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		<title>Publications:Gradual Typing for Functional Languages - Revision history</title>
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		<title>Slawek: Created page with &quot;&lt;div style='display: none'&gt; == Do not edit this section == &lt;/div&gt; {{PublicationSetupTemplate|Author=Jeremy Siek, Walid Taha |PID=588266 |Name=Siek, Jeremy (University of Color...&quot;</title>
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				<updated>2014-06-26T03:45:00Z</updated>
		
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|Title=Gradual Typing for Functional Languages&lt;br /&gt;
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|ISBN=978-354073588-5;978-3-540-73589-2&lt;br /&gt;
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|Abstract=&amp;lt;p&amp;gt;Static and dynamic type systems have well-known strengths and weaknesses. In previous work we developed a gradual type system for a functional calculus named $\lambda^?_\to$. Gradual typing provides the benefits of both static and dynamic checking in a single language by allowing the programmer to control whether a portion of the program is type checked at compile-time or run-time by adding or removing type annotations on variables. Several object-oriented scripting languages are preparing to add static checking. To support that work this paper develops $\mathbf{Ob}^{?}_{&amp;amp;lt;:}$, a gradual type system for object-based languages, extending the Ob &amp;amp;lt; : calculus of Abadi and Cardelli. Our primary contribution is to show that gradual typing and subtyping are orthogonal and can be combined in a principled fashion. We also develop a small-step semantics, provide a machine-checked proof of type safety, and improve the space efficiency of higher-order casts.&amp;lt;/p&amp;gt;&lt;br /&gt;
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