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We investigate the problem of fully abstract compilation, i.e., compilation that both preserves and reflects observational equivalence. In particular, we prove that typed closure conversion for the polymorphic lambda-calculus with existential and recursive types is fully abstract. Our proof uses operational techniques in the form of a step-indexed logical relation and construction of certain wrapper terms that ``back-translate'' from target values to source values.
Although the fact that typed closure conversion is fully abstract had not been in doubt, we are not aware of any previous result that actually proves this.
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