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Under consideration for publication in Math. Struct. in Comp. Science Operational Aspects of Untyped
 

Summary: Under consideration for publication in Math. Struct. in Comp. Science
Operational Aspects of Untyped
Normalization by Evaluation
KLAUS AEHL I G y and FEL I X JOACH I MSKI y
Mathematisches Institut der Ludwig-Maximilians-Universitat Munchen
Theresienstrasse 39, 80333 Munchen, Germany
Received 15 April 2003
A purely syntactic and untyped variant of Normalization by Evaluation for the
-calculus is presented in the framework of a two-level -calculus with rewrite rules to
model the inverse of the evaluation functional. Among its operational properties gures
a standardization theorem that formally establishes adequacy of implementation in
functional programming languages. An example implementation in Haskell is provided.
The relation to usual type-directed Normalization by Evaluation is highlighted, using a
short analysis of -expansion that leads to a perspicuous strong normalization and
con uence proof for "-reduction as a byproduct.
Introduction
Normalization by Evaluation uses the evaluation mechanism of a metalanguage to nor-
malize terms, typically of the -calculus. By means of an interpretation function [[]]  ,
terms are embedded into this metalanguage; an \inverse of the evaluation functional"
(Berger and Schwichtenberg, 1991) # serves to recover terms from the semantics. The

  

Source: Aehlig, Klaus T. - Institut für Informatik, Ludwig-Maximilians-Universität München

 

Collections: Mathematics; Computer Technologies and Information Sciences