Affiliation:
1. INRIA Saclay and École Polytechnique, Cedex, France
Abstract
Λμ-calculus is a Böhm-complete extension of Parigot's Λμ-calculus closely related with delimited control in functional programming. In this article, we investigate the meta-theory of untyped Λμ-calculus by proving confluence of the calculus and characterizing the basic observables for the Separation theorem,canonical normal forms. Then, we define Λs, a new type system for Λμ-calculus that contains a special type construction for streams, and prove that strong normalization and type preservation hold. Thanks to the new typing discipline of Λs, new computational behaviors can be observed, which were forbidden in previous type systems for λμ-calculi. Those new typed computational behaviors witness the stream interpretation of Λμ-calculus.
Publisher
Association for Computing Machinery (ACM)
Subject
Computational Mathematics,Logic,General Computer Science,Theoretical Computer Science
Reference28 articles.
1. Ariola Z. M. Herbelin H. and Sabry A. 2007. A type-theoretic foundation of delimited continuations. Higher-Order Symb. Comput. 10.1007/s10990-007-9006-0 Ariola Z. M. Herbelin H. and Sabry A. 2007. A type-theoretic foundation of delimited continuations. Higher-Order Symb. Comput. 10.1007/s10990-007-9006-0
2. Baba K. Hirokawa S. and Fujita K.-E. 2001. Parallel reduction in type free lambda/mu-calculus. Electron. Notes Theoret. Comput. Sci. 42. Baba K. Hirokawa S. and Fujita K.-E. 2001. Parallel reduction in type free lambda/mu-calculus. Electron. Notes Theoret. Comput. Sci. 42.
3. Böhm C. 1968. Alcune proprietà delle forme β η-normali nel λK-calcolo. Publicazioni dell'Istituto per le Applicazioni del Calcolo 696. Böhm C. 1968. Alcune proprietà delle forme β η-normali nel λK-calcolo. Publicazioni dell'Istituto per le Applicazioni del Calcolo 696.
4. David R. and Py W. 2001. λμ-calculus and Böhm's theorem. J. Symb. Logic. David R. and Py W. 2001. λμ-calculus and Böhm's theorem. J. Symb. Logic.
5. Lecture Notes in Articifial Intelligence;de Groote P.
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