Correct (for the execution) program might be untypable : let stupid n =. if n=n+1 then 27 else trué Etienne Miquey Realizing arithmetical formulae Classical realizability Realizability game Zoology Gender equality Introduction Curry-Howard Correct (for the execution) program might be untypable : let stupid n =. if n=n+1 then 27 else trué Etienne Miquey Realizing arithmetical formulae Classical ...

Motivated by considerations about Krivine’s classical realizability, we introduce a term calculus for an intuitionistic logic with record types, which we call the CPS target language. We give a reformulation of the constructions of classical realizability in this language, using the categorical techniques of realizability triposes and toposes. We argue that the presentation of classical realiza...

We present a general notion of realizability encompassing both standard Kleene style realizability over partial combinatory algebras and Kleene style realizability over more general structures, including all partial cartesian closed categories. We show how the general notion of realizability can be used to get models of dependent predicate logic, thus obtaining as a corollary (the known result)...

We introduce the notion of almost realizability, an arithmetic generalization realizability for integer sequences, which is property counting periodic points some map. characterize intersection between set Stirling sequences (of both first and second kind) realizable sequences.

A service choreography defines a set of permitted sequences of message events as a specification for the interaction of services. Realizability is a fundamental sanity check for choreographies comparable to the notion of soundness for workflows. We study several notions of realizability: partial, distributed, and complete realizability. They establish increasingly strict conditions on realizing...

The relative realizability toposes that Awodey, Birkedal and Scott introduced in [1] satisfy a universal property that involves regular functors to other categories. We use this universal property to define what relative realizability categories are, when based on other categories than of the topos of sets. This paper explains the property and gives a construction for relative realizability cat...

A choreography describes the interaction between services. It may be used for specification purposes, for instance serving as a contract in the design of an interorganizational business process. Typically, not all describable interactions make sense which motivates the study of the realizability problem for a given choreography. In this paper, we show that realizability can be traced back to th...

Two notions of primitive recursive realizability for arithmetic sentences are considered. The first one is strictly primitive recursive realizability introduced by Z. Damnjanovic in 1994. We prove that intuitionistic predicate logic is not sound with this kind of realizability. Namely there exists an arithmetic sentence which is deducible in the intuitionistic predicate calculus but is not stri...