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Tradeoffs in the Intensional Representation of Lambda Terms
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Tradeoffs in the Intensional Representation of Lambda Terms
Chuck Liang5 and Gopalan Nadathur6 
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Department of Computer Science, Hofstra University, Hempstead, NY, 11550 |
| (6) |
Department of Computer Science and Engineering, University of Minnesota, 4-192 EE/CS Building, 200 Union Street SE, Minneapolis, MN, 55455 |
Abstract
Higher-order representations of objects such as programs, specifications and proofs are important to many metaprogramming
and symbolic computation tasks. Systems that support such representations often depend on the implementation of an intensional
view of the terms of suitable typed lambda calculi. Refined lambda calculus notations have been proposed that can be used
in realizing such implementations. There are, however, choices in the actual deployment of such notations whose practical
consequences are not well understood. Towards addressing this lacuna, the impact of three specific ideas is examined: the
de Bruijn representation of bound variables, the explicit encoding of substitutions in terms and the annotation of terms to
indicate their independence on external abstractions. Qualitative assessments are complemented by experiments over actual
computations. The empirical study is based on λProlog programs executed using suitable variants of a low level, abstract machine
based implementation of this language.
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