Explicit Substitution
In computer science, lambda calculi are said to have explicit substitutions if they pay special attention to the formalization of the process of substitution. This is in contrast to the standard lambda calculus where substitutions are performed by beta reductions in an implicit manner which is not expressed within the calculus. The concept of explicit substitutions has become notorious (despite a large number of published calculi of explicit substitutions in the literature with quite different characteristics) because the notion often turns up (implicitly and explicitly) in formal descriptions and implementation of all the mathematical forms of substitution involving variables such as in abstract machines, predicate logic, and symbolic computation.
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