Lambda De nability with Sums via Grothendieck Logical Relations

Lambda Definability with Sums via Grothendieck Logical Relations

We introduce a notion of Grothendieck logical relation and use it to characterise the deenability of morphisms in stable bicartesian closed categories by terms of the simply-typed lambda calculus with nite products and nite sums. Our techniques are based on concepts from topos theory, however our exposition is elementary.

A New Characterization of Lambda De nability

We give a new characterization of lambda deenability in Henkin models using logical relations deened over ordered sets with varying arity. The advantage of this over earlier approaches by Plotkin and Statman is its simplicity and universality. Yet, decidability of lambda deenability for hereditarily nite Henkin models remains an open problem. But if the variable set allowed in terms is also res...

Une étude des sommes fortes : isomorphismes et formes normales. (A study of strong sums: isomorphisms and normal forms)

A study of strong sums: isomorphisms and normal forms The goal of this thesis is to study the sum and the zero within two principal frameworks: type isomorphisms and the normalization of λ-terms. Type isomorphisms have already been studied within the framework of the simply typed λ-calculus with surjective pairing but without sums. To handle the case with sums and zero, I first restricted the s...

Pcf Deenability via Kripke Logical Relations (after O'hearn and Riecke)

The material presented here is an exposition of an application of logical relations to the problem of full abstraction for PCF. The point is to see Kripke logical relations as introduced by Jung and Tiuryn in [5] and used by O'Hearn and Riecke in [6] to give a logical characterization of sequentiality, within the mainstream of the classical notion of logical relations. The main di erence with r...

Weighted NP Optimization Problems: Logical De nability and Approximation Properties