Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
The categorical abstract machine
Science of Computer Programming
Elf: a language for logic definition and verified metaprogramming
Proceedings of the Fourth Annual Symposium on Logic in computer science
Constructions: A Higher Order Proof System for Mechanizing Mathematics
EUROCAL '85 Invited Lectures from the European Conference on Computer Algebra-Volume I - Volume I
An abstract machine for Lambda-terms normalization
LFP '90 Proceedings of the 1990 ACM conference on LISP and functional programming
Implementing typed intermediate languages
ICFP '98 Proceedings of the third ACM SIGPLAN international conference on Functional programming
HOL-λσ: an intentional first-order expression of higher-order logic
Mathematical Structures in Computer Science
Polymorphic lemmas and definitions in $\lambda$Prolog and Twelf
Theory and Practice of Logic Programming
Typed common intermediate format
DSL'97 Proceedings of the Conference on Domain-Specific Languages on Conference on Domain-Specific Languages (DSL), 1997
Abstract Conditions for the Confluence of Explicit Substitution Calculi
Electronic Notes in Theoretical Computer Science (ENTCS)
Implementing polymorphic typing in a logic programming language
Computer Languages
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A representation for lambda terms is described based on the scheme of de Bruijn for eliminating variable names. The new notation 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 that is used is, however, more complex than the usual so as to support the ability to examine subterms embedded under abstractions. A virtue of our representation is that it permits substitution to be realized as an atomic operation and thereby provides for efficient implementations of &bgr;-reduction. Operations on lgr;-terms are described based on our representation and the relationship of these to the conventional definitions are exhibited.