We have built the first family of tagless interpretations for a higher-order typed object language in a typed metalanguage (Haskell or ML) that require no dependent types, generalized algebraic data types, or postprocessing to eliminate tags. The statically type-preserving interpretations include an evaluator, a compiler (or staged evaluator), a partial evaluator, and call-by-name and call-by-value CPS transformers.Our principal technique is to encode de Bruijn or higher-order abstract syntax using combinator functions rather than data constructors. In other words, we represent object terms not in an initial algebra but using the coalgebraic structure of the λ -calculus. Our representation also simulates inductive maps from types to types, which are required for typed partial evaluation and CPS transformations. Our encoding of an object term abstracts uniformly over the family of ways to interpret it, yet statically assures that the interpreters never get stuck. This family of interpreters thus demonstrates again that it is useful to abstract over higher-kinded types.It should also be possible to define languages with a highly refined syntactic type structure.Ideally, such a treatment should be metacircular, in the sense that the type structure used in the defined language should be adequate for the defining language.
We propose a complete model for the oxidation of silicon germanium. Our model includes the participation of both silicon and germanium atoms in the oxidation process and the replacement by silicon of germanium in mixed oxides. Our model is capable of predicting, as a function of time, the oxide thickness, the profile of the silicon in the underlying alloy, and the profile of germanium in the oxide. The parameters of the model vary with temperature, alloy composition, and oxidizing ambient. The model shows excellent agreement with published results, with model parameters following trends consistent with the physical phenomena hypothesized. The presence of germanium catalyzes both the silicon and the germanium oxidation rates, and all reaction rates increase with increasing temperature. The resulting effective oxidation rate is enhanced, with respect to the oxidation of pure silicon, at all germanium concentrations. Mixed oxides form only in the case of high germanium concentrations, but at high temperatures the rapid growth of a thick oxide results in a slowing of oxidant diffusion, and the oxide composition switches back to a pure silicon oxide.
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