Termination Casts: A Flexible Approach to Termination with General Recursion

Details Termination Casts: A Flexible Approach to Termination with General Recursion Termination Casts: A Flexible Approach to Termination with General Recursion

2010-12-22

arxiv.org/abs/1012.4900v1

EPTCS 43, 2010, pp. 76-93

Computer Science

Programming Languages

In Proceedings PAR 2010, arXiv:1012.4555

Scientific paper

10.4204/EPTCS.43.6

This 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.

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