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A Notation for Lambda Terms I: A Generalization of Environments
 THEORETICAL COMPUTER SCIENCE
, 1994
"... A notation for lambda terms is described that is useful in contexts where the intensions of these terms need to be manipulated. This notation uses the scheme of de Bruijn for eliminating variable names, thus obviating ffconversion in comparing terms. This notation also provides for a class of terms ..."
Abstract

Cited by 34 (12 self)
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A notation for lambda terms is described that is useful in contexts where the intensions of these terms need to be manipulated. This notation uses the scheme of de Bruijn for eliminating variable names, thus obviating ffconversion in comparing terms. This notation also provides for a class of terms that can encode other terms together with substitutions to be performed on them. The notion of an environment is used to realize this `delaying' of substitutions. The precise mechanism employed here is, however, more complex than the usual environment mechanism because it has to support the ability to examine subterms embedded under abstractions. The representation presented permits a ficontraction to be realized via an atomic step that generates a substitution and associated steps that percolate this substitution over the structure of a term. The operations on terms that are described also include ones for combining substitutions so that they might be performed simultaneously. Our notatio...
A Definite Clause Version of Categorial Grammar
, 1988
"... We introduce a firstorder version of Categorial Grammar, based on the idea of encoding syntactic types as definite clauses. Thus, we drop all explicit requirements of adjacency between combinable constituents, and we capture wordorder constraints simply by allowing subformulae of complex types to s ..."
Abstract
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We introduce a firstorder version of Categorial Grammar, based on the idea of encoding syntactic types as definite clauses. Thus, we drop all explicit requirements of adjacency between combinable constituents, and we capture wordorder constraints simply by allowing subformulae of complex types to share variables ranging over string positions. We are in this way able to account for constructio6s involving discontin uous constituents. Such constructions are difficult to handle in the more traditional version of Cate gorial Grammar, which is based on propositional types and on the requirement of strict string adjacency between combinable constituents.