A function which is hyperstrict in some argument will fully evaluate that argument. To fully evaluate an object, evaluate it to WHNF and if it is a constructed data object (e.g. a list or tuple) then fully evaluate every component and so on recursively. Thus a hyperstrict function will fail to terminate if its argument or any component or sub-component of its argument fails to terminate (i.e. if its argument is not "total").
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Nearby terms: Hyperscript « hyperspace « HyperSPARC « Hyperstrict » HyperTalk » hypertext » hypertext link