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Abstract: . It is well-known that the type system of ML is overly restrictive in its handling of recursion: certain intuitively sound terms do not pass ML's type-check. We formalise this intuition and show that the restriction is semantical: there are computable (semantical) functions which cannot be expressed by well-typed (syntactical) terms. Keywords: definability, polymorphism, recursion, ML, completeness 1 Introduction and Outline Are all computable functions definable in ML? One should think so,... (Update)
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...sensible programs which would never go wrong is inevitable but not everyone is so willing to accept a loss such as this. Stefan Kahrs in [Kah96] discusses the notion of completeness programs which never go wrong can be type checked which complements Milner s notion of...
.... functions [MTH90] Of course, all of these are computable, but not all computable functions of a given type are SML expressible [Kah96]. Putting these together (the decision to interpret S specifications using classes of P models and the imposition of computability and...
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BibTeX entry: (Update)
Stefan Kahrs. Limits of ML-definability. In Proceedings of Eighth International Symposium on Programming Languages, Implementations, Logics, and Programs, September 1996. http://citeseer.ist.psu.edu/kahrs96limits.html More
@inproceedings{ kahrs96limits,
author = "Stefan Kahrs",
title = "Limits of {ML}-Definability",
booktitle = "{PLILP}",
pages = "17-31",
year = "1996",
url = "citeseer.ist.psu.edu/kahrs96limits.html" }
Citations (may not include all citations):788 Rewrite systems - Dershowitz, Jouannaud - 1990 ACM DBLP
384 The Definition of Standard ML (context) - Milner, Tofte et al. - 1990 ACM
126 Type inference with polymorphic recursion - Henglein - 1993 ACM DBLP
101 Lambda calculus notation with nameless dummies (context) - de Bruijn - 1972
87 Operational Semantics and Polymorphic Type Inference (context) - Tofte - 1988
47 Two extensions of Curry's type inference system (context) - Cardone, Coppo - 1990
1 About the completeness of type systems (context) - Kahrs - 1996
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