The authors consider the problem of metacircularity in the polymorphic &lgr;-calculus. They first present an encoding of the Girard-Reynolds second-order polymorphic &lgr;-calculus in the third-order polymorphic &lgr;-calculus, and then they apply a similar technique for the &ohgr;-order polymorphic &lgr;-calculus. In the proposed representation, abstractions are represented by abstractions, evaluation is definable, only well-typed terms can be represented, and type inference need not be explicitly defined. Unfortunately, the metacircularity obtained does not provide a useful framework for typed metaprogramming, that is, the construction of statically typed programs (called metaprograms) that construct and manipulate other programs (called object programs). For examples of metacircularity in untyped or dynamically typed languages, the reader may refer to Reynolds [1].

The paper is clearly written and provides a useful introduction to the subject for the reader interested in the field.