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Denotational semantics with other notions of convergenceIn a typical domaintheoretic denotational semantics, a primitive value converges when it is non__, and functions converge in the limit, pointwise. Are there similar denotational semantics out there in which convergence is defined differently? I've found myself thinking "Why just non__ for values?" I can answer the question, partially: it makes semantic approximation order easy to define, and monotonicity with respect to the order is easy to ensure (anything finitely computable, I think). To do it otherwise would require every value to belong to a metric space with a metric that convergence happens with respect to, a way to specify what a function returns at any finite approximation level, and monotonicity would be hard to ensure. Monotonicity might be too restrictive to be useful anyway... But it might be cool. In languages defined with non__ convergence, you can't, say, define a value that depends on all the values of an infinite list, even when it's welldefined. Infinite sum, for example. You can make a list of prefix sums and carry out the limit yourself, but I'd like the language to do it for me. If it doesn't converge, that's like writing an infinite loop: my fault. By Neil Toronto at 20100701 21:36  LtU Forum  previous forum topic  next forum topic  other blogs  3756 reads

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