This article presents an alternative method of type-directed partial
evaluation, which is simpler and more efficient than previous methods.
Unlike previous methods, it is straightforwardly applicable to
functional languages with various powerful type systems.  As an
extreme instance, this article mainly deals with a dynamically-typed
functional language like Scheme.  The key idea is to extend primitive
value destructors such as function application and pair destruction
(car and cdr), so that they generate residual code when their operands
are dynamic.  It unnecessitates an operation in type-directed partial
evaluation called reflection, which was the major cause of
complication and inefficiency in previous methods.

We formalize our method as an extension of two-level lambda-calculus,
and prove it correct.  Furthermore, we show that our type-directed
partial evaluator can be derived from a simple online syntax-directed
partial evaluator with higher-order abstract syntax, by the same
transformation as an offline program-generator-generator (cogen) is
derived from an offline syntax-directed partial evaluator.  This
clarifies why type-directed partial evaluation is faster than ordinary
syntax-directed partial evaluation, and implies that we can obtain
more powerful partial evaluators by replacing the underlying
syntax-directed partial evaluator with more sophisticated ones.