Recent ground-breaking efforts such as CompCert have made a convincing case that mechanized verification of the compiler correctness for realistic C programs is both viable and practical. Unfortunately, existing verified compilers can only handle whole programs-this severely limits their applicability and prevents the linking of verified C programs with verified external libraries. In this paper, we present a novel compositional semantics for reasoning about open modules and for supporting verified separate compilation and linking. More specifically, we replace external function calls with explicit events in the behavioral semantics. We then develop a verified linking operator that makes lazy substitutions on (potentially reacting) behaviors by replacing each external function call event with a behavior simulating the requested function. Finally, we show how our new semantics can be applied to build a refinement infrastructure that supports both vertical composition and horizontal composition.

Abstract. We give explicit constructions of some finite-dimensional representations of generalized double affine Hecke algebras (GDAHA) of higher rank using R-matrices for U q (sl N ). Our construction is motivated by an analogous construction of Silvia Montarani in the rational case. Using the Drinfeld-Kohno theorem for Knizhnik-Zamolodchikov differential equations, we prove that the explicit representations we produce correspond to Montarani's representations under a monodromy functor introduced by Etingof, Gan, and Oblomkov.

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