Paper Info
Title
A typed context calculus
Abstract
This paper develops a typed calculus for contexts i.e., lambda terms with "holes". In addition to ordinary lambda terms, the calculus contains labeled holes, hole abstraction and context application for manipulating first-class contexts. The primary operation for contexts is hole-filling, which captures free variables. This operation conflicts with substitution of the lambda calculus, and a straightforward mixture of the two results in an inconsistent system. We solve this problem by defining a type system that precisely specifies the variable-capturing nature of contexts and that keeps track of bound variable renaming. These mechanisms enable us to define a reduction system that properly integrates&brg;-reduction and hole-filling. The resulting calculus is Church-Rosser and the type system has the subject reduction property. We believe that the context calculus will serve as a basis for developing a programming language with advanced features that call for manipulation of open terms. Copyright 2001 Elsevier Science B.V.
Year
DOI
Venue
2001
10.1016/S0304-3975(00)00174-2
Theor. Comput. Sci.
Keywords
DocType
Volume
Type system,lambda calculus,fi-renaming,ordinary lambda term,context calculus,subject reduction property,reduction system,context application,first-class context,Lambda-calculus,inconsistent system,Context,Alpha-renaming,context,lambda term,type system
Journal
266
Issue
ISSN
Citations 
1-2
Theoretical Computer Science
26
PageRank 
References 
Authors
1.14
12
2
Name
Order
Citations
PageRank
Masatomo Hashimoto1685.97
Atsushi Ohori2261.14