Related papers: Realizing realizability results with classical con…
During the last twenty years or so a wide range of realizability interpretations of classical analysis have been developed. In many cases, these are achieved by extending the base interpreting system of primitive recursive functionals with…
We consider different classes of combinatory structures related to Krivine realizability. We show, in the precise sense that they give rise to the same class of triposes, that they are equivalent for the purpose of modeling higher-order…
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…
We give a method to transform into programs, classical proofs using a well ordering of the reals. The technics uses a generalization of Cohen's forcing and the theory of classical realizability introduced by the author.
We investigate a framework of Krivine realizability with I/O effects, and present a method of associating realizability models to specifications on the I/O behavior of processes, by using adequate interpretations of the central concepts of…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
We develop a number of variants of Lifschitz realizability for CZF by building topological models internally in certain realizability models. We use this to show some interesting metamathematical results about constructive set theory with…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
In this paper we treat the specification problem in classical realizability (as defined in [20]) in the case of arithmetical formul{\ae}. In the continuity of [10] and [11], we characterize the universal realizers of a formula as being the…
In a recent paper, Herbelin developed a calculus dPA$^\omega$ in which constructive proofs for the axioms of countable and dependent choices could be derived via the encoding of a proof of countable universal quantification as a stream of…
In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel…
We develop a notion of realizability for Classical Linear Logic based on a concurrent process calculus.
We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Lof's type theory (hence…
Realizability notions in mathematical logic have a long history, which can be traced back to the work of Stephen Kleene in the 1940s, aimed at exploring the foundations of intuitionistic logic. Kleene's initial realizability laid the ground…
We define a variant of realizability where realizers are pairs of a term and a substitution. This variant allows us to prove the normalization of a simply-typed call-by-need $$\lambda$-$calculus with control due to Ariola et al. Indeed, in…
In the landscape of approaches toward the simulation of Lattice Models with complex action the Complex Langevin (CL) appears as a straightforward method with a simple, well defined setup. Its applicability, however, is controlled by certain…
We introduce a novel technique for checking reachability in Petri nets that relies on a recently introduced compositional algebra of nets. We prove that the technique is correct, and discuss our implementation. We report promising…
In this article, we investigate the arithmetical hierarchy from the perspective of realizability theory. An experimental observation in classical computability theory is that the notion of degrees of unsolvability for natural arithmetical…
In "Extensional realizability for intuitionistic set theory", we introduced an extensional variant of generic realizability, where realizers act extensionally on realizers, and showed that this form of realizability provides "inner" models…
In this paper, we introduce a semantics of realisability for the classical propositional natural deduction and we prove a correctness theorem. This allows to characterize the operational behaviour of some typed terms.