Binding-time analysis determines when variables and expressions in a program can be bound to their values, distinguishing between early (compile-time) and late (run-time) binding. Binding-time information can be used by compilers to produce more efficient target programs by partially evaluating programs at compile-time. Binding-time analysis has been formulated in abstract interpretation contexts and more recently in a type-theoretic setting. In a type-theoretic setting binding-time analysis is a type inference problem: the problem of inferring a completion of a-term e with binding-time annotations such that e satisfies the typing rules. Nielson and Nielson and Schmidt have shown that every simply typed-term has a unique completion e that minimizes late binding in TML, a monomorphic type system with explicit binding-time annotations, and they present exponential time algorithms for computing such minimal completions. 1 Gomard proves the same results for a variant of his two-level-calculus without a so-called "lifting " rule. He presents another algorithm for inferring completions in this somewhat restricted type system and states that it can be
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