Download PDFOpen PDF in browserTermination Casts: A Flexible Approach to Termination with General Recursion17 pages•Published: May 15, 2012AbstractThis paper proposes a type-and-effect system called Teqt, which distinguishes terminating terms and total functions from possibly diverging terms and partial functions, for a lambda calculus with general recursion and equality types. The central idea is to include a primitive type-form ``Terminates t'', expressing that term t is terminating; and then allow terms t to be coerced from possibly diverging to total, using a proof of Terminates t. We call such coercions termination casts, and show how to implement terminating recursion using them. For the meta-theory of the system, we describe a translation from Teqt to a logical theory of termination for general recursive, simply typed functions. Every typing judgment of Teqt is translated to a theorem expressing the appropriate termination property of the computational part of the Teqt term.Keyphrases: dependent types, general recursion, type theory In: Ekaterina Komendantskaya, Ana Bove and Milad Niqui (editors). PAR-10. Partiality and Recursion in Interactive Theorem Provers, vol 5, pages 84--100
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