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We define an interpretation of Standard~ML into type theory. The interpretation takes the form of a set of elaboration rules reminiscent of the static semantics given in \textit{The Definition of Standard ML}. In particular, the elaboration rules are given in a relational style, exploiting indeterminacy to avoid over-commitment to specific implementation techniques. Elaboration consists of identifier scope resolution, type checking and type inference, expansion of derived forms, pattern compilation, overloading resolution, equality compilation, and the coercive aspects of signature matching. The underlying type theory is an explicitly-typed $\lambda$-calculus with product, sum, function, and recursive types, together with module types derived from the translucent sum formalism of Harper and Lillibridge. Programs of the type theory are given a type-passing dynamic semantics compatible with constructs such as polymorphic equality that rely on type analysis at run-time. This document supercedes the previous CMU CS technical reports CMU-CS-96-136 and CMU-CS-96-136R. The revision reflects our experience in implementing the specified elaborator, and includes several essential corrections and simplifications to the presentation.