We present a shallow embedding of the Object Calculus of Abadi and Cardelli in the lambda-Pi-calculus modulo, an extension of the lambda-Pi-calculus with rewriting.  This embedding may be used as an example of translation of subtyping.  We prove this embedding correct with respect to the operational semantics and the type system of the Object Calculus. We implemented a translation tool from the Object Calculus to Dedukti, a type-checker for the lambda-Pi-calculus modulo.
['Raphaël Cauderlier', 'Catherine Dubois']
Objects and Subtyping in the Lambda-Pi-Calculus Modulo