We describe a systematic method to build a logic from any programming language described as a Pure Type System (PTS). The formulas of this logic express properties about programs. We define a parametricity theory about programs and a realizability theory for the logic. The logic is expressive enough to internalize both theories. Thanks to the PTS setting, we abstract most idiosyncrasies specifi...

Scenario-based speciications such as message sequence charts (MSC) ooer an intuitive and visual way of describing design requirements. MSC-graphs allow convenient expression of multiple scenarios, and can be viewed as an early model of the system that can be subjected to a variety of analyses. Problems such as LTL model checking are known to be decidable for the class of bounded MSC-graphs. Our...

The purpose of this short paper is to sketch the development of a few basic topics in the history of Realizability The number of topics is quite limited and re ects very much my own personal taste biases and prejudices Realizability has over the past years developed into a subject of such dimensions that a comprehensive overview would require a fat book Maybe someone some day ought to write suc...

We present a logical calculus which imposes a grading on a sequent-style calculus to account for the runtime of the programmes represented by the sequents. This system is sound for a notion of polynomial-time realizability. An extension of the grading is also considered, giving a notion of \dependant grades", which is also sound. Furthermore, we deene a notion of closed graded multicategory, an...

The realizability problem in requirements engineering is to determine the existence of an implementation that meets the given formal requirements. A step forward after realizability is proven, is to construct such an implementation automatically, and thus solve the problem of program synthesis. In this paper, we propose a novel approach to program synthesis guided by k-inductive proofs of reali...

We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by adding temporal operators equipped with parameters that bound their scope. LDL itself was proposed as an extension of Linear Temporal Logic (LTL) that is able to express all ω-regular specifications while still maintaining many of LTL’s desirable properties like intuitive syntax and semantics and a ...

In this paper we study the isotropic realizability of a given regular gradient field ∇u as an electric field, namely when ∇u is solution of the equation div (σ∇u) = 0 for some isotropic conductivity σ > 0. The case of a function u without critical point was investigated in [5] thanks to a gradient flow approach. The presence of a critical point needs a specific treatment according to the behavi...

UML collaboration diagrams (called communication diagrams in [8]) provide a convenient visual model for specifying Web Service choreographies. A choreography specifies the desired set of interactions among a set of Web services. We formalize the interactions among Web services as conversations, i.e., the sequence of messages exchanged among the services, recorded in the order they are sent. Thi...

In the €rst parts of this thesis, we introduced several calculi for which we gave a Krivine realizability interpretation. Namely, in addition to Krivine’s λc -calculus, we presented interpretations for the callby-name, call-by-value and call-by-need λμμ̃-calculi, for dLt̂p and for dLPAω . Amongst others, we could cite Munch-Maccagnoni’s interpretation for System L [126], Lepigre’s interpretation ...

PLCA is a framework for qualitative spatial reasoning that uses symbolic objects and the relationships between them. The second and third authors introduced inductive constructions to show construction of a PLCA expression. They also proved that expressions obtained by inductive constructions are planar (planarity) and that planar PLCA expressions can be obtained using inductive constructions (...