize non-Hausdorff topologies, like those arising from…

We prove a Model Existence Theorem for a fully infinitary logic for metric structures. This result is based on a generalization of the notions of approximate formulas and approximate truth in normed structures introduced by Henson and…

We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent…

This text gives a rough, but linear summary covering some key definitions, notations, and propositions from Lambda Calculus: Its Syntax and Semantics, the classical monograph by Barendregt. First, we define a theory of untyped extensional…

The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called "Lambek's restriction," that is, the antecedent of any provable…

We study normalising reduction strategies for infinitary Combinatory Reduction Systems (iCRSs). We prove that all fair, outermost-fair, and needed-fair strategies are normalising for orthogonal, fully-extended iCRSs. These facts properly…

In this paper we consider the class of truth-functional many-valued logics with a finite set of truth-values. The main result of this paper is the development of a new \emph{binary} sequent calculi (each sequent is a pair of formulae) for…

The linguistic applications of the Lambek calculus suggest its semantics over algebras of formal languages. A straightforward approach to construct such semantics indeed yields a brilliant completeness theorem (Pentus 1995). However,…