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Typing termination in a higher-order concurrent imperative language

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Title: Typing termination in a higher-order concurrent imperative language
Authors: Boudol, Gérard1 gbo@sophia.inria.fr
Source: Information & Computation. Jun2010, Vol. 208 Issue 6, p716-736. 21p.
Subjects: Imperative programming, Concurrent Aggregates (Computer program language), Computer software termination, ML (Computer program language), Recursion theory, Mathematical analysis
Abstract: Abstract: We propose means to predict termination in a higher-order imperative and concurrent language à la ML. We follow and adapt the classical method for proving termination in typed formalisms, namely the realizability technique. There is a specific difficulty with higher-order state, which is that one cannot define a realizability interpretation simply by induction on types, because applying a function may have side-effects at types not smaller than the type of the function. Moreover, such higher-order side-effects may give rise to computations that diverge without resorting to explicit recursion. We overcome these difficulties by introducing a type and effect system for our language that enforces a stratification of the memory. The stratification prevents the circularities in the memory that may cause divergence, and allows us to define a realizability interpretation of the types and effects, which we then use to establish that typable sequential programs in our system are guaranteed to terminate, unless they use explicit recursion in a divergent way. We actually prove a more general fairness property, that is, any typable thread yields the scheduler after some finite computation. Our realizability interpretation also copes with dynamic thread creation. [Copyright &y& Elsevier]
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Database: Engineering Source
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Abstract:Abstract: We propose means to predict termination in a higher-order imperative and concurrent language à la ML. We follow and adapt the classical method for proving termination in typed formalisms, namely the realizability technique. There is a specific difficulty with higher-order state, which is that one cannot define a realizability interpretation simply by induction on types, because applying a function may have side-effects at types not smaller than the type of the function. Moreover, such higher-order side-effects may give rise to computations that diverge without resorting to explicit recursion. We overcome these difficulties by introducing a type and effect system for our language that enforces a stratification of the memory. The stratification prevents the circularities in the memory that may cause divergence, and allows us to define a realizability interpretation of the types and effects, which we then use to establish that typable sequential programs in our system are guaranteed to terminate, unless they use explicit recursion in a divergent way. We actually prove a more general fairness property, that is, any typable thread yields the scheduler after some finite computation. Our realizability interpretation also copes with dynamic thread creation. [Copyright &y& Elsevier]
ISSN:08905401
DOI:10.1016/j.ic.2009.06.007