Forwarding is a technique for providing default attribute definitions in attribute grammars that is helpful in the modular implementation of programming languages. It complements existing techniques such as default copy rules. This paper introduces forwarding, and shows how it is but a small extension of standard higher-order attribute grammars. The usual tools for manipulating higher-order attribute grammars, including the circularity check (which tests for cyclic dependencies between attribute values), carry over without modification. The closure test (which checks that each attribute has a defining equation) needs modification, however, because the resulting higher-order attribute grammars may contain spurious attributes that are never evaluated, and indeed that need not be defined.

Algebraic properties of logical relations on partially ordered sets are studied. It is shown how to construct a logical relation that extends a collection of base Galois connections to a Galois connection of arbitrary higher-order type. "Theorems-for-free" is used to show that the construction ensures safe abstract interpretation of parametrically polymorphic functions. The properties are used to show how abstract interpretations of program libraries can be constructed.

Abstract.A definition of the semantics of attribute grammars is given, using the lambda calculus. We show how this semantics allows us to prove results about attribute grammars in a calculational style. In particular, we give a new proof of Chirica and Martin's result [6], that the attribute values can be computed by a structural recursion over the tree. We also derive a new definedness test, which encompasses the traditional closure and circularity tests. The test is derived by abstract interpretation.

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